Center for Advanced Medical Imaging Sciences, Division of Nuclear Medicine and Molecular Imaging, Massachusetts General Hospital, Boston, Massachusetts 02114 and Department of Radiology, Harvard Medical School, Boston, Massachusetts 02114.
Med Phys. 2013 Oct;40(10):102501. doi: 10.1118/1.4819821.
Our research goal is to develop an algorithm to reconstruct cardiac positron emission tomography (PET) kinetic parametric images directly from sinograms and compare its performance with the conventional indirect approach.
Time activity curves of a NCAT phantom were computed according to a one-tissue compartmental kinetic model with realistic kinetic parameters. The sinograms at each time frame were simulated using the activity distribution for the time frame. The authors reconstructed the parametric images directly from the sinograms by optimizing a cost function, which included the Poisson log-likelihood and a spatial regularization terms, using the preconditioned conjugate gradient (PCG) algorithm with the proposed preconditioner. The proposed preconditioner is a diagonal matrix whose diagonal entries are the ratio of the parameter and the sensitivity of the radioactivity associated with parameter. The authors compared the reconstructed parametric images using the direct approach with those reconstructed using the conventional indirect approach.
At the same bias, the direct approach yielded significant relative reduction in standard deviation by 12%-29% and 32%-70% for 50 × 10(6) and 10 × 10(6) detected coincidences counts, respectively. Also, the PCG method effectively reached a constant value after only 10 iterations (with numerical convergence achieved after 40-50 iterations), while more than 500 iterations were needed for CG.
The authors have developed a novel approach based on the PCG algorithm to directly reconstruct cardiac PET parametric images from sinograms, and yield better estimation of kinetic parameters than the conventional indirect approach, i.e., curve fitting of reconstructed images. The PCG method increases the convergence rate of reconstruction significantly as compared to the conventional CG method.
我们的研究目标是开发一种算法，直接从投影数据重建心脏正电子发射断层扫描（PET）动力学参数图像，并比较其性能与传统的间接方法。
根据具有真实动力学参数的单室动力学模型，计算 NCAT 体模的时间活动曲线。使用该时间帧的活性分布模拟每个时间帧的投影数据。作者通过优化成本函数，直接从投影数据重建参数图像，该成本函数包括泊松对数似然和空间正则化项，使用具有所提出的预条件器的预处理共轭梯度（PCG）算法。所提出的预条件器是一个对角矩阵，其对角元素是与参数相关的放射性的参数与灵敏度的比值。作者比较了直接方法重建的参数图像与传统间接方法重建的参数图像。
在相同偏差下，直接方法分别在 50×10（6）和 10×10（6）检测到的符合计数时，标准偏差的相对降低幅度分别为 12%-29%和 32%-70%。此外，PCG 方法仅在 10 次迭代后即可有效达到恒定值（在 40-50 次迭代后达到数值收敛），而 CG 则需要 500 多次迭代。
作者已经开发了一种基于 PCG 算法的新方法，可直接从投影数据重建心脏 PET 参数图像，并比传统的间接方法（即，重建图像的曲线拟合）更好地估计动力学参数。与传统的 CG 方法相比，PCG 方法显著提高了重建的收敛速度。
