Spatial Eigenmodes and Synchronous Oscillation: Co-Incidence Detection in Simulated Cerebral Cortex

C. L. Chapman, J. J. Wright, P. D. Bourke
J. Math. Biol. (Springer-Verlag) Volume 45, Issue 1, 57-78, 2002.
Doi: 10.1007/s002850200141


Zero-lag synchrony arises between two points on the cerebral cortex when these receive concurrent independent inputs and has generally been ascribed to nonlinear mechanisms. We report results obtained by Principal Component Analysis (PCA) applied to simulations of cerebral cortex which exhibit zero-lag synchrony and realistic spectral content, and show that synchrony can arise by distinct and separable linear and nonlinear mechanisms. For lower levels of cortical activation synchrony between the sites of input can be accounted for by the eigenmodes associated with the wave activity generated by the inputs. The first spatial eigenmode arises from even components in the independent input signals and the second spatial eigenmode arises from odd components in the inputs. Together these account for most of the signal variance, while the predominance of the first mode over the second within the near-field of the inputs accounts for zerolag synchrony in the neighbourhood of the inputs. Thus the simulated cortical surface acts as a coincidence detector with regard to concurrent, but uncorrelated, inputs. Synchronous response in the extended cortical field to changes in the inputs occurs on a time-scale of a few milliseconds.

At a critical point of increasing cortical activation, local damped oscillation in the gamma band undergoes a transition to highly nonlinear undamped activity at 40 Hz dominant frequency. Such activity ``locks'' between active sites to create patterns of activity with segregated phases.

The complementary character of the synchrony dependent on damped wave interactions, and that attributable to locked nonlinear oscillations may permit speedy organisation of synchronous patterns and partition of multiple patterns of activity within the same field of neurons.

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Figure 1
Cross-correlation results for 20 x 20 version of Average model with two driving sites (black diamonds) input asynchronous Gaussian noise. (a) Grey scale spatial plots of maximum cross-correlation, of the site marked `x', with every other site for lags of +-100 time steps, (b) Delay associated with the cross-correlation maximum at each site bar indicating +-2 milliseconds.

Figure 2
Cross-correlation results. Physiological model 20 x 20 lattice with toroidal boundary conditions. Two specifically driven input sites (centred in black diamonds) received Gaussian mean zero white noise. Non-specific cortical activation (Qns) set at 20.0. Cross-correlations computed with regard to the site marked `x'}

Figure 3
First two mean eigenvectors for 25 different noise seeds for PCA done over an interval of 20000 time steps (2 seconds) on the 20 x 20 lattice simulation of physiological model. Input and other conditions as for Figure 2. The numbers beneath the images indicate the percentage of variance associated with each eigenvector and the standard error on the basis of 25 runs.

Figure 4
Power spectra of first two temporal principal component vectors associated with the eigenmodes shown in Figure 3. Ordered from top to bottom, Qns=0, Qns=20, Qns=40 and Qns=50. Ensemble averages over 10 runs. Time step is 0.1 ms.

Figure 5
First two eigenvectors for PCA done over a 10000 time step (1 second) interval for site separations 5, 11 and 19 intervening elements.

Figure 6
First and second eigenmodes where driven sites have greater coupling strength than the case shown in Figure 5.

Figure 7
Time taken to separate the two principal component temporal trajectories calculated for the system under two noise cases described in the text. Plot of magnitude of difference of two standardised series as a function of time `- -'. The point at which the noise input to the two lattices became different is indicated in the diagram as a solid vertical line. The dotted `.' vertical line indicates 30 time steps after the change in noise input and a second dotted line is 40 time steps later. Where the dashed `- -' curve crosses the solid horizontal line indicates when the deviation became "large" as defined in text.

Figure 8
Phase relationships between the left hand driving site and every other element of the lattice at a stage in which limit cycle oscillations are present. Qns=50.

Figure 9
Typical element temporal delay plots for of voltage output x(i) vs x(i+lag) for Various Qns values for case of Qs=0.8 to driving sites.

Figure 10
Transitions from limit cycle to stochastic bursting with input of noise. Qns=40 and a Qs DC of 0.6 Gaussian white noise (zero mean and standard deviation 0.1) to two driving sites located on the 11th row on the 20 x 20 lattice simulation (toroidal boundary conditions). Plots on the left-hand side are with respect to the leftmost driving site over different length time scales. Plots on the right-hand side are with respect to the rightmost site on the first row of the lattice, over different length time scales.


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