Numerical study of oxygen diffusion from capillary
to tissues during hypoxia with external force effects

Srivastava, V; Tripathi, D; Beg, A

Abstract

A mathematical model to simulate oxygen delivery through a capillary to tissues under the influence of an external force field is presented. The multi-term general fractional diffusion equation containing force terms and a time dependent absorbent term is taken into account.
Fractional calculus is applied to describe the phenomenon of sub-diffusion of oxygen in both transverse and longitudinal directions. A new computational algorithm, i.e., the new iterative method (NIM) is employed to solve the spatio-temporal fractional partial differential equation subject to appropriate physical boundary conditions. Validation of NIM solutions is achieved
with a modified Adomian decomposition method (MADM). A parametric study is conducted for three loading scenarios on the capillary-radial force alone, axial force alone and the combined case of both forces. The results demonstrate that the force terms markedly influence the oxygen diffusion process. For example, the radial force exerts a more profound effect than axial force on sub-diffusion of oxygen indicating that careful manipulation of these forces on capillary tissues may assist in the effective reduction of hypoxia or other oxygen depletion phenomena.

Citation

to tissues during hypoxia with external force effects. Journal of Mechanics in Medicine and Biology, 17(2), 1750027.1-1750027.20. https://doi.org/10.1142/S0219519417500270

• Journal Article Type: Article
• Acceptance Date: Mar 20, 2016
• Online Publication Date: Jan 23, 2017
• Publication Date: Jan 23, 2017
• Deposit Date: May 11, 2016
• Publicly Available Date: Jan 23, 2018
• Journal: Journal of Mechanics in Medicine and Biology (jmmb)
• Print ISSN: 0219-5194
• Electronic ISSN: 1793-6810
• Publisher: World Scientific Publishing
• Volume: 17
• Issue: 2
• Pages: 1750027.1-1750027.20
• DOI: https://doi.org/10.1142/S0219519417500270
• Publisher URL: http://dx.doi.org/10.1142/S0219519417500270