Self-Organized Criticality Model for Brain Plasticity

Networks of living neurons exhibit an avalanche mode of activity, experimentally found in organotypic cultures. Here we present a model that is based on self-organized criticality and takes into account brain plasticity, which is able to reproduce the spectrum of electroencephalograms (EEG). The model consists of an electrical network with threshold firing and activity-dependent synapse strengths. The system exhibits an avalanche activity in a power-law distribution. The analysis of the power spectra of the electrical signal reproduces very robustly the power-law behavior with the exponent 0.8, experimentally measured in EEG spectra. The same value of the exponent is found on small-world lattices and for leaky neurons, indicating that universality holds for a wide class of brain models.

Figure 1

Total current flowing in one square lattice configuration ($L=1000$, $\alpha =0.03$, ${\sigma }_t=0.0001$, $v_{\max }=6$) as a function of time in a sequence of several thousand stimuli. In the inset we show the asymptotic value of the percentage of active bonds as a function of $\alpha$ for $L=100$. The value of the parameters is ${\sigma }_t=0.0001$ and $v_{\max }=6$.

Figure 2

Log-log plot of the distribution of avalanche size $n(s)$ ($L=1000$, $\alpha =0.03$ and 0.08, $N_p=10$, $v_{\max }=6$) for the square lattice (lines) and the small-world lattice (*, $L=1000$, $\alpha =0.05$, $N_p=1000$, $v_{\max }=8$) with 1% rewired bonds. The data are averaged over 10 000 stimuli in 10 different configurations. The dashed line has a slope 1.2. For $\alpha =0.3$ and random input site the slope is 1.5.

Figure 3

Power spectra for experimental data and numerical data ($L=1000$, $\alpha =0.03$, $N_p=10$, $v_{\max }=6$) for the square lattice (middle line) and the small-world lattice (bottom line, $L=1000$, $\alpha =0.05$, $N_p=1000$, $v_{\max }=8$) with 1% rewired bonds. Spectrum for the square lattice $\alpha =0.3$ and leaky neurons (*, $\gamma =0.01$). The experimental data (top line) are from Ref. 19 and frequency is in $Hz$. The numerical data are averaged over 10 000 stimuli in 10 different network configurations. The dashed line has a slope 0.8.