Theoretical framework for quantitatively estimating ultrasound beam intensities using infrared thermography

In the characterization of high-intensity focused ultrasound (HIFU) systems, it is desirable to know the intensity field within a tissue phantom. Infrared (IR) thermography is a potentially useful method for inferring this intensity field from the heating pattern within the phantom. However, IR measurements require an air layer between the phantom and the camera, making inferences about the thermal field in the absence of the air complicated. For example, convection currents can arise in the air layer and distort the measurements relative to the phantom-only situation. Quantitative predictions of intensity fields based upon IR temperature data are also complicated by axial and radial diffusion of heat. In this paper, mathematical expressions are derived for use with IR temperature data acquired at times long enough that noise is a relatively small fraction of the temperature trace, but small enough that convection currents have not yet developed. The relations were applied to simulated IR data sets derived from computed pressure and temperature fields. The simulation was performed in a finite-element geometry involving a HIFU transducer sonicating upward in a phantom toward an air interface, with an IR camera mounted atop an air layer, looking down at the heated interface. It was found that, when compared to the intensity field determined directly from acoustic propagation simulations, intensity profiles could be obtained from the simulated IR temperature data with an accuracy of better than 10%, at pre-focal, focal, and post-focal locations.