Abstract of disseration
A state bearing strong similarities to Rapid Eye Movement
(REM), often described as active or indeterminate
sleep, is dominant during the perinatal period in all mammals.
It is characterized by episodes of high variability, bursting
and intermittent activity in the brainstem and by spontaneous
phasic behavioral events such as REMs, periods of loss of cervical
muscle tone (nuchal atonia) and myoclonic twitching1. This REM-like
state is the principal behavioral state during fetal and neonatal
life and is apparently indispensable; REM deprivation during this
period can lead to long lasting behavioral defects in adult life2.
Spontaneous prenatal behaviors including twitching and other REM
associated phasic phenomena are often treated as the independent
random events of a Poisson distribution with the assumption that
correlations between events decay exponentially in time as in
a Markoff process. The central focus of this doctoral research
is the ontology of the temporal structure of spontaneous sequences
of nuchal atonia associated with REM or active sleep in late gestation
fetal sheep (E121-133) to determine if these processes are independent
random events described by Poisson distributions. The nature of
the variability of these spontaneous REM processes 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. The temporal coherence of episodes
of nuchal atonia with other markers of REM sleep such as eye movements
and electrocorticogram and breathing pattern changes is consistent
with their use as a marker of this sleep state. In addition, nuchal
atonia episode numbers and durations recorded in this study demonstrated
the expected developmental changes reported for other REM sleep
markers.
Correlations hidden within natural time series with short- and long-term fluctuations (e.g., annual patterns of riverflow, rainfall, tree rings, etc.) can be uncovered and comparsions made among diverse phenomena using Hurst's Rescaled Range Analysis (Range normalized by S.D. or R/S).3 Many natural processes with short- and long-term fluctuations are best described as fractals in time4. The word fractal refers to patterns in space or time, such as the cluster within cluster appearance of nuchal atonia, which contain detail recursively nested like the layers of an onion. Fractal patterns are impossible to measure accurately with one set scale due to the emergence of greater detail at finer magnifications; this necessitates the collection of multiple measurements over a range of scales. Hurst's analysis examines how the R/S for the entire time series is related to the R/S for a number of smaller time windows. A log-log plot of the average R/S for non-overlapping windows of 4, 8, 16....2048 points vs the size of the windows yields a line with a slope (H) that ranges from 0 to 1. Time series of independent random statistical processes have H = 0.5 indicating no correlations. Time series with positive correlations result in H > 0.5, indicating the existence of long-run correlations (i.e.,fractals in time). These processes have long clusters of events in time that are more likely to be followed by long clusters of events, than short clusters, in a pattern termed "persistence"4.
To determine if time series of nuchal atonia durations had non-random
fluctuations, episodes of NA were estimated from nuchal EMG sampled
in utero at 1Hz from fetal sheep (five subjects). Analysis
of 70 24hr records containing at least 2048 NA episodes yielded
a mean H = 0.70 that did not change significantly over days 121
to 133 of gestation. H values derived from 5 min segments of the
nuchal EMG of neonatal rats P2 to P10 (collected for 2hr @ 300
Hz) ranged from 0.65 to 0.87 and were very similar to H values
reported for fetal sheep. These results suggest the first major
finding of this work: spontaneous periods of nuchal atonia, and
via inference, REM-like sleep have similar temporal structure
across two distinct mammalian groups. This was also supported
by the common probability densities of these two species.
Another property of fractals in time is the non-convergence of
statistical moments of a time series. A special space of "convolutionally
stable" distributions, called Lévy space, can express
the relationship between time series with a non-convergent mean
and variance and the more well known normal or Gaussian distribution5.
A distrubution within this Lèvy space 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. 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 ; = 2 which by the Central Limit
Theorem converge to a finite mean and variance with sufficent
sample size. The most remarkable feature of stable Lévy
distributions in the range 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. The probability distributions
of spontaneous nuchal atonia events in both species were found
to be well described by convolutionally stable Lévy distributions,
suggesting deviations from Central Limit Theorem assumptions and
non-convergent 2nd moments, ruling out a Poisson process. In fact,
; was 1.822 and 1.830, respectively, for 121-3 and 131-3 day fetal
sheep and 1.875 and 1.882, respectively for 2-day and 10-day-old
rats, with nearly identical 's. This finding is striking in that
it implies that phasic REM processes are not Poisson processes,
and supports the finds of Edward Evarts almost 30 years ago who
observed spontaneous discharges of single pyramidal track neurons
during REM sleep in adult monkeys differed from a Poisson distribution
because of an excess of short and long interspike intervals (Evarts,
1967)6.
To summarize thus far, the following properties of nuchal atonia
episodes in both species were inconsistent with a Poisson process:
1) mean and variance; 2) H equals 0.5; 3) probabilities were in
the family of non-finite moment Lèvy stable distributions
with a characteristic (tail) exponent of ; < 2.0 ( ; alpha
equals1.8). One way to ascertain the functional significance of
these observations is to observe how manipulations of experimental
conditions might perturb the values of these measures.
One confound of measuring nuchal atonia in 2 to 10-day-old rats
is introducing the variable of maternal deprivation into the experimental
design. Neonatal rats were subjected to 2 hours of maternal deprivation
as a result of the measurement procedure. This augmented the mean
length of inactivity associated with a nuchal atonia event and
decreased the number of episodes observed, with a concomitant
increase in the Hurst exponent H equals 0.75 to 0.86 and a decrease
in the Lévy exponent from ; alpha equals 1.8 to 1.6 indicating
that behavior became more clustered in time. This represents the
second major finding of this work: maternal deprivation results
in alterations of the Hurst exponent and the Lévy exponents,
shifting distributions from their normal species invariant values.
In the remaining portion of this abstract I will discuss many
of the implications of these two major findings in terms of the
insights they provide in understanding the developmental origins
and function of REM sleep
.
In 1963 Guiseppi Morruzzi7 first functionally divided REM sleep
events in adult cats into brief phasic (e.g., rapid eye movements,
PGO spikes, pyramidal tract discharges) and longer tonic events
(desynchronization of the cortical EEG, nuchal atonia, depression
of spinal reflexes). In fetal sheep nuchal atonia is characterized
by clusters of bursts similar to adult phasic events. Based on
this observation, I propose that these fractal sequences of clusters
of nuchal atonia coalesce developmentally into the tonic periods
of atonia observed in adult REM sleep and that failure to coalesce
may underlie developmental disorders such as autism. Tanguay et
al8. found that eye movements (EM) 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 to coalesce where as the
effects of maternal deprivation result in abnormal coalescence,
both effects that could be detected by examining shifing Hurst
and Lévy exponents.
A more general hypothesis that emerges from these observations
is that the variability of REM-associated nuchal atonia episodes
and of other spontaneous motor events reflects the fractal time
signature of a global fetal REM sleep state that may serve as
a transient behavioral ontogenetic adaptation to changing developmental
environments. Ontogentic adaptations are age specfic behavioral
patterns (e.g. Suckling, imprinting) that emerged during evolution
to solve the environmental demands resulting from morphological
and physiological immaturity9. In addition, the fractal time structure
of spontanous activity at different 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).
For example, spontaneous nuchal events in both species were also
found to be described by convolutionally stable self-similar Lévy
distributions, suggesting that other phasic 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.
This fractal time description of spontaneous prenatal behaviors
also has 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.
The term "behavioral neophenotypes" was coined by Zing-Yang
Kuo to refer to striking deviations from normality that can result
from alterations of normal developmental experience10. The effects
of these early alterations could result, as Gillbert Gottlieb
has proposed, in enhanced brain size, learning ability, exploratory
behavior, resistance to stress and ultimately lead to evolutionary
change that precedes genetic change11. Indeed the existence of
long-range fractal correlations in spontaneous prenatal behaviors
and their interaction with 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
.
In conclusion, spontaneous phasic episodes of nuchal atonia in
fetal sheep and neonatal rats were not found to be independent
random events described by Poisson distributions. Instead, these
REM sleep-associated behaviors were found to be convolutionally
stable distributions containing long range correlations similar
to other processes in nature described as fractals in time. In
addition, a general hypothesis was proposed that these spontaneous
motor events associated with perinatal REM sleep serve as a global
sleep state that may represent a transient behavioral ontogenetic
adaptation to changing developmental environments and a source
of behavioral plasticity for the emergence of novel phenotypes
without the requirment for genetic change.
---------------------------
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Inc., New York.
2 Mirmiran, M. (1986) The importance of fetal/neonatal REM sleep.
European Journal of Obstetrics Gynecology and Reproductive
Biology, 21: 281-291.
3 Bassingthwaighte, J.B., Liebovitch, L.S. and West B.J. (1994). Fractal Physiology. Oxford University Press, New York.
4 Mandelbrot, B. B. (1983). The Fractal Geometry of Nature. New York : W.H.Freeman.
5 Takayasu, H. (1989). Fractals in the physical sciences. Nonlinear science: Theory and applications. Manchester, Manchester University Press.
6 Evarts, E.V. (1967). Unit activity in sleep and wakefulness, In: G.C. Gardner, T. Melnechuk and F.O. Schmitt (Eds.), The Neurosciences: A Study Program, (pp. 545-556), New York: Rockefeller University Press.
7 Morruzzi
8 Tanguay, P.E., Ornitz, E.M., Forsythe, A.B., and Ritvo E.R. (1976). Rapid eye movement (REM) activity in normal and autistic children during REM slee Journal of Autism and Childhood Schizophrenia, 6:275-288.
9 Oppenheim, R.W. (1981). Ontogenetic adaptations and retrogressive processes in the development of the nervous system and behavior: A neurobiological prespective. In K. J. Connelly and H.F.R. Prechtl (Eds.). Maturation and development: Biological and psychological perspectives (pp.1-54). Philadelphia: Lippincott.
10 Kuo, Z. Y. (1976). The dynamics of behavior development.
New York: Plenum Press.
11 Gottlieb, G. (1992). Individual Development and Evolution:
The Genesis of Novel Behavior. New York: Oxford University
Press.