Abstract
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Objectives: Direct reconstruction of parametric PET image estimates voxel-based physiological kinetic parameters, which can potentially achieve superior performance compared with traditional indirect methods. Conventional direct estimation calculates kinetic parameters without any spatial or joint constraints on parametric images, although the quality of parametric image is very sensitive to the variation of pixel-based time activity curves due to the severe ill-poseness of non-linear fitting problem. To address this issue, we propose a novel penalized direct estimation method using a patch-based joint similarity penalty of parametric images to improve the accuracy and robustness of the direct estimation, and applied the proposed method to 18F-FDG study. Furthermore, we developed a method only using partial dynamic data of first and last 15 mins for patients who cannot stay long time in a scanner. We compared the performance of the proposed method with conventional indirect method and penalized direct estimation using a 3-D total variation (TV) penalty in kinetic images; we also compared the performances of the proposed direct estimation method using full and partial dynamic data.
Methods: The cost function of proposed method contains the Poisson likelihood, ridge regression and patch-based joint similarity penalty with kinetic images. We used a separable quadratic surrogate (SQS) algorithm to minimize the Poisson likelihood. Ridge regression is applied to estimate kinetic parameters from dynamic images using non-linear least square (NLS) fitting. To optimize the cost function, we exploit an alternating direction method of multipliers (ADMM) algorithm that provides the convergent solution for optimizing multiple penalty terms in our cost function. To evaluate the proposed method, a healthy subject (a 26 year old, male) was studied with 18F-FDG and imaged in HRRT scanner (Siemens). A bolus injection of 18F-FDG with 185 MBq was administered to the subject via intra-venous and data acquisition was performed in a dynamic scan mode for 90 mins. The image size is 256x256x207 with a pixel resolution of 1.218 mm. We extract the artery region from the image at 1 min as shown in figure 1(a) and the image-based input function is exploited. Full data with 90 mins and partial data with first and last 15 mins were used as shown in figure 1(b). Input function is also partially used in the study with partial dynamic data and two-tissue compartment model is used (K1, k2, k3, k4). We compared qualities of binding potential images (k3/k4) using the conventional indirect reconstruction (NLS after OSEM reconstruction with 8 mm FWHM Gaussian filtering), the penalized direct estimation using a 3-D TV penalty in kinetic images, the proposed method with full data and the proposed method with partial data.
Results: In comparison of binding potential (BP) images in figure 1(c), the quality of BP image using the proposed method was significantly improved and outperforms other methods. In the BP image of indirect method, we could not identify any details. Although the penalized direct estimation using the TV penalty showed better results, the blurring effect was higher because the human brain image is not piece-wise constant. In the proposed method, we could observe the cortex structures and continuously connected in the BP images. Furthermore, the image quality of the proposed method using partial dynamic data was very similar to the result using the full data, which demonstrates the feasibility to estimate the parametric image using only partial data.
Conclusion: The penalized direct estimation of parametric image reconstruction using a patch-based joint similarity penalty outperforms the conventional direct reconstruction methods. Penalized direct estimation using a partial dynamic data can be very useful in clinics, specifically for sick and old patients. In the near future, we will thoroughly validate the proposed method using clinical data. Research Support: