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THE FRACTAL TIME BEHAVIOR OF SPONTANEOUS PERINATAL BEHAVIORS ASSOCIATED WITH REM SLEEP: A POSSIBLE ONTOGENETIC ADAPTATION AND SOURCE OF PLASTICITY UNDERLYING THE EMERGENCE OF BEHAVIORAL NEOPHENOTYPES

Carl M. Anderson

A Dissertation Submitted to the Faculty of

The College of Science

in Partial Fulfillment of the Requirements for the Degree of

Doctor of Philosophy

Florida Atlantic University

Boca Raton, Florida

December 1995

This dissertation was prepared under the direction of the candidate's dissertation advisor, Dr. Leslie M. Terry, Department of Psychology and has been approved by the members of his supervisory committee. It was submitted to the faculty of the College of Science and was accepted in partial fulfillment of the requirements for the degree of doctor of philosophy.

SUPERVISORY COMMITTEE:

___________________________________

Dr. Leslie M. Terry

Chairperson of dissertation committee

___________________________________

Dr. Arnold J. Mandell

___________________________________

Dr. Ingrid B. Johanson

_______________________________ ___________________________________

Chairperson, Department of Psychology Dr. Larry S. Liebovitch

_______________________________ ___________________________________

Dean, College of Science Dr. Timothy J. Iverson

_______________________________ ___________________________________

Dean of Graduate Studies and Research Date

Acknowledgements

The work and concepts expressed in this dissertation owe a great debt in large part to hundreds of people. I attempt here to spontaneously list and describe then in the order in which they occur to me. To Mary, my wife, I owe more than I say for all of her love, cheer, motivation, intellectual stimulation and unsurpassed editorial guidance, without you nothing would exist. To Corinna, my daughter, I owe the inspiration of her laughter and the joy of her spontaneity. I also thank my parents, Corrine, Gene and my brother Arthur Anderson for their love, support and uncritical acceptance through all the long years. I thank my in-laws, Margaret and Carl Pfeiffer, Jim Kolodny and Susan Thompson for all of their support and understanding throughout my endless education.

I would also like to acknowledge a huge debt to Dr. Leslie M. Terry, my longtime friend, chairperson and coadvisor who took me under her wing at the 87 Neuroscience in Dallas, to my first ISDP meeting, to dinner after my poster and has been unselfish in her support ever since. Thanks for letting me go my own way. To Dr. Clinton "Clint" Kilts, I owe the excellent mentorship and friendship and encouragement to proceed with my scientific career. To my coadvisor Dr. Arnold Mandell, for letting me play 1/f my way in your band and really listening. Arnold, thanks for all of your hard work over the years, particularly "Toward a neuropharmacology of habituation: a vertical integration" which inspired me to have that long talk with you and Karen at Santa Fe and to come to FAU and work with you. Thanks also for creating the "Bagels and cream cheese seminar in mathematical neuroscience and psychology" by which the early intuitions embodied in my 1992 talk "1/f noise in rapid eye movement sleep a developmental hypothesis" caught the flame that burns brightly to this day. Many thanks also to Dr. Karen Selz for her skill with cartoons and Lévy fits. Also I would like to thank all those in the Department of Psychology and the Center for Complex Systems for your help all these years. Among them, Bill McLean for your courage and help with the activity monitor, Tom and Kieko Holroyd and Colin Brown for my hours of friendship and tutoring. Also Pam Case, Gene Wallenstein, John Buchanan, Paul Treffner, Sue and Betty for your friendship. Special thanks to Dr. Larry Liebovitch for teaching me Hurst analysis and helping with the programming. Also to Alison Tannenbaum, thanks for your help in securing the Grass 7P511 and the Metaphane. Thanks also to Mingzhou Ding and Steve Bressler for the excellent courses and conversation. Thanks again to Dr. Ted Hall who put me on course to Dr. Ingrid Johanson's office and FAU. Thanks to Ingrid for her instruction and the generous use of the lab and materials. Thanks also to Dr. Tim Iverson for many helpful discussions about kids and how this work may benefit them. Thank you Jane Roberts and Rob Butts for your efforts and the idea that spontaneous activity informs conscious action. Last but not least, thanks to Dr. Bill Smotherman for his friendly comments and the Binghamton and Cornell groups for having the foresight to collect the data that comprises a sizable part of this dissertation, and generosity in allowing my access to it.

ABSTRACT

Rapid Eye Movement (REM) sleep in adult and neonatal mammals is characterized by episodes of high variability and bursting in brainstem sites associated with spontaneous tonic and phasic behavioral events such as REMs, nuchal inactivity and twitches of the body. REM sleep is the principal behavioral state during fetal and neonatal life and as has been demonstrated by various REM deprivaiton proceedures to be indispensable during this period and to lead to long lasting behavioral defects in adult life. The guiding hypothesis throughout this dissertation is that the variability of REM-associated nuchal atonia episodes and other spontanous motor events reflects the fractal time patterns of a global fetal REM sleep state over mutiple timescales serving as a transient behavioral ontogenetic adaptation to changing developmental environments. Further, spontanous activity over many levels of

organization, including phasic REM motor activity during ontogeny, could play a fundamental role in the development of appetitive behavioral processes (e.g., searching and orienting) and other forms of neuroplasticity (e.g., learning and dynamic regulation of receptor fields and maps). The nature of this variability was investigated by measuring the durations of nuchal atonia over extended periods in fetal sheep and neonatal rats, species which are in a REM sleep-like state > 50% of the time. Hurst's rescaled range analysis, which affords comparisons between natural time series with short- and long-term correlated fluctuations, indicated that variability in both species over short time scales is statistically similar to longer time scales (i.e., is fractal in time) and remarkably stable over the developmental periods examined. Spontaneous nuchal events in both species were also found to be described by convolutionally stable self-similar Lévy distributions, suggesting that activity associated with fetal REM sleep could provide a stable, scale invariant source of correlated stimulation, facilitating integration of new neural changes into developing motor and cortical networks over gestation. These fractal time descriptions of spontaneous prenatal behaviors have implications for conceptualizing the evolutionary mechanisms underlying heterochrony (shifting self-affine relationships between the timing of gene expression and behavioral activity) and the plasticity essential to the genesis of behavioral neophenotypes.

To Mary, Corinna And The World As Dream

Table of Contents

I. INTRODUCTION..........................................................................1

FRACTAL TIME AND SPONTANEOUS PRENATAL BEHAVIOR.....4

REM SLEEP IN FETUSES AND NEONATES AS AN

ONTOGENETIC ADAPTATION..............................................16

II. EXPERIMENT 1: ANALYSIS OF NUCHAL ATONIA SEQUENCES IN FETAL SHEEP: AN EXAMPLE OF THE FRACTAL TIME STRUCTURE OF A SPONTANEOUS PRENATAL BEHAVIOR.........................................21

SPECIFIC METHODS..........................................................22

RESULTS.........................................................................29

DISCUSSION....................................................................52

III. EXPERIMENT 2: ANALYSIS OF NUCHAL INACTIVITY SEQUENCES IN NEONATAL RATS: AN EXAMPLE OF THE FRACTAL TIME STRUCTURE OF A SPONTANEOUS POSTNATAL BEHAVIOR.................................60

SPECIFIC METHODS..........................................................73

RESULTS.........................................................................75

DISCUSSION...................................................................108

IV. GENERAL DISCUSSION: ORDER AND RANDOMESS IN BIOLOGICAL SYSTEMS AND SPONTANEOUS NEONATAL BEHAVIORS.................114

THE ORIGIN AND FUNCTION OF FRACTAL TIME PATTERNS ASSOCIATED WITH FETAL REM SLEEP: A TRANSIENT BEHAVIORAL ONTOGENETIC ADAPTATION TO CHANGING ENVIRONMENTS?.......117

FRACTAL TIME, FETAL REM SLEEP, HETEROCHRONY AND THE GENESIS OF BEHAVIORAL NEOPHENOTYPES................................129

THE FRACTAL TIME NATURE OF SPONTANEOUS PRENATAL BEHAVIORS: PARALLELS WITH CRITICAL POINT FLUCTUATIONS AND OTHER COMPLEX SELF-ORGANIZING SYSTEMS............................133

THE FRACTAL TIME ORIGINS OF SPONTANEOUS APPETITIVE BEHAVIORS: REM SLEEP, NEURAL PLASTICITY AND THE ORIENTING RESPONSE...............................................................................137

THE RETICULAR FORMATION, REM SLEEP, ORIENTING AND DEVELOPMENT: A GUIDING IMAGE.............................................139

THE UTILITY OF FRACTAL DESCRIPTIONS OF SPONTANEOUS PRENATAL BEHAVIOR ..............................................................165

V. CONCLUSIONS.........................................................................167

VI. REFERENCES...........................................................................170

INTRODUCTION

Intermittent spontaneous prenatal behavior has long been recognized as an integral component of fetal development (Coghill, 1929a; 1929b; Corner, 1977; 1978; 1990; 1994; Hamburger, 1963; 1973; Hall and Oppenheim, 1987; Preyer, 1885; Robinson and Smotherman, 1988) and has been proposed as a transient ontogenetic adaptation to the in ovo or in utero environment (Oppenheim, 1981; 1984). Wihelm Preyer, in his monumental 1885 work Specielle Physiologie des Embryo. Untersuchunge üher die Lebensersc heinungen vor der Geburt , "Special physiology of the Embryo: Investigations of the Phenomena of Life before Birth," called these spontaneous movements "impulsive movements" because of the distinctiveness of their uncoordinated, aimless, seemingly nonadaptive nature (Gottlieb, 1973). The underlying motivation behind much of Preyer's developmental work was the problem of "psychogenesis" or the genesis of mind. Through his motor primacy theory, Preyer proposed a central role for these impulsive, autogenous movements in physiogenesis and ultimately in psychogenesis.

George Coghill, who greatly admired Preyer as a behavioral embryologist, translated and republished portions of Specielle Physiologie des Embryo, and in a similar fashion sought to understand the nature of spontaneity and its relation to the development of more complex behaviors. In a philosophical dialogue with the famous neuroanatomist C. Judson Herrick (Herrick, 1948), Coghill refers to the "integration and spontaneity that can be recognized throughout both the organic and the inorganic realms (p.222)" as the source of mind or psychogenesis in Preyer's terms. Coghill further clarifies the roots of his Gestalt view of development of embryonic motility in Amblystome as the "progressive

expansion of a perfectly integrated total pattern and the individuation within it....[of] degrees of discreteness (Coghill, 1929, p. 38)." In a further quote from this dialogue: "This thing that we agree upon is that integrative experience, as you call it, and mentation, as I call it, is a total-pattern type of activity common to all organisms and that there has been progressive expansion and individuation of this pattern in evolutionary history and in personal development (Herrick, 1948, p. 216)."

In this dissertation I will attempt to reanimate the germs of these ideas with the concepts of fractal geometry by demonstrating that the same distinctive spontaneous perinatal activities perceived by Preyer and Coghill, which lack a unique measurement scale in time or space in which to fully capture their true nature, can be described as fundamental biological processes intrinsically associated with adult REM sleep. It is my contention, and the subtext of this dissertation, that the true wellspring of creative spontaneity and cognitive flexibility that serves as the foundation of consciousness has its source in the fractal time nature of recurrent phasic REM processes over a lifetime. And furthermore, that the rich creativity, diversity, adaptability and impulsivity of vertebrate forms result from what Coghill describes as "....a perfectly integrated total [fractal] pattern " of interactions over time and space that is first manifested in spontaneous perinatal behaviors.

Endogenously generated spontaneous activity, as opposed to evoked activity, is common to all vertebrate embryos, larvae and fetuses and it is associated with emergent behavioral and neurobiological processes from which adult REM originates (Blumberg and Lucas, 1994b; in press; Corner, 1978; 1990; Mirmiran, 1986) although true autonomous activity is only observed in fish and bird embryos (Hamburger, 1973). This spontaneous activity, whether movements (Coghill, 1929a; 1929b; Corner, 1977; Dawes, 1988; Oppenheim, 1982), neuronal activity (Corner and Crain, 1972; Corner, 1994; Ripley and Provine, 1972; Sharma, Provine, Hamburger, Sandel, 1970) or state changes (Prechtl, 1990) is often described as a sequence of independent random events lacking the coordination found in adult species-typical motor patterns (Bekoff and Lau, 1980; Blumberg and Lucas, 1994b; Corner, 1978; Gottlieb, 1976; Hamburger, 1973; Narayanan et al., 1970; Oppenheim, 1981; Windle, 1944; Robinson and Smotherman, 1988). Implicitly, species-typical adult behavior is conceptualized as originating from "...the activation of a neuronal circuitry that to a large extent has its origins in a basic neurobiological substrate laid down in the embryo and whose functional manifestation is spontaneous prenatal behavior...; Hall and Oppenheim, 1987, p.96." If this theoretical assumption is correct, how can this ontogenetic organizing capability of apparently uncorrelated random prenatal behavior be identified and characterized? Can the biological process giving rise to spontaneous prenatal behavior be a truly independent random process if spontaneous prenatal behavior arises over many scales of space and time in the fetus and ultimately results in global behavioral patterns over a range of space and time scales? Why do fetuses spend most of their time and energy in a state similar to adult REM sleep (Nijhuis, Martin and Prechtl, 1984; Richardson, 1991; Roffwarg, Muzio and Dement, 1966) if it only results in the spontaneous generation of independent random sequences of behavior? This dissertation attempts a comparative approach to investigating the time structure of spontaneous prenatal behavior and its inferred role in development. By demonstrating the recurrence of invariant temporal patterns in spontaneous prenatal behavior of the sheep fetus or the postnatal rat, I am suggesting that "impulsive" spontaneous behaviors need not be conceptualized as independent random processes. Perhaps the ontogenetic organizing capability of spontaneous prenatal behavior resides in a subtle attribute of its time structure.

FRACTAL TIME AND SPONTANEOUS PRENATAL BEHAVIOR

Many apparently random processes in nature have been demonstrated to have fractal order in space and time (Mandelbrot, 1982; 1983). If spontaneous prenatal behavior is not an independent random process but instead is correlated over many time scales (i.e, is fractal in time), then the intra-organism correlations provided by spontaneous prenatal behavior may illustrate a previously unrecognized form of non-cyclic, non-mode-locked coherence in time-dependent developmental systems (Mandell and Shlesinger, 1990; Smotherman, Seltz and Mandell, in press) which could represent a transient behavioral ontogenetic adaptation to the fetal environment and a substrate for the generation of novel behavioral pheotypes.

What is fractal time? This statistical concept is perhaps best described within the context of determining characteristic times from a series of observables such as sums of sequences of one spontaneous perinatal behavior, such as nuchal atonia durations, investigated at length in this work. Nuchal atonia or the loss of nuchal muscular tone in the primary anti-gravity muscles of the neck is a key indication of the onset of REM sleep in many animal species. If is an independent random process with a finite mean and variance, , the serves as one characteristic time of the nuchal atonia episode sequence. Another time, t, is derived from the product of two nuchal atonia

episodes computed over increasing numbers of intervals along the sequence, the autocorrelation function, . yields a characteristic time of decay of the amplitude of the joint products over the nuchal atonia episode sequence; an independent random sequence would proceed exponentially , where k is a constant. If the nuchal atonia sequences lack well defined central moments, say , then we would be without as a characteristic time, but instead, would have some probability distribution of times with a "stretched exponential" tail, or a "power law" tail, (see Schroeder, 1991 for a discussion of power laws and fractals). The decay of autocorrelations, , in this sequence without a well defined characteristic time is slower than exponential, often approximated by in which b also has a fractional value, 0 < b < 1.

Processes of this sort without a characteristic scale of time , or event correlation time, , have times of all orders which can often be described by distributions and correlation functions with fractional exponents. A fractal measure provides a single quantity to describe behavioral fluctuations over many scales of space or time. For example, if a process is fractal in time then the correlations among or similarity in the variations of a measured property of the process at one sampling rate (e.g., fluctuations of fetal behavior at one second) is statistically similar to the correlation or similarity in the variations of a measured property at a lower sampling rate (e.g., fluctuations of fetal behavior over an hour). This repetition of "self-likeness" in behavioral variation can be described in several ways. In geometric terms, if variation at different scales of measurement occur along one dimension, such as time, it is called "self-similar ". If the similarity dimensions of fluctuations are greater than one, such as time and amplitude, they are termed "self-affine". In this circumstance, the time series is invariant under a transformation that scales different coordinates by different amounts (for more detailed descriptions of these terms, see Barton & La Pointe, 1995a &b; Bassingthwaighte, Liebovitch and West, 1994; Fan, Neogi, and Yashima 1991; Feder, 1988; 1991; Hastings and Sugihara, 1993; Nonnenmacher, Losa and Weibel 1994; Peitgen, Jürgens and Saupe, 1992; Peters, 1991; and references therein). Naturally occurring self-affine processes (i.e., fluctuations in atomic clocks and sand hour glasses, wobbling of the earth on its axis, current fluctuations in electrical components, etc.) are called fractal or scaling noises (see Jensen, Todoeschuck, Crossley and Gregotski, 1991; West and Shlesinger, 1989; Voss, 1988a &b; 1992). Although, fractal time behavior was originally observed and defined for physical systems (Mandelbrot, 1982; 1983; see also Montroll and Shlesinger, 1984; Shlesinger, 1987; 1988), fractal time fluctuations in biological systems can be characterized by the same methods used to describe non-biological fractal time fluctuations. These "statistical fractals" may quantify the similarity of intermittent behavior across several different time scales, an example of which is the clustering within clusters of some fetal behaviors (Szeto, Dwyer, Cheng and Decena, 1990; Szeto et al., 1992).

Fluctuations of fetal behavior often appear as clusters in time, possibly self-affine, observed in spontaneous motility in the chick (Ripley & Provine, 1972) and other species (Corner, 1978) as well as in fetal breathing (Szeto et al., 1992) and nuchal electromyographic EMG recordings (see Figure 1), both markers of fetal REM sleep in sheep. This intermittent clustering in time among episodes of fetal behavior over minutes, hours or days can be distinguished from randomly ordered sequences by Hurst's rescaled range analysis (the Range of the sum of deviations from a local mean divided by the

Figure 1. On E123 of gestation, erratic intermittent bursting is apparent in nuchal activity with intervening periods of atonia. Nuchal EMG activity along the abscissa (2 volt range normalized to 250 standard units), plotted over 100 minutes on the ordinate (top trace). Rescaling the amplitude, abscissa, and time, the ordinate, over a 600 second subset of the original series (middle trace) reveals smaller clusters within larger clusters of both muscle discharges and atonia. Rescaling both dimensions again over 65 seconds (bottom trace) demonstrates similar qualitative "self-affinity" which is bounded from below by the sampling rate

Standard deviation from the local mean; R/S) developed by the British hydrologist Harold E. Hurst and popularized by Mandelbrot and Wallis (1968, 1969a-d and 1995).

Hurst needed to determine from historical records if the yearly flows of the Nile were random or clustered from year to year, for the construction of the Aswan dam (Bassingthwaighte et al. 1994, Bassingthwaighte and Raymond, 1994; Feder, 1988; 1991; Hurst, Black and Simaika, 1965). If high and low Nile flows were random over successive years (i.e., did not cluster in sequences of high or low years), then the reservoir size estimate could be based on the average of the recorded flows. On the other hand, if years of large Nile flows were not independent, but clustered or demonstrating serial dependency over successive years, then the "memory", or carry over between a series of wet years, could create a situation where reservoir capacity would have to be larger than the estimate based on the mean. Hurst examined 800 years of Nile flows recorded at the Roda gauge and determined they were not random but tended to cluster in runs of high or low years, supporting the need for a larger reservoir. He also examined 837 records of other natural phenomena (e.g., annual river levels, rainfall, temperature and pressure records, tree rings, varves, sunspot activity) finding non-random positive correlations in most of them (Hurst et al., 1965; see also Bassingthwaighte and Raymond, 1994; Mandelbrot and Wallis, 1995; and Peters, 1991 for Hurst analysis of capital markets).

Hurst's R/S analysis thus provides a measure of sequential dependency in the increments of records of natural fluctuations over different time scales of observation, . Mandelbrot and Wallis (1968 and 1969a-d) and Mandelbrot and Van Ness (1968) generalized and extended Hurst's R/S analysis to a class of Gaussian Brownian motions called fractional Brownian motions (fBm), which need not conform to the condition of serial independence of Brownian motion. The dependency between increments in fBm is quantified by H (called the Hurst exponent by Mandelbrot in honor of Hurst's work) which is calculated from the slope of the log-log relationship between the ratio R/S and the length of the record examined; R/S varies as .

To distinguish between statistically independent and dependent increments in a discrete time record, the difference in magnitude between two consecutive increments (e.g., nuchal atonia durations) DM = M(t2) - M(t1) is related to their difference in time = t2 - t1 by the scaling exponent H, or DM = (Dt)H (see eq. 9-23 in Feder 1988). This can be determined simply for the time record by plotting the ratio R/S versus increasing in a log-log plot and calculating its slope. For Brownian motion, fBm with H = 0.5 indicates that there is no dependency between steps (generated by flipping an unbiased coin and accumulating steps to the left or right, or recording points along the trajectory of a pollen grain in water). The sum of the independent steps or increments leads to a rescaled range of variation that scales with the square root of the number of steps or units of time : R/S . Due to the absence of positive or negative correlations between steps, the scaling exponent H equals 0.5 (Feller. 1951). Fractional Brownian motions with a scaling exponent H 0.5 indicate the presence of serial dependencies in the time series. When H > 0.5, positive correlations or dependency exists between the cumulative increments. Mandelbrot (1983) termed this "persistence" because increases (or decreases) are more likely to be followed by increases (or decreases) when observed at any time scale. In contrast, some biological processes such as closed loop control of upright stance or heart beat intervals have fluctuations with H < 0.5, called "antipersistence" because increases (or decreases) are more likely to be followed by decreases (or increases) when observed at any time scale (Collins and De Luca, 1993, 1995; Peng et al., 1993). The cumulative variation in a Gaussian distribution of increments in classical Brownian motion is proportional to the time between increments, which in the case of H = 0.5, classical Brownian motion, reduces to . H, by relating the variance-normalized cumulative deviation from a Gaussian zero-mean process over increasing time windows, provides a statistically scale invariant measure of correlation or dependency between increments over different time periods. In addition, H can be related to the coefficient of correlation between successive increments by the formula [see Bassingthwaighte et al., 1994 or Hastings and Sugihara, 1993 for a discussion of the relationship between H and the Pearson product moment correlation and coefficient of correlation] or to the slope, , of the spectral density function or power spectrum by the formula (Bassingthwaighte et al., 1994; Mandelbrot and Van Ness, 1968; Tatom, 1995; Voss, 1988a&b, 1989). Hurst's key discovery that many apparently irregular natural records could not be treated as the sums of independent random processes has still not had a great impact on the field of statistics (Bassingthwaighte and Raymond, 1994). This may in part be due to the non-convergence of the moments (see Hays, 1963 for a good treatment of statistical moments) in these fractal time series (non-finite mean and/or variance) and the absence of non-finite variance distribution-dependent tests of significance.

The distributions of times, , in a fractal time process with non-finite variance and long tails nonetheless manifest invariants with respect to indices on their identically distributed sums. The accumulated increments distribute like the probabilities of any single one of its motions. These Lèvy distributions without finite variance (and sometimes without a convergent mean as well) are in this way invariant across summation; this defining property is called "convolutional stability" (Lèvy, 1937; Gnedenko and Kolmogorov, 1968; Montroll and Badger, 1974; Takayasu, 1989). The Lèvy distribution is typically represented as a complex valued, exponential distribution function with four parameters indicating, respectively, location, symmetry, global scale, and rate of convergence of the tail (Mandelbrot 1982; 1983; 1993, Montroll and Shlesinger, 1984; Peters, 1991; Takayasu, 1984; 1987; 1989). Disregarding the location and symmetry and letting , the Lèvy distribution can be represented more simply as in which controls the relative size and the rate of convergence of the tail of across the range of values of t. In a Gaussian process with finite variance, ; if , the variance is nonconvergent but the mean, , can be computed; is the well known Cauchy distribution. If , the process is without a finite mean and will require the use of the median of interquartile indicators to locate the center of the distribution. Gaussian distributions are thus special stable Lévy distributions, with characteristic exponents a = 2 which by the Central Limit Theorem (Winer, Brown and Michels, 1991) converge to a finite mean and variance with sufficent sample size (Takayasu, 1989). For experimentalists who are accustomed to ignoring outliers in their data, the most remarkable feature of stable Lévy distributions is that the longer the period of observation, the greater the value for an outlier that might be observed. This signature, common to many fractal time processes, is the antithesis of the Central Limit Theorem governing normal stable Gaussian processes; that is, as more data points are accumulated, the variance and, in some cases, the mean are divergent. Can spontaneous fetal behavior such as nuchal atonia, a marker of fetal REM sleep, be described as a fractal time process?

I examined episodes of nuchal atonia, strongly associated with REM sleep in fetal sheep, with Hurst's rescaled range analysis to test whether this spontaneous fetal behavior would qualify as an independent random process. Developmentally, during embryonic days (E) 95-107, eye movements, nuchal muscle activity, breathing movements, and desynchronized low voltage fast (DLVF) electrocorticographic activity (ECoG) are almost continuous. Nuchal atonia first appears with differentiation of ECoG into synchronized high voltage slow (SHVS) waves and an increased mean amplitude of DLVF ECoG beginning near E120. At this time tonic nuchal activity starts to break up into periods of atonia. From E107 until E120 nuchal activity is actually increased during eye movement and breathing episodes. Following E120, long contractions of the nuchal muscles only accompany SHVS ECoG and are less active or absent during low-voltage activity (Clewlow et al., 1983). This reorganization of tonic nuchal activity into alternating periods of atonia and activity appears analogous in a general way to the emergence of spontaneous electrophysiological responses in early chick muscle primordium (Landmesser and Morris, 1975) or coordinated sequences of muscle contractions seen during later spontaneous motility in the maturing embryo (Bekoff, 1981). In addition, from about E120 on, spontaneous changes in fetal movements (e.g., rapid irregular fetal breathing, mouth and tongue, diaphragmatic, and isolated body twitches and generalized bursts of limb movements, changes in tracheal and arterial pressure) are correlated with most of the criteria of REM sleep in adult sheep (e.g., rapid eye movements, DLVF, increased cerebral blood flow; nuchal atonia; myoclonic twitches; Dawes, Fox, Leduc, Liggins and Richards, 1972; Parks, 1991; see figure 23-4, Rigatto, 1989; Szeto and Hinman, 1985). The sheep fetus, like other mammalian fetuses, is in DLVF sleep with atonia 40-60% of the time, proportionately more than time spent in any other behavioral state (Dawes et al., 1972; Rigatto, Moore, and Cates, 1986; Szeto and Hinman, 1985). Also, micturition, myoclonic twitches complex bursts of body movements and increased variability in heart rate and blood pressure fluctuations appear more likely to accompany periods of DLVF and atonia than SHVS ECoG (Robertson, 1987; Ruckebusch, 1971; Ruckebusch, Gaujouz and Eghbali, 1977; Wlodek, Thorburn and Harding, 1989). In accordance with these observations, in the third trimester of both sheep and humans, fetal REM has been suggested to provide a global organizing framework for perinatal behavioral states (Hofer, 1988; Kohyama, Shimohira and Iwakawa, 1994). The occurrence of nuchal atonia episodes, therefore, would appear to provide a primary index of this global fetal REM state.

Nuchal atonia in the late gestation sheep fetus probably originates from activity in behavioral state dependent neuronal populations in the reticular formation (RF), a brainstem structure which plays an important role in other phasic REM sleep phenomena in adults (Chase and Morales, 1990; Glenn, 1985). It therefore provides a convenient external marker of multiple state-dependent processes involving the adult RF, such as changes in single unit activity (Glenn and Dement, 1982; Peterson, Pitts and Fukushima, 1978) which are strongly associated with REM sleep. Although the neuroanatomical substrates responsible for phasic REM processes such as nuchal atonia are largely uninvestigated in the RF of fetal sheep, Peterson et al. (1978) observed that the probable origins of nuchal atonia in the adult cat involved large lateral inhibitory reticulospinal fibers originating in nucleus reticularis ventralis that project caudally as far as neck motor neurons, producing strong IPSPs in nuchal motor neurons when electrically stimulated. Atonia episodes result from a cluster of spontaneous phasic-event-related hyperpolarizing potentials invading motor neurons from these reticulospinal fibers and reducing the tonus of the nuchal muscle contraction (Glenn and Dement, 1982). Nuchal atonia is also a sensitive measure of the disruption of ECoG sleep patterns by infusions of drugs such as methadone or cocaine (Burchfield, Graham, Abrams and Gerhardt, 1990; Derks et al., 1993; Szeto, 1983; Szeto and Hinman , 1983), as well as, other dopamine and noradrenergic agonists or antagonists (Bamford, Dawes and Ward 1986 and Bamford, Dawes, Denny and Ward, 1986). These drugs are associated with the induction of a prolonged state of arousal in the sheep fetus. The presence of nuchal tone accompanied by DLVF ECoG (Ioffe, Janson, Russell and Chernick, 1980) is routinely used to distinguish this "arousal-like" state from REM sleep (Clewlow et al., 1983; Szeto, 1985). Therefore, transitions in nuchal EMG activity indicative of REM sleep are possibly representative of the state dependent reorganization of firing patterns in multiple sub-regions and neurotransmitter specific sub-populations in the RF (Hobson and Steriade, 1986; Sakai, 1985).

The interrelationships among the above mentioned fetal REM markers and nuchal atonia are often characterized as inconstant (Dawes et al., 1973; Parks, 1991), suggesting these fluctuations might be more completely described as fractal patterns in time. As I will describe spontaneous sequences of atonia episodes, over one embryonic day, have a clustered fractal structure in time that is different from random independent sequences. Statistical analysis of nuchal atonia episodes encompassing the observed gestation period demonstrated that longer episodes were observed with increased sample size resulting in nonconvergent cumulative means and standard deviations, the signature of fractal processes (Bassingthwaighte et al., 1994). Also, consistent with a developmental role for this clustered fractal time structure of atonia sequences, and inconsistent with other findings of Poisson random process for spontaneous prenatal behavior (Narayanan et al., 1970), distributions of atonia episodes were found to be well approximated by stable Lévy distributions over the gestational period examined, suggesting these may be invariant properties indicative of more general developmental processes.

REM SLEEP IN FETUSES AND NEONATES AS AN ONTOGENETIC ADAPTATION

The use of the term ontogenetic adaptation attempts to bring an ecologically valid perspective to interpretations of morphogenic and behavioral changes undergone during different developmental stages of an organism (e.g., embryonic, fetal, larval, postnatal and juvenile stages; Oppenheim, 1981, 1984). In essence the adaptive aspect of ontogenetic adaptation refers to those neurobehavioral and neurophysiological developmental patterns, processes and traits that enhance an individual's chances of perpetuating its genes. Although, as Oppenheim points out: "...there is always some danger in assuming that all traits of an organism are both adaptive and the direct result of natural selection...[and] it is not possible in most cases to test experimentally for the adaptiveness of a trait. In almost any discussion of adaptations one is forced...to rely on logical arguments [just so stories], inference and the consensus of fellow scientists as to whether or not a trait is adaptive (1984; p. 18)."

The core problem of developmental biology is the study of the temporal cause and effect relationship between transient antecedent structures (e.g., pharyngeal arches or gills, the pronephros, the egg-tooth) or behaviors (e.g., motility patterns, suckling, play) and more mature forms of those structures (e.g., adult facial features) and behaviors (crawling, walking, sleep-wake cycles, feeding, social interactions). Oppenheim's central purpose in introducing the concept of ontogenetic adaptation was to propose that viewing developmental change as a series of genetically controlled transient adaptations rather than a simple cumulative progression of developmental innovations provides a useful explanation

of the origins of age specific behaviors and structures in terms of meeting the unique ecological demands stemming from the organism's morphological and physiological immaturity (Oppenheim, 1984; Hall and Oppenheim, 1987). As Hofer (1988) points out: "The concept of ontogenetic adaptation can be useful to organize and understand many of the special features of the intrauterine period, as well as some of the features of subsequent development" ( p.6). In particular, in light of the fact that the occurrences of behavioral ontogenetic adaptations grossly characterize the developmental stages of an organism, they can also be used to assess the viability of the developing nervous system.

Why is REM sleep considered an ontogenetic adaptation? The dominance of REM sleep in fetal and infant behavioral states during prenatal and early postnatal life was first noted by Roffwarg and co-workers in the mid 1960's. Roffwarg et al. (1966) proposed that developmental neurobiologists "give consideration to the possibility that REM sleep plays a role in stimulating structural maturation and maintenance within the central nervous system" (p.617). REM sleep is the most metabolically active state of the brain in the fetus (Abrams, Hutchison, Jay, Sokoloff, & Kennedy, 1988; Richardson, 1991) and if it did not represent an adaptive innovation to the fetal (whether egg, pouch or uterus) or postnatal environment (nest or nursing niche), it would likely have been abandoned early in evolution for metabolic reasons; instead, it is ubiquitous in vertebrates and has analogous forms in higher invertebrates (Karmanova, 1982). An underlying experimental-theoretical foundation for understanding the how or why of this highly energetic REM state with its associated behavioral manifestations and the role it plays during ontogeny is almost completely lacking.

Corner (1990) has reviewed the connection between ultradian motility patterns in the embryos of vertebrates and invertebrates, their brainstem origins and the ontogeny of sleep states. He suggests a robust connection between the ontogenetic coalescence of body twitches, REM's, breathing moments, EEG, etc. in the developing animal and the maturation of the brainstem. The importance of REM is also supported by the observation that deprivation of sleep, especially REM sleep, in developing animals can have detrimental effects. Electrolytic lesions of pathways from the reticular core to the lateral geniculate nucleus (LGN) in kittens, which isolate the LGN from REM associated patterns of neuronal activity, were found to impair the structural and physiological maturation of cells in the LGN (Davenne and Adrien, 1985) Also, selective REM deprivation in kittens by non-invasive awakening produced anatomical changes in the LGN similar to eyelid occlusion (Shaffery et al., 1993). Rat pups deprived of REM sleep over the first three postnatal weeks with clonidine or alpha-methyl dopa, when tested as adults, showed a constellation of behavioral abnormalities such as hyperactivity, hyperanxiety, attentional distractability, sleep disturbances, reduced sexual performance and reduced cerebral cortical size (Mirmiran, 1986).

Hofer (1988) has referred to REM sleep as an ontogenetic adaptation "whereby early neural function acts as a vital ingredient in the developmental plan of the organism. Presumably, as the infant grows older, its interaction with the environment increasingly takes the place of this state specific internal stimulation. From its peak in the late fetal period, REM sleep proportion declines rapidly during the first postnatal year [in the human infant], possibly representing the decline of its role in neural development " (p. 16). This decline of the increased proportion of REM over the developmental period is analogous to the disappearance of other ontogenetic adaptations (i.e., shedding the fetal membrane and placenta at birth, the loss of sucking or crawling behaviors with the development of independent ingestion and walking).

If the REM sleep associated activity patterns represent an ontogenetic adaptation, then genetically homogeneous individuals would be expected to show similar patterns. Using a variety of methods for describing the temporal patterns of sleep in adults, several investigators have observed that general sleep structure as well as REM associated events exhibit a genetic component. Using Markov analysis, Zung and Wilson (1967) found almost complete concordance between all night EEG and REM patterns in adult monozygotic twins but not in dizygotic twins. Using standard methods, Webb and Campbell (1983) found significant correlations between the structural measures of sleep (e.g., onset latencies, awakening measures, stage changes and rapid eye movement amounts) in adult monozygotic but not in dizygotic twins. Using different standard methods, Hori (1986), in agreement with Webb and Campbell, found that the number of body movements associated with REM sleep were significantly correlated between adult monozygotic twins. However, Hori also found more similarities between structural measures of sleep in dizygotic twins than Webb and Campbell (1983). In a recent non EEG observational study of one neonatal pair of conjoined twins, both were found to have almost identical REM epochs per sleep bout and identical lengths of intervals between bouts, but temporal patterns of the occurrence of bouts were strongly individual (Sackett and Korner, 1993). Thus, these studies argue that the number of REM related activity patterns may have some genetic component, but that the temporal patterns of occurrence of these events is a characteristic of the individual. It is possible however, that these characteristic activity patterns show long run correlations in time, not detected in previous studies, that are invariant among members of a species and between species. Support for this conclusion comes from the work of Thoman, Zeidner and Denenberg (1981) who found commonalities among analog recordings of state-related motility patterns from rats, rabbits and humans scored by different observers, suggesting cross-species invariance in state-related motiltiy patterns.

Addressing the patterns of REM-associated activity, as well as motility during awake states, Thoman et al. (1986) have pioneered the interpretation of characteristic breathing and body movements signifying rest-activity cycles or "patterns of state behaviors" as an indicator of neurobehavioral stability in infants. Known associations between neurological defects and patterns of state behaviors furnish further evidence for these interpretations. For example, Tanguay, Ornitz, Forsythe and Ritvo (1976) found that eye movements (EM) in normal children did not become organized into bursts until 40 weeks gestational age; thereafter changes in the clustering of the bursts of EM were correlated with developmental age. From 2 to 24 weeks postnatal, as total REM decreases, the number of EM's remain constant resulting in an increase in the mean number of EMs/sec of REM. Between 3 months and 5 years of age, the major organizational change in the patterns of EMs is the increasing tendency of bursts of EMs to cluster, with more and shorter EMs packed into bursts within bursts. However, autistic children show substantially less clustering of EMs. In fact, no significant differences between burst structure in 2-5 year old autistics and younger (<18 month) normal children could be found. Thoman and colleagues have also found significant correlates between the stability of activity patterns and different developmental disorders (e.g., low stability scores were associated with major developmental disorders such as aplastic anemia, infantile seizures, hypsarrhythmia, SIDS and hyperactivity). The only criticism of the work of Thoman or predecessors such as Tanguay is not with the phenomena, because it has been so well supported in the literature, but with the use of standard methods of analysis (e.g. calculation of statistical moments such as the mean and variance under the possibly incorrect assumption of convergence) for biological processes that may not have convergent moments. Therefore, other methods of analysis sensitive to the temporal strucure of these activity patterns that do not rely on these standard statistical assumptions may provide new insights into their developmental roles.

EXPERIMENT 1: ANALYSIS OF NUCHAL ATONIAL SEQUENCES IN FETAL SHEEP: AN EXAMPLE OF THE FRACTAL TIME STRUCTURE OF A SPONTANEOUS PRENATAL BEHAVIOR

In the first of two studies, I examined spontaneous sequences of nuchal atonia associated with REM sleep behavior in late gestation fetal sheep (E121-133) with Hurst's rescaled range analysis, which affords comparisons between natural time series with short- and long-term correlated fluctuations (e.g., annual patterns of riverflow, rainfall, tree rings). This analysis indicats that nuchal atonia sequences over short time scales are statistically similar to longer time scales (i.e., is fractal in time). Hurst exponents (H) are distributed around 0.70 (H in an independent random process = 0.5) suggesting an invariant measure among animals and across age. Longer nuchal atonia durations are observed as more likely to be followed by longer durations, and shorter nuchal atonia events by shorter durations in a pattern called persistence. Several properties of nuchal atonia episodes are inconsistent with a Poisson process: 1) mean variance; 2) H 0.5; 3) probabilities are in the family of non-finite moment Lèvy stable distributions with a characteristic (tail) exponent of a < 2.0 ( a 1.8). Nuchal atonia has temporal coherence with other markers of REM sleep such as eye movements and electrocorticogram and breathing pattern changes consistent with its use as a marker of this sleep state. Based on the experimental findings detailed below I conclude that the fractal time patterns of nuchal atonia sequences appear to reflect the temporal structure of the global fetal REM sleep state over mutiple timescales which serves as a transient behavioral ontogenetic adaptation to changing developmental environments.

SPECIFIC METHODS

Subjects. Five time-mated pregnant ewes (Ovis aries, Rambouillet Columbia stock) obtained from the Cornell University breeding facility provided fetuses for this study. Ewes were acclimatized to the laboratory for one week prior to surgery. Ewes were housed in individual metabolism stalls, which permitted a range of movements and body postures but prohibited turning around so as not to damage catheters and electronic leads.

Preparation of Pregnant Ewes and Fetal Subjects. All surgeries were performed at E112-114 using ketamine (5-10mg/kg) and glycopyrollate preanesthetic and tracheal halothane which also anesthetizes the fetus. An antibiotic treatment of 1g ampicillin sodium (Polycilin-N; Bristol Laboratories, Syracuse, NY) was administered prophylactically, and 1g chloramphenicol sodium succinat (LyphoMed Inc., Melrose Park, Il) was administered i.v. to the ewe at surgery. Midline laparotomy and incision through the uterine wall provided access to the fetus. Chronic catheters were placed in the external jugular of mother and fetus to monitor blood gases as a means of determining preparation viability. EMG stitch-electrodes were placed on nuchal and geniohyoid muscles to enable recording of electro-myographic activity. Fetal electrocortical activity (ECoG) was monitored through gold electrodes placed on the dura overlying the parietal lobes to left and right of midline (see Robinson et al., 1995 and [Gluckman and Parsons, 1984], for more extensive details of the surgical procedures).

Data Acquisition and Analysis. Raw measurements from fetal EMG and ECoG leads were recorded in a computerized data acquisition system. Specifically, 50-200 mV

signals were amplified up to 2 volt full scale deflections and bandpass filtered (3-30 Hz for ECoG or 80 to 300 Hz for EMG signals), full wave rectified and low pass filtered at 10 Hz to create the envelope of signals. Fetal EMG and ECoG were then resampled with a 12 bit A/D converter at 32Hz and averaged over 1-sec intervals. Nuchal tone and ECoG measurements were normalized to 0 to 250 amplitude units and recorded continuously from E121 to 133. A 200 Hz EMG recoding made prior to low pass filtering was examined.

Two partitions of nuchal EMG were examined to distinguish baseline noise artifacts and to determine an unbiased estimate of atonia episode duration. The first partition (P1) was constructed by observing the range of variation of baseline EMG amplitudes across 13 days (typically 3-7 out of a possible 250 amplitude units) and recording the durations of EMG amplitude threshold range (e.g., values < 7 would count as atonia; events of amplitude > 8 would not). The second more stringent partition (P2) was contingent on the total absence of nuchal tone and was applied by observing the lowest EMG amplitude across the record and counting the duration in seconds of atonia.

Statistical Properties of Nuchal Atonia Episodes. Changes in mean nuchal atonia episode length and number over E121-E133 were assessed by 2-way ( 2 Partions ¥ 13 Fetal Days) Analysis of Variance (ANOVA ), with Fetal Day as the repeated measure. Simple main effects were analyzed by 1-way (Fetal Day) ANOVAs. Orthogonal linear trend analysis was used to further examine developmental trends for the number and average mean nuchal atonia episode length and number over the period of observation.

To examine the statistical properties of the Moments (e.g., cumulative mean and variance) a 3-way (2 Moments ¥ 2 Partions ¥ 13 Fetal Days) ANOVA was calculated, with Fetal Day as the repeated measure, for data sets ranging from 1 to 13 days in length. In addition, the cumulative means and standard deviations for each partition were tested individually for statistical convergence over development by 1-way ( 13 Fetal Days) ANOVA, with Fetal Day as the repeated measure. The criterion for type 1 errors was set on all comparisons at 0.05 and the Huhyn-Feldt procedure was used to assess violations of circularity (Winer, Brown and Michels, 1991).

Hurst's Rescaled Range Analysis. The Hurst exponents were estimated by the following segmentation procedure which is visually illustrated in Figure 2: (1) the mean over the total available record was calculated. (2) A lag () or window up to and including the total record length (i.e., 2048, 1024, 512, 256,128, 64, 32, 16, 8, 4) was chosen. (3) The local accumulated differences for nonoverlapping segments of length equal to were determined by subtracting episode length from the mean of the total record. (4) The local range (R), standard deviation (S) and ratio R/S determined for each was then calculated. (5) Local R/S ratios were then averaged. (6) The procedure was repeated for all window sizes or 's. (7) The logarithms of the average R/S values are then plotted against the logarithms of the fraction of points in the time window (e.g., for a 4 increment window out of 4096 increments the fraction would be 4/4096 or 0.0097). The linear regression of this line results in the slope which is equal to the Hurst exponent (H).

Two methods of validating Hurst analysis were used. The first involved randomizing the data set by the following procedure to destroy the correlations present in the data (Collins and De Luca, 1994 and 1995; Peters, 1991; Rapp, 1994). To accomplish this, a set of random numbers was generated for each file analyzed that ranged from zero to the size of the data set N and was stored in a parallel array. The random numbers were sorted in ascending order by size. In this way the random number corresponding to a particular N was used as an index to reorder the values of a original nuchal atonia data file. The reordered nuchal atonia data file or first order surrogate data set (Rapp, 1994) was then resubjected to Hurst analysis. Hurst and randomized exponent estimates were then

Figure 2. Diagrammatic representation of the processes of rescaled range analysis. The top line represents the entire analysis period (4096 sequential nuchal atonia episodes) where the first estimate of R/S is obtained by dividing the range by the standard deviation. Subsequent lines represent subsets of the original set which have undergone the same procedure to obtain multiple estimates that are then averaged. Average estimates of R/S are then plotted on a double logarithmic plot, and the slope determined by linear regression.

compared by a one factor (2 exponent estimates) ANOVA. The second method involved testing the Hurst algorithm on artificial data sets of fractional Brownian motion as generated by a spectral synthesis method with known values of H as described by Feder (1987) and Peters (1991).

Developmental changes in estimated Hurst exponents for original and randomized data sets were compared by 2-way (2 Partions ¥ 13 Fetal days) ANOVA, with Fetal day treated as a repeated measure. Developmental trends were tested by orthogonal linear trend analysis of average H values over the period of observation.

Estimating the Lévy Tail Exponent. I approximated the normalized density distributions of atonia episodes from each animal for E121-123 and 131-133 (i.e., for two 72 hour recording periods relatively early and late in fetal development) with parametrically fitted algebraic Lévy curves of the form , where C is a constant (Mantegna, 1991). I used a Simplex, direct search minimization of quadratic (i.e., sum of least squares) error (O'Neill, 1971; Griffiths and Hill, 1985) with larger initial step sizes (i.e., tolerances) designed to avoid local least squares minima while fitting and in combination. This is an exhaustive, "brute force" fitting procedure with relatively large but bounded regions of the parameter space (i.e., ). As noted below, the results of fitting to the density distributions of the nuchal atonia durations yielded which is consistent with processes termed anomalously diffusive in statistical mechanics; . Whereas the range of the summed increments of a subset of Lévy processes composed of Gaussian (or Poisson) independent random events with individual increments distributed such that grows with time in a process called normal diffusion, Lévy processes with individual events distributed such that are called superdiffusive (Shlesinger, 1987) and are consistent with the observed absence of finite (see results).

Nonlinear estimation is an art form. The pitfalls are many; parameter interdependencies and local minima among them. Here I have used variable, larger tolerances (i.e, 10-5 to 10-2) to test, and therefore avoid most local minima. The Simplex method of nonlinear estimation is robust in the presence of many discontinuities, as opposed to other methods (e.g., Quasi-Newton). Similarly, Simplex does not require that the model is differentiable in the parameter region of interest . The Simplex method is also immune to round off error because it recomputes estimates at each iteration.

The asymptotic standard errors were computed by central differencing finite estimation of the Hessian matrix after the parameter estimates were completed. Using this "final" matrix, rather than an iteratively updated one, I avoided the tolerance and iteration history dependence of some asymptotic standard error estimates.

RESULTS

Nuchal EMG records. Recordings of fetal sheep nuchal muscle potentials as normalized mVs over time appear at first glace to have little structure. However, after rescaling in both the dimensions of amplitude and time (see Figure 1, p. 7) 60 sec periods appeared qualitatively similar to those of 600 seconds which in turn resembled those over 60 minutes in a relation called self-affinity. In addition, this fractal time structure of nuchal atonia sampled at 1Hz appears to extend to nuchal muscle potentials recorded at 200Hz (see Figure 3, p. 30). The scaling structure of the irregular patterns of intermittent bursts of nuchal muscle activity and their absence appeared to have psychobiological significance: they corresponded roughly with other indicators of REM sleep including low voltage faster activity in the ECoG, eye muscle activity in the EOG, muscle activity in the geniohyoid

group, and changes in fetal breathing patterns recorded as tracheal pressure (see Figure 4, p.32 ).

Developmental Changes in Statistical Properties of Nuchal Atonia Episodes. Overall the results of the analysis suggest two main findings: As the fetus matures, there is a reduction in the number of nuchal atonia episodes (Figure 5a) and an increase in the mean length of nuchal atonia periods (Figure 5b). Without exception, application of the stringent partition P2 resulted in larger numbers of atonia events with shorter durations than with the less stringent partition P1 (Figure 5a and 5b). This may be due to small baseline fluctuations in EMG amplitudes which resulted in fragmentation of longer periods of atonia. Two 2-way ANOVAs ( 2 Partitions ¥ 13 Fetal days) comparing Partitions for

Figure 3. Nuchal EMG activity along the abscissa (2 volt range normalized to 25 standard units) plotted over 30 seconds on the ordinate (top trace). Rescaling time, the ordinate, over a 5 second subset of the original series (bottom trace) reveals smaller clusters within larger clusters of muscle discharges. Notice the similarity with (figure 1, p. 8) suggesting that clustering in muscle unit activity over milliseconds is self-affine with clustering in nuchal atonia events over hours

Figure 4. Digitized analog recordings from a representative sheep fetus on day E133 of gestation portray nuchal atonia episodes as a low or nearly flat baseline in nuchal EMG trace. Fetal REM sleep is characterized by lower nuchal muscle tone and increased geniohyoid EMG and eye movement EOG potentials corresponding roughly in time with lower voltage faster frequency patterns in the electocorticogram record, ECoG. Periods of decreased geniohyoid EMG and eye movement EOG potentials overlap with increased nuchal tone and higher voltage lower frequency ECOG.

Figure 5. Developmental changes over days E121-E133 in mean number of atonia episodes (a) and mean length of atonia episodes (b) over a day for the lower amplitude, more sensitive partition (P1) and higher amplitude, less sensitive partition (P2) in all animals. Error bars indicate the standard error of the mean for each day.

mean nuchal atonia episode length and for nuchal atonia number revealed significant main effects of Partition, F(1,4) = 2.502, p<.05, e = 1, and F(1,4) = 8.954, p<.01, e = 1, respectively. A significant main effect of Fetal Day was also present for atonia event number F(12,48) = 9.285, p<.01, e = 0.223, but not for mean length F(12,48) = 1.664, p>.05, e = 0.213. This suggests there is a strong developmental trend for decreasing nuchal atonia episode number over gestation which was evident with further 1-way tests of Partition and Day. The number of atonia events was found to significantly decrease with Fetal Day for P1, [F(4,12) = 10.460, p<.0001, e = 1] and for P2 [ F(4, 12) = 4.879, p<.05, e = 0.222], (p<.0001 before correcting for violation of the assumption of circularity) over the period of observation. In agreement with reports showing a decline in fetal DLVF ECoG with development (Dawes et al., 1983; Clewlow et al., 1983; and Szeto, 1985), trend analysis indicated linear developmental trends for decreases in the number of atonia events with P1 F(1,48) = 113.755, p<.0001,e = 1 and for P2 F(1,48) = 49.119, p<.001,e = 0.222, which accounted for 90.62% and 83.89% of the variance while departures from linearity accounted for 9.38% and 16.11%, respectively, of the remaining variance but did not reach criterion.

Although, the main effect of Fetal Day on mean nuchal atonia episode length was not significant, as a result of the large variability of atonia episodes, further analysis by 1 way (Fetal days) ANOVA resulted in an apparently significant effect of Fetal Day on P1 [F(4, 12) = 19.755, p<.05]. However, after corrections for a departure from the assumptions of circularity, this was found not to be significant , p >0.05, e = .624. Analysis of P2 was also non-significant [F(4, 12) = 19.755, p >.05 ,e = .118]. A priori trend analysis, justified by an apparent trend in the data (Figure 5b) indicated a linear increase in episode length with developmental age in mean nuchal atonia episode length for both P1[ F(1,64) = 12.831, p<.005,e = .624] and P2 [ F(1,64) = 43.117, p<.01,e = .118] which accounted for 54.15% and 68.42% of the variance, while departures from linearity did not reach criterion.

To test whether sequences of nuchal atonia are statistically similar to a Poisson process (e.g., for a Poisson process the mean equals the variance) in addition to the effects of Partition and Day, the cumulative Moments (e.g., mean and varience of nuchal atonia events summed progressively over 13-days) were analyzed by a 3-way ANOVA (2 Moments ¥ 2 Partitions ¥ 13 Fetal Days) with Fetal Day as the repeated measure. This

test detected a significant main effect of cumulative Moments [F(1,4) = 43.043, p<.0028, e = 1]. None of the 2 or 3-way interactions, however, proved to be significant. The nature of the effect of Moments is evident in Figure 6a and b where the magnitude of difference between the cumulative mean and variance for both Partitions over 24 hrs and development is seen to be quite large. Specifically, the magnitude of the difference is greater for P2 than P1. The difference between the cumulative mean and variance for P1 (M = 14.104 vs. V = 355.357 seconds) was significant [F(1,4) = 47.159, p<.005, e = 1] by 2-way repeated measures ANOVA (2 Moments ¥ 13 Fetal days). For P2, however, although the cumulative variance (V= 585.666 seconds) was larger than the cumulative mean (M = 8.539 seconds) and significantly different [F(1,4) = 12.069, p<.05, e = 1], the significance level was smaller. The extreme difference between the cumulative mean and variance argue against the possibility that nuchal atonia is a Poisson process.

To investigate whether the cumulative means and variance demonstrated any

Figure 6. (a)The cumulative mean duration and variance derived for both partitions over increasing numbers of nuchal atonia episodes for the five subjects during 24hr and (b) over increasing days of development E121-133, both of which fail to demonstrate the expected convergence of the variance in general and the mean in particular of a Poisson process.

statistical convergence with development both partitions were tested by a priori trend analysis following a 1-way ANOVA (Moment). None of the main effects of the 1-way ANOVAs were significant after corrections for departures from the assumptions of circularity. However, the cumulative mean and variance of P1 significantly increased with development [F(1,64) = 20.178, p<.05, e = .168] and [F(1,64) = 11.208, p<.005,e = .204], which accounted for 42.037% and 23.351% respectively, of the varience while other trend components were not significant.

To summarize the findings thus far, significant developmental decreases in the nuchal atonia episode number across all subjects were observed. This is compatible with previous reports of developmental declines in fetal REM sleep (Dawes et al., 1983; Clewlow et al.,1983; and Szeto, 1985). The cumulative mean duration and variance of atonia episodes were significantly different, highly variable and non-convergent in terms of the central limit theorem because the mean and variance consistently increased with sample size. The high variability also contributed to the finding of a non-significant effect of days on mean atonia length, although a priori trend analysis indicates a highly significant developmental increase in the length of atonia periods. These data are consistent with the hypothesis that REM sleep periods, when indexed by nuchal atonia, tend to consolidate into longer clusters with increasing age.

Results of Hurst Analysis of Nuchal Atonia Sequences. Hurst analysis, quantified by H, measures long-run statistical dependency or correlations within a timeseries (Bassingthwaighte et al., 1994). Hurst exponents greater than 0.5, which are significantly different than Hurst exponents from randomized surrogate data sets, suggest that the assumption of statistical independence between events can be rejected. Hurst exponents calculated for P1 ranged from 0.553 to 0.779 and from 0.620 to 0.843 for P2 during the period of observation (Figure 7), suggesting the presence of long-run dependency between Figure 7. The least squares fits of the mean of the Hurst exponents illustrate the changes in persistence (defined by H > 0.5) for the original sequences of nuchal atonia episodes for each partition. The R represents the Hurst values (H 0.5) computed in the same way following randomization of the sequences data for partition 1 and 2 over development, reflecting the expected loss of long range correlations following shuffling of the sequences.

nuchal atonia episodes over 24 hours. A histogram of the distribution of Hurst exponents for both P1 and P2, original and randomized is displayed in Figure 8a and 8b. A 2-way ANOVA (2 Partions ¥ 2 Fetal days) was used to assess the effects of Partition and Fetal Day on estimated Hurst exponents. This analysis indicated the significant main effect of Partition F(1,4) = 11.169, p>0.05,e = 1 and Day F(12,48) = 4.377, p>0.0001,e =1. Over all days examined, Hurst exponent estimates for P2 were higher than those for P1 (Figure 7). In addition, a substantial decreasing linear trend of Hurst exponent estimates with Day was evident regardless of Partition F(1,129) = 47.533, p<.0001,e =1.

Hurst exponents calculated from randomized surrogate data sets of P1 and P2 ranged from 0.430 to 0.587 and 0.408 to 0.590, respectively. Hurst exponent estimates from the original data sets were found to be significantly different, independent of Partition, from estimates derived from randomized surrogate data sets by 2-factor ANOVA (2 Hurst Estimates ¥ 2 Partitions) P1[ F(1, 4) = 572.221, p<.0001, e = 1] and P2 [F(1, 4) = 723.525, p<.0001, e = 1] confirming the existence of long-run dependency. A priori trend analysis also indicated strong linear trends for decreases for both P1 [F(1,64) = 12.831, p<.005, e = .624] and P2 [F(1,64) = 43.117, p<.01, e = .118] which accounted for 73.13% and 67.16% of the variance while trend components were not significant.

In summery, the magnitudes of Hurst exponent estimates were dependent on the Partition. Hurst exponent estimates from original timeseries were significantly different from Hurst exponent estimates from randomized surrogate data for both partitions and all days. In keeping with the strong developmental decline in nuchal atonia episode number, a significantly decreasing linear trend in Hurst exponent estimate magnitudes with day was observed. This decline is not unexpected due to the developmental decrease in nuchal

Figure 8. The distribution composed of all the 24 hour values of Hurst exponent (H) estimates for (a) original and (b) randomized sets for both P1 and P2 partitions over the period of gestation examined. The largest probability mass of the Hurst exponents for the original sequence was in the neighborhood of H 0.70. H 0.5 for the randomized set.

atonia event numbers and the effects of smaller sample sizes on Hurst estimates (see Bassingthwaighte and Raymond, 1994). Therefore, higher resolution measurements of

nuchal atonia events are needed to counter the developmental effect of the declining number of nuchal atonia events before the existence of a developmental trend in the Hurst exponents can be confirmed.

The probability density distributions describing nuchal atonia. To test the hypothesis that nuchal atonia episodes might not be described by normal Gaussian distributions, the goodness of fit to other Lévy distribution curves, as indexed by the derived characteristic exponents a and g, was examined. Fitting the probability distribution yielded estimates of a ranging from 1.8224 to 1.8300 and g's from 3.0062 to 3.0745 across animals and days. The single parameter Simplex estimates converged quickly and had small asymptotic standard error estimates (all A.S.E. < 0.008). No consistent changes in a or g were found between animals or within each animal across gestational days. Also, the finding that the normalized probability density distributions of atonia episodes calculated for the two partitions were generally similar in form over development (see Figure 9) is consistent with both the unbiased nature of the estimation of atonia events by the partitioning procedure and the finding of invariance in the characteristic exponents with maturation.

Figure 9. The log-linear plots of the probability density distributions for nuchal atonia episode durations on representative days of a representative animal demonstrate the highest densities at the lower bounds of the resolution of its sampling rate in animal A, as in a Poisson process. In addition, they display long tails which failed to converge over sample length or days. This distribution remained invariant over the 13 days of observation for all fetuses despite a shift in the average length of nuchal atonia episodes.

DISCUSSION

Fractal description is useful in developmental psychobiology because it unifies experimental accounts of diverse and apparently independent random events of behavior by representing relations among these patterns over many scales of space or time. The erratic cluster-within-clusters appearance of nuchal EMG activity in Figure 1 would seem to portend large within-group variances and concomitant difficulty discerning developmental trends using traditional methods of analysis. However, when this EMG activity is viewed at different timescales, a new symmetry of similar erratic behavior independent of timescale

is evident. Many neurobiological and behavioral processes appear, at first glance, similarly erratic over time. For example, ion channel currents (Liebovitch and Tóth, 1990), interspike intervals (Gerstein and Mandelbrot, 1964; Selz and Mandell, 1992; Teich, 1989), animal search behavior (Coughlin, Strickler, and Sanderson, 1992; Cole, 1991; Fourcassié, Coughlin and Traniello, 1992) plant and animal population dynamics (Hassell, Comins and May, 1991; Tilman and Wedin, 1991) and even taxonomic diversity (Burlando, 1990;1993) all have this self-affine signature of clusters within clusters. The analysis of the intervals of atonia of Figure 1, or nuchal atonia associated with REM sleep, revealed surprising statistical properties, such as cumulative moments that are non convergent with larger samples (i.e., violate the law of large numbers). Nuchal atonia is therefore neither Gaussian nor Poissonian, but highly ordered in that statistical interdependence extends between these intervals of atonia over many time scales. Another implication of this novel descriptor "fractal time" is that there is no natural time scale for the measurement of spontaneous prenatal behavioral patterns. This perspective on

the measurement of biological processes should be considered when examining complex patterns of behavior. Conversely, the measurement of a spontaneous prenatal behavior pattern, such as a nuchal atonia episode sequence or perhaps spontaneous motility, then depends on the time scale of measurement. This intrinsic variability of developmental fractal processes with time scale may underlie some of the difficulties in defining fetal behavioral states.

The implications of fractal time descriptions for defining fetal states. The definition of REM sleep and other states in the fetus is problematical because it is defined in relation to a prototypical adult state, with implicit assumptions that may be inappropiate when applied to the changing behavioral state of fetal REM sleep. In defining REM sleep in the fetus, characteristic markers used in the adult definition have either not matured or have greater variability in the fetus. In terms of REM sleep, the similarities with the adult state are many: DLVF ECoG (Clewlow et al, 1982); increased brain metabolism (Richardson, 1991), nuchal atonia (Ioffe et al, 1980; Szeto and Hinman, 1983), rapid eye and irregular fetal breathing movements (Dawes et al, 1972; Ruckebusch, 1972) -all classical indicators of REM in adult sleep physiology. However, the extent to which REM sleep markers correlate with other state-markers is much more variable in fetal or neonatal animals (Briem, 1986; Ruckebusch, 1972; Parks, 1991). Thus efforts to unambiguously delineate the behavioral states of sleep and wakefulness in fetal sheep or any fetus are beset from the start by the conceptual bias introduced by backwards generalization from adult states to fetal states. Further complications mark any attempt to define the in utero state of alert wakefulness in studies of fetuses where behavioral or drug manipulations have disturbed the fetus and its environment. In these instances of fetal disruption, DLVF becomes disassociated from nuchal atonia, and this is considered indicative of a state of arousal which has been reported in utero (Clewlow et al, 1983; Szeto and Hinman, 1983). Parks (1991) points out the dangers of circular arguments in using descriptions of fetal activity to test the validity of criteria for behavioral states and concludes that fetal "states" identical to coma, sleep or wakefulness do not exist in utero and are unique to adults.

My observation of increased variation with additional nuchal atonia episodes, a hallmark of fractal processes, suggests that difficulties of delineating the behavioral states of sleep and wakefulness in fetal sheep may result from the presence of fractal processes. The pattern of fetal behavioral states, if fractal in form, would not have a single natural time scale, and measurement of changes in these states would depend on the timescale of measurement or the size of time window used to classify an electrocorticogram tracing (Dement and Mitler, 1974). In support of this viewpoint, recent analysis of heart rate variability in the human fetus has demonstrated fractal structure in time (Gough, 1992; 1993; Shono et al.,1991), suggesting that the absence of a single natural time scale for making measurements may underlie the difficulties associated with diagnosing fetal distress and may partially explain the parallel increase in use of cesarean surgery with the availability of fetal monitoring (McCutcheon-Rosegg and Rosegg, 1984; Szeto, Personal Communication).

Nuchal atonia as a marker of REM sleep in fetal sheep. I have reviewed behavioral and neurophysiological studies supporting nuchal atonia as a correlate of REM sleep in adult species. The findings of the present study also support nuchal atonia as a marker of a REM sleep-like state in the sheep fetus. I observed a significant developmental pattern of decline in the number of nuchal atonia episodes across all animals and partitions with maturation, analogous to the ontological consolidation of markers of REM sleep in other species (Jouvet-Mounier, Astic and Lacote 1970; Roffwarg et al., 1966). I also observed a significant difference in the number of atonia episodes depending on the method of partitioning EMG activity, with P2 showing significantly more events that P1. I believe this difference is due in part to the sensitivity of P2, the most rigorous partition, to low amplitude digitization noise, resulting in the interruption of an ongoing absence of EMG activity and an associated generation of multiple atonia periods from single events. Also, for both partitions,the possibility exists that in some cases atonia periods were terminated prematurely by fetal movement artifacts from other channels, although this seems unlikely due to time lags observed between limb EMG and nuchal or ECoG recordings at higher resolution (data not shown). If, however, movement artifacts are present, my bias is that these occurrences represent in all likelihood concurrent phasic REM phenomena that could be confounded with nuchal atonia measurements without significantly affecting or invalidating the conclusions concerning the fractal nature of fetal REM associated processes. In fact, I would hypothese that other fetal behaviors (e.g. leg, trunk, and eye movements; breathing, heart beats) could be described as fractal time processes with similar Hurst exponents.

How does the presence of fractal correlations and non-Gaussian distributions influence the validity of statistical procedures, such as repeated measures ANOVA which are used to assess developmental changes in nuchal atonia? This is a fundamental problem that is at present unresolved. Fractal biological processes can run counter to the basic statistical assumptions involved in estimating stable population means or variances from stable sample means or variances because these processes do not show convergence with increasing sample size (Bassingthwaighte et al. 1994). Nuchal atonia distributions are stable over the course of development as was demonstrated by the invariance of the characteristic exponents and the form of the normalized probability distribution. This suggests that these processes are at least stationary over long periods of development. These confounds of non-convergent moments would prove more severe for non-repeated measures comparisons. Non-repeated measures ANOVA procedures allow comparisons between groups of uncorrelated means under the assumption that the means are normally distributed and have homogeneity of variance. Repeated measures ANOVA, however, by definition, compare correlated means and attempt to correct the F-test and probability levels for violations of assumptions by approximations such as the Hunyh-Feldt epsilon (Winer et al., 1991). The large partition dependent variations in both length and number of within subject atonia episodes probably contributed to the observed violations of the assumption of circularity. The observed violations of circularity are assumed to be another indication, along with the non-convergence of the cumulative moments, of the dissimilarity of fractal sequences of nuchal atonia episodes from normal Gaussian processes.

Given the above considerations, I conclude that nuchal atonia episodes investigated in this study are indicative of REM sleep for the following reasons: 1) At least one other REM associated state marker (low fast ECoG, EOG activity, tracheal pressure changes, movements of mouth or limbs) was usually observed to be coincident with nuchal atonia events, although this was not rigorously quantified for all days and animals; 2) the percent decline in total nuchal atonia developmentally, about 65% for E121 to 50% for E133, calculated by totaling atonia episode lengths over 24 hours, is similar to other reports of total REM time for sheep fetuses in this gestational range (Dawes et al., 1983; Clewlow et al., 1983; and Szeto, 1985); 3) A significantly linear trend of increasing nuchal atonia mean length with development suggests the possible consolidation of short nuchal atonia episodes into longer duration episodes, a trend reported for the clustering of rapid eye moments in human infants (Petre-Quadens, De Lee and Remy, 1971; Tanquay, Ornitz, Forsythe and Ritvo, 1976).

Non-convergence of Non-Poissonian Nuchal Atonia Episode Sequences. As I have reported, one key descriptive characteristic of nuchal atonia episode sequences is their deviation from normal probability distributions and the central limit theorem assumptions. This may seem abnormal given the pervasive use of Gaussian distributions. However, when viewed from the perspective of all Lévy distributions, the properties of normal Gaussian distributions, such as convergence of the mean and variance with increased sample size, are seen as unusual in a space of distributions where non-convergence of one or both moments is the norm (Takayasu, 1989). For one partition of nuchal atonia events, P1, I found the cumulative mean and variance were significantly non-convergent. I also report that, although nuchal atonia might appear, by the shape of the probability distribution, to be a Poisson distributed process (see Figure 9), the cumulative mean and standard deviation are significantly different for both P1 and P2. Therefore, nuchal atonia episodes are not consistent with a Poisson random process for the following reasons: 1) The cumulative mean is significantly different from the cumulative standard deviation; 2) The long tails of atonia distributions contribute to increased variance which does not converge with a larger "n", unlike the "law of large numbers" for Gaussian processes; 3) The Hurst exponent is > 0.5, suggesting long range correlations or dependency in the increments which violate assumptions of statistical independence.

Spontaneous Prenatal Behaviors as Non-Poisson Fractal Time Processes. Spontaneous prenatal behaviors such as spontaneous motility have been described previously and conceptualized as stochastic processes. Narayanan, Fox and Hamburger (1971), for example, reported that episodes of spontaneous motility in the E17-20 rat fetus could not be statistically distinguished from a Poisson random process. Recently, Blumberg and Lucas (1994a; 1994b) reported that limb twitching in normal and spinal transacted 5- and 8-day old rat pups also displayed Poisson random behavior as indicated by log-survivor analysis. The results of these experiments appear to differ from my findings that nuchal atonia events are not Poisson distributed.

One possibility is that traditional data collection methods are biased in that they are not sensitive to infrequent events (Fagen & Young, 1987) because an extended observation period or higher sampling of a fractal process would inevitably result in the appearence of outliers and higher variances. For example, Narayanan et al. recorded the length of periods of spontaneous unevoked activity and atonia in and ex utero for 15 minutes only. In their analysis of the distribution of spontaneous activity, the 15 minute observation time was divided into 45 periods of 20 seconds during which the number of movements was recorded. This method effectively high-pass-filters behavioral observations, restricting them to one "characteristic" timescale, 20 seconds, which effectively eliminates long periods of movement and restricts short movements to the sampling rate. Examining all relevant timescales is critical to obtaining a complete overview of temporal patterns of behavior. For example, in the analysis of behavioral repertoire size, the complexity of a species behavior repertoire increases with the sample size and length of the period of observation, thus necessitating very long records to adequately estimate the full range of behaviors (Fagen, 1987). When Fagen (1987) analyzed different distributions of complex behavior repertoires for optimum curve fits, the lognormal distribution, a prototypical fractal distribution (Montroll and Shlesinger, 1982; 1984; West and Shlesinger, 1990) was found to provide the best fit.

Validating the results found for fetal sheep, analysis of surface EMG recording of spontaneous motility from 2- and 5-day old rat pups collected at high sampling rates (300Hz) over long sampling times (one hour) reveal non-Poisson distributions and Hurst exponents similar to the sleep nuchal atonia (See Experiment 2). Similar to findings reported here for the clustering of nuchal atonia events are descriptions of clustering in the spontaneous discharge of single pyramidal track neurons during REM sleep in adult monkeys that have been shown to differ from a Poisson distribution because of an excess of short and long interspike intervals (Evarts, 1964; 1967). Evarts was able to demonstrate the non-random nature and behavioral state dependency of these discharge patterns by using an extensive range of counters and recording continuously from subjects over long periods. Consequently, spontaneous prenatal behaviors should be investigated with longer observation times or finer sampling rates along with the proper statistical tools (Bassingthwaighte et al., 1994; Rapp, 1994) such as Hurst analysis, before conclusions about the random nature of these developmental processes can be accurately drawn.

Hurst Analysis of Fractal Time Nuchal Atonia Sequences. The presence of Hurst exponents of greater than 0.5 for nuchal atonia episode sequences for all data partitions, days and subjects, indicating correlations between REM processes over many timescales, is an important finding of this study. Due to the necessity of examining 24 hr records (defined as one fetal day), I was limited to three orders of magnitude of nuchal atonia episodes in my Hurst analysis. Recent work by Berge et al. (1994) concerning Hurst analysis of particle flow through a single pore argues for five or more orders of magnitude to rule out crossover effects; these can lead to a spread in different Hurst estimates for the same subject or experiment situation resulting in a distribution of estimates centering on an effective H @ 0.75 (see figure 4.19 in Bassingthwaighte et al., 1994). I found, similarly, a distribution of Hurst estimates centering on H @ 0.70. Further investigation of these possible crossover effects, as reported by Berge et al., over time periods longer than 24hr in this data may prove valuable in elucidating the developmental emergence of circadian rhythmicity in the fetus (Robertson, 1988) which current results do not address. Another difficulty with Hurst analysis reported here is the developmental decline in number of nuchal atonia events from E121 to E133. Hurst analysis of short correlated sequences results, spuriously in H @ 0.5 (Bassingthwaighte and Raymond, 1994). A possible solution to the problem of nuchal atonia episode number influences on Hurst estimates would be to observe nuchal EMG at higher sampling rates (e.g., average over 500, 250 or 100 msecs). Anmuth, Goldberg and Mayer (1994) report fractal scaling relationships between EMG structure and muscle activation in humans with high sampling rates. Analysis of interspike intervals from single motor units may also be informative (Rapp, et al. 1993). Any of these procedures would enable high resolution examination by Hurst analysis for possible periodic ultradian processes which I did not observe in the current analysis. In addition, all physical and biological fractals have an effective range of timescales or spacescales over which they manifest scaling behavior (Bassingthwaighte et al. 1994). Addressing this issue, analysis of 200 Hz recordings of nuchal activity from other sheep fetuses (illustrated in Figure 3, p.31) indicate that the scaling relationships reported here for 24 hours are present with similar H values over time periods of 5 seconds (Anderson et al., unpublished). In order to determine if patterns of nuchal activity as indexed by the Hurst exponent and distrubutional charateristics would be similar in different species a series of observations of nuchal inactivity sequences in infant rats were carried out and are reported in the next section.

EXPERIMENT 2: ANALYSIS OF NUCHAL INACTIVITY SEQUENCES IN NEONATAL RATS: AN EXAMPLE OF THE FRACTAL TIME STRUCTURE OF A SPONTANEOUS POSTNATAL BEHAVIOR

Neonatal rats display spontaneous movements or twitches of the limbs, the trunk, the head and tail indicative of a state of REM sleep (Blumberg and Lucas, in press; Gramsbergen, Schwartzen and Prechtal, 1970; Jouvet-Mounier, Astic and Lacote,1970; Tamásy, Korányi and Lissák, 1980; Van Someren et al. 1990). These movements are associated with fluctuations of muscle tone which reflect central processes associated with the induction of muscle inactivity and REM sleep. Over the first postnatal week, one key indicator of REM DLVF ECoG is difficult to record reliably due to masking by EMG artifacts. In fact, the other classical indicators of REM, loss of nuchal muscle tone and paroxysmal musclar twitches accompanied by rapid conjugate eye movements (observable on PN 5-6), are the only reliable indicators of this state in infant rats (Jouvet-Mounier et al., 1970).

In this experiment, I investigated the temporal structure of spontaneous fluctuations of nuchal muscle tone in the form of inactivity sequences in infant rats on postnatal (PN) days 2, 4, 6, 8, and 10 with Hurst's rescaled range analysis, a statistical technique that distinguishes between natural time series with correlated and uncorrelated fluctuations (Mandelbrot and Wallis, 1995). I chose the term nuchal inactivity rather than nuchal atonia to distinguish the recording technique used here from that used to measure nuchal atonia in fetal sheep (e.g., surface EMG as opposed to intramuscular wire EMG). My analysis indicates that nuchal inactivity sequences are fractal patterns in time and that

over short time scales are statistically similar to those over longer time scales as in the nuchal atonia sequences found in fetal sheep. Hurst exponents (H) are distributed around 0.77 for the 0 hr deprivation condition and 0.80 for the 2 hr deprivation condition over all ages (H for an independent random process would = 0.5). The mean H exponent is within 0.07 units of the H values for fetal sheep, strongly suggesting that the H exponent is measuring a process associated with neonatal REM sleep across age and species. Further supporting the finding that the fractal nature of these patterns of nuchal inactivity sequences are inconsistent with a Poisson process are the following observations: 1) the mean does not equal the variance; 2) H 0.5; and 3) probabilities are in the family of non-finite moment Lèvy stable distributions with a characteristic (tail) exponent of a < 2.0 ( a 1.8). The early postnatal rat has been proposed to bear similarities to the third trimester fetus, suggesting it may spend a similar amount of time in a REM state similar to that of the fetal sheep. Based on the experimental findings detailed below, I conclude that these fractal time patterns of nuchal inactivity sequences represent an extension of the temporal structure of the global fetal REM sleep state into the postnatal period. This extension supports the notion that these properties may serve as a transient behavioral ontogenetic adaptation to changing developmental environments. In addition, the change in the clustered patterns of nuchal inactivity (i.e., shift to more persistent and prolonged bouts of clusters) with 2 hours of maternal deprivation as indicated by the increase in H (increase in presistance) and decrease in the Lèvy tail exponent (increase in cluster size), further support the usefulness of fractal time measures as a window into heterochromatic mechanisms underlying the plasticity of developing organisms to changing environmental factors.

SPECIFIC METHODS

Subjects. Forty male and forty female infant rats from 26 litters were tested (25 of which are reported here) from the age groups postnatal day (P) 2,4,6,8 and 10. The average body weights of the animals used are represented in Figure 10. All infant rats were born to Sprague-Dawley females (Charles River CD strain) in the animal colony at Florida Atlantic University. Water and Purina Lab Chow (#5012) were provided ad libitum. All animals were housed under temperature- and humidity-controlled conditions (21-23oC and 40-70% relative humidity) on a 14:10 hour light:dark cycle (lights on at 0700 hrs). Infant rats were raised in litters culled to 14 rats within 2 days after birth (day of birth = Day 0). Larger litters were used to ensure that littermates remaining after removals would not grow excessively large. Due to the necessity of collecting 2-hour-long time series recordings, only 2-3 infant rats/litter were examined per age.

Preparation of Subjects. Infant rats were quickly collected from the dam to minimizing disturbance to the the subject and remaining littermates. The subjects were transported in a small covered container (to attenuate thermal shock) filled with home cage bedding and then quickly weighed on an electronic balance before beginning electrode placement. Electrode placement and design was informed by Loeb and Gans (1986). Small amounts of Nuprep (D.O. Weaver & Co., Aurora Co), a cleaning abrasive, were applied to the neck and dorsal trunk to remove oils and lightly abrade the skin to improve electrode conductance. Three small electrodes (fabricated by cutting 4 mm [approx.] section from the tip of a conical microcentrifuge tube, inserting coiled 1mm bare silver wire through the

Figure 10. Bar chart of average body weights and standard errors of subjects used in these experiments illustrates the normal developmental changes in body weight. Doubling of body weight over this postnatal period is evident from linear trend analysis indicating a strong linear increase in weight with Postnatal Day F(1,16) = 158.457, p<.0001, which accounted for 99.46% of the variance.

tube wall and filling with electrode paste) were attached to the sites by super-glue. Two electrodes were applied bilaterally to the neck region approximately 5mm lateral to the midline, and the ground electrode was applied to the base of the tail. Anatomical guides were used to define nuchal muscle in the infant by extrapolating from the adult rat (Greene, 1963, p. 35; Hebel and Stromberg, 1976, p. 19; and Wingerd 1988, p. 19).

Soon after this procedure (the entire process takes less than 5min), the subjects were placed in a jacketed chamber with the temperature and relative humidity maintained close to thermoneutrality (between 34.5-35.8oC and 50%-64%, respectively) for testing (Satinoff, 1991). Subjects responded well to the procedure and appeared to enter REM sleep quickly after being placed in the testing chamber, as evidenced by the rapid appearance of twitches (Szymusiak, Stinoff, Schallert and Whishaw, 1980). Unlike the fetal sheep described in the last section, neonatal rats when removed from the dam are subject to maternal deprivation effects (see Anderson, 1991; Hofer, 1976). Maternal deprivation is therefore a treatment condition in these experiments.

Data Acquisition and Analysis. A Grass model 7P511L high performance AC amplifier in combination with a Grass model 7HIP5G high impedance probe was used to record neck surface EMG and movement artifacts generating an analog -5 to 5mV signal proportional in amplitude to the µV range biological source signal. Additional recordings of movements detected with a electrostatic motion sensitive device were also made. In this case movement patterns were detected and converted into analog 0-1V signals proportional in amplitude to the movements by a capacitive proximity sensor monitored by a radio-frequency circuit using a phase-locked-loop in the 1 megHz frequency range. The voltage output from one or both amplifiers was sent to a MacADIOS II jr 12-bit A/D (equipment, GW Instruments, Inc., Somerville, MA) sampled at 300 Hz and processed offline.

Nuchal inactivity sequences were detected by first full wave rectifing the 300 Hz

Figure 11. A segment of raw unrectified nuchal EMG (-5 to 5 mV) showing intermittent bursts of nuchal activity from 6194 to 6218 seconds. At 6218 seconds a large sustained burst of nuchal muscle contraction ensues. The regions of intermittent bursting of nuchal EMG associated with behavioral twitching would result in the detection of long episodes of inactivity. The sustained burst of EMG associated with behaviors such as orienting head movements would result in many short episodes of inactivity.

EMG signals. An example of the raw unrectified nuchal EMG can be found in Figure 11.

Two partitions of the resulting signal were then examined to distinguish baseline noise

artifacts and to determine an unbiased estimate of the duration of inactivity episodes. The first partition (P1) was constructed by observing the range of variation of baseline EMG amplitudes (typically 0 to 0.1 mVs after rectifying) and then recording the durations of EMG amplitude threshold range (e.g., values < 0.1 mV would count as inactivity; events of amplitude > 0.2 would not). The second partition (P2) examined the range of 0.1 to 0.5

mVs. Other partitions, 0.5 to 1.0 and 1.0 to 2.0 mVs, were also examined but are not reported here. These partitions were well above the background noise levels ( < 0.01 mVs) in most cases. In addition, two periods of the recording, the first 5 and last 5 minutes of the 2 hour recording session were compared to determine the effects of maternal deprivation on nuchal inactivity episodes. Representative histograms generated from these partitions are illustrted in Figure 12. In anesthetized subjects (Methoxyflurane[Metafane Pittman Moore, Washington Crossing, NJ]), complete loss of muscle tonus was observed and no segmentation of nuchal inactivity occurred (see Figures 15a and b). This manipulation constitutes a control for non-specific noise resulting from the instrumentation as well as heart beat artifacts.

Statistical Properties of Nuchal Inactivity Episodes. Changes in mean nuchal inactivity episode length and number over P2-10 were assessed by 3-way ( 2 Partitions ¥ 5 Postnatal Days ¥ 2 Deprivation conditions) Analysis of Variance (ANOVA ). Orthogonal linear trend analysis was used to further examine developmental trends for the number and average mean nuchal inactivity episode length over the period of observation.

To examine the statistical properties of the Moments (i.e., cumulative mean and variance) a 2-way (2 Moments ¥ 2 Partitions ) ANOVA was calculated for data sets 5

Figure 12. Representative histograms of inactivity episodes generated from partition P1 [0.1- 0.2 mV] in (a), P2, [0.1- 0.5 mV] in (b) and a partition at [0.5- 1.0 mV] in (c) are illustrated for a 10-day-old subject after 2 hrs of deprivation. The log of episode number per bin size is plotted on the ordinate and the length of inactivity episodes in time units (300/sec) is represented on the abscissa. Notice how the number of short inactivity episodes decreases with increasing partition threshold and the number of long inactivity episodes increases with partition threshold.

minutes in length. The criterion for type 1 errors was set on all comparisons at p = 0.05 and the Huhyn-Feldt procedure was used to assess violations of circularity when repeated measures were used (Winer, Brown and Michels, 1991).

Hurst's Rescaled Range Analysis. The Hurst exponents were estimated by the segmentation procedure detailed for fetal sheep (p.24). Validation of Hurst analysis was accomplished by the randomization procedure described for fetal sheep (p.24). Developmental changes in estimated Hurst exponents for original and randomized data sets were compared by 2-way (2 Partitions ¥ 13 Fetal days) ANOVA, with fetal day treated as a repeated measure. Developmental trends were tested by orthogonal linear trend analysis of average H values over the period of observation.

Estimating the Lévy Tail Exponent. I approximated the normalized density distributions of inactivity episodes for all animals for each age P 2 -10 with parametrically fitted algebraic Lévy curves as described for fetal sheep (p. 27). The asymptotic standard errors were computed as was described for fetal sheep. For neonatal rats, these matrices were singular (i.e., not all positive with nonzero roots), and the standard errors of the multparameter estimates were not computable. A common solution to this problem is to set one of the model parameters constant and refit the simpler model. Because my primary concern was the parameter and because the convergent values varied little across the 10 files (5 days ¥ 2 partitions), I set = 3.1, its mean value across all files. The single parameter Simplex estimates converged quickly and as was described for fetal sheep had small asymptotic standard error estimates (all A.S.E. < 0.008).

RESULTS

Nuchal EMG records. Recordings made of neonatal rat nuchal muscle potentials appear remarkable similar to intramuscular potentials in fetal sheep (see Figure 13, compare with Figure 1 p. 8). Self-affinity is evident when rescaling in both the dimensions of amplitude and time so that 20 second periods appear qualitatively similar to those of 2 seconds which in turn resemble those over the time scale of minutes. This fractal time structure of nuchal muscle potentials sampled at 300 Hz in the neonatal rat appears to be very similar to nuchal muscle potentials recorded at 200 Hz in fetal sheep (see Figure 3, p. 31). As in examination of the fetal sheep, the scaling structure of the irregular patterns of intermittent bursts of nuchal muscle activity and inactivity appeared to also have psychobiological significance: they corresponded roughly with other indicators of REM sleep such as muscle twitches, here detected by changes in the electrical capacitance of the recording chamber (see Figure 14).

Statistical Properties of Nuchal Inactivity Episodes. Overall the results of the analysis suggest two main findings: As the neonate matures, there is: 1) a reduction in the number of nuchal inactivity episodes (Figure 16a) and 2) an increase in the mean length of nuchal inactivity periods (Figure 16b). This is concordant with the findings for nuchal atonia defined for 1Hz data over 24 hours in fetal sheep reported in experiment 1. This further supports the observation of the fractal nature of nuchal EMG which implies that behavioral activity, whether recorded at 200 Hz or 1Hz, displays the same time structure.

Figure 13. Erratic intermittent bursting is apparent in nuchal activity with intervening periods of inactivity in a rectified recording from a 2-day old neonatal rat. Nuchal EMG activity along the abscissa (rectified, 10 mvolt / division), plotted over 20 seconds (6000 points at 300 Hz) on the ordinate (top trace). Rescaling the amplitude, abscissa, and time, the ordinate, over a 2 second subset of the original series (middle trace), reveals smaller clusters within larger clusters of both muscle discharges and inactivity. Rescaling both dimensions again over .67 seconds (bottom trace) demonstrates similar qualitative "self-affinity" which is bounded from below by the sampling rate.

Figure 14. The top plot illustrates changes in electrical capacitance of the recording chamber (in mVolts on the ordinate) due to a burst of twitching behavior in a 3-day-old infant rat (in msecs on abscissa). The bottom plot corresponds to the EMG of nuchal muscle (in mVolts on the ordinate) during the time (same scale as above) that twitches were observed in the burst of the top plot indicative of the state of REM sleep. The EMG recording was made before a high impedance probe was available, resulting in the high level of background noise.

Figure 15. This figure illustrates the control condition of anaesthesia. The subject, a 10-day-old pup, was administered Metafane shortly before being placed in the testing chamber. After a complete loss of muscle tonus was observed the electrode leads were connected and the EMG record in Figure 15a was recorded. Figure 15b was recorded 120 seconds after 15a and represents partial recovery from the Metafane. One long period of nuchal inactivity resulted without any interruptions. This manipulation constitutes a control for non-specific noise resulting from the instrumentation as well as heart beat artifacts and suggests that data presented only represents nuchal and movement events

Figure 16. Developmental changes over P2-10 in (a) mean number of nuchal inactivity episodes and (b) mean length of episodes over the non-deprived 5min recording period for the lower amplitude, more sensitive partition (P1) and higher amplitude, less sensitive partition (P2) in all animals. Error bars indicate the standard error of the mean for each 5min period.

Figure 17. Developmental changes over P2-10 in (a) mean number of nuchal inactivity episodes and (b) mean length of nuchal inactivity episodes over the deprived 5 min recording period for the lower amplitude, more sensitive partition (P1) and higher amplitude, less sensitive partition (P2) in all animals. Error bars indicate the standard error of the mean for each 5min period.

Two hours of maternal deprivation result in: 1) a reduction in the number of nuchal inactivity episodes at all ages (Figure 17a) compared with no deprivation and 2) a larger increase in the mean length of nuchal inactivity periods at all ages (Figure 17b) suggestive of larger clusterings of inactivity events. Without exception, application of the lower partition P1 resulted in larger numbers of inactivity events with shorter durations than inactivity events in P2 (Figures 16a & b and 17a & b). This may be the result of noise in the EMG recordings which resulted in fragmentation of longer periods of inactivity. Two 3-way ANOVAs ( 2 Partitions ¥ 5 Postnatal days ¥ 2 Deprivation conditions) comparing Partitions for mean nuchal inactivity episode length and for nuchal inactivity number revealed significant main effects of Partition, F(1, 80) = 20.013, p<.0001, and F(1, 80) = 63.329, p<.0001, respectively. A significant main effect of Postnatal Day was also present for inactivity number F(4, 80) = 4.847, p<.005, and for mean length F(4, 80) = 4.735, p<.005. This was suggestive of a strong developmental trend for decreasing nuchal inactivity episode number over gestation which was evident with further trend analysis of Postnatal Day. In agreement with reports showing a decline in postnatal markers of REM sleep (such as DLVF ECoG) with development (Gramsbergen et al., 1970; Jouvet-Mounier et al., 1970; Tamásy et al., 1980; Van Someren et al., 1990), trend analysis indicated linear developmental trends for decreases in the number of nuchal inactivity events with Postnatal Day F(1,16) = 14.475, p<.0005, and mean nuchal inactivity episode length with Postnatal Day F(1,16) = 14.479, p<.0005, which accounted for 74.66% and 76.45% of the variance. Departures from linearity accounted for 25.34% and 23.55%, respectively, of the remaining variance but did not reach criterion. In addition, a significant main effect of Deprivation condition was also present for nuchal inactivity number[ F(1, 80) = 9.416, p<.005] and for nuchal mean length [F(1, 80) = 7.630, p<.01] suggesting that the amount of time spent away from the dam could be a critical influence on nuchal inactivity episode patterns. Finially, a 2-way interaction of Partitions of nuchal inactivity number with Deprivation conditions proved to be significant: F(1, 80) = 4.811, p<.05 . A test of the effect of partitioning on nuchal inactivity number was found to be significantly different by orthogonal contrast [F(1, 96) = 9.416, p<.0029] under the condition of deprivation but not under non-deprived conditions.

To test whether sequences of nuchal inactivity are statistically similar to a Poisson process (e.g., for a Poisson process the mean equals the variance) and to test the effects of Partition and Postnatal Day, the cumulative Moments (i.e., mean and variance of nuchal inactivity events summed progressively over the 5 minute recording window) were analyzed by a 3-way ANOVA (2 Moments ¥ 2 Partitions ¥ 5 Postnatal Days). This test detected a significant main effect of cumulative Moments [F(1, 180) = 5.104, p<.05] and Partitions [F(1, 180) = 3.987, p<.05]. None of the 2 or 3-way interactions, however, proved to be significant. The nature of the effect of Moments is evident in Figure 18a and b where the magnitude of difference between the cumulative mean and variance for both Partitions over development is seen to be quite large for both the non-deprived (Figure 18a) and deprived conditions (Figure 18b). Also, the magnitude of the difference between the cumulative mean and variance is greater for P2 than P1. The large differences between the cumulative mean and variance strongly argue against the possibility that nuchal inactivity is a Poisson process and confirms the findings of large differences between the cumulative mean and variance in fetal sheep.

Summarizing the findings so far, significant developmental decreases in the nuchal inactivity episode number were observed over the developmental period examined. This is compatible with previous reports of developmental declines in REM sleep with development in the rat (Gramsbergen et al., 1970; Jouvet-Mounier et al., 1970; Tamásy et al., 1980; Van Someren et al., 1990). The second partition (.1-.5 mV) demonstrated the

Figure 18 The cumulative mean duration and variance (a) derived for both partitions over increasing numbers of nuchal inactivity episodes for the five subjects during the non-deprived period and (b) during the deprived period. Both of these conditions fail to demonstrate the expected convergence of the variance in general and the mean in particular of a Poisson process and are completely concordat with similar findings in fetal sheep (Figures 6 a&b, p. 39).

largest change with development. In the non-deprived condition, nuchal inactivity episode number went from 7500 events to 3500 events (Figure 16a), and in the deprived condition from 7500 to 2200 events (Figure 17a). In addition, the change in mean length of nuchal inactivity was also larger for P2, where it tripled from 5 to 15 points (16.7 to 50 msecs) in the non-deprived condition compared with 2.5 to 27 points (8.3 to 90 msecs) for the deprived condition. The cumulative mean duration and variance of inactivity episodes were significantly different from each other and highly variable, as indicated by the large standard errors, and possibly non-convergent in terms of the central limit theorem although longer sequences of nuchal inactivity episodes (>5min) should be examined to see if the mean and/or variance converge with sample size. These data are consistent with the hypothesis that REM periods, when indexed by nuchal inactivity periods, lack a charateristic timescale like other fractal time processes and tend to consolidate into longer clusters with increasing age.

Results of Hurst Analysis of Nuchal inactivity Sequences. Hurst exponents calculated for different partitions of the nondeprived condition ranged from 0.687 to 0.856 for P1 and from 0.648 to 0.846 for P2 during the period of observation (Figures 19a and b), suggesting the presence of long-run dependency between nuchal inactivity episodes over 5 minutes. For the deprived condition, Hurst exponents ranged from 0.741 to 0.867 for P1 and from 0.701 to 0.866 for P2. Histograms of the distribution of Hurst exponents for both P1 and P2, original and randomized, are displayed in Figures 20a and 20b for the non-deprived condition and in Figures 21a and 21b for the deprived condition.

A 3-way repeated measures ANOVA (2 Partitions ¥ 2 Deprivation Conditions ¥ 2 Hurst Estimates [original and randomized]) was used to assess the effects of Partition and Deprivation Conditions on estimated Hurst exponents. This analysis indicated the significant main effect of Deprivation Condition F(1,24) = 5.692, p>0.05,e = 1 and Hurst Figure 19. The least squares fits of the mean of the Hurst exponents for the non deprived (a) and deprived conditions (b) illustrate the changes in persistence (defined by H > 0.5) for the original sequences of nuchal inactivity episodes for each partition. The R represents the Hurst values (H 0.5) computed in the same way following randomization of the sequences data for partition 1 and 2 over development, reflecting the expected loss of long range correlations. Notice the similarity with Hurst values from fetal sheep (Figure 8, p. 43). Notice also that H values for the deprived condition (b) are higher than the non-deprived (a)

Figure 20. The distribution composed of all the 5 min values of Hurst exponent (H) estimates for (20a) original non-deprived and (20b) randomized sets for non-deprived for both P1 and P2 partitions over the postnatal period examined. The largest probability mass of the Hurst exponents for the original non-deprived sequence was in the neighborhood of H 0.78 for deprived. H0.55 for the randomized set.

Figure 21. The distribution composed of all the 5 min values of Hurst exponent (H) estimates for (a) original deprived and (b) randomized sets for deprived for both P1 and P2 partitions over the postnatal period examined. The largest probability mass of the Hurst exponents for the original non deprived sequence was in the neighborhood of H 0.80 for deprived subjects which was significantly different from the non-deprived estimates. H 0.55 for both randomized partitions.

Estimates F(1,24) = 1502.990, p>0.0001,e =1. In addition, a 2-way interaction of Deprivation Condition and Hurst Estimates was also significant F(1,24) = 6.653, p>0.05,e = 1, indicating that deprivation increased the magnitude of the normal Hurst exponents suggesting an increase in behavioral clustering. A test of the effect of Deprivation on the magnitude of the normal Hurst exponent was found to be significantly different by orthogonal contrast F(1, 196) = 5.385, p<.0029, under the condition of deprivation but not under non-deprived condition (see Figure 19b, p. 97).

Hurst exponents calculated from randomized surrogate data sets of P1 and P2 ranged from 0.483 to 0.586 and 0.438 to 0.573, respectively, for the non-deprived condition and from 0.458 to 0.584 and 0.474 to 0.585, respectively, for the deprived condition. Hurst exponent estimates from the original data sets were found to be significantly different from estimates derived from randomized surrogate data sets, independent of Partition, confirming the existence of long-run dependency.

In summary, the magnitudes of Hurst exponent estimates were dependent on the deprivation condition, with 2hrs of deprivation resulting in larger estimates. As a demonstration of the statistical validity of these estimates, Hurst exponents derived the from original time series were significantly different from Hurst exponent estimates from randomized surrogate data for both partitions and deprivation conditions.

The probability density distributions describing nuchal inactivity episodes. To test the hypothesis that nuchal inactivity episodes, as with fetal sheep nuchal atonia episodes, might not be described by normal Gaussian distributions, the goodness of fit to other Lévy distribution curves, was examined, by the derived characteristic exponents a at fixed g. Fitting the probability distribution yielded estimates of a for each postnatal day examined. Nuchal inactivity intervals from Partion 2 were examined. The values of a for non- deprived animals were 1.5839 for postnatal day 2; 1.5076 for postnatal day 4; 1.6125 for postnatal day 6; 1.5749 for postnatal day 8 ; and 1.6050 for postnatal day 10 at g = 3.0062. The values of a for deprived animals were 1.8750 for postnatal day 2; 1.8656 for postnatal day 4; 1.8916 for postnatal day 6; 1.8809 for postnatal day 8 ; and 1.8823 for postnatal day 10 at g = 3.0062. Non-deprived animals collapsed across age were found to be significantly different from deprived animals by 1-way repeated measures ANOVA (Deprivation Conditions), F(1, 4) = 415.028, p>0.0001, e = 1, suggesting that deprivation changes the nature of the underlying probability density distributions by shifting them toward vaules of a where both the first and second moment are non-convergent. The non deprived a value is remarkably similar to that found for fetal sheep (p. 49). In addition, the normalized probability density distributions of nuchal inactvity episodes calculated for the two partitions were found to be remarkably similar in form over species and development (compare Figure 22 with Figure 9, p. 51) which is consistent with both the unbiased nature of the estimation of inactivity events by the partitioning procedure and the finding of invariance in the characteristic exponents with maturation.

Figure 22. The log-linear plots of the probability density distributions for nuchal inactivity episode durations in representative 5 min periods for partition P1 and P2 post-deprivation demonstrate the highest densities at the lower bounds of sampling rate resolution in a 2- and 10-day-old subject, as in a Poisson process. In addition, they display long tails which failed to converge over the sample period. This distribution remained invariant over the 9 days of observation for subjects despite a shift in the average length of nuchal inactivity episodes, concordant with the findings in the sheep fetus (compare with Figure 9, p. 50).

DISCUSSION

The erratic cluster-within-clusters appearance of nuchal EMG activity over the 100 minute period illustrated in Figure 1 from the E123 sheep fetus is barely distinguish-able from the intermittent bursting behavior of nuchal activity recorded from the 2-day-old neonatal rat over 20 seconds in Figure 13. This observation is striking in that it suggests that developing biological systems are richly endowed with multiple levels of order extending over a spectrum of timescales and that the study of the fractal temporal structure of organisms is as important as the study of spatial organization in understanding the roles of behavioral processes such as REM sleep in adaptations throughout development. Another surprising conclusion from this comparison is that nuchal activity recorded over 100 minutes in one species is similar to nuchal activity recorded over 20 seconds in another species. In fact, all of the findings derived from 24 hr data in sheep fetuses are almost identical to the findings derived from infant rats over a 5 minute period. This observed self-similarity affords several important implications: 1) the electro-physiological behavior of the nuchal muscle is statistically similar over 4 orders of magnitude in the sheep and probably in the neonatal rat; 2) similarly, REM related behavior is statistically correlated over many timescales; 3) different species, possibly including humans, share this invariant time structure. The principal conclusion from both experiments is that normal statistical analysis of this data (e.g., not investigating order over many different scales of time) would most likely not be sensitive to this developmental invariant. The analysis of the intervals of inactivity of Figure 13 also revealed surprising statistical properties, such as

non-convergent cumulative moments, not found in normally distributed data. Nuchal inactivity in the rat, like atonia in the fetal sheep, is therefore neither Gaussian nor Poissonian, but is highly ordered in that statistical interdependence extends between these intervals of inactivity over many time scales.

Nuchal inactivity as a marker of REM sleep in neonatal rats. I have reviewed behavioral and neurophysiological studies supporting nuchal atonia as a correlate of REM sleep in adult species and fetal sheep. The findings of Experiment 2 also support nuchal atonia as a marker of a REM sleep-like state in the neonatal rat, which more closely resembles the third trimester fetus than other precocious rodents such as the hamster. I observed a significant developmental pattern of decline in the number of nuchal inactivity episodes and increase in mean length across all animals and partitions with maturation, analogous to the ontological consolidation of markers of REM sleep in other species (Jouvet-Mounier et al., 1970; Roffwarg et al., I also observed a significant difference in the number of inactivity episodes depending on the method of partitioning EMG activity, with the more sensitive (lower absolute threshold) P1 showing significantly more events that P2. I believe this difference is due in part to the sensitivity of more sensitive partition to low amplitude noise events in the EMG not observed in the control experiment (see Figure 15a), resulting in the interruption of an ongoing inactivity event and resulting in the generation of multiple inactivity periods from single events. Also, for both partitions, inactivity periods could have possibily been terminated prematurely by startle and twitching movement artifacts (see Figure 14). I believe these movement artifacts are present, and that these occurrences represent concurrent phasic REM phenomena with a similar fractal structure that could be confounded with nuchal inactivity measurements without significantly affecting or invalidating the conclusions concerning the fractal nature of neonatal REM sleep just as described for the fetal sheep observations.

Nuchal inactivity distributions also appear stable over the course of development in the postnatal rat as was demonstrated by the invariance of the characteristic exponents and the form of the normalized probability distribution. This suggests that these concurrent phasic REM phenomena are at least stationary over long periods of development. In addition, the relatively large number of nuchal events observed in this study may be due in part to the normal polyneuronal innervation of skeletal muscle that has been observed in the newborn rat (Brown, Jansen and Van Essen, 1976). Brown et al. found a rapid drop in the precentage of soleus muscle fibres innervated by more than one motor neuron axon after day 10, suggesting activity dependent synaptic elimination resulting in higher background activity. Brown et al. also observed much greater fluctuations in maximal end plate potentials from days 2 to 10 in muscle fibers which may be correlated with the greater quantity of twitching observed during this period (Jouvet-Mounier et al., 1970).

From a different perspective, Blumber and Lucas (in press), suggest that the "simple random firing mechanism" or "desynchronized" twitching during this period is critical in uniquely identifying different "cartels" (as defined by Colman and Lichtman, 1993) of motor neurons actively competing with each other to "monopolize" innervation of muscle fibers. I will detail my objections to the notion of random mechanisms in a later section; here, however, I propose that a view of activity patterns as having order imparted by fractal time processes does provide a richer perspective from which to view these complex interactions occurring within and among the components of cytoplasm, membranes, neuromuscular junctions, muscle fibers, motor neuron "cartels", muscles, muscle groups, etc. In fact, just the possibility of common fractal patterns in the activity of both muscles and the motor neurons that innervate them would be more suggestive of vertical and horizontal co-interactions and cooperation than competition and monopolization.

Given the above considerations, I conclude that nuchal atonia episodes investigated in this study are indicative of REM sleep for the following reasons: 1) Other REM associated state markers (twitches of the limbs, the trunk, the head and tail ) were usually observed to be coincident with nuchal inactivity events, although this was not rigorously quantified for all days and animals; 2) the decline in nuchal inactivity events from about 7500 for postnatal day 2 to 3500 for postnatal day 10 , calculated over 5 minutes, is similar to other reports of the decline of REM markers for neonates in this gestational range (Jouvet-Mounier et al., 1970); 3) A significantly linear trend of increasing nuchal inactivity mean length with development suggests the possible consolidation of short nuchal inactivity episodes into longer duration episodes, a trend reported for the clustering of rapid eye moments in human infants (Petre-Quadens et al., 1971; Tanquay et al., 1976).

Non-convergence of Non-Poissonian Nuchal Inactivity Episode Sequences. As I have reported for the fetal sheep, one key descriptive characteristic of nuchal atonia episode sequences is their deviation from normal probability distributions and the central limit theorem assumptions. This also is the case for nuchal inactivity sequences in neonatal rats. For both partitions of nuchal inactivity events and deprivation conditions, I found the cumulative mean and variance to be significantly non-convergent (see Figures 18a and 18b). Also the cumulative mean and standard deviation are significantly different for both P1 and P2. Therefore, nuchal inactivity episodes are not consistent with a Poisson random process for the following reasons: 1) The cumulative mean is significantly different from the cumulative standard deviation; 2) The long tails of atonia distributions contribute to increased variance which does not converge with a larger "n", unlike the "law of large numbers" for Gaussian processes; 3) The Hurst exponent is greater than 0.5, suggesting long range correlations or dependency in the increments which violate assumptions of statistical independence.

Nuchal Inactivity Events and Spontaneous Prenatal Behaviors as Non-Poisson Fractal Time Processes. The results of these experiments do not appear to support the findings of Narayanan et al. (1971) or Blumberg and Lucas (1994a; 1994b) [discussed on page 57] that spontaneous motility is a stochastic process. Once again these data suggest that examining all relevant timescales is critical to obtaining a complete overview of temporal patterns of behavior. Consequently, spontaneous prenatal behaviors should be investigated with longer observation times or finer sampling rates, before conclusions about the random nature of these developmental processes can be accurately drawn.

Hurst Analysis of Fractal Time Nuchal Inactivity Sequences. The presence of Hurst exponents of greater than 0.5 for nuchal inactivity sequences for all data partitions, days and subjects indicates correlations between REM processes over many timescales and confirms similar findings in fetal sheep (Experiment 1). Also similar to the findings in the fetal sheep, the estimated Hurst exponent estimates for the neonatal rats appear to be constant from postnatal days 2 through 10, suggesting that this measure may define an invariant of development. In addition, the Hurst exponent was shifted upward by maternal deprivation, suggesting that one compensatory response to this drastic change in environment is that REM processes become more persistent. This increased persistence may be due to changes in overall behavioral patterns observed in maternally deprived neonates (Anderson, 1992; Hofer, 1976). Deprivation tends to elevate levels of activity and to decrease habituation to stimuli (Anderson, Kilts, Miller and Hall 1991; Hofer, 1976). The subjects in this experiment tended to show more convulsive struggling for longer periods with deprivation. It is conceivable that the longer bouts of convulsive struggling activity resulted in more persistent Hurst estimates.

Lévy distributions and probability density distributions describing nuchal inactivity episodes. The hypothesis that nuchal inactivity episodes, as with fetal sheep nuchal atonia episodes, are not described by normal Gaussian or Poisson distributions was strongly confirmed by the results summarized above (pp.104-105). The estimated characteristic exponents found for the non-deprived condition were nearly identical to those found for fetal sheep (p. 49). Deprivation had a strong influence on the estimated characteristic exponents, shifting the underlying probability density distributions toward values of a where both the first and second moment are non-convergent. This finding also strongly dissociates fractal sequences of nuchal inactivity episodes from normal Gaussian or Poissonian processes where the underlying behavioral process is expected to converge on a larger distribution. Instead, in biological systems, the underlying distributions may show behavioral state dependent shifts in Lévy space between convergent and non-convergent moments (see Mandell, 1986 for neurobiological examples of Lévy or Pareto distributions). Shifts in the variables of the stable Lévy distribution in response to changes in the local environment many represent one critical difference between living and non living systems with statistical self-similarity.

The shift in the estimated characteristic exponents with deprivation fit well with the observed changes in the Hurst exponent, which would be expected to become more persistent with smaller a. For example, the probability density distribution for a periodic function such as the sine function would be represented by a "U" shaped as opposed to a bell shaped distribution. This is because the largest probability mass falls within the tails of the plot, meaning the sine function is only at zero every 2 periods, while it is greater and less than zero for the remaining time. Hurst analysis of a rectified sine wave time series sampled many times faster than the period, generating very long trends, would show strong persistence and long tails in the probability density distribution.

The general implications of experimental observations of fractals in time and the conceptual ramifications for understanding the order underlying spontaneous and appetitive behavior of animals and other living systems will be explored in greater depth in the following sections

GENERAL DISCUSSION

ORDER AND RANDOMESS IN BIOLOGICAL SYSTEMS AND SPONTANEOUS NEONATAL BEHAVIORS

One tacitly accepted null hypothesis in the biological sciences is that the behavior in time of living systems on different levels of description from the molecular (i.e., the movement of a water molecule in the cytoplasm) to macroscopic (i.e., the searching behavior of a hungry rat ) is no different from a random independent process until proven otherwise (e.g., that it shows cyclicity or coordination). This implicit assumption also seems prevalent in behavioral neuroembryology. In many cases spontaneous prenatal behaviors have been interpreted as independent random processes. E.B. Holt (1931), for example, in his hypothesis about early embryonic development, proposed that because of the lack of preformed connections in the developing nervous system, the earliest movements of organisms are "utterly random movements" (Gandelman, p.14). As discussed above (p. 57), Narayanan et al. (1971) reported that episodes of spontaneous motility in the E17-20 rat fetus could not be statistically distinguished from a Poisson random process. Also, Blumberg and Lucas (1994) reported that limb twitching in normal and spinal transected 5- and 8-day old rat pups also displays Poission random behavior. Robinson and Smotherman (1988), using arguments similar to those of Holt, have argued that random processes must play an inportant role in the early establishment of neural connections and that the "[r]andom production of seemingly organized activity, such as the chance synchrony of simple movements and random transition between behavioral categories provides the stuff from which the patterning that is so evident in species-typical

action patterns and goal-directed behavior in general is sculpted" (p.110).

The question of whether prenatal behavioral patterns are random and develop in a "haphazard" or "orderly manner" was central to Coghill's investigations of Amblystoma. In speaking of his early inspiration to study the parallel development of behavior and nervous system, he recalled that: "[i]t seemed to me basic to a scientific study of behaviour to know whether the behaviour pattern of an animal develops haphazard or in an orderly manner; and that, if it should be found that behavior develops in an orderly manner, then there should be a corresponding order of development structurally and functionally in the nervous system. Should such correlation be found to occur, it seemed to me that the development of behaviour would offer a new basis for the interpretation of nervous structure and function, and that the development of the nervous system would throw new light on problems of behavior. (1929; p. vii)" During the 1930's and 1940's the idea that spontaneous movements might provide a source of order to the developing fetus was anathema to the prevailing stimulus-driven reflex-integration movement of the time. As Provine (1986) states, "....because ongoing behavior was considered to be evoked, little attention was given to spontaneous movements....Indeed, the report of a spontaneous process was considered by some to be either an admission of ignorance of the causative agent or the acceptance of biological mysticism (p.215)."

All of these investigators appear to support the notion that spontaneous prenatal behaviors play an important role in development. However, they all prefer to invoke randomness as the mechanism underlying the generation of order. This is tantamont to invoking "instinctive" or "innate" as an explanation of animal behavior (see Lehrman [1970] for an excellent account of this issue). Perhaps, to take a note from Lehrman, the underlying problem resides in the informal uses of such terms such as "random", "spontaneous", "patterning" and "order" in behavioral neuroembryology. Bohm and Peat (1987) commented on how a breakdown in communication in scientific work can result from different and incompatible ways in which the informal language of science is used. For example random numbers from a computer random number generator appear to lack any degree of order, when in fact the numbers are generated in a very ordered and deterministic fashion. Therefore the meaning of random is dependent on the context in which it is observed or imbedded. The definition of randomness as lacking all order "has no real meaning...[because]....random events do happen to take place in a definable and describable sequence and can be distinguished from other random events....in this elementary sense they obviously have an order (Bohm and Peat, p. 128)." Perhaps a working hypothesis that many levels of spatial and temporal order exist in biological systems which will tend to generate patterns of great complexity that may not yield to methods of analysis such as Fourier analysis (with its implicit assumptions of periodicity, unitary time scales or stationarity in time) would best serve psychobiologists until proven otherwise. This would ring true to the spirit of the original work of both Coghill and Preyer and is one of the philosophical positions adopted in the following wide ranging disscussion of the findings of fractal time in fetal and neonatal REM sleep.

THE ORIGIN AND FUNCTION OF FRACTAL TIME PATTERNS ASSOCIATED WITH FETAL REM SLEEP: A TRANSIENT BEHAVIORAL ONTOGENETIC ADAPTATION TO CHANGING ENVIRONMENTS?

By what mechanisms do the observed complex patterns of statistical inter dependence in episodes of nuchal atonia originate? What new perspectives does the observation of fractal time patterns provide for understanding the role of phasic REM sleep processes and other spontaneous prenatal behaviors as possible transient behavioral ontogenetic adaptations? Due to the very high percentage of REM sleep during early life, and the detrimental effects of its deprivation during pre- or postnatal life (Corner et al., 1990; Hofer, 1988; Mirmiran et al., 1986; Roffwarg et al., 1966), several investigators have proposed that REM sleep plays an essential role in physical and neural development. But how is this accomplished and through what neurobiological mechanisms does it operate?

Nuchal atonia periods appear to be one manifestation of ongoing activity in the reticular formation (RF) that provides a simple fetal state indicator. The Hurst analysis reported here demonstrates that the timing of a nuchal atonia event has some degree of dependency on the occurrence of the last 1, 10 or 1000 episodes of nuchal atonia or inactivity. The early RF and spinal cord may be one of the preeminent neuronal sites for the vertical amplification of fractal processes from the cellular level (e.g., fluctuations in ion channels and resting membrane potentials) and the horizontal convergence and association of fractal neural firing patterns (Svozil, Felix and Ehrenberger, 1994). Neurons in the RF and spinal cord, by virtue of their early ontogeny (Lumsden and Keynes, 1989; Sholomenko and O'Donovan, 1995), extended spatial connections throughout the neural

axis, and their cardinal role in the activated brain state of REM sleep in fetuses and adults (Verties, 1990), can establish widespread temporal correlations between coupled networks supervising multiple organ systems (Langhorst, Schulz, Schulz & Lambertz, 1983; Langhorst, Lambertz, Schulz, & Stock, 1987). Similar to the origins of fractal time in river levels, coupling between a diverse range of neurotransmitters and neural networks of various sizes and complexities in the RF and spinal cord could create the multiplicative dependency between interconnected neural events which results in the observed fractal time characteristic of fetal behavior (Pellionisz, 1991). The unique developmental morphology of the reticular core (Scheibel, Davies and Scheibel, 1973; Figure 23) may reflect functional considerations that require neural interactions over multiple timescales without primary topological constraints.

Examples of the vertically integrative origins of this self-similar multiplicative dependency across all levels of RF and spinal cord organization are: 1) The influence of fractal binding kinetics on signal amplification at cellular and neurotransmitter binding sites (Savageau, 1993) resulting in nonlinear rather than proportionate transmission of information; 2) the influence of fractal resting membrane potential fluctuations (Churilla et al., 1994; Gottschalk et al., 1993; Strassberg and DeFelice, 1993) on the observed spontaneous burst firing of neurons (Chay, Fan and Lee 1995; Roeder, 1955; Spitzer, Olson and Gu, 1995) in the developing spinal cord and in concert with spontaneous movments (Provine, 1972; 1986; Provine and Rogers, 1977; Ripley & Provine, 1972); 3) fractal time patterns of impulse activity in different monoamine groups and their key regulatory enzymes examined by Mandell (1978; 1983; 1984; 1992) and Selz and Mandell (1991; 1993a; 1993b). The latter have found that different catecholamine cell body groups can be classified by the frequency range over which they manifest fractal patterns. Adrenergic cells bracket the low frequency range, dopaminergic cells, the high frequencies, and noradrenergic cells, a middle range (Mandell and Selz, 1990). One possible property of cells displaying fractal time behavior are random walks with self-similar clusters described by stable Lèvy distributions (Hughes, Shlesinger and Montroll, 1981) which would have invariant behavior over different scales of time and space. Fractal time behavior present in neuronal bursting at the catecholamine cell body level could be affine to fractal time behavior in the global clustering of spontaneous prenatal behavior (Mandell and Selz, 1993a). A similar vertical integration hypothesis has been put forth by Lowen and Teich (1993) and investigated in simulations by Svozil et al. (1994) relating the observed fractal interspike interval patterns observed in the auditory nerve to the well known spontaneous burst firing patterns of auditory hair cells (Hudspeth, 1985). They propose that this vertically convergent integration of activity from the cellular level provides a broadband fractal carrier wave to match and efficiently sample natural sounds and supports a mechanism to quickly resolve the intrinsic structure of broadband correlations in natural sounds (Teich, 1989) many of which can be described as fractal in time (Voss, 1989). Fractal time behavior in developing RF and spinal cord networks may function during fetal REM sleep in an analogous way to match and efficiently sample multiscale broadband internal signals and external uterine patterns in order to ensure adequate innervation and regulation of developing motor neuron populations (Provine, 1986), spinal cord pathways (Kudo, Furukawa and Okado, 1993; Rinaman and Levitt, 1993) and transient sensory neurons (Oppenheim, 1981); fractal time patterns of monoaminergic neurons in the RF may provide a way of correlating and dispersing information over many spatial and temporal scales in the forebrain, RF and spinal cord.

How might neurochemical mechanisms influence the fractal time structure of nuchal atonia patterns of fetal REM sleep? Extensive studies in adult animals have demonstrated that REM sleep and other sleep states are predominantly regulated by brainstem monoamines and cholinergic processes (Hobson and Steriade, 1986). Fetal brainstem and behavioral states also appear to be influenced by and regulated in some sense by these same neurotransmitters, although possibly in a markedly different fashion (see, for example, Qulligan, Clewlow, Johnston and Walker, 1981). Cholinergic processes, central to the induction of REM sheep in adults (Vertes, 1990), are present early in ontogeny (Semba, 1992), although little information exists as to their role in fetal and neonatal REM sleep. Adrenergic neurons appear functional at E14 in the rat brainstem with epinephrine concentrations at adult values or higher (Foster et al., 1987). Evidence from neonatal rat brain stem slice (Greene, Gerber, Hass & McCarley, 1989) and cat fetuses (Shuleikina and Raevsky, 1974) supports a possible REM-enhancing effect of noradrenergic neurons in fetal and neonatal animals (Bamford et al., 1986) which become REM-suppressive in adults (Bier and McCarley, 1994). The activity of locus coeruleus neurons in the in utero rat are responsive to tactile stimulation (Kimura and Nakamura, 1985; Sakaguchi and Nakamura, 1987). If fetal sheep show similar responsivity to in utero stimuli , then, in combination with the findings that serotonergic neurons show transient regulation by b receptors during the early postnatal period in rats (Laurence and Adrien, 1988), this suggests a mechanism by which brain noradrenergic neurons may convert stimuli from the tactile stimulation provided by uterine contractions into behavioral state transitions (Nathanielsz et al., 1980).

There are several possible functional advantages of a transient behavioral ontogenetic adaptation with fractal time characteristics. For example, spontaneous neural activity has been implicated in the functional segregation and topological organization of retinal-lateral geniculate nucleus-visual cortical pathways (Goodman and Shatz, 1993; Wong, Chernjavsky, Smith and Shatz, 1995) as well as the functional organization of the skeletomuscular system (Blumberg and Lucas, 1994b; in press), both systems with complex component systems extending throughout the brain or body. Aside from observed correlated bursting activity in the postnatal ferret retina (Wong, Meister and

Figure 23. This rendering of an illustration of a Golgi section of the dorsal medial medulla oblongata from Scheibel et al. (1973) depicts not only the complex net-like structure of the RF in the 1-day-old kitten but also the dramatic developmental changes that take place here during postnatal life (compare with adult cat). Scheibel et al. noted the appearance of many exuberant heteromorphic protospines on the dendrites and soma of neurons in the nucleus reticularis parvocellularis and magnocellularis in the neonate which were pruned to smooth soma surfaces and condensed into dendritic bundles forming the "net like" reticulum of the adult. This image serves as a guiding metaphor in this section of the inherent connection between sleep, learning, dynamics and spatial and temporal fractal processes during ontogeny.

Shatz, 1993; Wong et al., 1995) and the avian auditory system (Lippe, 1994), most descriptions of spontaneous neural activity in other developmental systems have emphasized the independent random, asynchronous nature of this activity. However, these

descriptions often approach the complex fractal patterns of spontaneous activity with inadequate signal processing techniques, resulting in binning, filtering and ensemble averaging that obscure the rich timescales inherent in the record. In addition, these descriptions do not propose any mechanism through which independent random activity can accomplish coordination over the many levels of organization in the developing brain or periphery (however, see Blumberg and Lucas, in press). Fractal time REM patterns may provide one mechanism that enables long range coordination through the following means: due to self-affinity, the interorganism correlations imparted by twitching over many timescales, and the properties of vertical and horizontal convergence tied to the convolutional stability of Lèvy distributions of the underlying biological processes bind spatially and temporally correlated clustering in a muscle or over the entire organism. This spontaneous binding would be analogous to broadband binding proposed for information processing (Anderson and Mandell, 1996). This binding of clusters of activity is similar to spatial clustering models based on the long-range correlations imparted by fractal growth processes, which, for example, have produced remarkably life-like simulations of the development of cerebellar Purkinje cells (Hamilton, 1993) and branching organisms (Kaandorp, 1994).

These long-range correlations may provide a transient behavioral ontogenetic adaptation during developmental changes in nuchal EMG activity over embryonic life. As described above, nuchal activity during the early embryonic period of sheep (E95-107) is described as continuous (Clewlow, Dawes, Johnston, and Walker, 1983). This may represent the active innervation and "competition" between innervating motor neuron axons (Colman and Lichtman, 1993; Purves, 1988) as described postnatally in the rat. If the inter-event firing patterns of the nuchal muscle mass has self-affinity and distributional convolutional stability to the firing patterns of local axon-muscle fiber elements, then fractal time patterns may provide a temporal scaffolding underlying the organization of the functional nuchal muscle and motorneuron groups, binding clusters of activity in the membranes of muscle fibers and innervating axons with global pattenrs of mass activity. Nuchal activity during the later embryonic period (E120 and beyond) starts to break up into periods of atonia. Based on my observations in the sheep, during this period muscle EMG observed at 200Hz has the same distribution and appears self-affine to atonia periods over 24 hrs. This appears to be the case for the postnatal rat as well. Therefore, fractal time patterns at this later stage may represent the hierarchial convergence of local vertically convergent processes at cellular, motor neuron and brainstem inhibitory levels. Their output picked up at the nuchal muscle electrode provides the envelope from which an emergent behavioral state is defined. Of course the mere association of fractal patterns with these developmental processes does not prove that they are providing this binding function. However, fractal time patterns may provide other adaptive advantages to the developing organism.

I propose that endogenous fractal activity patterns may mimic or provide a "fractal forgery" of temporal correlation patterns found in the postnatal environment, providing broad-band synchronous stimulation to promote afferent segregation in immature sensory and associative networks of neurons (Anderson & Mandell, 1996) as well as other developing organ systems. This would provide not just desynchronized stimulation but desynchronized stimulation with statistically self-similar patterns common to natural objects and processes (Voss, 1988a). Developing premotor networks important in postnatal attentional and orienting response movements (Grantyn, Olivier and Kitama, 1993) may require stimulation patterns with the long-range dependency provided by fractal REM sleep to ensure selective sensitivity to the broad range of stimuli encoutered at birth. In short, examples of activity dependent segregation of axonal connections abound that suggest only random asychronous stimulation during development is necessary and sufficient for normal function; however the fractal time character of endogenous activity has not been sufficiently investigated to rule out a role for self-similar patterning in the binding and tuning of neuronal structures to the salient natural fractal patterns of intra- and extrauterine stimulation.

Many organ systems with branching structures have self-similar and self-affine symmetries (West and Goldberger, 1987). Fractal bouts of breathing occurring during fetal REM sleep (Szeto et al., 1990) may coordinate the developmental organization of fractal branching systems in the body, for example, the branching pattern of the lung or circulatory system . The intermittent clustering of fetal breath episodes may create local areas of turbulent fluid flow in fetal lungs that enlarge and further extend branching bronchial buds, thus suggesting one possible explanation for observed fetal breathing during DLVF ECoG sleep (Dawes et al., 1972). Szeto (1992) found that inter breath intervals (IBIs) in these fetal breathing episodes also have fractal time characteristics which were described as an exponential inverse power law for longer intervals greater than a second (low frequency), supporting the idea that these patterns may be necessary for lung development and activity-dependent organization of brainstem systems for respiratory coordination.

Convolutionally stable patterns of spontaneous activity associated with fetal REM sleep could also provide a stable, scale invariant source of correlations that may facilitate integration of new neural changes into developing or existent motor networks, thereby stabilizing new pathways and eventually, during the normal phasic activity of adult REM, provide a recurrent, stable reference for memory consolidation or dynamic regulation of receptive fields and maps (Weinberger, 1995). The work of Evarts (1964; 1967) would support the view that spontaneous non-Poisson patterns of inter-spike-interval activity are recurrent during REM sleep in pyramidal track neurons of adult monkeys. Also, REM sleep in adult animals has been implicated in strengthening long-term memory processes, possibly by allowing the replay during sleep of temporally compressed correlations between cells established during learning in the waking state (Wilson & McNaughton, 1994). Correlations between population activity patterns in these cells in the hippocampus and neocortex have been found to be especially high during REM sleep in adult rats (Moore et al., 1994). Thus, if the correlations present in the fractal time processes of fetal REM sleep are viewed as a predecessor to adult REM sleep, the important role of this sleep state in the conservation of neural plasticity naturally emerges.

Disruption of RF development or maturation - in terms of the behavioral generation of statistical interdependence and clustering in phasic sleep processes - may interfere with the ability to match and efficiently sample multiscale internal signals and external uterine patterns. Such disruption could underly developmental disorders such as autism. Autistic children show poor attentional habituation to environmental changes, a possible indicator of disruption of long-range interaction in the RF. As discussed in the introduction, Tanguay et al. (1976) found that eye movements in normal children do not become clustered into bursts until 40 weeks gestational age. As total REM decreases during development, the number of EM's remain a constant resulting in an increase in the mean number of EMs/sec of REM. However, autistic children show substantially less clustering of EMs. In fact, no significant differences between burst structure in 2-5 year old autistics and younger (<18 month) normal children could be found by Tanguay et al. This lack of clustering may be explained by the developmental failure of multi-timescale correlational mechanisms involving the vertical integration of fractal time patterns from monoaminergic groups. The resulting behavioral patterns of abnormal fixation on narrow frequency bands of stimuli and stereotypic self-stimulatory motor patterns may represent the external manifestation of loss of multi-timescale correlations in the maturing RF. Measurement of parametric shifts in self-affine clustering over development (Hughes et al., 1981) in observable behaviors such as EM's, myoclonic twitches, daytime nighttime sleep/activity patterns and nuchal atonia patterns could be preformed noninvasively, thus enabling the diagnosis of developmental delays in self-affine clustering behavior. Parametric shifts in self-affine clustering behavior are describe by Hughes et al. on a continuum from diffusive clusters, close together in time, to tighter clusters, further apart in time. The behavior observables of children with different psychiatric disorders may map to different points in this scaling continuum allowing an objective means of generating diagnostic categories. How might disruptions of the self-affine clustering of spontaneous prenatal behaviors desplaying fractal-time characteristics interfere with normal development?

If spontaneous behavioral activity is the carrier of fractal time patterns throughout the embryo or fetus, then the elimination of this activity should prevent the transfer of this information. A number of experiments have examined various levels of deprivation of spontaneous behavioral activity in normal amphibian and avian fetal development. Pharmacological suppression of the behavior of amphibian embryos during development does not impair the ability of the tadpole to display normal swimming behavior (Haverkamp and Oppenheim, 1986). Similar experiments involving a transient reduction of spontaneous behavioral activity and sensory input in the chick embryo (Oppenheim, Pittman, Gray, and Maderdrut, 1978) have not resulted in behavioral impairments, although long periods of immobility result in impairment of joint development (Drachman and Sokoloff, 1966) and disruptions of neural-muscular development (Purves, 1987). One interpretation of this remarkable adaptability of the fetus to insult involves the repetitive nature of fractal patterns over many time scales. Fractal time, by definition, allows temporal patterns to be repeated at many different time scales, and this may account for resistance to periods of interruption. Thus fractal patterns of spontaneous behavioral activity may only need to be expressed transiently, depending on the species, in order to provide the necessary coordination. In addition, fractal time patterns that arise from vertical and horizontal integration of activity over many levels in a fetus, from subcellular and cellular processes such as spontaneous calcium transients (Spitzer, 1994) to cell networks coupled by gap junctions could provide resistance to these insults while maintaining cellular patterns of activity (Guthrie and Gillula, 1989). Therefore, fetal REM sleep in mammals and spontaneous motility in lower vertebrates may represent a fractal information system that serves as a transient behavioral ontogenetic adaptation, providing activity with the pertinent time structure for the coordination of simultaneous self organizing processes at many time scales in the fetal brain, lung, kidney, muscle and joints, as well as for receiving and integrating feedback from the uterine environment. This may partially explain the greater prevalence of REM during development, in addition to providing a new perspective for understanding its essential role in adult animals (Rechtschaffen et al., 1989) and its role in evolution.

FRACTAL TIME, FETAL REM SLEEP, HETEROCHRONY AND THE GENESIS OF BEHAVIORAL NEOPHENOTYPES

Heterochrony, described by de Beer (1958) as the shifting in time of the appearance of embryonic structures during ontogeny has been proposed as a fundamental mechanism in evolution (Gould, 1977). A developmental behavioral basis for heterochronological change has been proposed by Gottlieb (1992) who detailed the implications of supragenetic factors such as experiential alterations in the genesis of behavioral neophenotypes. Gottlieb's central idea is that behavior-phenotypic changes precede genetic changes due to "random" mutations. The term "behavioral neophenotype" was first used by Zing-Yang Kuo (1976) to refer to large behavioral deviations that could be induced by altering the early developmental experience of an animal. Altering what is considered normal species typical "instinctive" behavior by unusual early developmental experience, Kuo was able to create "neophenotypes" such as male dogs without sexual interests in female dogs in heat and other behavioral oddities. How does Kuo's work change our preconceptions about the genetically determined view of evolution? The critical modification of the population genetic synthesis of modern evolutionary theory proposed by Gottlieb is that the untapped heterochronic flexibility of living systems can provide a basis for evolutionary change through the genesis of behavioral neophenotypes before population-genetic change, thereby relegating genetic change to "a secondary or tertiary consequence of enduring behavioral changes brought about initially by supragenetic alterations of normal or species-typical development (p.175)".

How can the concept of fractal time provide new insights into the mechanisms of behavioral change afforded by heterochrony? Mandell and Selz (1990,1992) have

interpreted nonlinear changes in phenotypic traits such as the self-regulation of brain enzyme kinetics or the number of digits in the hind limb of the salamander in terms of a new view of heterochrony as the absence of a single characteristic time scale (i.e., fractal time) in biological systems. The possibility exists that spontaneous prenatal behaviors as fractal patterns in time may also suggest a mechanism for heterochrony (i.e., shifting self affine relationships between the timing of gene expression and behavioral activity) and as a source of the behavioral plasticity underlying the creation of neophenotypes as described by Gottlieb (1992).

This evolutionary and behavioral plasticity may originate from bidirectional interaction between fractal spontaneous prenatal behaviors, the spatial-temporal dynamics of gene expression, in utero patterns of stimulation, as well as postnatal experience, to generate behavioral neophenotypes. One element of this complex interaction may involve long-range spatial fractal correlations that have recently been described in both introns and exons (Voss, 1992) along strands of DNA. These correlations may be related to the spatial structure of the chromosome (Bludyrev, Goldberger, Havlin, Peng and Stanley, 1994) and may in turn play a role in the regulation of gene expression. Another aspect of this interaction may involve the responsiveness of fetal noradrenergic neurons to sensory stimuli such as uterine contractions, maternal heart beat and breathing. It is also possible that these patterns of maternal stimuli are fractal in time as well (Bludyrev et al., 1995), and that horizontal interactions between maternal and fetal fractal patterns provide a source of relative coordination similar to that proposed for autonomic discharge coupling in the adult RF (Langhorst et al., 1983; Langhorst et al., 1987). Further noradrenergic regulation of serotonergic neurons could modulate REM durations and subsequent activity patterns. Alterations in or prolonged disruptions of fetal activiy can have wide ranging effects on phenotype (see for example Hall, 1986). Prenatal and neonatal exposure to drugs or hormones and alterations in dietary cofactors or essential amino acids such as tryptophan may alter REM structure (Qulligan et al., 1981) and induce functional changes in the fetal and neonatal RF and other brain structures resulting in life long changes in behavior (Mirmiran et al., 1986). The RF and temporal lobe areas are particularly sensitive anatomical sites for experiential change, as indicated by the wide ranging role the RF has in startle responding, learning, sleep state and emotional regulation and the common comorbidity of disruptions of these behaviors in abused and traumatized children (Anderson et al.,1995; Finkelhor, 1990; Glod et al.,1995). How might environmental, genetic and behavioral information such as spontaneous phasic REM associated activity inform developmental processes to generate behavioral neophenotypes during ontogeny?

On the celluar level, spontaneous calcium transients (spikes and cellular waves) have been found to regulate neuronal plasticity during develoment in Xenopus (Spitzer, Olson and Gu, 1995), the chick spinal cord (Spitzer, 1994) and the rat neocortex (Yuste and Katz, 1991) and many other systems (Spitzer, 1994) over a wide range of time-scales. Nerve membrane fluctuation events have long been known to have fractal time properties (Verveen and Derksen, 1968). In the chick spinal cord, calcium fluctuations are most likely generated in synaptically driven motor neurons during bursting events correlated with spontanous motility (Provine and Rogers, 1986). I hypothese that these developmentally critical spontaneous calcium transients will share the same convolutionally stable patterns seen in inter-spike-interval, fetal and neonatal associated phasic REM events which occur recurrently during adult REM sleep during the dynamic regulation of receptive fields and maps in the sensory cortex and limbic areas associated with learning. Therefore, alterations in these same convolutionally stable pattens, as seen for maternally deprived rats, could have broad spectrum effects on fractal time bursting patterns resulting in functional behavior changes (i.e, habituation, startle responding, etc.) and morphological alterations (Ito et al., 1993; Teicher, Glod, Surrey and Swett, 1993). In additon, the existence of long-range fractal correlations in spontaneous prenatal behaviors, spontaneous calcium transients, genetic regulation and their interaction with fractal stimuli from the mother and environment during pre- and postnatal development may provide the key to understanding the dual phylogenetic origins of REM sleep and exploratory behavior so prevalent among mammals (Gottlieb, 1992; p.187).

Coevolution of fractal time interactions within and between organisms and the environment is also an important concept that emerges from this new perspective of behavioral neophenogenesis. This may explain to some extent the observed fractal geometery of phylogenetic trees (Burlando, 1990; 1993). The coevolution of insect size and shape with plant leave size and shape may explain the observed fractal scaling relations between insect population density, body weight and their terrestrial habitats (Birdi, 1993). The wide ranging occurrence of spatial and temporal fractals in both non-biological and biological systems suggest that the plasticity underlying the interplay between ontogenetic adaptations and environmental factors in the development of phenotype during evolution consists of a complex interaction or resonance between external and internal spatial and temporal fractal processes (Anderson and Mandell, 1996). In a profound way the evolution of all spontaneous animal behavior including human consciousness could be conceptualized as having originated in "universal" spontaneous fractal time fluctuations such as critical point fluctuations and 1/f noise proceses that were present in the first proto cellular membranes (Mandell, 1986; Verveen and Derksen, 1968), these same fluctuations continue to this moment and beyond.

THE FRACTAL TIME NATURE OF SPONTANEOUS PRENATAL BEHAVIORS: PARALLELS WITH CRITICAL POINT FLUCTUATIONS AND OTHER COMPLEX SELF-ORGANIZING SYSTEMS.

The long range correlations observed between nuchal atonia events suggests similarities between the behavior of this REM related process and that of other complex systems. Any complex self-organizing system such as (a sheep fetus or neonatal rat) is actively involved in the coordination of processes with different characteristic time scales (e.g., neural membrane events, population events in the RF, motor unit activity, etc.) and, therefore, may in a limited way be analogous to other complex physical systems displaying scaling, critical point phenomena and long-range correlations. Examples of these include velocity distributions in turbulence (Kadanoff, 1990; Takayasu, 1984), phase transitions in magnetism (Peitgen and Richter, 1986), self-organized criticality or diffusion in amorphous solids which are also described by fractal time correlations and long-tailed Lévy distributions (Bak and Chen 1991; Montroll and Shlesinger, 1984; Shlesinger, 1987; 1988). Similarly, Prigogine (1980) has proposed that the origins of order, or long range correlations, in far-from-equilibrium systems (e.g., biological systems) are due to the breakdown of the law of large numbers, and the shift from Poissonian to long tailed non Poissonian distributions (Prigogine and Stengers, 1984; Nicolis and Prigogine, 1989).

How can I visualize the formation of these complex patterns of statistical interdependence? What mechanisms create correlations or the "memory" effect in physical phenomena? River flows, for example, are dependent on weather events over many scales of space and time from droplet formation to the jet stream, and their interaction with geophysical structures over millennia. Each of these processes can also be described in

terms of spatial and temporal fractals (turbulent fluid flows in the atmosphere, multifractal rain and cloud fields; see Jenson et al., 1991 and others in the same volume). Also, multiple time and space scales contribute to river formation; rain falls on fractal river basins and percolates through fractal soils (Barton and La Pointe, 1995a & b; Takayasu, 1993). The multiplicative dependency between these diverse factors and degrees of freedom in this long stream of interconnected events, from drop formation to river level measurements, results in complex patterns of statistical interdependence and the observed fractal time behavior. How does memory arise in the river system? As Feder (1988) explains: "The discharge of the river depends on not only the recent precipitation but also on earlier rainfalls. The flow in a large river system such as the Nile, or the discharge of Lake Albert, must depend on the water content in a large drainage area. The amount of water stored in the drainage area will increase in prolonged periods of higher than average precipitation. The excess amount of water stored will then contribute to the discharge in drier years [The carryover of excess water generates the "memory" effect] " (p. 161). The memory, or carryover between wet years, causing a persistent increase in the flow, is the source of the correlations. A pattern consisting of a series of low years or high flood years creates the fractal time behavioral sequence of river flows as well as mud layers in sedimentary deposits over decades, centuries and millennia. Critical point phenomena in physical systems also exhibit a rich variety of fluctuations with long-range correlations over many scales of space and time.

Fluctuations in behavior analogous to the fractal time behavior of REM sleep, but in much more homogeneous substrates, can be found in critical or second order phase transitions between magnetic and non-magnetic states in magnets and liquid or gas phases in water. For the less complicated case of magnets, an application of the concept of self similarity called renormalization theory allows descriptions of self-similar states of matter. The relationship between different levels of observation in a homogeneous system can be described by a renormalization transformation equation (RTE). Simply, it means that because magnets look the same, or are fractal, over different ranges of length, a model magnet can be simplified by reducing the degrees of freedom (number of atoms) by rescaling. A magnet at one scale of measurement can be compared to a magnet at a new scale of measurement, but the temperature (or fluctuations) at one scale may not be the same at the other scale. To have a valid model I must renormalize the temperature from the old scale to the new scale, and this is done with the RTE. A magnet is made up of many smaller atomic magnets that, when lined up in parallel, create a strong magnetic field. When a magnet is heated to a particular temperature, the Curie temperature, it starts to lose its magnetic properties and becomes non-magnetic. This is due to an increase in thermal fluctuations that disorder the parallel order, leading to a loss of long-range order, correlation or coherence over many spatial and temporal scales. At this special temperature the RTE is a constant. A unique situation exits with thermal fluctuations occurring over all ranges in a self-similar fashion creating the same temperature over all ranges. In the language of dynamical systems, when the RTE is a constant, it is a basin boundary or repellor between two states in this case between low temperature magnetism and high temperature with a loss of magnetism (Peitgen & Richter, 1986). Temperature is said to be a parameter that moves the system from magnetic, before the Curie temperature or critical state, to non-magnetic, when long-range interactions break down.

As it happens, analogous critical states in dynamical turbulent fluid flows, where a continuum of states having multifractal behavior exists, may be even closer to the reticular formation phenomenon (Kadanoff, 1990). Turbulent fluid flows have fractal time structure and generate charateristic patterns of intermittency. One model of fully developed turbulence regards this state as the velocity field produced by fractally distributed sources of circulation such as vortex filaments (Takayasu, 1984). An important theoretical finding in this area is that these fractally distributed vortices have velocity distributions that are Lévy stable with characteristic exponents which depend on the fractal dimension of the turbulence. Looking at Figure 23 it is not hard to imagine that complex patterns of activity in the developing RF might have properties similar to fully developed turbulent fluid flows and that the resulting intremittency would be the fetal and neonatal REM fluctuations I observe. It even appears that the flows of turbulent patterns of activity would result in the prononced anatomical changes observed over development.

Turbulent fluid flows and critical point phenomena in physical systems also share 1/f spectral patterns which originate in the long range correlations between different parts of the system in particular states. The RF also shows 1/f spectral density patterns during different behavioral states which it shares with turbulent fluid flows and critical point phenomena in physical systems RF function during fetal REM may show similar patterns based on spectral studies of cell firing patterns during different behavioral states in adult cats (Kodama et al., 1989). Kodama et al., observed a loss of long-range correlations which was evident during slow wave sleep and quiet wakefulness, while during REM sleep and orienting, long-range correlations and 1/f spectral density patterns were found to be present in the same cells. An experimental test of the hypothesis that the fetal RF during fetal REM sleep has a change in correlational state, inspired by the Kodama et al. study, could utilize methodology similar to that used in the analysis of long range correlations in turbulent fluid flows or the heart used by Bayly et al. (1993). In this study a 22 ¥ 23 unipolar electrode array was placed on the heart, and the correlation length, a measure of critical scaling states (Peitgen, 1986), was examined between all regions of the array during the transition to fibrillation. Thus, a similar study in the in utero fetal RF may elucidate the structure of spatial and temporal correlations and their behavioral state dependent changes, giving a four-dimensional view of dynamic brainstem self-organization during spontaneous prenatal behavior.

THE FRACTAL TIME ORIGINS OF SPONTANEOUS APPETITIVE BEHAVIORS:

REM SLEEP, NEURAL PLASTICITY AND THE ORIENTING RESPONSE

The term appetitve behavior, which has its roots in the latin for a longing for, is used by Craig (1918) and later by Lorenz to describe the restless, searching behavior characteristic of animals expressing a mounting internal drive state (Roeder, 1955). Kenneth Roeder in his 1955 article "Spontaneous activity and behavior" described the occurrence of non-sensory evoked spontaneous self-excitatiory activity in the nervous systems of many invertebrates and vertebrates and proposed that the apparently random nature of appetitive search behavior was in part a result of this spontaneous neural activity. In the abstract I stated that "spontaneous activity over many levels of biological organization, including phasic REM motor activity during ontogeny, could play a fundamental role in the development of appetitive behavioral processes (e.g., searching and orienting) and other forms of neuroplasticity (e.g., learning and dynamic regulation of receptor fields and maps)". As I have shown, spontaneous activity associated with REM sleep is not an independent random process, but contains invariant hierarchical correlations over many levels of organization in development.

In this section I will explore in further detail what I percive to be a connection between spontaneous prenatal behaviors first manifest in the fetus as concurrent bioelectrical activity and spontaneous motility and the nature of neuroplasticity and appetitive behses such as the orienting response in developmentally mature organisms. Two new concepts will be explored: 1) A behavioral response of an organism, (such as habituation) to a repeated stimulus can be conceptualized as movement in an of

attractor with complex boundries; 2) A new definition of homeostatsis in terms of the fractal time nature of biological systems which allows flexible rescaling in time to enviromental stimuli and conditions.

The following section results from a personal struggle over the last seven or eight years to conceptualize in some coherent fashion the observation that maternally deprived infant rats do not habituate normally to an artificial odor (Anderson, 1992). During these years I have observed that developing rat pups along with most other animals typically generate highly variable spontaneous behavior. In rat pups, examples of this include convulsive, uncoordinated myoclonic jerks and irregular patterns of spontaneous whole body activity or motility exhibited when sleeping in a warm incubator. In other cases the fluctuations of responses during an olfactory habituation testing session and the spontaneous choices that 16 day-old pups make when handled for removal from their home cage were also distinctive. Exposure to the ideas of fractal geometry and non-linear dynamics has provided me with a context for the belief that a new and pervasive order may underlie the apparently erratic behavior of pups sleeping or orienting to an odor, and this fractal time order may have important implications for deciphering and unifying the processes underlying the developmental organization of behavior. What follows in this section is part of an ongoing free play of ideas toward the formulation of testable hypotheses concerning the connection between fetal and neonatal REM sleep phenomena, neuroplasticity and appetitive processes such as orienting and habituation.

THE RETICULAR FORMATION, REM SLEEP, ORIENTING AND DEVELOPMENT: A GUIDING IMAGE

Before I proceed further let me share with you an image that embodies the core of this section: The RF during an orienting response as a vast collection of regions, subregions and complex fractal neurons interconnected in a network (literally "net-like" see Figure 23) interacting over all scales, activated or aroused by incoming multimodality sensory input. A state almost identical to this (except that the evoking stimulus and physical movements associated with orienting are suppressed) exists in the RF during the behavioral state of REM sleep, as if the two highly activated states were identical (see Morrison, 1979 for a stimulating discussion of this connection). The RF during these states could be said to contain coherent fluctuations of neuronal firing (or activated loops or pathways) at all time and space scales woven together, small groups of fluctuating neurons imbedded in larger fluctuations between nuclei, in a self-similar fashion over the entire brainstem, indeed, coherent with all cortical and subcortical areas.

One image for the aroused state of the RF during orienting or REM sleep could be a repeller or complex fractal basin boundary between different possible behavioral states of the RF and, by implication, behavioral states of the animal. If a novel stimulius, say, a caged bird, is presented to a cat, it will evoke a strong orienting response. When the bird cage is removed from the cat's sight, the orienting response and arousal will fade, leaving the cat in a state of quiet or attentive wakefulness. The RF dynamics in this situation are similar to those of a point entering an attractor at a complex fractal basin boundary as opposed to a basin bounded by a smooth curve. The analogy here is to the dynamics of the Curie point in magnetism (p. 135) where coherent fluctuations of all ranges are woven

together, small fluctuations imbedded in larger ones, on and on to the smallest length scales. As time changes, the point will follow a pathway along the boundary, taking longer to land in the stable attractor (the homeostatic state of quiet wakefulness). After many presentations, the stimulus is no longer novel to the cat and it is said that the cat has habituated to the bird; the next presention will evoke less orienting. This waning of the response may be due in part to neurochemical changes, perhaps in RF-forebrain pathways. Habituation in this case might be visualized as a smoothing of the complexity of the fractal basin boundary, so that a point entering now takes less time to find the stable attractor. Or in the case of the magnet, the dynamics has moved off the Curie point and the RTE is in the domain of fewer and fewer scales. Imagine that a habituation parameter (analogous to temperature in the magnet example) might be 5-HT concentrations or firing rate, and that increasing [5-HT] might make the behavioral state of quiet wakefulness a smoother bounded attractor for initial points (stimuli) similar to the habituated state. Therefore, under these conditions the behavior of the animal quickly finds the attractor, habituating rapidly. Conversely, what if the animal were given a 5-HT synthesis inhibitor, which interferes with habituation? This parameter change may reduce the predictability of the attractor by making the fractal basin boundary more complex, causing the animal to take longer to habituate. What then determines the long term shape of the fractal boundary of the habituation attractor, genetics or experience or some complex interplay between these and other factors? I propose that the shape of the fractal boundary is due to many factors, with the fractal time structure of fetal REM sleep patterns playing an important role in the interplay between genetics and experience. Referring back to Figure 23, the observed change in the complexity of the RF during development might reflect alterations experientially derived in the properties and parametric characteristics of the complex fractal basin boundaries between different possible behavioral states. In the RF the activity of many types of neurotransmitters, neuromodulators and hormones in the RF interacting during pre- and postnatal periods with spontaneous convolutionally stable fractal time phasic processes could create in every REM period a long-range developmentally similar pattern of stimulation, which when superimposed on the dramatic morphological changes observed (Figure 23) would endogenously regenerate the complex internal correlations or fractal structure of the basin boundaries. So REM sleep provides a kind of self-similarity over development, functionally superimposed on anatomical changes. The complexity of the fractal boundaries would be the result of interplay between daily experience and periodic REM events, becoming self-modifying fractal basin boundaries through the animal's interaction with the environment. Perhaps some kind of two-way interactive hierarchy of fractal basins within basins could be used to model long- and short-term learning. Habituation over trials would entail smoother boundaries within this interactive hierarchy. For example, large lesions of the RF destroy long-term habituation over sessions versus short-term habituation within a session (Jordan, 1989). The disorder and loss of anatomical connectional correlations caused by lesions in the hierarchy would not interfere with elemental basins, only the complex interactions within the hierarchy.

One of the predictions of the presence of plastic complex fractal basin boundaries in the internal behavior of the RF is that 1/f-like power spectra or fractal time behavior would be observed in behavior originating there. This has been observed in single unit activity in the RF during orienting and REM sleep and in a model of the RF (Yamamoto et al.,1983; 1986; 1993 ). Also Szeto et al. (1992) have observed 1/f-like power spectra behavior in the instantaneous breathing rate of fetal sheep, which only breathe during REM sleep (Dawes, 1972). This is supported by the findings (described in the experiments of this dissertation) that fractal long-range time correlations and Lévy stable distributions are observed in the patterns of nuchal atonia and nuchal inactivity in fetal sheep and neonatal rats, both in association with REM sleep. The prolonged occurrence of phasic REM associated activity in the fetal state during developmental processes such as axon migration and synapse formation and elimination may ensure that the fractal boundry does not get too complex (by removing the heteromorphic protospines from growing dendritic surfaces), which may happen in the case of chronic drug induced sleep deprivation during postnatal life resulting in defects in habituation and appetitive behaviors into adulthood (Mirmiran, et al., 1983; 1986).

The next section attempts to conceptually tie together the phenomena of spontaneous motility associated with REM sleep and the neural-behavioral process of habituation through the concept that homeostasis in biological systems (and in brain structures such as the RF; see Dell, 1963 and Klemm, 1990 for discussions of this old but interesting concept) occurs through the generation of correlations over many timescales which is facilitated by the phasic activity of REM sleep. Specifically, homeostasis reflects the ongoing modifications of the complex dynamic interactions over many time and space scales between neurons, networks in the RF and forebrain sites (see Rooney and Laming, 1988, for an excellent account of the effects of removing telencephalic inputs on RF mediated habituation). The concept of physiological homeostasis can be applied readily to the RF because it is inherently self-similar over many levels of biological description, from ionic homeostasis in cells, to body temperature homeostasis, to the homeostasis of animal populations.

The fractal basin boundary or critical state description is one of many possible descriptions of the dynamics of RF neuronal interactions. Any worthwhile description and experimental approach to the involvement of the RF in phasic REM processes should consider the application of measures sensitive to the existence of a wide range of correlations over different timescales such as in ultradian activity patterns of spontaneous movements from neonatal rats over short- and long-timescales and their alteration by postnatal maternal deprivation or other insults. For example, maternal deprivation or other insults (e.g., cocaine) appear to increase correlations, as measured by the Hurst exponent (see Figure 19b, p. 97), associated with the fractal-time behavior of nuchal inactivity episodes with concomitant disruption of habituation to an olfactory stimulus (Anderson, 1992). Commensurate with the increases in persistence are changes in the Lévy stable distributions between deprived and non-deprived animals, indicative of longer distributional tails due to outliers which result from the generation of larger clusters of phasic activity. This would reflect complexity changes in the fractal basin boundaries, and/or changes in the ability of the organism to internalize and efficiently sample multiscale internal signals and match them with external patterns from the enviroment. The fetal and neonatal animal may be more dependent on REM to maintain RF homeostasis. Maternal deprivation may disrupt neonatal REM sleep (Hofer, 1976), causing a compensatory increase in phasic activity which, under normal litter conditions, may result in the pup's approach to the dam or other appetitive behaviors. In addition, this may help to explain habituation defects indictive of fetal distress (Leader, Baillie, Martin and Vermeulen, 1982) as a loss of RF homeostasis due to REM disruptions.

This new perspective afforded by the fractal basin boundary description of habituation, homeostasis and development will be integrated with themes explored in earlier sections in the following ways: 1) The recurrence of stable fractal time behavior during REM processes in the RF throughout the life span of an animal facilitates long-term memory and behavioral flexibility by reinstating homeostatsis and keeping fractal basins from becoming too complex or by regenerating the flexibility of the internalization process. 2) Conceptualizing habituation and sensitization processes as the consolidation or internalization (in the RF and forebrain areas) of stimuli induced-reorganization of the ongoing maximization of correlations in biological systems, whether in fractal basin boundaries of the dynamics of the RF or global networks of the CNS, allows a simplification of dual processes theory and accommodation of other unexplained observations such as the "missing stimulus effect" in habituation of orienting responses. 3) This model can provide an image in terms of dynamical systems theory for unifying a large data base of observations of REM processes, habituation of orienting responses and other behaviors in developmental and adult experimental systems.

HOMEOSTASIS, HABITUATION AND THE IMPORTANCE OF REM SLEEP IN THE GENERATION OF LONG-RANGE CORRELATIONS

Based on observations of physical systems showing critical point behavior, I propose as a primary hypothesis that biological dynamical systems after encountering a stimulus tend to self-order in a way that maximizes the range of scales over which temporal and spatial correlations can occur and that this process is dependent on the long-range correlations imparted by REM-associated processes. This self-ordering is also similar to the notion of homeostasis. Homeostasis, when abstracted from the specific physiological context of a given organ system, can be given a more general meaning. A more general definition was proposed at a symposia of the Society for Experimental Biology in 1963 entitled "Homeostasis and Feedback Mechanisms": "Homeostasis in its widest context includes the co-coordinated physiological processes which maintain most of the steady states in organisms. Similar general principles may apply to the establishment, regulation and control of steady states for other levels of organization. It must be emphasized that homeostasis does not necessarily imply a lack of change, because the 'steady states' to which the regulatory mechanisms are directed may shift with time. But throughout the change they remain under more or less close control. Such a concept can therefore be applied to organizations at cellular, organ system, individual and social levels. It may be considered in relation to time intervals ranging from milliseconds to millions of years. Its essential feature is the interplay of factors which tend to maintain a given state at a given time. (p.vii)" Homeostasis or the maintenance of a relatively stable internal environment or equilibrium in an organism, population or ecosystem, requires compensatory feedback mechanisms on many different time and space scales. In creating homeostasis, biological systems appear to generate long-range temporal and spatial order through the generation of correlations between different scales of time. REM sleep processes could supply correlational order over many scales, as measured by Hurst analysis and Lévy exponents. The similar values of the Hurst estimates and Lévy exponents across species reported in this dissertation many reflect this common role in homeostatic stability.

The behavioral manifestation of homeostatic stability is the tendency of an organism to become habituated over time to stimuli in its environment. Habituation is a fundamental biobehavioral process, recurrent at many levels of phylogenetic, behavioral and neuropsychological description (e.g., from cellular events to interactions of animal populations; Mandell 1986). Habituation is simply defined as the decrementing of a response with repetition of an eliciting stimulus, or simply learning to ignore a stimulus (Groves and Thomson, 1970). In nature, habituation is often long lasting and can have a critical role in various adaptive processes for organisms, including stimulus recognition and selective perception (Hinde, 1970; Thorpe, 1963).

It follows from the primary hypothesis that perturbations of biological dynamical systems away from homeostasis can interfere with the ongoing maximization of correlations over temporal and spatial scales. In these terms a fundamental relationship between the generation of and/or consolidation of correlations over temporal and spatial scales in the organism and the behavior of the organism exposed to a changing environment can be proposed. It can also be proposed that as the organism shows habituation to the changing environment, information about the changing environment influences the ongoing generation of and/or consolidation of correlations. In this way the organism internalizes new correlations with the changing environment. This may partially explain the need for frequent sleep in predator species which explore large regions of space searching for food (Campbell and Tobler, 1984). In fact, it would be highly adaptive for the organism to internalize environmental correlations (which in the wild would probably have many fractal properties) during REM periods in terms of relationships in time and space between food, shelter and mates to ensure survival. In addition, internal factors that modulate habituation to environmental changes (arousal, sleep deprivation, hunger, 5-HT, NE, etc.) can be described in a universal way in terms of their influence on the process of maximization or the complexity of fractal basin boundaries governing the dynamics. One further implication of these concepts is that changes in correlations involving habituation and homeostasis could be measured in the fractal time behavior of the organism.

MAXIMIZATION OF FRACTAL TIME CORRELATIONS AND THE INTERSTIMULUS INTERVAL (ISI): DISRUPTION OF CORRELATIONS BY AN ACOUSTIC STARTLE STIMULUS

A concrete example of this concept of maximization of correlations will be discussed below in terms of the habituation of the startle response (Davis, 1970). The startle response is a stereotyped, reflexive sequence of muscular responses elicited by a sudden, intense stimulus. The amplitude of the response is directly related to the intensity of the stimulus, and the decrease in amplitude with repeated presentation of the stimulus is the key measure of learning or habituation. In terms of speed of response decrement to a number of startle stimuli, the shorter the interstimulus interval (ISI), the higher the rate of decrement when tested with short ISIs. (Keep in mind that training and testing occur with the same stimulus, and therefore the ISI is the training interval and the testing interval, confounding the training and testing parameters; Davis, 1970). The rate of habituation is inversely related to the ISI when testing is performed with the opposite ISI. For example, Davis found in rats, that with 1000 presentations of 2 sec ISI's vs 16 sec ISIs, the 2 sec ISI produced the greater decrement. However, when the animals were tested 1 min or 24 hrs later with different ISIs, startle responses were lower (the animal showed more learning) with 16 sec ISIs than 2 sec ISIs. How can I explain habituation to longer and shorter ISIs, as well as enhanced learning with longer ISIs vs shorter ISIs with independent testing, in terms of maximization of correlations over temporal and spatial scales in the CNS of the rat?

THE TIMING OF ISI'S AND THE RATE OF RETURN TO THE CRITICAL STATE

What is the animal's correlational baseline? According to the primary hypothesis, prior to the first startle stimulus, assuming the animal is habituated to the testing situation, the animal would be in a maximized state. At the moment the animal startles, the homeostatic state is disrupted and experiences a loss of correlations. The effect of the startle stimulus is to disrupt the ongoing maximization of correlations by triggering auditory sensory activity, which because of its amplitude and suddenness (e.g., 90dB within 12 msec), elicits reflex activation of a number of pathways. Davis (1982) describes this auditory pathway in great detail. Briefly, the auditory stimulus enters the brain at the ventral cochlear nucleus; passing through the lateral lemniscus it enters the reticularis pontis caudalis (RPC) in the pontomedullay RF. The RPC projects locally to other RF areas (paramedian pontine RF and nuclei of the medial RF core) and to interlaminar and midline thalamus, fields of Forel, zona incertal and the lateral hypothalamic/MFB bundle and amygdaloid nuclei as well as extensively to the spinal cord (Klemm, 1990). This results in movement and the likely release of stress hormones, which in turn causes changes in the activation of reticular and forebrain areas setting off the trigger for an orienting reflex and the 1/f power spectal density and fractal time patterns associated with the critical state that is also similar to the REM sleep state. After stimulus ends, the response fades and all parts of the system return to homeostasis, similar to the prestimulus state. This new state would be a reorganized version of the prestimulus state, the stimulus having altered synaptic strengths, the release properties of many neurotransmitters, firing rates of NE and 5-HT centrifugal systems and reorganized dynamic assemblies of cortical and subcortical loops, as well as having changed autonomic variables such as heart-rate, breathing, vasoconstriction, gastric motility, etc. In short, the neurons (glia too) involved in the response, as well as those not involved, and their interactions have been altered by the stimulus. Therefore the stimulus, by momentarily decorrelating the system, forces the system to re-self-order in the critical state of the orienting response, in terms of the stimulus and its history and characteristics of the local environment (cage). The fractal time correlations imparted by REM sleep are crucial to the normal habituation process.

How is a sequence of stimuli driven behavioral states such as .../ crtical state/ to /stimulus-disrupted-state/ to / critical state/...altered with multiple stimulus events during a habituation session? The key idea is the nonlinear rate of return to the critical state after decorrelation. Because this rate is a reflection of the overall correlational structure (integrity) of the animal, it would be fairly constant over a training-testing session. Even if the animal is momentarily disrupted by the stimulus, it has a reservoir of correlations in its multiscale structure. Long ISIs give the animal ample time to recover the critical state between stimuli and reproduce the startle response. The animal will continue responding until the stimulus is internalized. With short ISI's the animal habituates in a shorter time to the stimulus as compared with the longer ISIs. Short ISIs quickly overwhelm the nonlinear rate of return to the critical state, and the animal is unable to integrate the response. The inability to internalize the stimulus is revealed with subsequent testing with different ISI's. Animals trained with long ISIs show less responding or greater learning when tested one minute or one day later with the same or shorter ISIs. Training with short ISIs, however, that overwhelm the nonlinear rate of return to the critical state, (possibly even changing or slowing the rate), render the animal unable to fully integrate historical correlations with the new correlational state formed. Therefore, on retesting one minute or one day later with the same or longer ISI's, less learning (e.g., savings or long-term integration) is present behaviorally. In brief, short ISI's, by effectively altering the rate of return to the maximized state, disrupt the establishment of long and short term correlations (disruptions over many time scales distort fractal time), creating apparent learning by disrupting responding but preventing long-term learning whether one minute or 24 hrs later. Alternatively, the animals exposed to short ISIs were forced into a prolonged state of loss of correlation, which was more disruptive of homeostasis, preventing internalization of correlations. The idea of remaximizing intercorrelations or internalization is similar to a consolidation hypothesis discussed by Davis (1970): "Another possibility might be to assume that some process similar to consolidation may operate during habituation training. Stimulus exposure may always result in a tendency to reduce subsequent responding to that stimulus, unless otherwise disrupted by another stimulus presented shortly thereafter. When stimuli are presented at short ISIs, the habituation produced by Stimulus n may not have sufficient time in which to consolidate by virtue of being followed too closely by Stimulus n + 1. With long ISIs, however, each stimulus would be expected to have a longer time to consolidate, so that the total habituation produced under such conditions should be greater. (p.190)" In these terms, ongoing maximization of correlations during orienting and internalization is equivalent to consolidation. Another way of conceptualizing these results is to consider ISI length as a probe of the plasticity of the animal; when plasticity is low, the ISI length needed to disrupt learning would be longer compared with the ISI length that would be needed with an animal having normal plasticity.

DISRUPTION OR FACILITATION OF CORRELATIONAL MAXIMIZATION:

MODULATION OF SENSITIZATION OF STARTLE RESPONSES BY NOISE OR NEUROTRANSMITTER SYSTEMS

Groves and Thompson (1970) explained the disruption effect of short ISIs in terms of dual process theory by assuming that shorter ISIs produce more sensitization in the animal. Further supporting a role for a sensitization process is the observation that under certain circumstances, repetition of the startle stimulus can lead to increments in startle responses as opposed to decrements (Davis & Wagner, 1969). To explain this effect, Davis and Wagner proposed that the startle stimulus elicits both incremental and decremental processes that interact in determining the final response levels. The key assumption is that both effects are the result of the startle stimulus. However, other factors in the experimental situation could also interfere with ongoing maximization of correlations. For example, high background noise (Gaussian white noise 80dB) causes progressive increments in response (Davis, 1974). Thus the background noise could be disrupting the ongoing maximization of correlations due to its lack of correlations (each time point in a Gaussian white noise process is uncorrelated with or independent of the last point) and intensity (overwhelming sensory adaptation or habituation) to such an extent that the rate of maximization becomes negative. On the contrary, music or fractal sounds with long-range correlations might enhance startle habituation. This suggests that in some cases (e.g., stressors) sensitization is a result of the reoccurence of phasic REM like activity to reinstate maximization and homostasis in a situation where an actual loss of correlations over many time scales is occurring. The implications of the original hypothesis, at least in the example of habituation of startle responses, are to simplify dual process theory into one process, the maximization of correlations or fractal time behavior contributed by the phasic nature of REM sleep-like states. Strangely, this also implies that the critical state of orienting closely resenbles a REM sleep state (Morrison, 1979). This simplication of habituation concepts can also overcome another difficulty of dual process theory, the "missing stimulus effect" (Sokolov, 1960), where the omission of a stimulus during habituation of the orienting response results in the return of orienting (this will be explored further in the section on orienting responses).

How can the modulatory effects of manipulations of various neurotransmitter systems such as the NE and 5-HT systems on habituation of the startle response be conceptualized in terms of disruption or facilitation of the ongoing maximization of correlations? Davis (1980) investigated neurochemical modulation of the startle response in rats with chronically implanted stimulating electrodes in two key segments of startle pathway, the auditory nucleus posteroventral cochlear nucleus (VCN) and part of the pontomedullary RF, the ventromedial region of the nucleus reticularis pontis caudalis (RPC). Bilateral lesions of both of these areas eliminated acoustic startle responses both acutely and chronically. Electrical stimulation of these sites elicits short latency startle responses which, in the case of RPC, increment in mean response amplitude during the session. The RPC has heavy descending projections to the spinal cord and receives substantial projections from more anterior reticular nuclei. In addition, reticulo-reticular projections to anterior reticular nuclei might activate the cell bodies of ascending and descending NE and 5-HT axons. Interestingly, acoustically responsive RPC neurons in the cat display discharge activity during muscle twitches in REM sleep. Other neurons in the RPC may play a role in muscle atonia during REM sleep (Lai, Clements and Siegel, 1993; Kungel, Ebert, Herbert and Ostwald, 1994).

Davis found that intrathecal NE or 5-HT increased startle under the condition of background white noise. When the 5-HT synthesis inhibitor p-chlorophenylalanine (PCPA) was infused before the session, RPC stimulation induced increments were not affected and remained high throughout the session. However the infusion of a a1 adrenergic antagonist, WB-4101, blocked RPC stimulation induced increases in startle. Taken together, these experiments demonstrate the central role of NE in preventing habituation. I found evidence for a similar role of NE in preventing habituation of olfactory orienting in infant rats (Anderson, 1992).

In contrast, the tonic activity of dorsal raphe 5-HT neurons (except during orienting responses or REM sleep) suggests some role in homeostasis. Activation of NE neurons seems to be associated with arousal, and on first examination would seem to play a role in disruption of ongoing maximization of correlations (Rasmussen, Morilak and Jacobs, 1986). The startle response work of Davis supporting a role of 5-HT in normal habituation would seem to suggest it might provide facilitation (at least in the spinal cord) of ongoing maximization of correlations as well. A parsimonious view would suggest that the coordinated interaction of these two major neurotransmitter systems would facilitate the generation of correlations during different behavior states (waking, orienting, quiet wakefulness and REM sleep).

Other work on startle responses in the cat (Wu and Siegel, 1990) supports a more definite role of 5-HT in startle decrementing. Wu and Siegel found substantial facilitation of startle over pre-drug levels 550% in cats treated for 4 days with PCPA. They reported that the cats suffered from initial insomnia (no REM sleep until day 3-4) and this may represent a confound (REM deprivation inpedes habituation). Over half of PGO events that appeared in wakefulness or SWS on day 4 were found to be preceded or followed by discrete head-body movements resembling orienting reflexes. Startle responses were also enhanced following PGO events. It was concluded that 5-HT produces a tonic suppression of startle responses and PGO amplitude in waking and that PGO spikes are associated with phasic facilitation of startle sensorimotor pathways. Curiously, PCPA dose not induce PGO during wakefulness in rats (Kaufman, 1983).

In conclusion, it is proposed here that the (Groves and Thompson) view of habituation in terms of competing sensitization and habituation processes can be restated within the theoretical framework of a unitary process involving maximization of correlations and the fractal time nature of REM sleep. Sensitization is therefore the result of an extreme stimulus induced failure of correlational maximization with compensatory induction of phasic REM processes, possibly caused by prolonged changes in coordination between increased NE as well as decressed 5-HT release associated with behavioral arousal. Remaximization of correlations or normal habituation following stimulus presentations with long ISI's is facilitated by tonic 5-HT release, which as acts a brake on phasic REM-like activity. The fact that these two neurotransmitter systems project to almost every region of the brain from the RF illustrates the role they play in this theoretical model as key positive and negative modulators of the ongoing maximization of correlations during wakefulness, in addition to their permissive role in REM sleep.

DISRUPTION OF HABITUATION, CORRELATIONS AND HOMEOSTASIS BY REM DEPRIVATION

Increased REM sleep has been demonstrated to be strongly associated with consolidation of associative learning (Pearlman, 1979; Smith & Wong, 1991). In humans it has been reported (West, 1964; see Discussion page 556) that the habituation of autonomic responses disappears during drowsiness caused by sleep loss and further "Insofar as habituation requires some sort of temporary storage of the effect of the stimulus, this again reflects a real defect in the temporary storage mechanism during sleep and drowsiness (p.556)." How would REM deprivation modulate the habituation of startle reflexes or orienting behavior? It appears from an extensive review of the research on learning and sleep deprivation that no systematic parametric study of the effects of REM deprivation on habituation patterns can be found. How can the results of REM deprivation the disruption of learning-possibly by disrupting consolidation as well as preventing habituation, be reconciled with the main hypothesis? I have suggested that fetal REM sleep and associated phasic activity may provide a stable, scale-invariant source of correlations that may facilitate integration of new neural changes into previous growth, thereby facilitating homeostasis, plasticity and behavioral flexibility (Anderson & Mandell, 1994). These fractal time REM patterns would also provide a stable reference for memory consolidation in older animals. This may explain the PGO burst associated activity of RPC neurons during REM sleep. This activity could be the result of recurrent activation of previously used reticular-spinal pathways, reinforcing long-range correlations in those pathways. Interestingly, phasic sleep events like sporadic muscle jerks in the neck on a background of atonia, saccades and myoclonic jerks around distal joints all correlated with erratic changes in heart rate and respiration have some apparent scaling in time over a night. For example, the bout-like architecture of nightly cycles of sleep episodes over 6 to 10 hours define the longest time scale. Within bouts are stages of near REM (NREM) followed by REM sleep alternating with a period of ~90mins. Although periods of REM are defined by standard EEG criteria, observations of phasic events occurring during REM sleep and its onset reveal a lack of a characteristic time scale (Dement and Mitler, 1974). REM sleep predominates in the last third of the night and is accompanied by body movements which have a distribution that appears statistically self-similar to the nightly cycles of sleep episodes (see Carskadon and Dement, 1989; Fig. 1-7 for example) over a time scale of 10 to 1000 seconds. These irregular body movements in turn result from faster activity in the pyramidal tract (Evarts, 1967) on the time scale of 2.5 to >150 msecs. All told, statistically self-similar fractal bunching may occur over 10 orders of magnitude in time scales from 104 to 10-6 seconds during sleep. This suggests a novel perspective for viewing the nightly reoccurrence of sleep as well as the ontogeny of sleep.

In a sense, REM provides the longest possible temporal correlations to an animal i.e., its entire life history. Disruption of the representation of these stable scale-invariant correlations, present during fetal development and remanifested in phasic and tonic REM in adult sleep processes, increases the effective ISI length needed to disrupt consolidation. Therefore, all ISIs are effectively rescaled to appear shortened to the animal. The animal loses timescales, and perceived time slows, while external time is unaffected. The disruption to correlations caused by the stimulus is therefore potentiated. In the next section the maximization of correlations will be generalized to habituation of orienting responses.

THE RELATIONSHIP OF REM SLEEP PROCESSES TO THE HABITUATION OF ORIENTING RESPONSES

Sharpless and Jasper (1956) introduced the idea of short-timescale "Phasic" and long-timescale "Tonic" processes in terms of habituation of orienting responses: "In interpreting the present results, it is helpful to distinguish between two kinds of activation reactions. One, the "phasic" reaction, rarely outlasts the stimulus by more than 10 or 15 seconds, it has a short latency, it is very resistant to habituation, and once habituated, it recovers within a few minutes. The other "tonic" reaction, varies in duration from a few seconds to many minutes, it is labile, subject to rapid habituation, and it tends to recover slowly, over periods of hours or days. [A note is made to the effect that Sokolov makes a similar distinction between two forms of the "orienting reflex"]. In normal animals, the two occur together and cannot be distinguished except in special circumstances-e.g., after partial habituation, when only the phasic type of reaction is elicited. However, the two types of reactions may be dissociated by brain-stem lesions. Thus, animals in which the primary sensory pathways have been severed at the collicular level so that the thalamus is deprived of direct auditory innervation are apt to exhibit long latency, tonic activation patterns which habituate extremely rapidly. On the other hand, animals in which the mesencephalic reticular system has been damaged leaving the sensory pathways to the thalamus intact exhibit only brief arousal patterns which barely outlast the stimulus. Unfortunately habituation has not yet been studied in preparations of the latter type. (p. 674)" In this section, the phasic startle response or reflex will be conceptualized as one extreme in a continuum of time scales from phasic (brief) to tonic (prolonged) behavioral responses to aversive or appetitive stimuli (e.g., eye blink to air puff, salivation to meat powder, rearing to a light, etc.), behaviors generally referred to in Pavlovian or classical conditioning as unconditional or unconditioned responses. Tonic orienting processes (e.g., a cat orienting to a bird) with a prolonged structure in time will, for the purposes of this section, be considered multi-component orienting responses, involving dynamic functional re-organization of brainstem-forebrain loops, as well as multiple reflex pathways with a wide range of time scales (i.e., 10-2 seconds for a complete startle response in the rat to ~103 seconds for a cat making multiple orienting responses to a bird). A rough calculation gives many more startle responses in a rat during one period of multiple orienting events in the cat. It is proposed that tonic orienting processes represent a multitude of complex patterns of coordination involving the RF and its subnuclei, NE, 5 HT and Ach outputs, the intralaminar and midline thalamus (Groenewegen & Berendse, 1994), frontal cortex, ventral striatum and amygdaloid-temporal lobe structures to enable an animal to mantain a state of readiness behavioral options and internalize a stimulus without disruption of the ongoing maximization of correlations.

The orienting response, illustrated in behaviors such as turning one's head to discover "what is it?" [or as Pavlov would say "Shto eta takoe" -- "what is the nature of this thing?" (Kimmel, 1979)], could be conceptualized as consisting of a complex assembly of unconditional responses (e.g., changes in GER, blood pressure, heart rate, eye movements, head movements, rearings, changes in auditory processing, etc). For example, If you have ever owned a cat and observed its behavior when birds are nearby, you have probably observed the birds eliciting an orienting response in the cat. The orienting response is evoked when an animal is presented with a novel stimulus, and is manifested in a quick movement of the head toward the stimulus so that the eyes, ears and nose are facing the source of the stimulus. This orienting movement is frequently followed by exploratory or appetitive behaviors such as approach and sniffing as well as increased general arousal and activity. Orienting is also accompanied by autonomic arousal and increased heart rate, due to attenuation of the vagal component of the baroreceptor reflex, thereby temporarily increasing cardiac output to the brain (Schlor, Stumpf and Stock, 1984). Repeated presentation of the stimulus leads to habituation of the orienting response, with autonomic arousal decrementing more rapidly than the behavioral response (Martin, Sutherland and Zbrozyna, 1976). Orienting can be see as a complex self-organized behavior involving the integration of many central and peripheral subsystems. As Sokolov (1963) points out: " [a]ccording to some, the orientation reactions are but reflexes limited to the muscular apparatus of individual analyzers...[a]utonomic (e.g., vascular) reactions serve the same purpose as somatic reactions, and facilitate increase of analyzer sensitivity. The orientation reflex is, therefore, a complex combination of somatic and autonomic reactions forming a complete functional system (p. 12)."

PATTERNS OF COORDINATED ACTIVITY IN NE AND 5-HT SYSTEMS PARALLEL THE TIME COURSE OF THE ORIENTING RESPONSE AND REM SLEEP

Jacobs et al (1986;1992) has explored with single unit recordings the temporal contiguity between changes in firing patterns and changes in environmental, behavioral and physiological variables in cat NE and 5-HT neurons. A few interesting anatomical details concerning the NE cell body groups follow: 1) A6 or the LC is situated in the dorsal part of the pons on the lateral border of the fourth ventricle in all higher vertebrate species, with its ventral aspect continuous with the RF. 2) The other NE cell groups A1-A7 extend throughout the rostral-caudal extent of the RF, and have overlapping ascending and descending projections throughout the brain and spinal cord (Moore, 1980). 3) The number of NE neurons found in the LC covaries with cortical mass (e.g., frogs have only a few neurons; humans have 20,000). 4) The LC is the only source of NE for cortical regions and the olfactory bulb whereas A1-A7 overlap in their projections with the LC to many subcortical and spinal sites. 5) In some species of mammals (e.g., rats, monkeys and humans), the LC is very compact with few interspersed non-NE neurons. However, in others (e.g., cats and dogs), LC neurons are diffusely mixed with non-NE neurons of the dorsolateral pons. How these anatomical properties influence group interactions with Ach REM-ON cells or integration with RF afferents, as well as functional effects upon target neurons throughout the neuroaxis is unknown. Functionally, LC neurons, whether in the cat, rat or monkey, fire with a tonic pattern during low vigilance behaviors such as grooming, eating or quiet wakefulness. However, the most effective and reliable elicitor of phasic burst firing patterns in LC neurons are stimuli that disrupt ongoing behavior or evoke orienting responses (Aston-Jones, 1986). So LC activity may originate in the RF as a response to a change in state due to the disorganizing effect of the stimulus on RF homeostasis and changes in the multscale intrinsic patterns of inter nuclear coordination. Then the RF might by way of the LC send out a signal to the rest of the brain to open sensory channels in order to pick up environmental correlations and attempt to internalize the ongoing patterns of stimuls information, as well as, communicate the critical state existing in the RF throughout the brain.

LC activity in the adult seems to be tuned specifically to the significance of the stimulus, showing quick habituation to CS+ during non-aversive conditioning, but slower habituation to both CS+ and CS- with aversive conditioning (Sara & Segal, 1991). When the LC is in phasic burst firing mode, a general state of alertness results. This is evident by changes in neural activity on many space and time scales signifying a loss of habituation. For example, on the cortical cell level (1-10 msec range), by normal habituation is prevented to sensory input; on the local ensemble level (10-200 msec), measured by ERP's; and on the ensemble-regional level (103 msecs to 105 msecs) a loss of coherence indicated by EEG arousal (Foote, et al., 1991). In simpler terms the orienting stimulus evokes long-range temporal and spatial changes, similar to the critical state, that speed internalization of the stimulus (e.g., by way of LTP).

There are nearly 60,000 5-HT cell bodies in the cat and 20,500 in the rat spread on or near the midline and grouped into superior and bilateral inferior groups. The superior group consists of 4 main nuclei (B8 and B5) the median raphe and the dorsal raphe [B7 and B6]) and the inferior group of 5 main nuclei (B2, B1 & B4, B3, [B1/B3], and area postrema. Both 5-HT cell body groups provide the primary source of afferents to themselves, forming a complex network bilaterally and rostral-caudally. Generally the superior nuclei send ascending projections to the forebrain while the inferior group account for the 5-HT innervation of the spinal cord. The superior midline nuclei innervate dendrites in sensory-receiving and associational areas of the cortex (e.g., layer IV of primary sensory cortex; layers III and V of prefrontal cortex where thalamocortical and corticocortical converge) and limbic system (e.g., temporal lobe, amygdala, hippocampus), while the inferior group of nuclei innervate motor neurons of the axial rather than distal musculature in the ventral horn, or along with the superior nuclei the motorneurons of the large muscles of the jaw, face and neck. Jacobs (1993) has recently proposed a "tonic motor control hypothesis of 5-HT neurons" stating that the activity of 5-HT neurons is activated preferentially in association with tonic motor output, enhancing muscle tone during chewing, locomotion, grooming, and respiration. In addition, he proposes that while 5 HT is enhancing tonic motor activity, it is inhibiting sensory information processing by its actions on sensory-receiving and associational areas.

Perhaps the most interesting interaction between NE and 5-HT neurons occurs during orienting and REM sleep. In 5-HT neurons, for example if an arousing stimulus such as a loud click elicits an orienting response (indicated by interruption of ongoing tonic grooming behavior and phasic eye movements towards the source of the sound), activity in superior nuclei such as the dorsal and medial raphe stops for several seconds. At the same time NE neurons are in phasic burst firing patterns, exciting granule cell regions of the sensory and associational cortex and subcortical areas that were under tonic 5-HT suppression before the stimulus. The characteristic desynchronization of the cortical EEG (a-blocking effect) with onset of orienting is likely due to the loss of 5-HT inhabition of interhemispheric suppression of synchronous modes in favor of thalamocortical interactions (a-waves) (Read et al., 1994). In contrast to the increase firing of NE neurons during orienting, the RF, when disrupted by the stimulus and placed in a critical state, resorts to shutting off 5-HT cells in order to switch out of tonic motor mode and into full sensory mode grasping any environmental correlations. The primary influence of RF-REM activity states during development of the RF is the recurrent presentation of fractal patterns of activity that may aid the RF in the consolidation of synaptic changes or, in dynamical terms, reshape the fractal structure of the boundary during the prolonged critical state.

THE RELATIONSHIP OF REM SLEEP TO THE DEVELOPMENT OF THE ORGANIZATION OF ORIENTING RESPONSES

How are phasic and tonic REM processes involved in this dramatic reorganization during development? How might disruptions of REM processes effect these developmental processes and the habituation of orienting responses? How can we visualize long range correlations in the RF and there development? This section hopefully will give the reader some feel for the complexity and synergistic nature of RF interactions in adult cats, and apprecition of how sensory input may destablize the homostatic correlations between and amoung RF regions. Taking this hypothesis one step further, keeping in mind figure 23, how is developmental experience intergrated and at the same time the functionally of the RF mantained? Maybe the RF has such a vast reservoir of "graceful degradation" that it can accommodate great development alterations, possibity providing much flexibly to the neonate. In contrast with the above thought, the work of Ursin et al., (1967), on the habituation of orienting elicited by electrical stimulation of the RF, AMY, septal area and posterior suprasylvian gyrus, found that while the orienting response elicted from telencephalic, mesencephalic or by auditory stimuli was identical, the habituation of orienting was much slower from the RF. What I want to suggest is that the RF is a complex dynamicly changing fractal structure. It has great intergrative capacitys in terms of shaping response. However this complex homeostasis is dependent on phasic REM processes for coherence. The preponderance of REM in the neonate may be suggestive of the use of phasic REM processes as a stablizing input during these periods of dramatic change, allowing the fine tuning of orienting behavior and the integration in the RF of its complex synaptic pathways. This may make the developing RF particularly senstive to disruption during this period, by way of REM deprivation or trauma. This disruption would, like the results of electrical stimulation, cause a loss of correlation structure and attenuated habituation of orienting, leaving a long negative influence on behavior.

Evidence supporting a role for the RF in orienting is diverse. Kornbliuth et al. (1972) found that when unit activity in different regions of the RF was recorded during the learning of an appetitive classically conditioned task (tone-food pairing), the activity tended to be temporally correlated with the orienting response. Electrical stimulation of the RF induces a state of arousal in many species, and, in some cases, elicits movements of the head and neck. Drew et al. (1990) describes the motor organization of the RF: "[it] is probably organized so as to allow, both reinforcement of movements initiated at other regions of the neuraxis and to produce patterned postural responses in response to either voluntary movement or unexpected perturbations...[t]he fact that turning of the head to the stimulated side accompanies all limb movement suggests that it may also play an important role in orientation."

Grantyn et al. (1993) have recently explored the organization of tecto-reticulo-spinal neurons (TRSN) involved in the spatio-temporal transformations of orienting-related tectal efferent signals into orienting movements in awake behaving cats. Their work allows a visual explanation of the long range integrative interactions involved in orienting responses incorporating Scheibel's long projecting NCG cells and Kornblith's orienting specific activity, as well as Ursin's, Drew's and Sharpless & Jasper's observations of RF electrical stimulation evoked orienting. Using direct matching of movement-related firing patterns and fine anatomical resolution using intra-axon staining, Grantyn et al. found that TRSN have diverse connective arbors with abducens nucleus, and medial reticular formation where the burst neurons of the horizontal saccadic generator and the orienting-related reticulo-spinal output neurons (RSNs) are located. TRSN neurons show phasic bursting activity which, acording to Grantyn et al., are: "...events that contribute to the triggering of orienting synergies and contain information on the intended eye velocity and head acceleration (p.974)". These TRSNs and RSNs have complex fractal dendritic arbors and are described as providing widespread coherent facilitation of ocular, neck and facial motoreurons during orienting synergies.

Overall, spontaneous activity over many levels of organization, including phasic REM motor activity during ontogeny, could play a fundamental role in the development of appetitive behavioral processes (e.g., searching and orienting) and other forms of neuroplasticity. In 1986 Arnold Mandell published a review article entitled "Toward a neuropsychopharmacology of habituation: a vertical integration." This article represented a cross-disciplinary exploration of desensitization and habituation processes in the nervous system in terms of a dynamical systems language that emphasized the distributional ordering of spontaneous events such as protein conformational states, cholinergic receptor membrane conductance complexes and inter-spike-intervals to fluctuations in the EEG. Mandell proposed that habituation at different levels of organization in an organism would display self-similar statistical patterns in the temporal reordering of processes regardless of components involved. For example, Mandell (p. 841) detailed the work of Fatt and Katz (1950; 1952) who observed that spontaneous depolarization in membrane voltage manifested the same "irregular intervals" between events as was observed for end-plate potentials. They observed events that occurred over a frequency range of 0.1 to 100 Hz, but excluded the outliers at the high and low frequency ends, thus obtaining a fit to a Poisson. This led to the conclusion that these spontaneous events were statistically independent. However, other investigations of these processes (Van Der Kloot, Kita and Cohen, 1975) and reanalysis of the work of Fatt and Katz (Lewis, 1965) demonstrated that these spontaneous events showed reliable deviations from Poisson point process behavior.

How are these spontaneous non-Poisson processes related to habituation phenomena? Mandell proposed that habituation represents "...the shift from random [self similar] spontaneous neural discharges to rhythmic, oscillating membrane hyperpolarization waves...(p. 845)." The statistical properties of the system are reordered by the stimulation such that "[t]he effect of repeated stimuli on this ensemble[polysynaptic interneuron habituation in the dorsal horn] can be viewed as similar to that of electrotonic or low frequency depression disaggregating a Gaussian population into one or more subpopulations of autonomously oscillating coherent membrane proteins, creating a defect in ordering potential and resulting in membrane conductance burst kinetics (p. 847)."

Therefore, according to Mandell, habituation may represent a reordering in time of the interactions of units (membrane proteins, interneurons or the heart rate changes during an orienting reflex) independent of the level of observation.

The observation of significant changes in the Hurst and Lévy with maternal deprivation, indicating a shift in statistical clustering in nuchal atonia inactivity, when combined with early work (Anderson, 1992) showing an inability to habituate after periods of maternal deprivation in pups of the same ages, supports this notion that deprivation may alter habituation by reordering spontaneous processes in time and making them more persistent. Based on the coherence among these findings, and the work of Mandell, the investigation of habituation processes in terms of a statistical-mechanical approach (Kuba, 1957; Kuba, Koketsu and Kitahara, 1973) analyzing the effects of periodic stimuli on the fluctuation patterns of spontaneous REM related events, may provide a much richer perspective from which to explore the behavioral organization of living systems.

THE UTILITY OF FRACTAL DESCRIPTIONS OF SPONTANEOUS PRENATAL BEHAVIOR

Describing fetal behaviors such as spontaneous nuchal atonia or spontaneous motility as a fractal time process is no better than attributing this behavior to random processes if fractal descriptions cannot provide useful new developmental insights as well as an explanatory framework for understanding the development of brain and behavior. Based on results reported, Hurst analysis can provide one comprehensive measure of the long term structure of behavior. These findings suggest that, at least for this spontaneous prenatal behavior, the duration of an atonia event correlates significantly with the durations of nearby periods of atonia as well as with periods of atonia extending over three orders of magnitude of developmental time. Compared with log-survivor analysis (Fagen & Young, 1987), Fourier analysis or Markov based sequential analysis (Bakeman and Gottman, 1986), Hurst analysis is ideally suited for the analysis and comparison of long run correlations in long noisy data sets. Hurst analysis, by providing a global index of the correlations in a behavior over time, may be sensitive to disruptions or losses of internal correlations due to pathological situations. In addition, other measure theoretic approaches, developed for the statistical analysis of time series for deterministic physical nonlinear systems, may prove more sensitive to the nonlinearity underlying the organization of biological systems (Elbert et al, 1994; Mandell and Selz, 1994; Selz, Mandell, Anderson, Smotherman and Teicher, 1995; Smotherman, Selz and Mandell, 1995). The common occurrence of spontaneous behavior over different levels of organization in fetuses or adults is suggestive of a fundamental principle of biological organization. The concepts of fractals in space and time seem at least to provide a richer theoretical perspective than that of independent random activity for investigating the spontaneous behavioral events of mature organisms or of global fetal REM processes over many temporal and spatial scales (Anderson and Mandell, 1996).

SUMMARY AND CONCLUSIONS

REM sleep based on experimental studies and behavioral observations has for many years been suggested to play an important role during fetal and neonatal life. However, a strong theoretical or experimental basis for this role has remained for the most part obscure. I report in this dissertation that spontaneous motor activity events characteristic of fetal REM sheep in the sheep and neonatal REM sleep in the infant rat, which in the past have been described as independent random Poisson processes, appear to be better described as fractal time processes with long run correlations. These apparently erratic fluctuations had similar Lévy distributions across species, supporting the idea that the fractal time patterns of nuchal atonia and other spontaneous motor sequences reflect the temporal structure of a global REM sleep state, over multiple timescales, in the fetus and neonate, which may serve as a transient behavioral ontogenetic adaptation to changing developmental environments.

Physical and biological observables that lack a characteristic scale of time and have exponentially decaying autocorrelation functions were introduced as fractal processes in time. These processes typically display clustering or bursting fluctuation behavior which is statistically self-similar in time. Spontaneous perinatal behaviors such as spontaneous motility in fetuses or behaviors associated with REM sleep in neonates characteristically display the statistically self-similar fluctuations. To distinguish independent, Markov and other short-run dependent processes from self-similar patterns with persistence in nuchal atonia records in fetal sheep and nuchal inactivity records in neonatal rats, I applied Hurst's rescaled range analysis, R/S, which characterizes how the range scales with the sample

standard deviation. One advantage of R/S analysis over other statistical techniques is that the exponent derived for this analysis, H, is robust with respect to the marginal distribution. In other words, not only is R/S analysis useful for records that are nearly Gaussian but it continues to be effective when values of the record are so far from Gaussian that the moments of the distribution diverge. The central finding using R/S analysis was that nuchal events in the sheep fetus or neonatal rat have long-run dependency or correlations over many seconds, hours or days.

The moments for these records were also found to be divergent and the fitted characteristic exponents of convolutionally stable Lévy distributions were similar, supporting the conclusions of R/S analysis. In addition, for neonatal rats, maternal deprivation was found to shift the characteristic exponents of the Lévy distributions toward distributions that lack both the first and second moments. This was confirmatory of increases observed in the Hurst exponents as well, suggesting that changes in the activity of deprived neonatal rats were more persistent than non-deprived animals.

These findings were first discussed in the context of the interrelationships of fetal and neonatal state markers, which are often characterized as variable. This variability is due to the lack of a single timescale of observation that can uniquely capture the full structure existing over many timescales. I also suggested that the fractal time nature of the patterns of spontaneous perinatal behaviors may in fact represent an ontogenetic adaptation to the unique ecological demands of the fetal and neonatal environment, by providing a "fractal forgery" of the temporal patterns found in postnatal or post nest environment. Fractal time correlations may provide a temporal scaffolding for the developmental organization of muscles, synaptic connections, brainstem regulation and the formation of branching organ systems in the lungs and circulatory system. The properties of convolutionally stable patterns of spontaneous activity may facilitate integration of neural changes into developing networks and, later in life, memory consolidation and receptive field and map plasticity. A view of the possible evolutionary implications for fractal patterns in time within an organism and its utility in conceptualizing heterochrony were described. In addition, heterochrontic change as a source of plasticity underlying the genesis of behavioral neophenotypes was explored in detail.

Finally, spontaneous perinatal behaviors as fractal patterns in time and their parallels with phenomena found in physical complex systems with self-organizing properties such as velocity distributions in turbulence, second order phase transitions in magnetism with critical point fluctuations were illustrated. In addition, I focused on commonalities in the fluctuations associated with the behavioral states of REM sleep and appetitive orienting and the latter's habituation in terms of critical point fluctuations and attractors with fractal basin boundaries generating behavior with 1/f power spectral densities in the reticular formation. I explored the idea that reticular formation homeostasis can be conceptualized as involving self-similar processes dependent on the fractal time structure of REM sleep. The order imparted by these patterns allows flexible rescaling in time so that the reticular formation and brain is optimally responsive to environmental stimuli and conditions. In the last section I argued that the concepts of fractals, when applied to behavior in developing systems seem to provide a richer theoretical perspective for experimentally investigating spontaneous processes in living things than explanations based on independent random activity.

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