A Proposal to Clarify the Relationship Between the Thermal Index and the Corresponding Risk to the Patient

Abstract

The thermal index (TI) displayed on the screens of most modern diagnostic ultrasound machines is linearly proportional to the absorbed power or, equivalently, to the in-situ intensity or temperature rise. Users are instructed to interpret the TI as a “relative indication of bioeffect risk.” The thermal dose is a well-known empirical relationship between the temperature T of a biological system and the time t needed for that temperature to induce a deleterious effect. For any two temperatures, T 1 and T 2, and the corresponding times t 1 and t 2, required to produce the same level of effect, this general relation holds: t 1/ t 2 = R T 2 − T 1 , where R is the thermal normalization constant. Hence, it is experimentally determined that the rate of induction, or risk, of a thermal effect increases exponentially with temperature. Because exponential relationships are not intuitive to many users, there is a significant potential for underestimation of the thermal risk associated with exposure to diagnostic ultrasound. To better quantify this risk and thereby make the displayed information more useful, the current linear display of the calculated value of the thermal index, i.e., of TI cur, should be altered to an exponential form based on the thermal dose and representing the excess risk associated with the exposure: TI new = ( R TI cur − 1)/( R − 1). This expression has the advantage that for the usual choice of R = 4 for T ≤ 43° C, TI new ∼ TI cur in the range most often seen onscreen, i.e., TI cur < 1.2, minimizing any confusion during a transition from TI cur to TI new. For the relatively rare but potentially much more serious circumstances when TI cur > 3.5, the displayed TI new ≫ TI cur, consistent with empirical observations of the likelihood of harm. Additional advantages also obtain. (E-mail: cchurch@olemiss.edu)