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Int. J. Mol. Sci. 2015, 16(1), 2001-2019; doi:10.3390/ijms16012001

Meshless Method with Operator Splitting Technique for Transient Nonlinear Bioheat Transfer in Two-Dimensional Skin Tissues

1
Research School of Engineering, Australian National University, Acton, ACT 2601, Australia
2
Institute of Scientific and Engineering Computation, Henan University of Technology, Zhengzhou 450001, China
*
Author to whom correspondence should be addressed.
Academic Editor: Bing Yan
Received: 25 November 2014 / Accepted: 7 January 2015 / Published: 16 January 2015
(This article belongs to the Special Issue Advances in Anisotropic and Smart Materials)
View Full-Text   |   Download PDF [1499 KB, uploaded 16 January 2015]   |  

Abstract

A meshless numerical scheme combining the operator splitting method (OSM), the radial basis function (RBF) interpolation, and the method of fundamental solutions (MFS) is developed for solving transient nonlinear bioheat problems in two-dimensional (2D) skin tissues. In the numerical scheme, the nonlinearity caused by linear and exponential relationships of temperature-dependent blood perfusion rate (TDBPR) is taken into consideration. In the analysis, the OSM is used first to separate the Laplacian operator and the nonlinear source term, and then the second-order time-stepping schemes are employed for approximating two splitting operators to convert the original governing equation into a linear nonhomogeneous Helmholtz-type governing equation (NHGE) at each time step. Subsequently, the RBF interpolation and the MFS involving the fundamental solution of the Laplace equation are respectively employed to obtain approximated particular and homogeneous solutions of the nonhomogeneous Helmholtz-type governing equation. Finally, the full fields consisting of the particular and homogeneous solutions are enforced to fit the NHGE at interpolation points and the boundary conditions at boundary collocations for determining unknowns at each time step. The proposed method is verified by comparison of other methods. Furthermore, the sensitivity of the coefficients in the cases of a linear and an exponential relationship of TDBPR is investigated to reveal their bioheat effect on the skin tissue. View Full-Text
Keywords: transient nonlinear bioheat transfer; meshless method; operator splitting; radial basis function; method of fundamental solutions transient nonlinear bioheat transfer; meshless method; operator splitting; radial basis function; method of fundamental solutions
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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MDPI and ACS Style

Zhang, Z.-W.; Wang, H.; Qin, Q.-H. Meshless Method with Operator Splitting Technique for Transient Nonlinear Bioheat Transfer in Two-Dimensional Skin Tissues. Int. J. Mol. Sci. 2015, 16, 2001-2019.

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