Iterative Curve Fitting of the Bioheat Transfer Equation for Thermocouple-Based Temperature Estimation In Vitro and In Vivo.

Temperature measurements with thin thermocouples embedded in ultrasound fields are strongly subjected to a viscous heating artifact (VHA). The artifact contribution decays over time; therefore, it can be minimized at late temperature readings. However, previous studies have failed to demonstrate a rigorous method for determining the optimal time point at which the artifact contribution is negligible. In this study, we present an iterative processing method based on successive curve fittings using an artifact-independent model. The fitting starting point moves at each iteration until the maximum R2 indicates where the viscous heating is minimum. A solution of the bioheat transfer equation is used to account for blood perfusion, thus enabling in vivo measurements. Three T-type thermocouples with different diameters and sensitivities were assessed in an excised canine liver and in the mouse brain in vivo. We found that the artifact constitutes up to 81% ± 5% of wire thermocouple readings. The best-fit time varied in the liver samples ( n = 3 ) from 0 to 3.335 ± 0.979 s and in the mouse brain ( n = 5 ) from 0 to 0.498 ± 0.457 s at variable experimental conditions, which clearly demonstrates the need of the method for finding the appropriate starting time point of the fit. This study introduces a statistical method to determine the best time to fit a curve that can back-estimate temperature in tissues under ultrasound exposure using thermocouples. This method allows temperature evaluation in vivo and in vitro during a validation and safety assessment of a wide range of therapeutic and diagnostic ultrasound modalities.