Absence seizures as resetting mechanisms of brain dynamics
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| Zitieren: | Absence seizures as resetting mechanisms of brain dynamics / S.P. Nair, P.I. Jukkola, M. Quigley, A. Wilberger, D.S. Shiau, J.C. Sackellares, P.M. Pardalos, K.M. Kelly // Кибернетика и системный анализ. — 2008. — № 5. — С. 45-53. — Бібліогр.: 37 назв. — англ. |
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| author | Nair, S.P. Jukkola, P.I. Quigley, M. Wilberger, A. Shiau, D.S. Sackellares, J.C. Pardalos, P.M. Kelly, K.M. |
| author_facet | Nair, S.P. Jukkola, P.I. Quigley, M. Wilberger, A. Shiau, D.S. Sackellares, J.C. Pardalos, P.M. Kelly, K.M. |
| citation_txt | Absence seizures as resetting mechanisms of brain dynamics / S.P. Nair, P.I. Jukkola, M. Quigley, A. Wilberger, D.S. Shiau, J.C. Sackellares, P.M. Pardalos, K.M. Kelly // Кибернетика и системный анализ. — 2008. — № 5. — С. 45-53. — Бібліогр.: 37 назв. — англ. |
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| container_title | Кибернетика и системный анализ |
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UDC 519.68+519.8+612.821:51
S.P. NAIR, P.I. JUKKOLA, M. QUIGLEY, A. WILBERGER, D.S. SHIAU,
J.C. SACKELLARES, P.M. PARDALOS, K.M. KELLY
ABSENCE SEIZURES AS RESETTING MECHANISMS
OF BRAIN DYNAMICS
1
Keywords: Lyapunov exponents, absence seizure, brain dynamics, resetting.
1. INTRODUCTION
Epilepsy is one of the most common neurological disorders, second only to stroke,
affecting about 0.8% of the world’s population [1]. Although epilepsy occurs in all
age groups, the highest incidences are found in infants and the elderly. Absence
epilepsy is a subtype of generalized epilepsy manifested by seizures characterized by
brief periods of impaired consciousness (absence seizures). Human absence epileptic
seizures are typically associated with bursts of generalized 3 Hz spike-wave
discharges (SWDs) in the electroencephalogram (EEG). The usual duration is
3–10 sec, ranging up to a few minutes. The level of functioning during a SWD
depends in part on the duration of the seizure, and the recovery from such episodes
is usually fast, in the order of a few seconds.
Animal modeling of absence seizures has been conducted in numerous studies. The
defining EEG events in rodents are 7–12 Hz generalized SWDs (Fig. 1) of variable
duration with an abrupt onset and abrupt termination, which usually occurs during passive
wakefulness or sleep [2, 3]. In a previous study [4], numerous spontaneous bilateral cortical
7–9 Hz spike-wave discharges were recorded in control and brain-lesioned animals
spanning an age range from 2 to 30 months. As animals progress from mid-aged to aged
periods, they can experience hundreds of absence seizures per day [5].
A central feature of epilepsy is
that it is characterized by seizures that
are transient in nature and occur
spontaneously in a recurrent fashion.
Epilepsy has been described as a
dynamical disease with pathological
states characterized by the occurrence
of abnormal dynamics [6]. From a
dynamical perspective, a seizure may
represent self-organizing behavior in
which widespread cortical areas make
an abrupt transition to an ordered
state and reset to a normal state at the
end of the seizure [7]. Nonlinear
time-dependencies have also been
reported in the pattern of seizure
occurrence, which indicate that
seizures do not occur randomly, but
rather reflect determinism [8, 9].
In an effort to better understand the relationship between aging and the differential
expression of SWDs, we studied the dynamical EEG properties of the epileptic brain. The
concept of “brain dynamical resetting” may provide some insights into the mechanisms
ISSN 0023-1274. Êèáåðíåòèêà è ñèñòåìíûé àíàëèç, 2008, ¹ 5 45
Fig. 1. A sample of a generalized SWD recorded from a rat.
The F3, C3, and P3 abbreviations refer to skull screw
electrodes overlying left frontal, central, and parietal regions
of the animal’s brain, respectively; F4, C4, and P4 refer to the
brain areas on the right. An “F3-C3” label corresponds to an
EEG channel produced by the output of one differential
amplifier with inputs from the F3 and C3 electrodes
1This work was supported by an Epilepsy Foundation Targeted Research Initiative for Seniors award (SPN),
NINDS 5R01-NS046015 (KMK), and NIBIB R01EB002089 (JCS).
� S.P. Nair, P.I. Jukkola, M. Quigley, A. Wilberger, D.S. Shiau, J.C. Sackellares, P.M. Pardalos,
K.M. Kelly, 2008
underlying increased seizure susceptibility of the aged brain. One way to quantify the effect
of an event, e.g. a seizure, is to estimate how dynamical EEG properties change after the
event. A nonlinear measure that is closely related to the rate at which information is
produced, the short term maximum Lyapunov exponent (STLmax ), was utilized to extract a
dynamical profile of the EEG signal over time for each recording channel. This measure
has been found to be useful in capturing and predicting system (brain) dynamics associated
with transitions into and out of epileptic seizures [10–15]. The overall goal of this study
was to establish a clear relationship between changes in the dynamical EEG properties of
the brain and differences in the age-related expression of SWDs.
2. STATE SPACE TOPOGRAPHY AND ANALYSIS OF iEEG
The state space portrait of a signal (time series) provides a visual representation of its
evolution in a multidimensional space over time. Its characteristics reflect the original
characteristics of the signal, and ultimately the system that generates the signal. The
state space can be thought of as a collection of all possible states that a dynamical
state visits during its evolution. In general, the state space is identified with a
topological manifold. A p-dimensional state space is spanned by a set of
p-dimensional “embedding vectors,” each of which defines a point in the state space,
thus representing the instantaneous state of the system.
2.1. State Space Reconstruction. The theoretical basis for the relationship between
a signal and its state space representation generated by earlier work [16, 17] was
developed from the Whitney embedding theorem [18]. A state space portrait is created by
treating each time-dependent variable of the system as a component of a vector in a
multidimensional space. Each vector in the state space represents an instantaneous state
of the system. These time-dependent vectors are plotted sequentially in the state space to
represent the evolution of the state of the system over time. For many systems, this
graphical mapping creates an object confined over time to a sub-region of the state space.
The geometrical properties of these confined objects, called “attractors,” provide
information about the global state of the system. The vector reconstruction is achieved as
follows:
�
X x t x t x t p� � � �{ }( ), ( ),... , ( ( ) )� �1 ,
where x t( ) is the value at time t; � is a fixed time increment, and p is the embedding
dimension. Every instantaneous state of the system is therefore represented by the
vector X, which defines a point in the p-dimensional state space. The intracranial
EEG (iEEG), being the output of a multidimensional system, has both spatial and
temporal statistical properties. Components of the brain (neurons) are densely inter-
connected and there exists an inherent relation between the iEEG recorded from one
site and the activity at other sites. This makes the iEEG a multivariate time series.
The state space reconstruction of the iEEG signal in a three-dimensional state space
(Fig. 2) was done using the method of delays [17].
2.2. Embedding Parameters for iEEG Reconstruction. An accurate represen-
tation of the system in state space depends upon making appropriate choices of the
embedding dimension p and time delay �. The choice of p for experimental data such as
ours is not a straightforward issue. According to Takens [17], if d is the fractal dimension
of the attractor in a state space, the embedding dimension p should be at least equal to
2 1d � in order to correctly reconstruct the attractor. Therefore, one of the first steps in
characterizing the properties of a system is to estimate the fractal dimension of the
attractor. The dimension helps to determine the position of a point on the attractor to
within a certain degree of accuracy. In addition, it provides a lower limit to the number of
variables necessary to model the system.
To ensure that the ictal (seizure) dynamics were captured, we calculated the fractal
dimension and the time delay from the iEEG recorded during the ictal period. For any
attractor, the dimension can be estimated by looking at the manner in which the number
46 ISSN 0023-1274. Êèáåðíåòèêà è ñèñòåìíûé àíàëèç, 2008, ¹ 5
of points within a sphere of radius r scales as the radius shrinks to zero. The geometric
relevance of this observation is that the volume occupied by a sphere of radius r in the
dimension d behaves as rd . The correlation function or correlation integral C r( ) measures
the probability that two vectors on the attractor, selected at random, lie within a distance r
of each other. This function of two variables is an invariant on the attractor, but it has
become conventional to look only at the variation of this quantity when r is small. In that
limit, it is assumed that
C r rd( ) � ,
defining the generalized fractal dimension d when it exists. From the above equation,
d can be estimated in the limiting case as
d
C r
rr
�
�
lim
log[ ( )]
log[ ]0
.
In practice, we need to compute C r( ) for a range of small r over which we can argue
that the function log [ ( )]C r is linear in log[ ]r and then select the linear-like slope over the
range. Figure 3 shows a plot of
d C r
d r
log[ ( )]
log[ ]
versus log [ ]r for an ictal segment where
C r( ) denotes the correlation integral and r represents the attractor size. The curves
correspond to different values of the embedding dimension (p = 6, 7, 8, and 9) and a time
delay of 15 msec. The objective is to find a “middle” region in log [ ]r where the
derivative (slope) is consistent. The figure illustrates the difficulties in establishing a
clean, unsullied value of the correlation dimension for experimental data.
Therefore, following the values used in human studies, we have used an embedding
dimension p = 7 for the reconstruction of the phase space. This value of p may be too small
for the construction of a state space that can reconstruct all interictal attractors of the brain,
but it should be adequate for detection of the transition of the brain toward the ictal stage if
the epileptic attractor is active in its space prior to the occurrence of the epileptic seizure.
ISSN 0023-1274. Êèáåðíåòèêà è ñèñòåìíûé àíàëèç, 2008, ¹ 5 47
Fig. 2. (a) Ictal segment of a filtered iEEG recorded from the hippocampus of a rat , (b) Reconstructed iEEG
segment in 3-D state space
a
b
Time (sec)
U, �V
xn� 2
xn�1 xn
The embedding delay parameter � should be small enough to capture the shortest
change (i.e., highest frequency component) present in the data, but should also be large
enough to generate (with the method of delays) the maximum possible independence
between the components of the vectors in the state space. These two conditions are
usually addressed by selecting � as the first minimum of the mutual information between
the components of the vectors in the state space or as the first zero of the time domain
autocorrelation function of the data [19]. Theoretically, because the time span ( )p � 1 �
of each vector in the state space represents the duration of a state of the system, ( )p � 1 �
should be at most equal to the period of the maximum (or dominant) frequency
component in the data. For example, a sine wave (or a limit cycle) has � = 1, then a
p � � �2 1 1 3 is needed for the embedding, and ( )p � 1 � should be equal to the period
of the sine wave. Such a value of � would then correspond to the Nyquist sampling of the
sine wave in the time domain. In the case of the epileptic attractor, the highest frequency
present is 70 Hz (the iEEG data are low-pass filtered at 70 Hz), which means that if p � 3,
the maximum � to be selected is about 7 msec. However, because the dominant frequency
of the epileptic attractor (i.e., during the ictal period) in the animal iEEG was never more
than 15 Hz, according to the above reasoning, the adequate value of � for the
reconstruction of the state space of the epileptic attractor with p = 7 is ( )7 1 67� �� msec,
that is, � should be about 11 mseñ [20].
2.3. Positive Lyapunov Exponent in the iEEG. The Lyapunov exponents of a
system are a set of invariant geometric measures that describe the dynamical content of
the system. In particular, they serve as a measure of the ease of predicting the future state
of the system. Lyapunov exponents quantify the rate of divergence or convergence of
two nearby initial points of a dynamical system, in a global sense. A positive Lyapunov
exponent measures the average exponential divergence of two nearby trajectories,
whereas a negative Lyapunov exponent measures exponential convergence of two nearby
trajectories. A zero Lyapunov exponent indicates the temporal continuous nature of a
flow. If a discrete nonlinear system is dissipative in nature, then a positive Lyapunov
exponent quantifies a measure of chaos. Consequently, a system with positive exponents
has positive entropy in that trajectories that are initially close together move apart over
time. The more positive the Lyapunov exponents are, the faster they move apart.
Similarly, for negative exponents, the trajectories move together in time. A system with
both positive and negative Lyapunov exponents is said to be chaotic. Stated differently,
Lyapunov exponents quantify the amount of linear stability or instability of an attractor
or an asymptotically long orbit of a dynamical system.
Wolf et al. [21] proposed an algorithm for calculating the largest Lyapunov
exponent. First, the state space reconstruction is made and the nearest neighbor is
searched for one of the first embedding vectors. After the neighbor and the initial
distance (l) are determined, the system is evolved forward for some fixed time (evolution
48 ISSN 0023-1274. Êèáåðíåòèêà è ñèñòåìíûé àíàëèç, 2008, ¹ 5
Fig. 3. Derivative of the correlation function calculated for a rat iEEG ictal segment (2000 points) created
from vector spaces of dimension p = 6, 7, 8, and 9, with respect to ln ( )r . Consistency is observed in a broad
range of ln ( )r with slopes that lie in a range of values from 2 to 4
ln ( )r
d
C
r
d
r
[l
n
(
)]
/
[l
n
(
)]
time) and the new distance (
l ) is calculated. This evolution is repeated, calculating the
successive distances, until the separation is greater than a certain threshold. A new vector
(replacement vector) is searched as close as possible to the first one, having
approximately the same orientation of the first neighbor. The short term maximum
Lyapunov exponent (STLmax ) used in this study was estimated using the method
proposed by Iasemidis et al. [23], which is a modification of Wolf’s algorithm. The
measure was termed “short-term maximum Lyapunov exponent” to distinguish it from
those used to study autonomous dynamical systems studies. Modification of Wolf’s
algorithm was necessary to better estimate STLmax in small data segments that include
transients, such as interictal spikes. The modification is primarily in the searching
procedure for a replacement vector at each point of a fiducial trajectory.
The first step in the calculation of STLmax is to divide the iEEG signal recorded
from each electrode (a one-dimensional time series) into sequential, non-overlapping
segments of length 5.12 sec (1024 data points) and embed each segment in a
7-dimensional state space with a time delay � � 3 (15 msec), using the method of delays.
The computation of the largest Lyapunov exponent (Lmax ) involved the iterative selection
of pairs of points on the state space portrait and the estimation of the convergence or
divergence of their trajectory over time. More specifically, the largest Lyapunov
exponent is defined as the average of local Lyapunov exponents Lij in the state space,
that is
L
N
Lij
N
max � � �
1
,
where N is the necessary number of iterations for the convergence of the Lmax esti-
mated from a data segment of n points (n N t� �
), and
L
t
X t t X t t
X t Y t
ij
i j
i j
� �
� � �
�
1
2
log
| ( ) ( )|
| ( ) ( )|
,
where
t is the evolution time allowed for �0 ( ) | ( ) ( )|x X t X tij i j� � , the vector
difference, to evolve to �� ( ) | ( ) ( )|x Y t t Y t tk i j� � � �
, the new vector difference,
where
t k dt� � and dt is the sampling period of the data u t( ) . If
t is given in
seconds, Lmax is in bits/s. Details of this method, including the selection of
parameters for calculating STLmax , and a variation of Lmax for nonstationary signals
like iEEG, have been described previously by Iasemidis and colleagues [23, 24].
ISSN 0023-1274. Êèáåðíåòèêà è ñèñòåìíûé àíàëèç, 2008, ¹ 5 49
Fig. 4. STLmax values estimated from a single bipolar channel of EEG from a 4-month (a) and 20-month (b) old
animals, before, during, and following an absence seizure (SWD), each lasting approximately 5 sec. The
estimation of the STLmax values was made by dividing the signal into non-overlapping segments of 5.12 sec
each and using p = 7 msec and � � 15 msec for the phase space reconstruction. The onset of the seizure, at time
point 0, is associated with a drop in STLmax. In the immediate postictal period, STLmax has been reset to a value
exceeding that of the preictal period. Note: STLmax values are reset to a higher average postictal value
compared to the average preictal value in the 4-month old animal
a
b
Figure 4 demonstrates the STLmax profile derived from a single bipolar EEG
channel for a 4-month old animal and a 20-month old animal. The figure shows a drop in
the STLmax value during the SWD (both at time 0), and a postictal increase in values
compared to the average preictal value. Note that this postictal increase is more
significant in the younger (4-month old) animal.
3. SEIZURES AS INTRINSIC MECHANISMS OF CONTROL
It has been postulated that seizures may be intrinsic mechanisms that serve to reset
the brain from an abnormal state back to a more normal state [25, 26]. This theory
suggested that epileptic brains, being chaotic nonlinear systems, repeatedly make
abrupt transitions into and out of the ictal (ordered) state based on the following
observations: (i) a positive Lyapunov exponent in the EEG; (ii) presence of
nonlinearities in the ictal EEG; (iii) existence of spatiotemporal transitions (from
chaos to order); and (iv) resetting of spatiotemporal dynamics by the seizure (to a
more chaotic state). It follows intuitively that failure to sufficiently reset the brain by
a seizure may increase the susceptibility of the epileptic brain to a subsequent
seizure.
3.1. Resetting of Spatiotemporal Chaos: From Order to Chaos. A seizure can be
characterized by a significant drop in the value of the Lyapunov exponent associated with
it, thereby suggesting a sudden and brief transition to a highly ordered state. Following
the seizure, these values are reset to a larger value compared with the immediate preictal
values, suggesting that the seizure promotes the brain to revert to a normal functioning
state that is more chaotic. The above
observations constitute further support
for the working model of dynamical
state transitions underlying the
evolution of epileptic seizures proposed
in early literature [23–26]; this working
model explained the temporal evolution
of the maximum Lyapunov exponent in
terms of a modified “cusp catastrophe
model” [27–29] wherein a sudden
bifurcation in system dynamics occurs
when the system enters the local cusp of
singularity of a folded surface S, due to a change in intrinsic parameters. A plausible
hypothetical intrinsic feedback and resetting mechanism in the brain is shown in Fig. 5.
3.2. Resetting and Age-Related Seizure Expression. In animal studies, several
investigations using models of aging have shown an enhanced seizure susceptibility
associated with older animals. We postulated that the functional anatomy of the brain
changes as it ages resulting in global changes of brain operation that are reflected in part
by a changed expression of SWDs. One approach to characterize these global changes is
to employ dynamical measures of brain activity, which offers the possibility to
understand how changes in the dynamics of neuronal networks could result in SWDs -
sudden manifestations of paroxysmal widespread oscillations. To compare and contrast
the dynamical EEG properties of 4- and 20-month old male rats as a means to delineate
differences in age-related expression of SWDs, we estimated STLmax values to test for
differences in peri-ictal (surrounding a seizure) dynamical properties of the EEG.
Four young adult (4-month old) and four aged (20-month old) male rats were
included in the study. Fifty SWDs from each animal were used to estimate the dynamical
50 ISSN 0023-1274. Êèáåðíåòèêà è ñèñòåìíûé àíàëèç, 2008, ¹ 5
Internal State
Monitor
Intrinsic Feedback
Controller
System
Seizure
Generation
Circuitry
Fig. 5. Conceptual schematic showing intrinsic brain
feedback control responsible for seizure generation. Sei-
zure expression is determined by an internal feedback
control mechanism utilizing the brain state; the generator
is activated until the normal state is reached (effective re-
setting) by the intrinsic controller
properties during the peri-ictal period. We estimated the STLmax values for a 2-min EEG
epoch recorded before and after each SWD using the algorithms described above. The
values were computed for each EEG channel and averaged across electrodes to calculate
overall pre-ictal, post-ictal, and difference (STLmaxpost ictal�
–STL
maxpre ictal�
) values for each
SWD in each animal. A statistical comparison (by a nested two-way ANOVA test, where
the random factor (rats) is nested within an animal group) of dynamical values during the
pre-ictal period (2 min before a
SWD) showed no significant
difference between the 4- and
20-month old animals in STLmax
values (p > 0.05). However, the
same statistical test performed on
post-ictal dynamical values
(2 min after a SWD) revealed
a significant difference between
the two groups in STLmax values
(p < 0.05). To compare how
effective each SWD was in
resetting the animal’s brain to a
normal interictal state, we
computed the difference between average pre-ictal and post-ictal dynamical values. The
test of these “resetting” values suggested that the “resetting” was significantly more
effective in the 4-month old cohort compared with the 20-month old cohort, evident from
STLmax values (p < 0.05). Fig. 6 illustrates the comparison of the differences between
pre-ictal and post-ictal periods between animals in the two age groups.
4. CONCLUSION
As in human epilepsy, transitions from the interictal to the ictal state in the rat
involve a transition from a chaotic (high STLmax ) to a more ordered (lower values of
STLmax ) state. The transitions observed in the iEEG in human and rat temporal lobe
epilepsy are consistent with early publications that introduced the concept of
“dynamical diseases” [30–34]. This concept was introduced to explain how biological
systems can make transitions between normal and pathophysiological states. Periodic
state shifts observed in biological disorders, such as Cheyne–Stokes respiration,
periodic hematopoiesis, and penicillin-induced neuronal spiking, were demonstrated to
be similar to state transitions that occurred in certain mathematical models of
low-dimensional nonlinear systems [31, 35].
The mean STLmax difference values (post seizure–pre seizure) were significantly
different between 4-month old and 20-month old naive animals (4 months > 20 months;
p < 0.05), which suggested that the age-related increase in SWD expression is associated
with a decrease in seizure-related dynamical effect (resetting), as the animal ages. The
results of this study suggest that the recovery of the brain back to its normal interictal
state following SWDs was better in young adult animals compared with aged animals.
This interpretation is supported by higher post-ictal dynamical values as well as a larger
difference between post-ictal and pre-ictal dynamical values.
Mackey and Glass [30] speculated that certain periodic diseases arose because of a
ISSN 0023-1274. Êèáåðíåòèêà è ñèñòåìíûé àíàëèç, 2008, ¹ 5 51
Fig. 6. Age-related differences in resetting (difference between
post-ictal and pre-ictal STLmax values) between young (4-month
old) and aged (20-month old) animals
Age-related differences
(p < 0.05)
M
ea
n
S
T
L
m
ax
d
if
fe
re
n
ce
4 months 20 months
bifurcation in the behavior of a control system. Even in simple mathematical models of
such systems, transitions between normal and pathological states, or between ordered and
chaotic states, can result from small changes in the value of a control parameter [6, 30,
31, 33]. If dynamical diseases can be explained on this basis, then it may be possible to
use this information to construct optimal therapeutic responses based on manipulation of
a control parameter [33] or by external perturbations using techniques developed for the
control of chaotic systems. Furthermore, models of coupled chaotic oscillators have given
several insights into prediction of seizures and the resetting phenomenon [36]. Other
studies modeling dynamical transition in nonlinear coupled map lattice systems have also
shown similarities with the transitions in an epileptic brain [37]. Techniques applied for
controlling chaos in dynamical systems, such as coupled map lattice systems, may also
prove to be useful in controlling spatiotemporal chaos in the epileptic brain.
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| id | nasplib_isofts_kiev_ua-123456789-44252 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 0023-1274 |
| language | Russian |
| last_indexed | 2025-12-07T18:09:52Z |
| publishDate | 2008 |
| publisher | Інститут кібернетики ім. В.М. Глушкова НАН України |
| record_format | dspace |
| spelling | Nair, S.P. Jukkola, P.I. Quigley, M. Wilberger, A. Shiau, D.S. Sackellares, J.C. Pardalos, P.M. Kelly, K.M. 2013-05-27T14:13:21Z 2013-05-27T14:13:21Z 2008 Absence seizures as resetting mechanisms of brain dynamics / S.P. Nair, P.I. Jukkola, M. Quigley, A. Wilberger, D.S. Shiau, J.C. Sackellares, P.M. Pardalos, K.M. Kelly // Кибернетика и системный анализ. — 2008. — № 5. — С. 45-53. — Бібліогр.: 37 назв. — англ. 0023-1274 https://nasplib.isofts.kiev.ua/handle/123456789/44252 519.68+519.8+612.821:51 This work was supported by an Epilepsy Foundation Targeted Research Initiative for Seniors award (SPN), NINDS 5R01-NS046015 (KMK), and NIBIB R01EB002089 (JCS). ru Інститут кібернетики ім. В.М. Глушкова НАН України Кибернетика и системный анализ Системный анализ Absence seizures as resetting mechanisms of brain dynamics Article published earlier |
| spellingShingle | Absence seizures as resetting mechanisms of brain dynamics Nair, S.P. Jukkola, P.I. Quigley, M. Wilberger, A. Shiau, D.S. Sackellares, J.C. Pardalos, P.M. Kelly, K.M. Системный анализ |
| title | Absence seizures as resetting mechanisms of brain dynamics |
| title_full | Absence seizures as resetting mechanisms of brain dynamics |
| title_fullStr | Absence seizures as resetting mechanisms of brain dynamics |
| title_full_unstemmed | Absence seizures as resetting mechanisms of brain dynamics |
| title_short | Absence seizures as resetting mechanisms of brain dynamics |
| title_sort | absence seizures as resetting mechanisms of brain dynamics |
| topic | Системный анализ |
| topic_facet | Системный анализ |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/44252 |
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