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Để tạo ra tiềm năng hành động trong mô hình, phương trình 5,8 được tăng cường bởi các quy tắc mà bất cứ khi nào V đạt giá trị ngưỡng Vth, một tiềm năng hành động bị sa thải và khả năng thiết lập lại để Vreset. Phương trình 5,8 chỉ ra rằng khi Tức là = 0, thế màng thư giãn theo cấp số nhân | 12 Model Neurons I Neuroelectronics To generate action potentials in the model equation 5.8 is augmented by the rule that whenever V reaches the threshold value Vth an action potential is fired and the potential is reset to Vreset. Equation 5.8 indicates that when Ie 0 the membrane potential relaxes exponentially with time constant Tm to V EL. Thus EL is the resting potential of the model cell. The membrane potential for the passive integrate-and-fire model is determined by integrating equation 5.8 a numerical method for doing this is described in appendix A and applying the threshold and reset rule for action potential generation. The response of a passive integrate-and-fire t ms Figure 5.5 A passive integrate-and-fire model driven by a time-varying electrode current. The upper trace is the membrane potential and the bottom trace the driving current. The action potentials in this figure are simply pasted onto the membrane potential trajectory whenever it reaches the threshold value. The parameters of the model are El Vreset -65 mV Vth -50 mV Tm 10 ms and Rm 10 M . The firing rate of an integrate-and-fire model in response to a constant injected current can be computed analytically. When Ie is independent of time the subthreshold potential V t can easily be computed by solving equation 5.8 and is V t El RmIe V 0 - El - RmIe exp -t Tm 5.9 where V 0 is the value of V at time t 0. This solution can be checked simply by substituting it into equation 5.8. It is valid for the integrate-and-fire model only as long as V stays below the threshold. Suppose that at t 0 the neuron has just fired an action potential and is thus at the reset potential so that V 0 Vreset. The next action potential will occur when the membrane potential reaches the threshold that is at a time t tisi when V tisi Vth El RmIe Vreset - El - RmIe exp -tisi Tm . 5.10 By solving this for tisi the time of the next action potential we can determine the interspike interval for constant Ie or equivalently .
