Inverse problem in the hyperthermia therapy of cancer with laser heating and plasmonic nanoparticles

In this paper, laser-induced hyperthermia therapy of cancer is treated as a state estimation problem and solved with a particle filter method, namely the Auxiliary Sampling Importance Resampling algorithm. In state estimation problems, the available measured data are used together with prior knowledge about the physical phenomena, in order to sequentially produce estimates of the desired dynamic variables. Although the hyperthermia treatment of cancer has been addressed in the literature by different computational methods, these usually involved deterministic analyses. On the other hand, state space representation of the problem in a Bayesian framework allows for the analyses of uncertainties present in the mathematical formulation of the problem, as well as in the measured data of observable variables that might be eventually available. Two physical problems are considered in this paper, involving the irradiation with a laser in the near infrared range of a non-homogeneous cylindrical medium representing either a soft-tissue phantom or a skin model, both containing a tumour. The region representing the tumour is assumed to be loaded with nanoparticles in order to enhance the hyperthermia effects and to limit such effects to the tumour. The light propagation problem is coupled with the bioheat transfer equation in the present study. Simulated transient temperature measurements are used in the inverse analysis.