Kalman filter temperature estimation with a photoacoustic observation model during the hyperthermia treatment of cancer. (1st August 2022) - Alaeian, Mohsen; Orlande, Helcio R.B.; Lamien, Bernard
Abstract: Hyperthermia with laser heating can be a noninvasive treatment for tumors near the body surface. Thermal damage of tissues depends on temperature levels and time of exposure to high temperatures, thus requiring accurate techniques to measure the temperature in the target region of interest. In this computational work, we couple the laser hyperthermia treatment of cancer to the photoacoustic temperature measurement of internal tissues, by solving a state estimation problem with the Kalman filter. The region of interest is considered to be continuously heated by a laser for the hyperthermia treatment, while another laser is sequentially pulsed over the same heated surface to generate acoustic pressure waves. The observation model is derived from the photoacoustic problem, which is linear with respect to the local internal temperatures of the tissues. The evolution model given by the bioheat transfer problem is also supposed linear and uncertainties are modeled as additive and Gaussian. Therefore, the Kalman filter provides the optimal solution of the state estimation problem considered in this work. Simulated nonintrusive acoustic pressure measurements are used in inverse analyses for two test cases, with different dimensions and locations of a tumor in a two-dimensional region. The simulated tumors are supposed loaded with nanoparticles, in order to enhance the local absorption of the laser energy and to reduce thermal damage to healthy cells. The Kalman filter estimated accurate and stable temperature distributions, even in the tumor region that involved large gradients. Moreover, uncertainties in the Kalman filter estimates were smaller than those resulting from the direct simulation of the photoacoustic thermometry problem.