Mathematical modeling of the dilution curves for ultrasonographic contrast agents

Most techniques using sonographic contrast agents are based on introducing the agent intravenously. The sonographic changes occur over time and follow a characteristic "skewed gaussian curve," often referred to as the indicator dilution curve. This study uses principles of linear acoustics and tracer kinetics to develop a quantitative model for the indicator dilution curve. A rapid increase in image brightness occurs after bolus injection; brightness peaks after a time related to the blood flow and stability of the contrast agent, which is followed by an asymptotic decrease in image brightness. The net image enhancement, represented by the area under the dilution curve, increases nonlinearly with the injected dose. In stable contrast agents the peak-time and mean transit time are related directly to the flow rate. This relationship changes when the microbubbles of a contrast agent collapse. In an unstable contrast agent the indicator dilution curve is attenuated and peaks earlier than expected on the basis of flow rate. The extent of shift in the mean transit time varies with the half-life of the contrast agent and follows a sigmoid relationship. In conclusion, the properties of the time-videointensity (indicator dilution) curves are significantly affected by the attenuation and stability of the contrast agents. These factors must be taken into consideration in deriving flow related information.