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

JOURNAL OF COMPUTATIONAL PHYSICS

卷:252

Article

Amsallem, David¹  Nordstrom, Jan² 

[1] Stanford Univ, Dept Aeronaut & Astronaut, Stanford, CA 94305 USA

[2] Linkoping Univ, Dept Math, SE-58183 Linkoping, Sweden

关键词: High-order accuracy;    Hodgkin-Huxley;    Neuronal networks;    Stability;    Summation-by-parts;    Well-posedness;   

DOI  :  10.1016/j.jcp.2013.06.035

来源: Elsevier

【 摘 要 】

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. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free