Particle filter and approximation error model for state estimation in hyperthermia

Abstract

This work deals with numerical simulation of a hyperthermia treatment of skin cancer as a state estimation problem, where uncertainties in the evolution and measurement models, as well as in the measured data, are accounted for. A reduced model is adopted, based on a coarse mesh for the solution of the partial differential equations that describe the physical problem, in order to expedite the solution of the state estimation problem with a particle filter algorithm within the Bayesian framework of statistics. The so-called approximation error model (AEM) is used in order to statistically compensate for model reduction effects. The Liu and West algorithm of the particle filter, together with the AEM, is shown to provide accurate estimates for the temperature and model parameters in a multilayered region containing a tumor loaded with nanoparticles. Simulated transient temperature measurements from one sensor are used in the analysis.