Numerical Simulation Study On Electrical Stimulation Rugulating Neuronal Action Potential Based On MATLAB

Electrical stimulation regulating neuronal action potential provides an effective method for the treatment of neurological diseases such as epilepsy and Parkinson.Although this technology has been widely promoted and made some progress,mechanism is not yet clear,and selection and optimization of stimulation parameters need to be improved.In order to solve this problem,simulation studies are widely carried out.However,simulation parameters,especially the need for flexible adjustment of electrical stimulation parameters,are becoming increasingly prominent and have not been resolved.Hence,we take Hodgkin-Huxley model(HH model)and cable model as basic and construct an action potential conduction model.For the first time,we use MATLAB and M language to establish a numerical simulation platform for this conduction model and realizes simulation parameters arbitrarily flexible and adjustable.Moreover,based on the above mentioned numerical platform,characteristics of spatiotemporal distribution of neuronal action potentials under different electrical pulse stimulus are analyzed.Relationship between minimum intensity(intensity threshold)of electrical stimulus for action potential regulating and parameters of stimulation pulse are systematically explored.First of all,based on HH model and cable model,a neuronal action potential conduction model is constructed.This paper takes the lead in introducing matrix calculation method into the solution and constructed a numerical platform for action potential conduction by MATLAB and M language for the first time.The model is discretized,derived and solved using three different discrete methods: forward Euler method,backward Euler method,and Crank-Nicolson method.Through direct comparison with existing literature,the simulation platform is built and solved correctly and fully verified.Besides,results show that when time step Δt < 1 μs and space step Δx< 1 μm,truncation errors introduced by the three discrete methods show no difference on the simulation results.Secondly,study on electrical stimulus to activate action potential firing is carried out.Results show that strength thresholds for action potential activation both occurred in current and voltage pulses stimulus.When supra-threshold stimulus is applied,action potentials are activated and conducts along axial direction without attenuation.When subthreshold stimulus is applied,action potential activation fails and transmembrane potentials conducts along axial direction with attenuation.When high-frequency narrow pulse(frequency >100 Hz or pulse width less than 1 ms)is applied,minimum stimulation intensity(intensity threshold)for action potential activation decreases as pulse width or frequency increases.When low-frequency long pulse is applied,the intensity threshold hardly changes with the stimulus.Besides,cumulative effect in action potential activation is shown on high-frequency,narrow-pulse electrical stimulus.Furthermore,effects of electrical pulses on action potential conduction block is explored.Results show that intensity thresholds also occur in electrical stimulation for action potential conduction block.Supra-threshold stimulus prevents action potential at x= 0 mm conducts to x = 5 mm,and action potential conduction is blocked.Sub-threshold stimulus allows action potentials sequentially transmitted along axial direction.In addition,there is a "window parameter" for electrical pulses to block action potential conduction.Low-frequency electrical pulse stimulation cannot block action potential conduction.When high-frequency narrow(stimulation frequency greater than 1 k Hz and pulse width less than 3 ms),the intensity threshold of electrical pulse blocking action potential conduction decreases significantly with the increase of stimulation pulse width(or frequency).Electrical pulse stimulus blocks the opening of Na ion channels and prevents closing of K ion channels to suppress the release of action potentials and thus achieves action potential conduction block.Finally,results show that certain intensity of electrical pulse stimulation activates nerve excitation,while high-frequency,high-intensity electrical pulse stimulation is more conducive to achieving action potential conduction block.Minimum intensity of the electrical pulse stimulus to achieve neural regulation(activation and block)is pulse width and frequency dependent.Not only does this paper lay a foundation for a numerical platform for subsequent study on different forms of electrical pulse for neuronal action potential regulation,but also provide a theoretical support and guidance for the optimization and selection of electrical stimulation parameters in practical technical applications.