External excitatory stimuli can terminate bursting in neural network models

The concept of modulating or terminating seizure activity by brain stimulation is attracting considerable attention. The ability of such external excitatory stimuli to terminate repetitive bursting may depend upon identifiable parameters. We investigate the ability of external stimuli to terminate bursting under various conditions in defined neural network models. Networks of multiple neurons (n=90), with both inhibitory and excitatory synaptic connections were modeled using conductance-based models with a reduced number of variables. Each neuron in the network has synaptic connections from randomly chosen excitatory and inhibitory neurons. The type and number of connections were kept constant. The initial parameters of the networks were chosen to simulate synchronized repetitive bursting activity. Two basic models of repetitive bursting activity were developed. The first model is a single network with constant random excitatory input, the second incorporates two networks with no random background input, but with a feedback loop with a delay of 600-900ms connecting two networks. The ability of external excitatory stimuli to terminate repetitive bursting in each model was studied. External excitatory stimulation terminates repetitive bursting in both models; however, only in the models with a feedback loop, is the burst termination long-lasting. In the single network model with constant random excitatory input, termination is of short duration and recurrent bursting resumes. Timing of the application of the stimulus to the dual network model is critical; long-lasting termination occurs only when the stimuli to the first network are during a time when the connected network is still relatively refractory. The delay in the loop determines the exact timing of the stimulus. Synaptic inhibition is not required for burst termination. Neural network models provide systems for the study of burst termination and can help define the requirements for such stimuli to successfully terminate bursts. Studies in these models can guide the development and application of such stimuli in intact systems.