Assessing Ultrasound Safety: A Method for Correlating Stimulus Parameters With MI and TI

Diagnostic ultrasound safety indices, such as the mechanical index (MI) and the thermal index (TI), serve as approved risk estimators of bioeffects that can result from an ultrasound stimulus. However, especially in ultrasound-based indirect therapeutic applications, only the MI is reported while the TI is overlooked, possibly due to its complex calculation. To simplify the calculation, we present an analytical-numerical method for computing the TI, restricted to the -6-dB region of the ultrasound beam, based on equations provided by the International Electrotechnical Commission (IEC) standards. Central to this calculation is the assumption of a linearly propagating ultrasound wave with minimal nonlinear distortion. This assumption was verified by COMSOL simulations and hydrophone measurements in a two-layer setup consisting of water and a tissue-mimicking phantom (TMP) for a single-element, spherically focusing transducer with a central opening driven at a frequency of 950 kHz. For this configuration, the peak-rarefactional pressure (PRP) was evaluated up to 1.5 MPa. To facilitate the immediate assessment of ultrasound safety, MI and TI were mapped into characteristic diagrams, correlating them with pulse durations (PDs) between 0.1 and 3.5 ms at a pulse repetition period (PRPP) of 0.1 s and PDs between 0.01 and 0.35 ms at a PRPP of 0.01 s. These diagrams serve as a practical tool for determining whether an ultrasound stimulus adheres to diagnostic safety limits for MI and TI.