Bias-variance tradeoff of indirect versus direct parametric reconstruction for PET myocardial perfusion imaging

Objectives: The aim of this study was to assess the bias-variance tradeoff offered by direct and indirect parametric PET reconstruction with a quadratic penalty function for in-vivo myocardial perfusion imaging.

Methods: Dynamic PET MPI studies were performed on two healthy pigs using the whole-body Siemens Biograph mMR scanner. List-mode PET data were acquired following bolus injection of ~7-8 mCi of ¹⁸F-flurpiridaz, a myocardial perfusion agent. Fully-3D dynamic PET sinograms were obtained by sorting the coincidence events into 16 temporal frames covering ~5 min after radiotracer administration. Eight independent noise realizations of both scans - each containing 1/8^th of the total number of events - were generated from the original list-mode files. Dynamic sinogram data were then used to compute parametric maps using the indirect method and direct methods. For both cases, a one-tissue compartment model accounting for spillover from the left and right ventricle blood-pools was used to describe the kinetics of ¹⁸F-flurpiridaz. An image-derived arterial input function obtained from a TAC taken in the left ventricle cavity was used for tracer kinetic analysis. For the indirect method, frame-by-frame images were estimated using the One-Step Late Maximum a Posteriori (OSL-MAP) algorithm, which incorporates a quadratic penalty function. The parametric images were then calculated using voxel-wise weighted least-square fitting of the reconstructed myocardial PET TACs. For the direct method, parametric images were estimated directly from the dynamic PET sinograms using a maximum a posteriori (MAP) parametric reconstruction algorithm which optimizes an objective function comprised of the Poisson log-likelihood term, the kinetic model and a quadratic penalty function. Maximization of the objective function with respect to each set of parameters was achieved using a preconditioned conjugate gradient algorithm with a specifically developed pre-conditioner. The performance of the direct method was evaluated by comparing voxel-wise estimates of K₁, the tracer transport rate (mL.min^-1.mL^-1), to those obtained using the indirect method. The regularization parameters for the direct and indirect methods were empirically chosen in order to obtain similar mean K₁ across the myocardium and compare the standard deviation performance of each method at a similar level of bias. In addition, we studied the bias/standard deviation tradeoff offered by the direct and indirect methods by varying the values of the regularization parameters.

Results: At a similar level of bias, the direct method resulted in lower standard deviation of K₁ compared to the indirect method. For mean K₁at ~0.87 mL.min^-1.mL^-1, the direct method reduced the voxel-wise standard deviation of K₁ across all eight noise realizations by ~14.4% (averaged over two animals). For large values of the regularization parameters, the direct and indirect methods appear to offer similar performance in terms of standard deviation.

Conclusion: The direct method achieved a better bias-variance tradeoff than the indirect reconstruction methods. Research Support: This work was supported in part by NIH grant R01-HL118261.