The network model we considered is a model of synaptically connectedreduced neurons generating action potentials. Cells are modeled as a single compartment units using modified Av-Ron-Rinzel's reduced model equations[4]. The neuron model incorporates two inward currents - INa and ICa three outward potassium currents - delayed rectifier IK, Ca-dependent IK(Ca) and transient current IA, and leak current IL. The synaptic connection between cells is modeled by a synaptic current Isyn. The synaptic conductance is represented by a sum of two exponential functions[5]. The overall strength of a connection is represented by a single synaptic weight parameter and a delay parameter represents all delays between cells. We use a two dimensional array of up to 250 by 250 cells to simulate a two dimensional neural network (e.g. a thin slice or layer of neocortical tissue). We assume that there is no significant inhibition in the network. Each cell receives excitatory input from two of the nearest eight neighboring cells (Figure 1A); no inhibitory inputs were included. A pseudo-random generator was used to choose connections for each cell. This produced a network with no predefined structure of circuits. All connections have equal strength and delay. Individual cells and synapses have properties based on physiologic data. Repetitive firing activity in the network was triggered by one cell at the beginning of the simulation (i.e. the selected cell received a input current strong enough to evoke a burst of action potentials). The membrane potentials for selected cells and histograms of generated action potentials for all cells were recorded.
