Abstract

The main purpose of this chapter is to propose a novel boundary element modeling and simulation algorithm for solving fractional bio-thermomechanical problems in anisotropic soft tissues. The governing equations are studied on the basis of the thermal wave model of bio-heat transfer (TWMBT) and Biot’s theory. These governing equations are solved using the boundary element method (BEM), which is a flexible and effective approach since it deals with more complex shapes of soft tissues and does not need the internal domain to be discretized, also, it has low RAM and CPU usage. The transpose-free quasi-minimal residual (TFQMR) solver are implemented with a dual-threshold incomplete LU factorization technique (ILUT) preconditioner to solve the linear systems arising from BEM. Numerical findings are depicted graphically to illustrate the influence of fractional order parameter on the problem variables and confirm the validity, efficiency and accuracy of the proposed BEM technique.

Highlights

  • A large number of research papers in bioheat transfer over the past few decades have focused on an understanding of the impact of blood flow on the temperature distribution within living tissues

  • The dual reciprocity boundary element method has been used to solve the thermal wave model of bio-heat transfer (TWMBT) for obtaining the temperature distribution, and the BEM has been used to obtain the displacement and stress at each time step

  • A novel boundary element model based on the TWMBT and Biot’s theory was established for describing the bio-thermomechanical interactions in anisotropic soft tissues

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Summary

Introduction

Human body is a complex thermal system, Arsene d’Arsonval and Claude Bernard have shown that the temperature difference between arterial blood and venous blood is due to oxygenation of blood [1]. The boundary element method (BEM) [11–21] is one of the numerical methods used to solve the current general problem [22–31]. The main aim of this chapter is to propose a new boundary element fractional model for describing the bio-thermomechanical properties of anisotropic soft tissues. The dual reciprocity boundary element method has been used to solve the TWMBT for obtaining the temperature distribution, and the BEM has been used to obtain the displacement and stress at each time step. A brief summary of the chapter is as follows: Section 1 introduces the background and provides the readers with the necessary information to books and articles for a better understanding of bio-thermomechanical problems in anisotropic soft tissues Section 2 describes the BEM modeling of the bio-thermomechanical interactions and introduces the partial differential equations that govern its related problems.

Formulation of the problem
Boundary element implementation for bioheat transfer field
Boundary element implementation for the poro-elastic fields
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Numerical results and discussion
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Conclusion
Methods
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