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Meshless method with operator splitting technique for transient nonlinear bioheat transfer in two-dimensional skin tissues.

Zhang ZW, Wang H, Qin QH - Int J Mol Sci (2015)

Bottom Line: 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.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 Article: PubMed Central - PubMed

Affiliation: Research School of Engineering, Australian National University, Acton, ACT 2601, Australia. zewei.zhang@anu.edu.au.

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.

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Variation of temperature with time for the linear case of blood perfusion rate.
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ijms-16-02001-f005: Variation of temperature with time for the linear case of blood perfusion rate.

Mentions: Further, Figure 5 presents the temperature variation from t = 0 s to t = 2560 s at the point (1.875 mm, 0) on the x-axis for the case of a linear blood perfusion rate. It can be seen from Figure 5 that the variation of temperature with time from the proposed meshless method is almost identical to that obtained from ANSYS, although much less unknowns are used in the proposed method.


Meshless method with operator splitting technique for transient nonlinear bioheat transfer in two-dimensional skin tissues.

Zhang ZW, Wang H, Qin QH - Int J Mol Sci (2015)

Variation of temperature with time for the linear case of blood perfusion rate.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4307345&req=5

ijms-16-02001-f005: Variation of temperature with time for the linear case of blood perfusion rate.
Mentions: Further, Figure 5 presents the temperature variation from t = 0 s to t = 2560 s at the point (1.875 mm, 0) on the x-axis for the case of a linear blood perfusion rate. It can be seen from Figure 5 that the variation of temperature with time from the proposed meshless method is almost identical to that obtained from ANSYS, although much less unknowns are used in the proposed method.

Bottom Line: 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.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 Article: PubMed Central - PubMed

Affiliation: Research School of Engineering, Australian National University, Acton, ACT 2601, Australia. zewei.zhang@anu.edu.au.

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.

Show MeSH
Related in: MedlinePlus