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

Area of Science:

• Computational physics and biophysics
• Numerical methods in heat transfer
• Biomedical engineering

Background:

• Accurate modeling of transient nonlinear bioheat transfer in skin is crucial for understanding thermal therapies and injury.
• Existing numerical methods often face challenges with complex nonlinearities and boundary conditions in biological tissues.
• Temperature-dependent blood perfusion rate (TDBPR) significantly influences heat distribution in skin.

Purpose of the Study:

• To develop and verify a novel meshless numerical scheme for solving 2D transient nonlinear bioheat problems in skin.
• To incorporate temperature-dependent blood perfusion rate (TDBPR) with both linear and exponential relationships.
• To investigate the bioheat effect of perfusion coefficients on skin tissue.

Main Methods:

• A hybrid meshless numerical scheme combining operator splitting method (OSM), radial basis function (RBF) interpolation, and method of fundamental solutions (MFS).
• OSM decomposes the governing equation into simpler forms, approximated by second-order time-stepping schemes.
• RBF interpolation and MFS are used to solve the resulting linear nonhomogeneous Helmholtz-type governing equation (NHGE).

Main Results:

• The proposed meshless method successfully solves transient nonlinear bioheat problems in 2D skin tissues.
• The numerical scheme effectively handles nonlinearities arising from TDBPR.
• Sensitivity analysis reveals the significant bioheat effect of coefficients in linear and exponential TDBPR relationships.

Conclusions:

• The developed meshless numerical scheme offers an accurate and efficient approach for bioheat transfer analysis in skin.
• The study highlights the importance of considering TDBPR in thermal modeling of skin.
• The findings contribute to a better understanding of heat transport phenomena in biological tissues.