Paired stereoisomer model for quantifying receptor concentrationin vivo

Abstract

In vivo receptor imaging currently uses two main methodologies to quantify receptor concentration in the brain: Nonlinear regression and graphical analysis. The purpose of this article is to suggest an alternative set of operational procedures and analysis. The paired stereoisomer method (SM) combines elements of the two existing methodologies. It also takes advantage of a unique property of radiolabeled stereoisomer ligands, where the chemistry of the two isomers in the target tissue is identical with the exception of active binding to the receptor. Starting with a standard two-compartment model as an example, a set of operational equations is derived to evaluate a pair of PET/SPECT images of sequential radiolabeled ligand injections: One active, one inactive. The solution is derived in terms of an instantaneous and normalized supply term (activity X time) to more easily characterize model behavior. Also, a set of computer generated tissue curves for both rapid and prolonged plasma supply curves are generated. The data collection periods, needed to reach an accurate value for receptor concentration, are evaluated. An approximation to shorten the required data collection is developed and evaluated. The experimental requirements needed to obtain a matched pair of injections are discussed as well. The SM method, given enough time to capture the area under the tissue curves, eliminates the large impact of flow and brain permeability to accurately estimate receptor concentration. The analysis also shows that the solution is independent of scanner calibration, works for inactive isomers that have reduced affinity as well as no affinity, works for mixtures of isomers with different affinities, and, finally, works for multicompartment models where the chemistry of the isomers differ only by active binding to receptor. Tissue curve analysis (computer generated) shows that the data collection time required is as fast as the slowest dynamic of the system being evaluated. The experimental practicalities in obtaining a matched pair of injections (scale each tissue curve with respect to the supply for that injection) vary from simple to tedious depending on the whole body biodistribution of the two radioligands. However, this measurement is always theoretically achievable given the ability to directly measure plasma levels. The SM method reduces the error from many of the assumptions required in the graphical analysis method. It is a promising approach which deserves to be tested against actual clinical data. The potential advantages are the reduction in random error by using area measurements as well as the reduction in bias error by eliminating assumptions/measurements of scanner calibration, reference regions, and assorted equilibrium conditions. These advantages offer the possibility of a method with easier implementation and improved accuracy for the clinical in vivo measurement of receptor concentration.