Real-time estimation of the temperature field for invasive laser-induced thermal therapy employing a Kalman filter

Abstract

Laser-induced thermal therapy (LITT) represents a developing, minimally invasive approach used in the practice of oncology, has received attention in the field of therapeutic techniques for malignant tumors. Research and the development of LITT technology rely on the online calculation of a biological tissue's transient thermal field. This paper investigates the online estimation of the temperature field of biological tissues for the invasive LITT process is investigated based on Kalman filter theory. Firstly, thermal conduction model for tissue sample for the invasive LITT process is established based on Penne's biological heat transfer equation and the Beer-Lambert law, and the associated state space model is built on this basis. Subsequently, time-dependent temperature distribution within the tissue of interest is estimated in real-time by integrating the temperature measurement data from a singular measurement point within the treatment site and a state-space representation of thermal transport within tissue sample and KF algorithm. In this paper, the reliability of the constructed state-space representation of thermal transfer within tissue sample is verified with the help of published experimental data on laser irradiation of tissue sample, and the influence of laser radiation form, model mismatch, and the issue of measurement noise when estimating temporary temperature distributions in tissues is discussed through numerical experimentation. The test results indicate that the transient maximal temperature deviation of the estimated temperature field is 0.751 K and 0.731 K under different forms of laser irradiation, respectively, indicating that the scheme in this paper is universal and can effectively estimate the temperature distribution within biological issue under varied optical irradiation forms. When the standard deviation δr of the measurement noise is 0.7 K, the instantaneous error of maximum magnitude pertaining to the estimation of the temperature field is about 0.75 K. The root means square error (RMSE) and MRE of the temperature estimation results are always lower than 0.30 K and 0.5 %. This scheme can provide a more accurate reckon of the inherent thermal distribution in tissue of interest better when model mismatch occurs in the offline link.