NUMERICAL STUDY OF OXYGEN DIFFUSION FROM CAPILLARY TO TISSUES DURING HYPOXIA WITH EXTERNAL FORCE EFFECTS

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 a...

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Bibliographic Details
Published inJournal of mechanics in medicine and biology Vol. 17; no. 2; p. 1750027
Main Authors SRIVASTAVA, V., TRIPATHI, D., ANWAR BÉG, O.
Format Journal Article
LanguageEnglish
Published Singapore World Scientific Publishing Company 01.03.2017
World Scientific Publishing Co. Pte., Ltd
Subjects
Axial forces
Boundary conditions
Computer simulation
Cybernetics
Diffusion
Fractional calculus
Hypoxia
Iterative methods
Mathematical models
Oxygen
Partial differential equations
Time dependence
general fractional diffusion equation
axial-radial forces
hypoxia
new iterative method
Capillary-tissue diffusion
spatio-temporal concentration plots
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Summary: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.
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content type line 14
ISSN:0219-5194
1793-6810
DOI:10.1142/S0219519417500270