Noninvasive temperature estimation in tissue via ultrasound echo-shifts. Part I. Analytical model

Temperature changes in tissue, caused by high-intensity focused ultrasound, cause time shifts in the echoes that traverse the heated tissue. These time shifts are caused by thermally induced changes in the distribution of the velocity of sound and by thermal expansion within the tissue. Our analytical model relates these shifts to changes in temperature distribution. It is proposed that these relationships can be used as a method for the noninvasive estimation of temperature within the tissue. The model shows that the echo shifts depend mostly on changes in the mean velocity along the acoustical path of the echoes and that no explicit information about the shape of the velocity distribution is required. The effects of the tissue thermal expansion are small in comparison, but may be significant under certain conditions. The theory, as well as numerical simulations, also predicts that the time shifts have an approximately linear behavior as a function of temperature. This suggests that an empirical linear delay-temperature relationship can be determined for temperature prediction. It is also shown that, alternatively, the distribution of temperature in the tissue can be estimated from the distribution of echo delays along the acoustical path. In the proposed system, low-level pulse echoes are sampled during brief periods when the high-intensity ultrasonic irradiation is off, and thus linear acoustic behavior is assumed. The possibility of nonlinear aftereffects and other disturbances limiting this approach is discussed.