Reconstruction for Gated Dynamic Cardiac PET Imaging Using a Tensor Product Spline Basis

A maximum likelihood reconstruction algorithm for gated dynamic cardiac PET studies was developed and evaluated. A two dimensional tensor product spline basis spanning the time and gate domain is proposed. The activity variations introduced by the biochemical kinetics and cardiac motion are modeled as conic combinations of the B-spline basis functions. The basis explicitly takes the cyclic nature of the heart motion into account. We make use of the expectation-maximization (EM) algorithm to derive a closed form iteration scheme for the reconstruction. The proposed algorithm is validated through computer simulations of the dynamic NCAT beating heart phantom and the kinetics of $^{13}{\rm N}$-ammonia uptake. We used the Monte Carlo simulator GATE to simulate a typical PET scanner. We qualitatively found that a reconstruction using cubic splines resulted in smoother images while better delineating the myocardial wall. Fourth order spline modeling reduced the mean squared error (MSE) of binned reconstruction by 56% whereas conventional Gaussian filtering reduced the MSE by 38%. Spline modeling in the gate domain reduced the MSE by 72% compared to a reduction of 47% obtained with filtering. Quantitative evaluation of the reconstructed motion information suggested that the number of basis functions in the gate domain could be reduced from 16 in a framed approach to 5 for reconstructions using a higher order spline interpolation.