Development and Experimental Validation of Mathematical Tools for Computerized Monitoring of Cryosurgery
Cryosurgery is the destruction of undesired biological tissues by freezing. Modern cryosurgery is frequently performed as a minimally-invasive procedure, where multiple hypodermic, needle-shaped cryoprobes are inserted into the target area to be treated. The aim of the cryosurgeon is to maximize cryoinjury within a target region, while minimizing damage to healthy surrounding tissues. There is an undisputed need for temperature-field reconstruction during minimally invasive cryosurgery to help the cryosurgeon achieve this aim. The work presented in this thesis is a part of ongoing project at the Biothermal Technology Laboratory (BTTL), to develop hardware and software tools to accomplish real-time temperature field reconstruction. The goal in this project is two-fold: (i) to develop the hardware necessary for miniature, wireless, implantable temperature sensors, and (ii) to develop mathematical techniques for temperature-field reconstruction in real time, which is the focus of the work presented in this thesis. To accomplish this goal, this study proposes a computational approach for real-time temperature-field reconstruction, combining data obtained from various sensing modalities such as medical imaging, cryoprobe-embedded sensors, and miniature, wireless, implantable sensors. In practice, the proposed approach aims at solving the inverse bioheat transfer problem during cryosurgery, where spatially distributed input data is used to reconstruct the temperature field. Three numerical methods have been developed and are evaluated in the scope of this thesis. The first is based on a quasi-steady approximation of the transient temperature field, which has been termed Temperature Field Reconstruction Method (TFRM). The second method is based on analogy between the fields of temperature and electrical potential, and is thus termed Potential Field Analogy Method (PFAM). The third method is essentially a hybrid of TFRM and PFAM, which has shown superior results. Each of these methods has been benchmarked against a full-scale finite elements analysis using the commercial code ANSYS. Benchmarking results display an average mismatch of less than 2 mm in 2D cases and less than 3 mm in 3D cases for the location of the clinically significance isotherms of -22°C and -45°C. In an advanced stage of numerical methods evaluation, they have been validated against experimental data, previously obtained at the BTTL. Those experiments were conducted on a gelatin solution, using proprietary liquid-nitrogen cryoprobes and a cryoheater to simulate urethral warming. The design of the experiment was aimed at creating a 2D heat-transfer problem. Validation results against experimental data suggest an average mismatch of less than 2 mm, for the hybrid of TFRM + PFAM method, which is of the order of uncertainty in estimating the freezing front location based on ultrasound imaging.