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Causal Measures of Structure and Plasticity in Simulated and Living Neural Networks

Figure 9

Comparison of Firing Rate and Pairwise Granger Causality Plasticity Measures.

The neural activity of rat cortical neurons were stimulated to induce plasticity and recorded using an 8×8 grid of MEA electrodes (shown earlier in Figure 1). The left, middle, and right panel represent plasticity suggested by changes (enhancement or depression) in firing rate, pairwise Granger causality for outgoing “source” and incoming “sink” relationships, respectively. Each panel presents in clockwise order the distribution of values, average total changes by spatial location, distribution of the direction of change, and changes by probe location for each of the three measures. The vertical axis represents the stimulation probe site among the 60 electrodes on the MEA. The horizontal axis represents the network's response at each electrode to each probe. Each pixel is color coded to indicate the magnitude and direction of any changes that occurred following the tetanus. Application of the tetanus resulted in substantial changes in the strength of connections among neurons in this network. Comparison of those changes using a firing rate based verses a Granger causality based measure indicates a great deal of similarity between each measure. Rows where spike rate was enhanced in left panel also tended show a stronger causal relationship in the right panel. Similarly, rows indicating depression were associated with depressed causal strength in the right panel. A black arrow along the vertical and horizontal axis denote the electrode that received the tetanizing stimulus to induce plasticity. The color scale has been set to +/−3 standard deviations for each plot.

Figure 9

doi: https://doi.org/10.1371/journal.pone.0003355.g009