Solving bioenergetics’ problems with the transmission-line modeling (TLM) method

Abstract. We propose use of transmission-line modeling (TLM) method for solving complex bioenergetics problems. The advantages of the TLM over the current numerical models is that the TLM solves the time-domain problem directly and its use does not require the assumption of a mathematical form of the solution. The previous TLM models for bioheat transfer have the drawback of requiring the refinement of an additional domain every time the domain of interest is refined. Our first proposed solution for this problem was the use of graded meshes that resulted in simulations of 9 times faster and 6 times less computational memory use compared to TLM‘s classical formulation. The graded meshes, although in a less extent, also have the drawback of requiring the refinement of an addition domain when the domain of interest is refined. We recently developed triangular and tetrahedral TLM nodes that do not have this drawback. The disadvantage of these nodes is that they require an additional assumption in the space discretization. The extent to how this additional approximation influences on the prediction of this new nodes is still an open question. Nonetheless, these nodes bring a new modeling philosophy to the field of solving bioheat transfer problems with the TLM model. They differ from the previous nodes because they allow the use of the previous nodes in conjunction with the new ones. Therefore, triangular and tetrahedral nodes can be used in regions of the problem that require fine discretization and the other nodes can be used in regions that do not have this requirement, hence, benefiting from the advantages of each approach.