Study of thermal behavior of a biological tissue: An equivalence of Pennes bioheat equation and Wulff continuum model

• Equivalence of Pennes bioheat equation and Wulff continuum model were established.
• A relationship between blood velocity and blood perfusion rate was derived.
• Consideration was given to 1-D geometry of tissue.
• Both the bioheat models were solved using the finite volume method.
• Numerical results were compared with experimental data.

Equivalence of Pennes bioheat equation (PBHE) and Wulff continuum model (WCM) is established for a 1-D planar tissue. The derived condition of equivalence is specific to tissue without metabolic heat generation. Mathematical analysis is carried out to relate blood perfusion rate and local mean blood velocity that are needed in the analysis of WCM. It is found that the local mean blood velocity in a tissue is a direct function of square root of blood perfusion rate. This functional dependence is also established numerically by having same solution obtained from PBHE and WCM. Analysis is also done to check how closely the derived relation can be used for practical cases of breast tissue with and without a tumor. Blood velocity is a very important physiological quantity. Its measurement is a difficult process and requires a state-of-the-art technique. The proposed relation allows its computation merely from the knowledge of blood perfusion rate.