The Hodgkin-Huxley model is a system of differential equations that describe the membrane voltage of an axon as it fires the basic signal of the nervous system: the action potential. When charge-carrying ions such as sodium, potassium, and others are enabled to cross a selectively permeable membrane, the resulting current propagates along the length of the axon as a wave of altered ionic potential. However, the degree to which the membrane is permeable to sodium and potassium is itself gated by voltage; therefore, voltage depends on permeability and permeability depends on voltage. This interdependent cellular system is expressed as a system of differential equations with experimentally obtained initial conditions, which must be solved numerically to model changes in the behavior of axons. Additionally, this project aims to solve the system of equations of the Hodgkin-Huxley Model using a novel time-parallel algorithm named the Parareal algorithm. Parareal is a method for solving initial value problems involving either partial or ordinary differential equations. It allows expensive computation to be carried out simultaneously for improved time efficiency and enables calculations to be completed in fewer iterations/evolutions than the equivalent sequential computing method.
Boerman, E., Pham, K., & Peltier, K. (2021). Parallel Computation of Action Potentials in the Hodgkin-Huxley Model via the Parareal Algorithm. Retrieved from https://digitalcommons.wcupa.edu/math_stuwork/4