Modeling of repeating freezing of biological tissues and analysis of possible microwave monitoring of local regions of thawing

Transient heat transfer problems typical of recent-day cryosurgery are considered. Relatively simple models are suggested to take into account different temperatures of freezing inside the biological cells and in the gaps between the cells. In the most complicated case of interpenetrating media, when there is a thermal contact between the cells and also between the gaps, the model one-dimensional problem is formulated and solved with a specific attention to the effects produced by repeated periods of freezing and thawing. It is shown that the latent heat of melting may lead to a significant difference between temperatures of the cells aggregates typical of tumors and the extracellular medium. It is important that the temperature inside the cell aggregate alternatively becomes less or greater than the ambient temperature. Such a temperature regime may lead to serious thermo-mechanical damage of the tumor cells not only due to ordinary thermal expansion during the freezing but also because of tensile stresses that arise at the surface of the frozen biological cells or their aggregates. Potential possibility of microwave monitoring of small local regions of thawing is analyzed on the basis of Mie theory calculations.