Theoretical Analysis of Optimal Conditions in Fquilibrium Imaging of in Vivo Receptors

A mathematical analysis is presented of the optimal conditions for the equilibrium imaging of a three-dimensional spatially varying distribution of receptor sites. The analysis considers both the properties of ligand-receptor binding and counting statistics. Results for realistic imaging conditions are presented as two-dimensional equi-error contours of the relative standard error for the estimation of total receptor within a volume of interest. Each contour is a function of total administered ligand in one dimension and a function of total receptor (within a volume of interest) in the other dimension. These results allow the determination of the optimal relationship between the three-dimensional spatial distribution of total receptor, the ligand-receptor dissociation costant, and the total amount of administered ligand, therefore, they should provide a basis for the rational choice of conditions in studies involving positron emission tomography, single photon tomography, and autoradiography.