Theoretical analysis of lesion detectability in penalized maximum-likelihood patlak parametric image reconstruction using dynamic PET

Detecting cancerous lesion is a major clinical application in emission tomography. In previous work, we have studied penalized maximum-likelihood (PML) image reconstruction for lesion detection in static PET. Here we extend our theoretical analysis of static PET reconstruction to dynamic PET. We study both the conventional indirect reconstruction and direct reconstruction for Patlak parametric image estimation. In indirect reconstruction, Patlak parametric images are generated by reconstructing a sequence of dynamic PET images first and then performing Patlak analysis on the time activity curves (TACs) pixel-by-pixel. In direct reconstruction, Patlak parametric images are estimated directly from raw sinogram data by incorporating the Patlak model into the image reconstruction procedure. PML reconstruction is used in both the indirect and direct reconstruction methods. We use a channelized Hotelling observer (CHO) to assess lesion detectability in the Patlak slope image. Simplified expressions for evaluating the lesion detectability have been derived and applied to the selection of the regularization parameter value to maximize the lesion detectability. The proposed method is validated using computer-based Monte Carlo simulation. Good agreements between theoretical predictions and Monte Carlo results are observed. The theoretical formula also shows the benefit of the direct method in dynamic PET reconstruction for lesion detection.