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

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. For each transaxial slicesets of sequential tomographic projections are reconstructed into a sequence of transaxial reconstructions using for each reconstruction in the time sequence an iterative MAP reconstruction to calculate the maximum a priori reconstructed estimate. Time-activity curves for a sum of activity in a blood region inside the left ventricle and a sum in a cardiac tissue region are generated. Also, curves for the variance of the two estimates of the sum and for the covariance between the two ROI estimates are generated as a function of time at convergence using an expression obtained from the fixed-point solution of the statistical error of the reconstruction. 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 of 99mTc-teboroxime 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