Journal of Ultrasound in Medicine, Vol 16, Issue 7 471-479, Copyright © 1997 by American Institute of Ultrasound in Medicine
Mathematical modeling of the dilution curves for ultrasonographic contrast agents
C. M. Sehgal and P. H. Arger
Department of Radiology, Hospital of the University of Pennsylvania, Philadelphia 19104-6010, USA.
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.
