Sparsity Constrained Direct Parametric Reconstruction in Dynamic PET Myocardial Perfusion Imaging

110 Objectives: Dynamic myocardial perfusion imaging (MPI) with PET serves an important role in diagnosis and prognosis of patents with suspected or known coronary artery disease. Conventional myocardial blood flow (MBF) quantification reconstructs a series of dynamic frames and applies a kinetic model to the reconstructed image sequences for measuring the tracer uptake rate K1. This approach leads to noisy K1 estimation due to very limited counts in individual time frames. The goal of this study is to develop a sparsity regularized direct parametric reconstruction algorithm, which collectively uses data from all the dynamic frames while imposing a dictionary learning (DL) based sparsity constraint on K1 spatial variation. Methods: The direct parametric reconstruction is accomplished by relating parametric images to dynamic PET data through a nonlinear transform containing the one-tissue compartment model and the imaging system matrix. To suppress the undesirable noise propagation in this ill-posed inverse problem, we impose a sparsity regularization on the K1 image leading to a penalized log-likelihood function for maximization. The sparsity constraint is constructed as the difference between the estimated K1 image and its sparse representation based on the learned dictionary from a self-created hollow sphere. A two-stage iterative approach is adopted to solve this optimization problem. In stage one, we calculate the sparse representation of the current estimation of K1 given the learned dictionary. In stage two, the penalized log-likelihood function is optimized with the sparsity penalty term fixed. Applying optimization transfer, we construct separable surrogate functions for the log-likelihood term and the sparsity constraint term, respectively. The combined surrogate function, which is solvable by convenient voxel-wise optimization is maximized by the damped Newton method. To evaluate the proposed algorithm, we simulated two sets of realistic Rb-82 dynamic MPI PET data, one with normal MBF (K1=1.48) and the other with regionally reduced MBF (K1=1.13). Using the XCAT phantom, PET image frames were created by assigning the activities integrated from the multiple organ time activity curves based on clinical measurement. We performed analytic simulations for the geometry of a GE RX PET scanner to generate 20 noise realizations for each dynamic dataset. By assessing the ensemble noise versus bias tradeoff of the normal and abnormal K1 on the region of interest, we compared the proposed method, the conventional method with and without post filtering, and a quadratic penalty regularized direct parametric reconstruction method. We also evaluated the tradeoff of the ensemble noise and the contrast between the normal and the defect K1 for abnormal MBF detectability. Results: For the regional normal K1 estimation, the mean and the ensemble normalized standard deviation (EnNSD) across 20 noise realizations obtained by the conventional method without and with post filtering, the quadratic penalty regularized direct algorithm, and the proposed method are 1.43+/-0.45, 1.10+/-0.21, 1.36+/-0.22, and 1.45+/-0.22. For the abnormal case, the corresponding regional mean+/-EnNSD are 1.13+/-0.64, 0.78+/-0.26, 1.02+/-0.27, and 1.07+/-0.27, respectively. In both cases, post filtering in the conventional method reduces noise at the cost of introducing large bias. The proposed sparsity constraint outperforms the quadratic penalty, achieving similar noise but reduced bias resulting in better recovered contrast. Conclusions: We developed a sparsity constrained direct parametric image reconstruction algorithm that incorporates the DL based regularization on the K1 parametric image. Using simulated dynamic MPI PET data, we demonstrated its better performance in K1 estimation and abnormal K1 detection compared with conventional methods. The proposed method shows its potential to advance MBF quantification in dynamic PET MPI.