A Comparative Analysis of Thermal Blood Perfusion Measurement Techniques

Abstract

The object of this study was to devise a unified method for comparing different thermal techniques for the estimation of blood perfusion rates and to perform a comparison for several common techniques. The approach used was to develop analytical models for the temperature response for all combinations of five power deposition geometries (spherical, one- and two-dimensional cylindrical, and one- and two-dimensional Gaussian) and three transient heating techniques (temperature pulse-decay, temperature step function, and constant-power heat-up) plus one steady-state heating technique. The transient models were used to determine the range of times (the time window) when a significant portion of the transient temperature response was due to blood perfusion. This time window was defined to begin when the difference between the conduction-only and the conduction-plus-blood flow transient temperature (or power) responses exceeded a specified value, and to end when the conduction-plus-blood flow transient temperature (or power) reached a specified fraction of its steady-state value. The results are summarized in dimensionless plots showing the size of the time windows for each of the transient perfusion estimation techniques. Several conclusions were drawn, in particular: (a) low perfusions are difficult to estimate because of the dominance of conduction, (b) large heated regions are better suited for estimation of low perfusions, (c) noninvasive heating techniques are superior because they have the potential to minimize conduction effects, and (d) none of the transient techniques appears to be clearly superior to the others.

A sensitivity analysis of the step-temperature technique for measurement of local tissue blood perfusion

“…However, this is impossible in practice, because the power supplied to the bead is limited by the maximum allowable power, i.e. a possible power, 1.5 times the steady state power supplied to the bead for a typical value used in previous experiments [14]. Additionally, the heat capacity of the bead is not infinitesimal.…”

“…Therefore, the blood perfusion prediction accuracy is enhanced with increasing measured blood perfusion. For low blood perfusion levels, the blood perfusion term in equation (7) is so small that the heat transfer of tissue is dominated by the thermal conduction [14]. The contribution of the blood perfusion for the probe bead thermal response is also small.…”

“…However, these are just the mathematical results caused by the assumption that the probe bead temperature rises from the initial equilibrium value of the probe and the surrounding tissue to a predetermined fixed increment value in an infinitesimally short time period [14]. In practice, both the supplied power and the heat capability of the bead are finite; it is impossible for the temperature of the bead to increase to the predetermined temperature in an infinitely short interval.…”

“…By comparing with the blood perfusion value measured by radioactive microspheres, Bowman [10] and Valvano et al [11] pointed out that the average measurement error using the step-temperature technique is 10.6%. Kress and Roemer [14] compared several thermal techniques for the estimation of blood perfusion including the step-temperature technique by introducing the concept of 'time window'; nevertheless they did not directly give a detailed sensitivity analysis. The total error in blood perfusion estimated using the steptemperature technique has two components: the measurement error, which is caused by errors in measurement values, such as the temperature measurement error and the supplied power measurement error; and the theoretical error (bias error), which is caused by the deviation of the model from the actual physical phenomenon.…”

“…The total error in blood perfusion estimated using the steptemperature technique has two components: the measurement error, which is caused by errors in measurement values, such as the temperature measurement error and the supplied power measurement error; and the theoretical error (bias error), which is caused by the deviation of the model from the actual physical phenomenon. The major sources for theoretical error are the assumptions that the probe bead temperature rises from the initial equilibrium value of the probe and the surrounding tissue to a predetermined fixed increment in an infinitesimally short time period [14], as well as the closed form solutions used in the measurement formula. General error analysis methods can be applied to investigate the measurement error directly; however, there are difficulties in dealing with the above-mentioned theoretical errors.…”