Model-Based Thermometry for Laser Ablation Procedure Using Kalman Filters and Sparse Temperature Measurements

In this work, we implement a data-assimilation Bayesian framework for the reconstruction of the spatiotemporal profile of the tissue temperature during laser irradiation. The predictions of a physical model simulating the heat transfer in the tissue are associated with sparse temperature measurements, using an Unscented Kalman Filter. We compare a standard state-estimation filtering procedure with a joint-estimation (state and parameters) approach: whereas in the state-estimation only the temperature is evaluated, in the joint-estimation the filter corrects also uncertain model parameters (i.e., the medium thermal diffusivity, and laser beam properties). We have tested the method on synthetic temperature data, and on the temperature measured on agar-gel phantom and porcine liver with fiber optic sensors. The joint-estimation allows retrieving an accurate estimate of the temperature distribution with a maximal error < 1.5 C in both synthetic and liver 1D data, and < 2 C in phantom 2D data. Our approach allows also suggesting a strategy for optimizing the temperature estimation based on the positions of the sensors. Under the constraint of using only two sensors, optimal temperature estimations are obtained when one sensor is placed in proximity of the source, and the other one is in a non-symmetrical position.