Model transformations to evaluate transient thermal responses at a tissue surface

For a spatially distributed model describing the transient temperature resp onse of a thermistor-tissue system, Wei et al. [J. Biomech. Eng., 117:74-85 , 1995] obtained an approximate transformation for fast analysis of the tem perature response at the tissue surface. This approximate transformation re duces the model to a single ordinary differential equation. Here, we presen t an exact transformation that yields a single differential-integral equati on. Numerical solutions from the approximate and exact transformations were compared to evaluate the differences with several sets of parameter values . The maximum difference between the exact and approximate solutions did no t exceed 15 percent and occurred for only a short time interval. The root-m ean-square error of the approximate solution was no more than 5 percent and within the level of experimental noise. Under the experimental conditions used by Wei et al., the approximate transformation is justified for estimat ing model parameters from transient thermal responses.