### Abstract

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.

Original language | English (US) |
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Pages (from-to) | 603-618 |

Number of pages | 16 |

Journal | Mathematical Biosciences and Engineering |

Volume | 16 |

Issue number | 2 |

DOIs | |

State | Published - Jan 1 2019 |

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### All Science Journal Classification (ASJC) codes

- Modeling and Simulation
- Agricultural and Biological Sciences(all)
- Computational Mathematics
- Applied Mathematics

### Cite this

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*Mathematical Biosciences and Engineering*, vol. 16, no. 2, pp. 603-618. https://doi.org/10.3934/mbe.2019029

**The effect of magnetic field on flow induced-deformation in absorbing porous tissues.** / Ahmed, Aftab; Siddique, Javed I.

Research output: Contribution to journal › Article

TY - JOUR

T1 - The effect of magnetic field on flow induced-deformation in absorbing porous tissues

AU - Ahmed, Aftab

AU - Siddique, Javed I.

PY - 2019/1/1

Y1 - 2019/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85061079019&partnerID=8YFLogxK

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U2 - 10.3934/mbe.2019029

DO - 10.3934/mbe.2019029

M3 - Article

C2 - 30861658

AN - SCOPUS:85061079019

VL - 16

SP - 603

EP - 618

JO - Mathematical Biosciences and Engineering

JF - Mathematical Biosciences and Engineering

SN - 1547-1063

IS - 2

ER -