Numerical study of tissue deformation behaviour under impact loading

Abstract

In this study, the theoretical analysis of tissues behaviour designates a common approach towards the bio-mechanical study, which is used to verify the interpretation of the experimental data along with the compression of different biological tissues. The previous investigations on the KLM (Kuan-Lai-Mow) theory always presented the swelling behaviour without considering the nature of organic fluid flow through the elastic porous medium of the tissues. In fact, isotropic behaviour has been implemented while deriving the power-law model occasionally, but its anisotropic nature still needs to accommodate in the case of power-law fluids. Some general assumptions are often provoked to formulate the complex multiphase deformation behaviour of the solid matrix. If a special kind of complex interconnection is not produced, then deformations produced in these dynamics are important for modelling point of view. To derive such a model, computational cost is the main factor of interest for the researcher. Keeping in view of such a problem, the multiphase deformation of soft tissues is moulded using the power-law model. A diffusion equation is applicable to the undirected swelling behaviour, which has been derived from the solid displacement based on the local fluid pressure. The governing nonlinear coupled system of equations is solved numerically before attaining the consolidation state that is a time-dependent problem, while considering the nonlinear permeability of the tissues. The purpose of the present study is to provide a reasonable direction into the tissues swelling behaviour and its dependence upon the class of organic fluid flow through the lateral boundaries.

Keywords:

• Tissue deformation
• KLM power-law model
• deformation theory
• convergent solution
• biomedical engineering

Mathematics Subject Classifications:

• 35E10
• 35Q30

Disclosure statement

No potential conflict of interest was reported by the author(s).

Data availability statement

Non-digital data available, however, Matlab Figures, Numerical Algorithm available on the request from the authors.

Additional information

Funding

This work partially supports the author J. I. Siddique by the Simons Foundation [grant number 401993] and Penn State York.