Independent variable time-step integration of individual neurons for network simulations.
Realistic neural networks involve the coexistence of stiff, coupled, continuous differential equations arising from the integrations of individual neurons, with the discrete events with delays used for modeling synaptic connections. We present here an integration method, the local variable time-step method (lvardt), that uses separate variable-step integrators for individual neurons in the network. Cells that are undergoing excitation tend to have small time steps, and cells that are at rest with little synaptic input tend to have large time steps. A synaptic input to a cell causes reinitialization of only that cell's integrator without affecting the integration of other cells. We illustrated the use of lvardt on three models: a worst-case synchronizing mutual-inhibition model, a best-case synfire chain model, and a more realistic thalamocortical network model.
Lytton
William W
WW
Department of Physiology, Pharmacology, and Neurology, State University of New York, Downstate, Brooklyn, NY 11203-2098, USA. billl@neurosim.downstate.edu
Hines
Michael L
ML
D000200:Action Potentials / Q000502:physiology*; D000465:Algorithms; D000818:Animals; D001921:Brain / Q000502:physiology; D002540:Cerebral Cortex / Q000502:physiology; D003344:Cortical Synchronization; D006801:Humans; D008959:Models, Neurological; D009415:Nerve Net / Q000502:physiology*; D009433:Neural Inhibition / Q000502:physiology; D016571:Neural Networks, Computer; D009434:Neural Pathways / Q000502:physiology; D009474:Neurons / Q000502:physiology*; D013569:Synapses / Q000502:physiology; D009435:Synaptic Transmission / Q000502:physiology*; D013788:Thalamus / Q000502:physiology; D013997:Time Factors