84 Wilson and Bower 
Computer Simulation o.f Oscillatory Behavior 
in Cerebral Cortical Networks 
Matthew A. Wilson and James M. Bower x 
Computation and Neural Systems Program 
Division of Biology, 216-76 
California Institute of Technology 
Pasadena, CA 91125 
ABSTRACT 
It has been known for many years that specific regions of the work- 
ing cerebral cortex display periodic variations in correlated cellular 
activity. While the olfactory system has been the focus of much of 
this work, similar behavior has recently been observed in primary 
visual cortex. We have developed models of both the olfactory 
and visual cortex which replicate the observed oscillatory proper- 
ties of these networks. Using these models we have examined the 
dependence of oscillatory behavior on single cell properties and net- 
work architectures. We discuss the idea that the oscillatory events 
recorded from cerebral cortex may be intrinsic to the architecture 
of cerebral cortex as a whole, and that these rhythmic patterns 
may be important in coordinating neuronal activity during sensory 
processing. 
I INTRODUCTION 
An obvious characteristic of the general behavior of cerebral cortex, as evident in 
EEG recordings, is its tendency to oscillate. Cortical oscillations have been observed 
both in the electric fields generated by populations of cells (Bressler and Freeman 
Please address correspondence to James M. Bower at above address. 
Computer Simulation of Oscillatory Behavior in Cerebral Cortical Networks 85 
1980) as well as in the activity of single cells (Llinas 1988). Our previous efforts 
to study this behavior involve the construction of realistic, large scale computer 
simulations of one particular cortical area, the piriform (olfactory) cortex (Wilson 
and Bower 1989). While the oscillatory behavior of this region has been known 
for some time (Adrian 1942; Bressler and Freeman 1980), more recent findings 
of oscillations within visual cortex (Eckhorn et a1.,1988; Gray et al. 1989) have 
generated increased interest in the role of oscillations in cerebral cortex in general. 
It is particularly intriguing that although these cortical areas receive very different 
kinds of sensory information, the periodic activity seen in both structures share a 
common principle frequency component in the range of 30-60 Hz. At the same time, 
however, the phase relationships of activity across each cortex differ. Piriform cortex 
displays systematic phase shifts in field potential responses to afferent activation 
(Freeman 1978; Haberly 1973), while correlations of neuronal activity in visual 
cortex indicate no such systematic phase shifts (Gray et al. 1989). 
In order to compare this oscillatory behavior in these two cortical systems, we have 
developed a model of visual cortex by modifying the original piriform cortex model 
to reflect visual cortical network features. 
2 MODEL STRUCTURE 
2.1 COMMON MODEL FEATURES 
Each simulation has at its base the three basic cell types found throughout cerebral 
cortex (Figure 1). The principle excitatory neuron, the pyramidal cell, is modeled 
here as five coupled membrane compartments. In addition there are two inhibitory 
neurons one principally mediating a slow K+ inhibition and one mediating a fast C1- 
inhibition. Both are modeled as a single compartment. Connections between mod- 
eled cells are made by axons with finite conduction velocities, but no explicit axonal 
membrane properties other than delay are included. Synaptic activity is produced 
by simulating the action-potential triggered release of presynaptic transmitter and 
the resulting flow of transmembrane current through membrane channels. Each of 
these channels is described with parameters governing the time course and ampli- 
tude of synaptically activated conductance changes. The compartmental models of 
the cells integrate the transmembrane and axial currents to produce transmembrane 
voltages. Excursions of the cell body membrane voltage above a specified thresh- 
old trigger action potentials. Details of the modeling procedures are described in 
Wilson and Bower (1989). 
Each model is intended to represent a 10 mm x 6 mm cortical region. The many mil- 
lions of actual neurons in these areas are represented by 375 cells of the three types 
for a total of 1125 cells. The input to each cortex is pr,rided by 100 independent 
fibers. 
86 Wason and Bower 
A 
rostral 10 mm caudal 
./.:'::'.....i:': _ ,ff.int collateral. .. j 
LO...ai..n. - - - '- - -::"::::-':::: 
10 mm 
B D 
roltrally directed eaudally directed 
mmociation fibera mmociation fibera 
mmoclatien fibera 
Figure 1: In the piriform cortex, input (A) and association fiber (B) projections 
make distributed lateral contacts with cells over the extent of the cortex. In the 
visual cortex model, input projections make local contact with cells over a 1 mm 
radius in a point-to-point fashion (C) and association fibers connect to cells within 
a limited radius (D). 
While both the piriform and visual cortex models reflect these basic features of 
cerebral cortical architecture, both also contain major structural simplifications. 
The model referred to as "visual cortex", is particularly simplified. Our objective 
was to reproduce cortical oscillations characteristic of visual cortex by modifying 
those basic architectural features that differ between these two brain regions. 
2.2 MODEL DIFFERENCES 
The principle differences between the model of piriform and visual cortex involve 
changes in the topography of input projections, and in the extent of intrinsic connec- 
tions within each model. In piriform cortex, afferent input from the olfactory bulb 
arrives via a tract of axons (LOT) projecting across the surface of the cortex (Fig. 
1A) with no topographic relationship between the site of origin of individual LOT 
axons in the olfactory bulb and their region of termination in the cortex (Haberly 
1985). In contrast, projections from the lateral geniculate nucleus to visual cortex 
are highly topographic, reflecting the retinotopic organization of many structures 
in the visual system (Van Essen 1979). In piriform cortex, excitatory intrinsic asso- 
ciation connections are sparse, distributed, and non-topographic, extending across 
Computer Simulation of Oscillatory Behavior in Cerebral Cortical Networks 87 
the entire cortex (Fig. 1C) (Haberly 1985). In the visual cortex, this association 
fiber system is much more limited in extent (Gilbert 1983). 
3 RESULTS 
Space limitations do not allow a complete discussion of previous results modeling 
piriform cortex. Readers are referred to Wilson and Bower (1989) for additional 
details. Here, we will describe data obtained from the modified piriform cortex 
model which replicate results from visual cortex. 
1 2 
1-2 
1 2 
2-2 
1-2 
0,12 
-aO -0 -40 -L)O 0 20 0 eO eO -60 0 0 
'rkne (msec) me (msec) 
Figure 2: Comparison of auto and cross correlations from modeled (middle) and 
actual (right) (modified from Gray et al. 1989) visual cortex. The left column shows 
a diagram of the model with the stimulus region shaded. The numbers indicate the 
location of the recording sites referred to in the auto (2-2) and cross (1-2) correla- 
tions. The correlations generated by presentation of a continuous and broken bar 
stimulus are shown in the upper and lower panels respectively. 
88 Wilson and Bower 
Figure 2 shows a comparison of auto and cross correlations of neuronal spike activ- 
ity taken from both simulated and actual (Gray et al. 1989) experimental data. In 
each case the two recording sites in visual cortex are separated by approximately 
6 mm. Total cross correlations in the modeled data were computed by averaging 
correlations from 50 individual 500 msec trials. Within each trial simulated activity 
was generated by providing input representing bars of light at different locations in 
the visual field. In these cases the model produced oscillatory auto and cross corre- 
lations with peak energy in the 30-60 Hz range. As in the experimental data, this 
effect is most clearly seen when the stimulus is a continuous bar of light activating 
cells between the two recorded sites (fig. 2). A broken bar which does not stimulate 
the intermediate region produces a weaker response (fig. 2), again consistent with 
experimental evidence. 
The oscillatory form of the the cross correlation function suggests coherent firing of 
neurons at the two recorded locations. In order to determine the degree of synchrony 
between modeled neurons, the difference in phase between the firing of cells in these 
locations was estimated by measuring the offset of the dominant peak in the cross 
correlation function. These values were consistent with measurements obtained 
both through chi-square fitting of a modified sinc function and measurement of the 
phase of the peak frequency component in the correlation function power spectra. 
These measurements indicate phase shifts near zero (< 3 msec). 
3.1 STIMULUS EFFECTS 
As shown in figure 2, correlations are induced by the presence of a stimulus. How- 
ever, in both experimental and simulated results these correlations cannot be ac- 
counted for through a simple stimulus locking effect. Shuffling the trials with respect 
to each other prior to calculating cross correlation functions showed oscillations 
which were greatly diminished or completely absent. At the same time, simulations 
run in the absence of bar stimuli produced low baseline activity with no oscillations. 
These results demonstrate that while the stimulus is necessary to induce oscillatory 
behavior, the coherence between distant points is not due to the stimulus alone. 
3.2 FREQUENCY 
The visual cortex model generates oscillatory neural activity at a frequency in the 
range of 30-60 Hz, consistent with actual data. As found in the model piriform 
cortex, the frequency of these oscillations is primarily determined by the time course 
of the fast feedback inhibitory input. Allowing inhibitory cells to inhibit other 
inhibitory cells within a local region improved frequency locking and produced auto 
and cross correlations with more pronounced oscillatory characteristics. 
3.3 COHERENCE 
In order to demonstrate the essential role of the association fiber system in establish- 
ing coherent activity, simulations were performed in which all long-range (> 1 mm) 
Computer Simulation of Oscillatory Behavior in Cerebral Cortical Networks 89 
association fibers were eliminated. Under these conditions the auto correlations at 
each recording site continued to show strong oscillatory behavior, but oscillations 
in the cross correlation function were completely eliminated. Increasing the range 
of association fibers from 1 to 2 mm restored coherent oscillatory behavior. This 
demonstrates that long-range association fibers are critical in establishing coherence 
while local circuitry is sufficient for sustaining oscillations. 
250.375 m 
0-125 mec 
-50 0 50 
Time (m ec) 
0-5(X)ms 
I UaOnltjmml  
o IO 2o  ,4o 54)   ao 
Frequency () 
0 I0  30  54) 60 70 60, 
Figure 3: Time course of cross correlation functions for relative association fiber 
coupling strengths of 200 (left) and 300 (right). Upper traces display correlations 
taken at successive 125 intervals over the 500 msec period. The bottom-most cor- 
relation function covers the entire 500 msec interval. The lower panels display the 
power spectra of the overall correlation function. 
90 Wilson and Bower 
3.3.1 Association Fiber Delay 
To examine the dependence of zero-phase coherence between distant sites on asso- 
ciation fibers characteristics, the propagation velocity for spikes travelling between 
pyramidal cells was reduced from a mean of 0.86 m/s to 0.43 m/s. Under these con- 
ditions the phase shift in the cross correlation function for a continuous bar stimulus 
remained less than 3 msec. This result indicates that the zero-phase coherence is 
not a direct function of association fiber delays. 
3.3.2 Coupling Strength 
As shown in figure 3, increasing the degree of association fiber coupling by increasing 
synaptic weights produced a transition from zero-phase coherence to a coherence 
with an 8 msec phase shift. Intermediate shifts were not observed. Figure 3 also 
illustrates the time course of coherence and phase relationships. There is a tendency 
for the initial stimulus onset period (0-125 msec) to show zero-phase preference. 
Later periods ( 125 msec) reflect the association coupling induced phase shift. 
For weak coupling which produces zero-phase behavior, the correlation structure 
decays over the 500 msec stimulus period. Increased coupling strength provides 
more sustained coherence, as does the addition of mutual inhibition. 
4 DISCUSSION 
Analysis of the behavior of the models shows that several components are particu- 
larly important in establishing the different phase and frequency relationships. A 
key factor in establishing zero-phase coherence appears to be the stimulation of a 
cellular population which can activate, via association fibers, adjacent regions in a 
symmetric fashion. In the case of the continuous bar, this intermediate region lies 
in the center of the bar. This is consistent with experimental results which indicate 
reduced coherence with bar stimuli which do not excite this region. The model also 
indicates that frequency can be effectively modulated by inhibitory feedback. The 
fact that inhibitory events with similar temporal properties are found throughout 
the cerebral cortex suggests that oscillations in the 30-60 Hz range will be found in 
a number of different cortical areas. 
Interpreting phase coherence from correlation functions produced from the average 
of many simulation trials pointed out the need to distinguish average phase effects 
from instantaneous phase effects. Instantaneous phase implies that the statistics 
of the correlation function taken at any point of any trial are consistent with the 
statistics of the combined data. Average phase allows for systematic within-trial and 
between-trial variability and is, therefore, a weaker assertion of actual coherence. 
This distinction is particularly important for theories which rely on phase encoding 
of stimulus information. Analysis of our model results indicates that the observed 
phase relationships are an average rather than an instantaneous effect. 
Based on previous observations of the behavior of the piriform cortex model, we 
have proposed that high frequency oscillations may reflect the gating of intrinsic 
Computer Simulation of Oscillatory Behavior in Cerebral Cortical Networks 91 
network integration intervals. This modulatory role would serve to assure that 
cells do not fire before they have received the necessary input to initiate another 
round of cortical activity. While this is clearly only one possible functional role 
for oscillations in piriform cortex, the model is being used to extend this idea to 
processing in the visual cortex as well. 
Acknowledgements 
This research was supported by the NSF (EET-8700064), 
N00014-88-K-0513), and the Lockheed Corporation. 
the ONR (Contract 
References 
Adrian, E.D. 1942. Olfactory reactions in the brain of the hedgehog. J. Physiol. 
(Lond.) 100, 459-472. 
Bressler, S.L. and W.J. Freeman. 1980. Frequency analysis of olfactory system 
EEG in cat, rabbit and rat. Electroenceph. clin. Neurophysiol. 50, 19-24. 
Eckhorn, R., R. Bauer, Jordan, M. Brosch, W. Kruse, M. Munk, and H.J. Reitboeck. 
1988. Coherent oscillations: A mechanism of feature linking in the visual cortex? 
Biol. Cybern. 60, 121-130. 
Freeman, W.J. 1978. Spatial properties of an EEG event in the olfactory bulb and 
cortex. Electroenceph. clin. Neurophysiol. 44,586-605. 
Gilbert, C.D. 1983. Microcircuitry of the visual cortex. Ann. Rev. Neurosci. 
6,217-247. 
Gray, C.M., P. Konig, A.K. Engel, W. Singer. 1989. Oscillatory responses in cat 
visual cortex exhibit inter-columnar synchronization which reflects global stimulus 
properties. Nature 338, 334-337. 
Haberly, L.B. 1985. Neuronal circuitry in olfactory cortex: anatomy and functional 
implications. Chem. Senses 10,219-238. 
Haberly, L.B. 1973. Summed potentials evoked in opossum prepyriform cortex. J. 
Neurophysiol. 36, 775-788. 
Kammen, D.M., P.J. Holmes, and C. Koch. 1989. Cortical architecture and oscil- 
lations in neuronal networks: Feedback versus local coupling. In: Models of Brain 
Function R.M.J. Cotterill, Ed. (Cambridge Univ. Press.) 
Llinas, R. 1988. The intrinsic electrophysiological properties of mammalian neurons: 
Insights into central nervous system function. Science 242:1654-1664. 
Wilson, M.A. and J.M Bower. 1989. The simulation of large scale neuronal net- 
works. In Methods in Neuronal Modeling: From Synapses to Networks C. Koch 
and I. Segev, Eds. (MIT Press, Cambridge, MA.) pp. 291-334. 
Van Essen, D.C. 1979. Visual areas of the mammalian cerebral cortex. Ann. Rev. 
Neurosci. 2, 227-263. 
