Implementation issues in approximate methods for stochastic Hodgkin-Huxley models

The Hodgkin-Huxley models with stochastic sodium channels can be implemented by three different algorithms, which include Strassberg and DeFelice, Rubinstein, Chow and White, and Fox. The first three algorithms utilize exact methods for describing channel kinetics with finite-state Markov process models, while the Fox algorithm uses stochastic differential equations (SDEs) to approximate the Markov process models. The simulation studies have revealed that the mean latency for the Fox algorithm is longer than that of the Chow and White algorithm at all stimulus currents. Mino and his colleagues have reported that the approximate method of Fox algorithm is around seven times faster than the Chow & White algorithm. The spike jitter for the Fox algorithm is much smaller than the jitter for the Chow & White algorithm, irrespective of the method of rounding sodium channels.