High-order accurate difference schemes for the Hodgkin-Huxley equations

  • Authors:

  • David Amsallem;Jan Nordström

  • Affiliations:

  • Department of Aeronautics and Astronautics, Durand Building, Room 028, 496 Lomita Mall, Stanford University, Stanford 94305-4035, USA;Department of Mathematics, Linköping University, SE-581 83 Linköping, Sweden

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2013

Quantified Score

Hi-index 31.45

Visualization

Abstract

A novel approach for simulating potential propagation in neuronal branches with high accuracy is developed. The method relies on high-order accurate difference schemes using the Summation-By-Parts operators with weak boundary and interface conditions applied to the Hodgkin-Huxley equations. This work is the first demonstrating high accuracy for that equation. Several boundary conditions are considered including the non-standard one accounting for the soma presence, which is characterized by its own partial differential equation. Well-posedness for the continuous problem as well as stability of the discrete approximation is proved for all the boundary conditions. Gains in terms of CPU times are observed when high-order operators are used, demonstrating the advantage of the high-order schemes for simulating potential propagation in large neuronal trees.