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

The morphology of cancerous breast tissue is characterized by tightly packed groups of small malignant cells, as found in most duct cell carcinoma. This special structure affects the osmotic responses of the cells to freezing and hence their probability of damage from cellular dehydration or intracellular ice formation. A mathematical model has been developed to study the microscale damage to these breast cancer cells during cryosurgery by accounting for their special structure. The model is based on a spherical unit comprised of an extracellular region that surrounds several layers of cancer cells, as experimentally observed of breast duct cell carcinoma by other researchers. Temperature transients in the breast cancer undergoing cryosurgery are calculated numerically using the Pennes equation. When subjected to various thermal histories, both cellular dehydration and intracellular ice formation in the unit structure are examined by considering the cell-to-cell contact and water transport at the microscale level. It is found that the cells in the inner layers hardly dehydrated while those in the outermost layer do greatly. The results help interpret the previously observed experimental phenomena that breast cancer tissues exhibit intracellular ice formation even at a slow cooling rate of -3 degrees C/min. In the attempt to better define an optimal procedure for breast cancer cryosurgery, various freezing protocols are simulated. The constant heat flux protocol induces greater cellular dehydration and higher intracellular ice formation probability simultaneously compared to the other protocols studied.