Simulating thermal dynamics in skin tissues using finite volume method: Insights for thermal therapies

Accurate prediction of the temperature field in breast tissue is central to thermal diagnostics and to hyperthermia treatment planning. This study develops a two-dimensional transient bioheat model based on the Chen-Holmes equation which, unlike the classical Pennes formulation, accounts for the directional transport of heat by blood flow. The governing equation is solved using an implicit finite volume method (FVM) on a rectangular tissue domain with isothermal conditions on the left and bottom boundaries, a zero-flux condition on the right boundary, and a convective condition at the skin surface (y = H). A uniform velocity field with horizontal dominance (u > v) is introduced to represent the predominantly lateral convective transport between the chest wall and the nipple. Three blood-perfusion laws, constant, linear and non-linear, are examined to capture the temperature-dependent vascular response. To the authors' knowledge, this particular combination of a horizontally dominant convective field, temperature-dependent perfusion laws and a convective skin boundary has not previously been examined together for breast tissue. The solver is verified by a grid-convergence study and benchmarked against published numerical results, showing close agreement throughout the transient and steady states, with tissue temperatures confined to the physiological 30 to 40 °C range; no experimental or clinical validation is undertaken. The results show that higher tissue and blood thermal conductivities, together with the horizontal-dominant velocity, produce faster and more uniform heat dispersion along the x-axis; raising the convective coefficient markedly increases surface cooling; and the non-linear perfusion model delivers the strongest temperature-dependent feedback, suppressing overheating in high-temperature regions while the constant model yields the most uniform but least adaptive field. Together these features offer a physically motivated description of heat transfer in perfused breast tissue and provide a basis for further work on thermal-therapy and diagnostic applications.