A Spherical Source Model for the Thermal Pulse Decay Method of Measuring Blood Perfusion: A Sensitivity Analysis

The thermal pulse-decay method, as developed and analyzed by Chen et al. [1–6], is a thermal clearance technique that uses a small thermistor probe for determining the blood perfusion and thermal conductivity of the tissue immediately surrounding the probe. They described the energy transfer of the probe/tissue system mathematically with a simple analytical model, the point source model, which assumes that the heating source is infinitely small. This paper introduces a new, more accurate analytical description that assumes the heating source is spherically symmetric with a finite radius. A numerical study of these two alternative mathematical models is presented in which the solutions of each model are compared to transient temperature decay data generated from a detailed finite difference simulation of the probe/tissue system. The accuracy and sensitivity of the predictions of each of these models to variations in tissue thermal conductivity and perfusion, probe characteristics, and heating time are presented. In all cases, the accuracy of the spherical source model was better than the point source model. It is also shown that the spherical source model can accurately predict low rates of perfusion (on the order of 1 kg/m³s) unlike the point source model. The spherical source model also allows for the possibility of the measurement probes to be calibrated for an “effective bead radius” which accounts for the nonideal characteristics of the probe, thereby giving even more accurate determinations of perfusion.