On the physical and stochastic representation of an indicator dilution curve as a gamma variate

The analysis of intravascular indicator dynamics is important for cardiovascular diagnostics as well as for the assessment of tissue perfusion, aimed at the detection of ischemic regions or cancer hypervascularization. To this end, indicator dilution curves are measured after the intravenous injection of an indicator bolus and fitted by parametric models for the estimation of the hemodynamic parameters of interest. Based on heuristic reasoning, the dilution process is often modeled by a gamma variate. In this paper, we provide both a physical and stochastic interpretation of the gamma variate model. The accuracy of the model is compared with the local density random walk model, a known model based on physics principles. Dilution curves were measured by contrast ultrasonography both in vitro and in vivo (20 patients). Blood volume measurements were used to test the accuracy and clinical relevance of the estimated parameters. Both models provided accurate curve fits and volume estimates. In conclusion, the proposed interpretations of the gamma variate model describe physics aspects of the dilution process and lead to a better understanding of the observed parameters, increasing the value and credibility of the model, and possibly expanding its diagnostic applications.