An accurate, convective energy equation based automated meshing technique for analysis of blood vessels and tissues

An automated three-element meshing method for generating finite element based models for the accurate thermal analysis of blood vessels imbedded in tissue has been developed and evaluated. The meshing method places eight noded hexahedral elements inside the vessels where advective flows exist, and four noded tetrahedral elements in the surrounding tissue. The higher order hexahedrals are used where advective flow fields occur, since high accuracy is required and effective upwinding algorithms exist. Tetrahedral elements are placed in the remaining tissue region, since they are computationally more efficient and existing automatic tetrahedral mesh generators can be used. Five noded pyramid elements connect the hexahedrals and tetrahedrals. A convective energy equation (CEE) based finite element algorithm solves for the temperature distributions in the flowing blood, while a finite element formulation of a generalized conduction equation is used in the surrounding tissue. Use of the CEE allows accurate solutions to be obtained without the necessity of assuming ad hoc values for heat transfer coefficients. Comparisons of the predictions of the three-element model to analytical solutions show that the three-element model accurately simulates temperature fields. Energy balance checks show that the three-element model has small, acceptable errors. In summary, this method provides an accurate, automatic finite element gridding procedure for thermal analysis of irregularly shaped tissue regions that contain important blood vessels. At present, the models so generated are relatively large (in order to obtain accurate results) and are, thus, best used for providing accurate reference values for checking other approximate formulations to complicated, conjugated blood heat transfer problems.