Mathematical Models of Action Potential

  • Boris Ja. KoganEmail author


Mathematical models of action potential first appear at the beginning and the middle of twentieth century as both models of analogy (Ostwald [1], Van Der Pol [2]), FitzHugh [3], Nagumo[4]) and pure phenomenological models ( Wienner and Rosenblut [5], Moe et al [6]., Krinski [7]) including models based on finite automata representations. With significant developments of experimental technique and computer technology, and due to classical pioneering research accomplished by a group of scientists lead by Hodgkin and Huxley [8-10], the semi phenomenological ionic models have received recognition and wide applications for nerve AP models and were then modified to cardiac AP models in fundamental investigations accomplished by D. Noble and his group [11-13].

All ionic AP mathematical models are based on a balance of the electrical currents through a cell membrane. The existing ionic mathematical models reflect different knowledge of ionic currents flowing through the membrane and are based on experimental finding that ionic channel currents have stochastic character. There exist two approaches (see Chapter 3) in formulating the probability that an ionic channel, s, is in the open state. The first, introduced by Hodgkin-Huxley [8], is based on the assumption of mutual independence in time of channel gate variable processes, which describe different possible states of a channel. It is important to note that there were many concerns [14] about the validity of this assumption.


Purkinje Fiber Pace Rate Diastolic Interval Restitution Curve Gate Variable 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Department of Computer ScienceUniversity of California, Los AngelesLos AngelesUSA

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