Fractional Modeling Applied to the Dynamics of the Action Potential in Cardiac Tissue

Fractal and Fractional

Carlos Alberto Valentim¹  Amar Debbouche²  Sergio Adriani David³ 

[1] Department of Biosystems Engineering, University of São Paulo, Av. Duque de Caxias Norte 225, Pirassununga 13635-900, SP, Brazil;Department of Mathematics, Guelma University, Guelma 24000, Algeria;Systems Dynamics Group, Department of Biosystems Engineering, University of São Paulo, Av. Duque de Caxias Norte 225, Pirassununga 13635-900, SP, Brazil;

关键词: fractional calculus;    partial differential equations;    cardiac conduction;    membrane potential;    simulation;   

DOI  :  10.3390/fractalfract6030149

来源: DOAJ

【 摘 要 】

We investigate a class of fractional time-partial differential equations describing the dynamics of the fast action potential process in contractile myocytes. The system is explored in both one and two dimensional cases. Homogeneous and nonhomogeneous solutions are derived. We also numerically simulate some of the proposed fractional solutions to provide a different modeling perspective on distinct phases of cardiac membrane potential. Results indicate that the fractional diffusion-wave equation may be employed to model membrane potential dynamics with the fractional order working as an extra asset to modulate electricity conduction, particularly for lower fractional order values.

【 授权许可】

Unknown