Boundary Element Algorithm for Modeling and Simulation of Dual-Phase Lag Bioheat Transfer and Biomechanics of Anisotropic Soft Tissues

2018 ◽  
Vol 10 (10) ◽  
pp. 1850108 ◽  
Author(s):  
Mohamed Abdelsabour Fahmy
Keyword(s):  
Boundary Element ◽  
Soft Tissues ◽  
Bioheat Transfer ◽  
Phase Lag ◽  
Dual Phase ◽  
Lu Factorization ◽  
Governing Equations ◽  
Complex Shapes ◽  
Incomplete Lu Factorization ◽  
Element Algorithm

The main aim of this paper is to propose a new boundary element algorithm for describing thermomechanical interactions in anisotropic soft tissues. The governing equations are studied based on the dual-phase lag bioheat transfer and Biot’s theory. Due to the advantages of convolution quadrature boundary element method (CQBEM), such as low CPU usage, low memory usage and suitability for treatment of soft tissues that have complex shapes, it is a versatile and powerful method for modeling of bioheat distribution in anisotropic soft tissues and the related deformation. The resulting linear systems for bioheat and mechanical equations are solved by Transpose-free quasi-minimal residual (TFQMR) solver with a dual-threshold incomplete LU factorization technique (ILUT) preconditioner that reduces the iterations number and total CPU time. Numerical results demonstrate the validity, efficiency and accuracy of the proposed algorithm and technique.

scholarly journals Boundary Element Modeling and Simulation Algorithm for Fractional Bio-Thermomechanical Problems of Anisotropic Soft Tissues

2021 ◽  
Author(s):  
Mohamed Abdelsabour Fahmy
Keyword(s):  
Modeling And Simulation ◽  
Boundary Element ◽  
Soft Tissues ◽  
Wave Model ◽  
Simulation Algorithm ◽  
Governing Equations ◽  
Element Modeling ◽  
Complex Shapes ◽  
Incomplete Lu Factorization ◽  
Internal Domain

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.

Modeling of Laser-Soft Tissue Interactions Using the Dual-Phase Lag Equation: Sensitivity Analysis with Respect to Selected Tissue Parameters

2017 ◽  
Vol 379 ◽  
pp. 108-123
Author(s):  
Ewa Majchrzak ◽  
Marek Jasiński ◽  
Łukasz Turchan
Keyword(s):  
Sensitivity Analysis ◽  
Soft Tissue ◽  
Laser Irradiation ◽  
Soft Tissues ◽  
Initial Conditions ◽  
Internal Heat ◽  
Bioheat Transfer ◽  
Phase Lag ◽  
Dual Phase ◽  
Coupled Equations

Thermal processes occurring in soft tissues are subjected to laser irradiation are analyzed. The transient bioheat transfer is described by the generalized dual-phase lag model. This model consists of two coupled equations concerning the tissue and blood temperatures supplemented by the appropriate boundary and initial conditions. The efficiency of the internal heat source connected to the laser irradiation results from the solution of the diffusion equation. This approach is acceptable when the scattering dominates over the absorption for wavelengths between 650 and 1300 nm, and just such a situation occurs in the case of soft tissues. Sensitivity analysis with respect to the parameters occurring in the mathematical model is done using the direct approach (differentiation of the basic equations and the boundary-initial conditions with respect to the parameter considered), especially the absorption coefficient and scattering coefficient of the soft tissue are considered. At the stage of numerical modeling the basic problem and additional problems connected with the sensitivity functions are solved using the finite difference method. In the final part the conclusions and examples of computations are presented.

scholarly journals The exact analytical solution of the dual-phase-lag two-temperature bioheat transfer of a skin tissue subjected to constant heat flux

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Hamdy M. Youssef ◽  
Najat A. Alghamdi
Keyword(s):  
Heat Flux ◽  
Analytical Solution ◽  
Exact Analytical Solution ◽  
Constant Heat Flux ◽  
Bioheat Transfer ◽  
Skin Tissue ◽  
Phase Lag ◽  
Dual Phase ◽  
Constant Heat ◽  
Two Temperature

Abstract This work is dealing with the temperature reaction and response of skin tissue due to constant surface heat flux. The exact analytical solution has been obtained for the two-temperature dual-phase-lag (TTDPL) of bioheat transfer. We assumed that the skin tissue is subjected to a constant heat flux on the bounding plane of the skin surface. The separation of variables for the governing equations as a finite domain is employed. The transition temperature responses have been obtained and discussed. The results represent that the dual-phase-lag time parameter, heat flux value, and two-temperature parameter have significant effects on the dynamical and conductive temperature increment of the skin tissue. The Two-temperature dual-phase-lag (TTDPL) bioheat transfer model is a successful model to describe the behavior of the thermal wave through the skin tissue.

scholarly journals Unconditional Stability of a Numerical Method for the Dual-Phase-Lag Equation

2017 ◽  
Vol 2017 ◽  
pp. 1-5
Author(s):  
M. A. Castro ◽  
J. A. Martín ◽  
F. Rodríguez
Keyword(s):  
Numerical Method ◽  
Numerical Solutions ◽  
Unconditional Stability ◽  
Bioheat Transfer ◽  
Phase Lag ◽  
Dual Phase ◽  
Stability Properties ◽  
The Stability ◽  
Transfer Problems ◽  
Uniformly Bounded

The stability properties of a numerical method for the dual-phase-lag (DPL) equation are analyzed. The DPL equation has been increasingly used to model micro- and nanoscale heat conduction in engineering and bioheat transfer problems. A discretization method for the DPL equation that could yield efficient numerical solutions of 3D problems has been previously proposed, but its stability properties were only suggested by numerical experiments. In this work, the amplification matrix of the method is analyzed, and it is shown that its powers are uniformly bounded. As a result, the unconditional stability of the method is established.

COMPARISON BETWEEN PENNES AND DUAL PHASE LAG MODELS FOR THE BIOHEAT TRANSFER AROUND A HEALTHY AND A TUMOROUS THYROID

2017 ◽  
Author(s):  
Tiago Pereira da Costa Bittencourt ◽  
BERNARD LAMIEN ◽  
Leonardo Antonio Bermeo Varon ◽  
Helcio Orlande
Keyword(s):  
Bioheat Transfer ◽  
Phase Lag ◽  
Dual Phase

scholarly journals Analysis of non-Fourier thermal behavior for multi-layer skin model

2011 ◽  
Vol 15 (suppl. 1) ◽  
pp. 61-67 ◽  
Author(s):  
Kuo-Chi Liu ◽  
Po-Jen Cheng ◽  
Yan-Nan Wang
Keyword(s):  
Heat Transfer ◽  
Wave Model ◽  
Bioheat Transfer ◽  
Phase Lag ◽  
Dual Phase ◽  
Order Partial Differential Equation ◽  
Transfer Equations ◽  
Lag Model ◽  
Fourier Equation ◽  
Good Agreement

This paper studies the effect of micro-structural interaction on bioheat transfer in skin, which was stratified into epidermis, dermis, and subcutaneous. A modified non-Fourier equation of bio-heat transfer was developed based on the second-order Taylor expansion of dual-phase-lag model and can be simplified as the bio-heat transfer equations derived from Pennes? model, thermal wave model, and the linearized form of dual-phase-lag model. It is a fourth order partial differential equation, and the boundary conditions at the interface between two adjacent layers become complicated. There are mathematical difficulties in dealing with such a problem. A hybrid numerical scheme is extended to solve the present problem. The numerical results are in a good agreement with the contents of open literature. It evidences the rationality and reliability of the present results.

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