Finite element modeling of cryosurgery with coupled phase change and thermal stress aspects

The freezing of biomaterials and the induced injuries play an important role in the field of medicine and biomedical engineering, especially in the treatment of ailments involving tissue and organ failure. One of the remarkable applications is cryosurgery, a surgical technique using controlled freezing to inflict localized tissue injury and destroy abnormal tissues. Modern cryosurgery has become a very promising therapy as an alternative to conventional surgery involving the destruction of tumors during cancer treatment following the early development of cryosurgical probes in the 1960's. Cryosurgery can now be applied to a slew of deep body configurations such as prostate, kidney, liver, breast and brain, with advances being made on cryosurgical devices (such as cryoprobes) and imaging techniques. The crucial aspect of cryosurgery for the treatment of a tumor is that all cancerous tissues must be discriminately killed without damaging the normal tissue that surrounds it. Therefore, the control on the freezing process including cryoprobe placements, cooling rates and freezing durations is important to the success of the treatment. However, the field of cryosurgery is still very much in an empirical form in which critical clinical decisions are subjective and mainly based on the surgeon's experience.A description of tissue freezing problem regarding both thermal and mechanical aspects is established within the framework of Continuum Mechanics. The differential equations arising from the model formulations are solved numerically based on the finite element method. In the thermal part of the model, the bioheat equation is computed and the internal moving boundary problem associated with tissue water phase change is solved on a fixed finite element mesh based on the Duvaut transformation [1]. On the other hand, with regard to the mechanical part, stresses and deformations are induced by thermal expansion or contraction due to temperature change and phase change while being computed in a quasi-static manner based on an elasto-plastic model. The developed numerical model, calibrated against benchmark problems, will subsequently be used to study cryosurgery cases for the treatment of prostate and kidney cancer. In order to determine the thermal characteristics of a cryoprobe typically used in cryosurgery where biological tissues are frozen, experimental investigations of ice ball formation around a single cryoprobe in various bulk solutions are conducted involving both optical and temperature measurements. The heat transfer coefficients of the cryoprobe, which will enter as input into the computational model, are determined based on the experimental data. To explore the effect of tissue microstructure on the freezing process, the experiments have been extended to freezing in micron-sized glass capillary tubes for the investigation of capillary freezing point depression due to surface tension. Finally, the developed numerical model and the experimentally determined thermal properties of the cryoprobe are applied to simulate cryosurgeries for the treatment of prostate and kidney cancer. The finite element grids are built based on the geometries of prostate and kidney reconstructed from Ultrasound and CT images, respectively. On the other hand, the cryoprobe placements and the cooling protocol are determined according to the images and data collected during cryosurgery. The numerical results show that the computed field variables such as tissue temperature, cooling rate, freezing exposure index and mechanical stresses can all work in concert to inflict tissue injuries. Also, predicted frozen zones are in good agreement with the ice ball region as seen on the surgery monitoring CT images, and the tumor shown on pre-operative CT images.In conclusion, it is expected that the developed simulation tool can be ultimately used to predict the freezing process for a particular cryosurgery case, and therefore assist surgeons to perform better cryosurgery planning.This PhD research work is motivated toward the modeling of freezing in porous media such as tissue and the development of a simulation tool for cryo-treatment that will allow surgeons to engage in treatment planning to improve the success of this procedure. This work is concerned with the development of a finite element based numerical model for cryosurgery, combined with the study of freezing in both bulk solution and micron-sized glass capillaries.