Phase Plane Analysis Of FCM Model And Its Response To Electrical Stimulation

Objects:Retinal ganglion cells (RGCs) are the only part of retina which can generate the action potentials and project to central nervous system (CNS). The physical activities and electrical responses of retinal ganglion cells play an important part in developing visual prostheses. In this paper, it was studied that the effect of electrical stimulation on the retinal ganglion cell model—a model developed by Fohlmeister, Coleman, and Miller, named FCM model, and the effect of ion channels during the generation of action potential in the model was analyzed by phase plane method, and these studies will provide support for the further study on the function of retinal ganglion cells and development of artificial visual prostheses.Methods:1. On base of MATLAB, the electrical activities of retinal ganglion cells was simulated, and analyzed by FCM model. And then on the basis of FCM model simulation, the conductance of calcium, the role of calcium ion channels and Ca-activated potassium channels in the firing process was studied.2. The effect of the different direct current electrical stimulation and sine current electrical stimulation chosen by us on the firing of retinal ganglion cells was analyzed; the propagation velocity of action potential on the axon of retinal ganglion cells was computed.3. The changes of ion channels' conductance during the generation of action potential and the differences of action potentials during the impulse firing was analyzed by phase plane method.Results:1. By analyzed the FCM model, the change of sodium channel, calcium channel, and three kind of potassium channel under clamped potential (Figure 3.1), and the channels played different roles in different action potential generation phases. And the calcium ions have specific influence both on membrane potential's frequency and on their size in FCM model by analyzing the FCM model.2. The firing frequency of FCM model was increasing by the larger of direct electrical stimulation, and the size of generated action potential had obvious change. As the increasing of sine current's frequencies, the firing pattern was changed to rhythmic discharge from bursting. And with the increasing of sine current stimulation's size, the firing frequencies of FCM model was increasing, and changed to non damping oscillation.3. There were different expressions of the firing of FCM model in phase plane plot.Conclusion:1. Through voltage control calcium channels and the calcium activated potassium channels, calcium ions have an influence on the firing and the shape of action potentials in FCM model. It interpreted the role of calcium ions on the shape of action potential and firing physical activities in retinal ganglion cells by model simulation.2. Because different electrical stimulation has different influence on FCM model, it is helpful for choosing electrical stimulation mode for the future prostheses by study the influence of different stimulation on FCM model.3. As an effective method to analyze the generation of action potential in FCM model, phase plane analysis can observe all the phase properties of action potential generation and the differences of action potentials during the impulse firing visually.