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

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.

Velocity and Blood Perfusion’s Impact on Transient Bioheat Transfer in Human Skin, a Numerical Investigation

“…In a state of equilibrium, the rate at which heat is generated and the rate at which heat is dissipated through conduction and convection are equal. Once the system reaches a state of equilibrium, the temperature profile remains unchanged 32 .…”

“…In brief, the technique of measuring the temperature distribution at various y positions while keeping the x coordinates constant in the transient Bioheat equation enables researchers and clinicians to investigate the temporal changes in temperature within specific areas of biological tissues. The temperature distribution has the potential to undergo temporal evolution, but it may ultimately converge to a state of equilibrium, characterized by a constant temperature that remains unchanged 32 . The comprehension of this knowledge holds significant value in diverse applications within the realm of bioheat transfer.…”

Meshfree and Particle Methods in Biomechanics: Prospects and Challenges

“…Tao and his colleagues solved various linear transient skin bioheat transfer problems using the meshfree method by combining the Laplace transform method and the RBF-MFS method in order to reduce the overall computation time [94]. Other approaches were also formed from the coupling of the method of fundamental solution (MFS) and either the dual reciprocity method (DRM) [95] or the operator splitting method (OSM) [96], to solve nonlinear steady state and transient bioheat transfer problems using a 2D nonlinear skin model with a temperature-dependent blood perfusion rate within the RBF meshfree framework. For details on the nonlinear skin bioheat model, interested readers can refer to [95,96] and the references therein.…”

Developing computational methods of heat flow using bioheat equation enhancing skin thermal modeling efficiency

“…Cui and Barbenel (1990) presented a one-dimensional multilayer model based on Penne's bioheat equation to calculate skin surface temperature distribution with fully constant physical properties at resting conditions and covering skin with an isolation layer, and the results were extracted numerically. Zhang et al (2015) proposed a meshless method to model heat transfer in skin tissue and validated their numerical results through comparison to the results obtained from Ansys software outputs. In this study, a linear mathematical relationship was applied to model the temperature dependence of blood perfusion rate.…”