A Novel Approach to Parametric Studies in Nuclear Medicine

Finding the rate constants (rates of transition) of radiopharmaceuticals between organs or different regions of interest (ROIs) in nuclear medicine quickly and accurately provides rich physiological data that is essential for determining drug dosages and performing precise radiation dosimetry. This article describes a novel exact analytical approach to achieving this goal. This can be done in a very short time period at the beginning of treatment with application of tracer levels of radiopharma, and using activities in the ROIs construct the rate constants. Here, using randomly chosen rate constants, time activity curves (TACs) for a four-compartment model are created, and using different sampling regimens of these TACs, the rate constants are reconstructed in a large number of simulations. The least square error (LSE) and relative LSE in the reconstructed parameters are shown to be better than $1\times {10}^{-4}$ . While studies based on optimization methods have been described previously, this paper achieves the rate constants accurately and robustly using analytical methods, thus improving on the clinical applicability of these methods.