Open AccessThe effect of magnetic field on flow induced-deformation in absorbing porous tissues
Author(s) -
Aftab Ahmed,
Javed Siddique
Publication year - 2019
Publication title -
mathematical biosciences and engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.451
H-Index - 45
eISSN - 1551-0018
pISSN - 1547-1063
DOI - 10.3934/mbe.2019029
Subject(s) - permeability (electromagnetism) , porous medium , magnetic field , materials science , mechanics , displacement (psychology) , fluid dynamics , nonlinear system , poromechanics , fluid pressure , porosity , deformation (meteorology) , tissue fluid , chemistry , physics , composite material , biomedical engineering , membrane , medicine , psychology , biochemistry , quantum mechanics , psychotherapist
In order to understand the interaction between magnetic field and biological tissues in a physiological system, we present a mathematical model of flow-induced deformation in absorbing porous tissues in the presence of a uniform magnetic field. The tissue is modeled as a deformable porous material in which high cavity pressure drives fluid through the tissue where it is absorbed by capillaries and lymphatics. A biphasic mixture theory is used to develop the model under the assumptions of small solid deformation and strain-dependent linear permeability. A spherical cavity formed during injection of fluid in the tissue is used to find fluid pressure and solid displacement as a function of radial distance and time. The governing nonlinear PDE for fluid pressure is solved numerically using method of lines whereas tissue solid displacement is computed by employing trapezoidal rule. The effect of magnetic parameter on fluid pressure, solid displacement and tissue permeability is illustrated graphically.