New Mathematical Model to Estimate Tissue Blood Perfusion, Thermal Contact Resistance and Core Temperature

Abstract

Analytical solutions were developed based on the Green’s function method to describe heat transfer in tissue including the effects of blood perfusion. These one-dimensional transient solutions were used with a simple parameter estimation technique and experimental measurements of temperature and heat flux at the surface of simulated tissue. It was demonstrated how such surface measurements can be used during step changes in the surface thermal conditions to estimate the value of three important parameters: blood perfusion (wb ), thermal contact resistance (R″), and core temperature of the tissue (Tcore ). The new models were tested against finite-difference solutions of thermal events on the surface to show the validity of the analytical solution. Simulated data was used to demonstrate the response of the model in predicting optimal parameters from noisy temperature and heat flux measurements. Finally, the analytical model and simple parameter estimation routine were used with actual experimental data from perfusion in phantom tissue. The model was shown to provide a very good match with the data curves. This demonstrated the first time that all three of these important parameters (wb , R″, and Tcore ) have simultaneously been estimated from a single set of thermal measurements at the surface of tissue.