A Bayesian Model for Organ Blood Flow Measurement with Colored Microspheres

The development of quantitative methods to measure organ blood flow is an active area of research in physiology. Under current protocols radiolabeled microspheres are injected into the circulation of an experimental animal and blood flow to an organ is estimated based on uptake of radioactivity. Growing concerns about environmental pollution, laboratory exposure to radioactivity and the increasing costs of radioactive waste disposal have lead to the development of microspheres labeled with non-radioactive colored markers. Because colored microspheres are new, little research has been devoted to developing statistical methods appropriate for the analysis of data collected from their use. In this paper we present a Bayesian approach to the problem of organ blood flow measurement with colored microspheres. We derive a Poisson-multinomial probability model to describe the organ blood flow protocol. The physical and biological information available to an investigator before an experiment is summarized in a prior probability density which we represent as a product of Dirichlet and log-normal probability densities. We derive the marginal probability density for the flow of blood to an organ conditional on the number of microspheres observed in the counting phase of the experiment. We apply a Monte Carlo Markov chain algorithm to compute the density. The Bayesian approach is used to estimate kidney, heart and total organ blood flow in a colored microsphere study performed in a male New Zealand white rabbit. The results from a Bayesian analysis are compared to those obtained from applying an approximate maximum likelihood procedure based on the delta method. The relation to current methods for organ blood flow estimation is described and directions of future research are detailed.