A microscale model for prediction of breast cancer cell damage during cryosurgery

Abstract

The morphology of most ductal carcinoma is characterized by tightly packed groups of small malignant cells. This special structure can make these breast cancer cells have different osmotic responses to freezing and affect the probability of damage from cellular dehydration and intracellular ice formation. A mathematical model has been developed to study the microscale damage of the breast cancer cells during cryosurgery by taking its unique structure into consideration. The model was built based on a spherical unit comprised of an extracellular region that surrounds several layers of cancer cells, as experimentally observed by other researchers. In this model, cell to cell contact and water transportation were both taken into consideration. Temperature transients in the breast cancer undergoing cryosurgery were calculated numerically using the Pennes equation. When subjected to various types of thermal histories, both cell dehydration and intracellular ice formation in the unit structure were examined at the microscale level using the model developed in this study. It was found that the cells in the inner layers hardly dehydrated while those in the outermost layer did greatly. The results were used to explain the experimental phenomena observed in freezing of breast cancer tissues that intracellular ice formation existed even at the slow cooling rate of -3°C/min. In the attempt to better define an optimal freeze-thaw cryosurgery procedure for breast cancer, both serious dehydration and intracellular ice formation (IIF) need to be considered. This study also found that use of constant heat flux is able to induce greater dehydration and higher IIF probability simultaneously. It is recommended that a constant heat flux protocol should be used in cryosurgery to ensure better treatment results.