Estimation of the parameter covariance matrix for a one-compartment cardiac perfusion model estimated from a dynamic sequence reconstructed using MAP iterative reconstruction algorithms

Abstract

In dynamic cardiac SPECT estimates of kinetic parameters of a one-compartment perfusion model are usually obtained in a two step process: 1) first a MAP iterative algorithm, which properly models the Poisson statistics and the physics of the data acquisition, reconstructs a sequence of dynamic reconstructions, 2) then kinetic parameters are estimated from time activity curves generated from the dynamic reconstructions. This paper provides a method for calculating the covariance matrix of the kinetic parameters, which are determined using weighted least squares fitting that incorporates the estimated variance and covariance of the dynamic reconstructions. Sequential tomographic projections are reconstructed into a sequence of transaxial reconstructions for each transaxial slice using for each reconstruction in the time sequence the fixed-point solution to the MAP reconstruction. Time-activity curves for a sum of activity in a blood region inside the left ventricle and a sum in a cardiac tissue region, for the variance of the two estimates of the sum, and for the covariance between the two ROI estimates are generated at convergence. A one-compartment model is fit to the tissue activity curves assuming a noisy blood input function to give weighted least squares estimates of blood volume fraction, wash-in and wash-out rate constants specifying the kinetics for the left ventricular myocardium. Numerical methods are used to calculate the second derivative of the chi-square criterion to obtain estimates of the covariance matrix for the weighted least square parameter estimates. Even though the method requires one matrix inverse for each time interval of tomographic acquisition, efficient estimates of the tissue kinetic parameters in a dynamic cardiac SPECT study can be obtained with present day desk-top computers.