Maximal conductances and reversal potentials, Mechanical Engineering

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By introducing their model of neural excitability in 1952, Alan Lloyd Hodgkin and Andrew Huxley not only shed light on the mechanism underlying a very important phenomenon in Physiology (i.e. the generation and propagation of electrical signals in neurones), but they also introduced a mathematical formalism for modeling similar phenomena in a large variety of excitable cells. Therefore, it is only natural that there is a large number of neural models that are built on the basic concepts introduced by the two aforementioned researchers. One such model is the following:

where IL, INa, IK, IA and ICaT are leakage, transient sodium, persistent potassium, transient potassium and transient calcium currents, respectively, and I(t) is any time-dependent externally injected current. The dynamic activation and inactivation variables x, where x 2 fm; h; n; a; b;M;Hg follow rst order relaxation kinetics:

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