Analytical theory of bioheat transport

Macroscale thermal models for biological tissues can be developed either by the mixture theory of continuum mechanics or by the porous-media theory. Characterized by its simplicity, the former applies scaling-down from the global scale. The latter uses scaling-up from the microscale by the volume averaging, thus offers the connection between microscale and macroscale properties and is capable of describing the rich blood-tissue interaction in biological tissues. By using the porous-media approach, a general bioheat transport model is developed with the required closure provided. Both blood and tissue macroscale temperature fields are shown to satisfy the dual-phase-lagging (DPL) energy equations. Thermal waves and possible resonance may appear due to the coupled conduction between blood and tissue. For the DPL bioheat transport, contributions of the initial temperature distribution, the source term and the initial rate of change of temperature are shown to be inter-expressible under linear boundary conditions. This reveals the solution structure and considerably simplifies the development of solutions of the DPL bioheat equations. Effectiveness and features of the developed solution structure theorems are demonstrated via examining bioheat transport in skin tissue and during magnetic hyperthermia.