Measurement of relative blood flow, transit-time distributions and transport-model parameters by residue detection when radiotracer recirculates

Abstract

The interpretation of tracer kinetic data obtained by external monitoring of radioactively-labeled indicators is generally based on mathematical models that ignore recirculation. An important limitation of these models is that they can be used successfully only in those situations in which the major portion of the response curves are obtainable prior to the onset of the first recirculation. A further complication that limits the usefulness of the models is due to interference from radiotracers carried by recirculation into adjacent perfused regions also within the field of view of the detector. In this paper, we develop a mathematical model applicable for measuring blood flow per unit volume and determining transit-time distributions by external monitoring when recirculation is not a late event and must be taken into consideration. Additionally, the model accounts for interfering recirculation of tracer to adjacent perfused regions in the field of view of the detector. Central to the model is the use of two injections of tracer: one upstream (arterial) and one downstream (venous) of the particular organ or region of interest. Thus, two residue curves are obtained. We develop equations indicating how to employ the two residue curves in order to determine the mean transit time of tracer through the vascular system of interest, as well as higher moments of the transit-time distribution if they are desired. These equations are natural generalizations of Zierler's residue-detection method in that they do not depend for their validity on any model of mass transport within the system of interest. The numerical calculations implied by our equations need not rely on curve-fitting of the data. In addition to mean flow per unit volume, our method can yield compartmental parameters if these are appropriate and desired.