A parametric model of radioisotopic tracer flow through the kidney

To assess the state of a kidney from radiological examination a dynamic model of flow of an isotopic tracer through the kidney, of a convolution type, is commonly used. It is a nonparametric model where the output is related to the input by an integral relation. In this paper a new parametric model of tracer flow through the kidney is presented. It takes to much bigger extent into account the physiology of the tracer flow in kidney than previously proposed compartmental models. It consists of the submodels of flow through nephrons which are in the form of ordinary differential equations with pure delays between input and the output flows. The delay is caused by the time of passage of the isotope through nephrons and depends on the nephron length. It is assumed that the distribution of nephrons of different length is exponential. The renal pelvis is described as the one-compartment model. The solutions of the equations are given for the assumed two-exponential decay of the isotope tracer in the blood following the bolus injection of the tracer. The formulae obtained are then used to simulate the influence of changes in the model parameters, representing the flow condition through the kidney, on the shape of the waveforms depicting time evolution of the amount of the isotope being in the kidney