Bounds on Thermal Dose Estimates using Ultrasonic Backscatter Monitoring of Heating

Diagnostic ultrasound provides a means for estimating the spatial distribution of temperature in tissue in response to HIFU therapy. One approach to estimating the temperature is to distort backscattered ultrasound between two frames, one preceding and one following the treatment, in a manner consistent with the heat equation, the exposure protocol, the beam pattern, and the specific material properties of the tissue. Ascribing a probability distribution to the measurements taken after treatment, the Cramer Rao bound may be determined for coefficient estimates in a functional expansion for the applied heating during therapy. This formulation also identifies the function with coefficient estimates having least variance, providing the lower bound. We study the implications of this characterization for heat deposition from a linear scan, examining how estimation accuracy is influenced by the lesion length and the delay following treatment and preceding acquisition. It is shown that for these studies, temperature estimates with accuracy well below 1 deg C are possible. In addition, the thermal dose can be estimated to tens of equivalent minutes, referenced to 43 deg C.