On numerical integration of the Hodgkin and Huxley equations for a membrane action potential
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A comparison of six numerical methods for integrating a compartmental Hodgkin-Huxley type model
2021, Applied Numerical MathematicsCitation Excerpt :Integration methods listed in Table 3 are intended for different contexts. At the same time there exist myriad examples of these methods being used to integrate generic HH models [5,6,8,10,23,28]. To be clear, we integrated ion channel states represented by equation (3) with ODE methods forward Euler, backward Euler and trapezoidal rule in place of PDE methods forward-time central-space (FTCS), backward-time central-space (BTCS) and HCN, respectively.
On the accuracy and computational cost of spiking neuron implementation
2020, Neural NetworksCitation Excerpt :Moreover, this kind of algorithms has not been incorporated into the SN simulation software, but only adaptive time step algorithms. Although several works, since Moore and Ramon (1974), have faced such a problem, this has not been treated as a multiobjective optimization one, and a general and unique solution has been intended to be found with no convincing results. Finding the optimal simulation parameters for SNs is still an open issue because we have an undetermined number of specific problems, a considerable number of NMs, firing frequencies, simulation windows, SN models, stimulation current types and intensities, and an infinite number of time steps.
Efficient partitioned numerical integrators for myocardial cell models
2020, Applied Mathematics and ComputationCitation Excerpt :The methods with the shortest and second-shortest execution times are given in Table 3 along with the ratio of the times. A direct comparison of RL (MRC1) and MRH (proposed by Moore and Ramon in [9]) is given in Table 4, in which the winning MME time is highlighted and the winning ratio of the slower time to the faster time is given. From these tables, we are able to make following observations.
Stochastic Pacing Inhibits Spatially Discordant Cardiac Alternans
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2007, Biophysical JournalCitation Excerpt :No-flux boundary conditions were used. The activation and inactivation variables were computed from their analytic formula (40). To increase computation speed, lookup tables were used for evaluation of the voltage-dependent rate constants or steady-state values and time constants.