Comparison of different mathematical models to analyze diminution kinetics of ultrasound contrast enhancement in a flow phantom

Ultrasound (US) energy leads to intensity- and frequency-dependent destruction of US contrast agent (UCA) microbubbles. When applying repeated US pulses, this phenomenon can be detected as contrast diminution over time. Contrast diminution kinetics depend on the replenishment of UCA into the sample volume. Thus, it is related to organ perfusion. To analyze the contrast diminution kinetics following pulsed harmonic US application (SONOS 5500, 1.8-3.6 MHz, MI: 1.6, frame rates: 2, 4, and 6.67 Hz), we performed an in vitro study using SonoVue® continuous infusion. Seven flow rates (4.5, 9, 13.5, 18, 22.5, 27 and 36 mL/min) were tested. Based on our results, three mathematical models (linear intensity decrease, exponential decay, and an exponential destruction/reperfusion model) describing diminution kinetics were compared. In 113 (89.7%) of 126 trials, a signal decrease was observed after US application. At higher flow rates (18 to 36 mL/min), curve fitting was not possible for the exponential models. For the linear model, intensity decrease depended significantly on the flow rate (p ≤ 0.005, n = 7). A logistic model was fitted to the data, defining the slope in the dynamic range of quasilinear dependence for the different frame rates, as well as the inflection point: The higher the frame rate, the higher the flow rate at the point of inflection. For the exponential model, the contrast half-life was dependent on the flow rate (r = 0.95, p = 0.03, n = 6) only at the highest frame rate (6.67 Hz). The perfusion coefficient derived from the destruction/reperfusion model was not significantly related to the flow rate. In conclusion, the linear intensity decrease correlates well with the flow rate (i.e., flow velocity) and defines optimum frame rates for diminution imaging at different flow velocities. The exponential models, which required curve-fitting procedures, were determined to be inappropriate to describe flow in our phantom. (E-mail: guenter.seidel@neuro.uni-luebeck.de)