Mathematical Descriptions of Damage to Cells and Tissues Following Heating

The cells of the cardiovascular system can experience temperature excesses of a few degrees during a diseased state or of tens of degrees during a thermal therapy treatment. These raised temperatures may be acute or of long duration. The multiple cell lines that compose each tissue then react, in approximate order of increasing thermal insult, by expressing heat shock proteins, undergoing apoptosis, or suffering necrosis. Mathematical models of the response of cells could aid in planning and designing thermal therapies. The multifactor nature of the cell response makes it challenging to develop such models. The models most used clinically are mathematically simple and based on the response of representative tissues. The model that might provide the most fundamental understanding of the biochemical response of cells requires many parameters, some of which are difficult to measure. None of the semiempirical models that provide improved prediction of cell fate have been widely accepted to plan therapies. There remain great opportunities for developing mathematical models cell response.