Triangular node for Transmission-Line Modeling (TLM) applied to bio-heat transfer

• Published in: Journal of thermal biology 2016-12, Vol.62 (Pt B), p.116-122
• Main Authors: Milan, Hugo F.M., Gebremedhin, Kifle G.
• Format: Article
• Language: English
• Subjects: Bio-heat Equation; blood; Body Temperature; Computer Simulation; equations; heat transfer; mathematical models; Models, Biological; Numerical Analysis, Computer-Assisted; Numerical Method; Pennes’ Equation; Pennes’ equation; temperature; Thermodynamics; Transmission-Line Modeling; Triangular node
• ISSN: 0306-4565; 1879-0992
• DOI: 10.1016/j.jtherbio.2016.07.003

Transmission-Line Modeling (TLM) is a numerical method used to solve complex and time-domain bio-heat transfer problems. In TLM, rectangles are used to discretize two-dimensional problems. The drawback in using rectangular shapes is that instead of refining only the domain of interest, a large additional domain will also be refined in the x and y axes, which results in increased computational time and memory space. In this paper, we developed a triangular node for TLM applied to bio-heat transfer that does not have the drawback associated with the rectangular nodes. The model includes heat source, blood perfusion (advection), boundary conditions and initial conditions. The boundary conditions could be adiabatic, temperature, heat flux, or convection. A matrix equation for TLM, which simplifies the solution of time-domain problems or solves steady-state problems, was also developed. The predicted results were compared against results obtained from the solution of a simplified two-dimensional problem, and they agreed within 1% for a mesh length of triangular faces of 59µm±9µm (mean±standard deviation) and a time step of 1ms. •Triangular node for TLM that can be used for heat transfer in biological systems.•Heat source, blood perfusion, and different boundary conditions are considered.•In the validation, accuracy was within 1% when convergence criteria was met.