Quadratic versus linear models to estimate the mean scattering spacing as a function of temperature in ex-vivo tissue

Previous works have shown the feasibility of temperature estimation during ultrasonic therapy using pulse-echo diagnostic ultrasound. These methods are based on the measurement of thermally induced changes in backscattered RF echoes due to thermal expansion and changes in ultrasonic velocity. They assume a joint contribution of these two parameters and a linear dependence with temperature. In this work, the contributions of velocity changes and thermal expansion to the evolution of the mean scatterer spacing of ex vivo bovine skeletal muscle tissue samples were decoupled. This was achieved by employing an experimental setup which allows measuring the absolute velocity value, using the through-transmission technique in a direct transmission configuration. The mean-scatterer spacing was estimated from spectral analysis of the backscattered signals obtained in pulse-echo mode. We propose a quadratic model of the thermal expansion coefficient to fit the evolution of the mean-scatterer spacing with temperature. The temperature increase estimated by the linear model, in the range of 29.5-47 °C, presents a percentage error (mean square error) of 11 %, while for the quadratic model the error is 4.8 %.