Results

The parameters of neuron and synaptic models were selected to allow for propagation of bursts of action potentials along the network. Periodic stimulation with a frequency in a range 2 - 10 Hz evokes periodic waves of activity that propagate through the network. Fig. 2 shows results of applying a periodic (7 Hz) rectangular stimulus pulse to three neurons in the center of the network. A regular pattern of traveling waves emerges. Not every stimulus is a source of a new wave and intervals between waves differ from intervals between stimuli. The frequencies of bursts computed from the voltage traces in single neurons (excluding the initially activated neurons) are independent of the frequency of stimulation (Table 1). The spike frequency adaptation process in neurons determines the burst frequency. Observed frequencies of bursts can vary over a range of 1.5 - 5Hz. The highest burst frequency in neurons is controlled by the recovery time from the afterhyperpolarization (AHP) process in neurons. In a network of 50x50 neurons short stimulation (e.g. duration 0.5 - 2.0 sec), regardless of frequency of stimulation, produces waves of activity only during stimulation. After the end of the stimulation activity continues only for a short time. Stimulations that last longer than the 2.0 sec produce repetitive bursts in individual neurons and complex spatiotemporal pattern in the network lasting for a long period after the stimulation (up to 10 min). The length of stimulus needed to induce these long-lasting pattern decreases with increasing network size. In the big networks (240x240) even a single pulse induces long-lasting activity. Varying the stimulus frequency (2-10 Hz) or the duration of the stimulation does not have an effect on the observed pattern of activity in the network. Fig. 2 shows the 10 seconds of activity evoked by 2 sec stimulation in a network of 240 by 240 neurons. Initial traveling ring-like waves, after several seconds evolve into more spiral-like and then irregular spatiotemporal patterns. This resembles behavior seen in a number of different distributed non-linear chemical systems. Similar patterns are observed in other types of models and in experimental data from drug-induced epilepsy. These changes in the spatiotemporal activity of the network are in contrast to the apparent regular firing pattern of individual neurons. Fig. 3 shows the firing pattern in two selected neurons during 10 seconds of simulation. The frequency of bursts measured in neurons does not change significantly after the period of initial stimulation, remaining constant with time (examined up to 10 minutes). Introducing the local inhibitory connection changes the dynamics of traveling waves. Inhibition influences the shape and the average velocity of activity of the waves and also may prevent generation of sustained activity in network after stimulation. Weak inhibition in the network does not alter the pattern of activity in the network considerably. When the strength of inhibitory synaptic connection increases, the number of neurons that fire synchronous APs decreases, as the wave propagates through the network. Fig. 4 illustrates the pattern of activity in a network with relatively strong inhibitory connections (wi=-75). The traveling activity wave is not as clear as on Fig. 2 and the average velocity of propagating waves in the network is decreased. Further increasing of inhibitory synaptic weights results in gradual disappearance of traveling waves. Inhibitory weights above 100 prevent propagation of activity in the network.