Exact Solutions to Cancer Laser Ablation Modeling

The present paper deals with the study of the fluence rate over both healthy and tumor tissues in the presence of focal laser ablation (FLA). We propose new analytical solutions for a coupled partial differential equation (PDE) system, which includes the transport equation modeling of light penetration into biological tissue, the bioheat equation modeling the heat transfer, and its respective damage. The present work could be the first step toward knowledge of the mathematical framework for biothermophysical problems, as well as the main key to simplify the numerical calculations due to its zero cost. We derive exact solutions and simulate results from them. We discuss the potential physical contributions and present respective conclusions about the following: (1) the validity of the diffusion approximation of the radiative transfer equation; (2) the local behavior of the source of scattered photons; (3) the unsteady state of the fluence rate; and (4) the boundedness of the critical time of the thermal damage to the cancerous tissue. We also discuss some controversial and diverging hypotheses.