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 bas ed models for the accurate thermal analysis of blood vessels imbedded in ti ssue has been developed and evaluated. The meshing method places eight node d hexahedral elements inside the vessels where advective flows exist, and f our 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 us ed. 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 surroundin g tissue. Use of the CEE allows accurate solutions to be obtained without t he necessity of assuming ad hoc values for heat transfer coefficients. Comp arisons of the predictions of the three-element model to analytical solutio ns show that the three-element model accurately simulates temperature field s. Energy balance checks show that the three-element model has small, accep table errors. In summary, this method provides an accurate, automatic finit e element gridding procedure for thermal analysis of irregularly shaped tis sue regions that contain important blood vessels. At present, the models so generated are relatively large tin order to obtain accurate results) and a re, thus, best used for providing accurate reference values for checking ot her approximate formulations to complicated, conjugated blood heat transfer problems.