Mathematical and Statistical Analysis Techniques for in Vivo Imaging Studies

在这一年里，我们改进了用L-1-C-11亮氨酸和正电子发射计算机断层扫描估计脑蛋白质合成速率的动力学模型分析方法。由于RCP在不同的生理条件下往往只有轻微的变化，因此动力学分析对RCP的测定达到尽可能高的准确度是至关重要的。 PET示踪剂的定量利用隔室模型，该隔室模型通常假设测量活动的组织区域相对于所有相关的生理参数是均匀的。L-1-C-11亮氨酸PET方法的动力学模型最初应用于感兴趣区数据，并包括关于氨基酸浓度、血流、氨基酸的运输和代谢速率以及蛋白质掺入速率的假设(Schmidt等人，2005年)。然而，由于PET的空间分辨率有限，大多数区域包含动态不均匀的组织成分混合物，这可能会对估计结果产生偏差。我们一直在不断改进我们的分析，以最大限度地减少组织异质性对动力学参数和RCP估计的影响。首先，基于组织区域体积的大幅减少应该减少组织异质性的影响的前提，我们开发了一种将均匀组织模型应用于体素水平的PET数据分析的方法(Tomasi等人，2009)。我们发现，在ROI上平均的RCP的体素水平估计比基于ROI时间-活动曲线与同质组织模型直接拟合的估计的偏差要小得多。组织时间-活度曲线的模型拟合表明，组织异质性的影响有所减少，但并未完全消除。然后，我们开发了第二种方法，该方法明确考虑了组织ROI内的异质性，即使用迭代过滤器进行频谱分析(SAIF)。当对ROI水平的数据进行优化并将其应用于ROI时，SAIF-ROI产生了RCP的低偏差、低方差估计(Veronese等人，2010年)。它与Tomasi等人的体素电平方法在计数正常时的表现相当，但在低计数时表现更好。虽然SAIF允许被分析的组织中的异质性，但它确实需要对非均质组织内的动力学参数之间的关系进行假定的约束，以便估计RCP。当ROI内不同组织的动力学最不相同时，这会产生最大的影响。在体素水平上组织之间的差异较小的前提下，我们扩展了SAIF方法并对其进行了优化以用于体素水平数据的分析(Veronese等人，2012)。在正常的国家研究中，使用SAIF-体素估计的RCP比使用SAIF-ROI分析估计的RCP大约高5-15%；受试者间的可变性是可比的。基于仿真研究，我们得出结论，这种差异主要是由于SAIF-ROI低估了RCP，即SAIF-VOXEL的性能更好。我们目前正在比较SAIF-体素和Tomasi等人的体素估计方法在正常和低比率研究中的性能。

In the current year we have refined our kinetic model analysis methods for estimation of rates of Cerebral Protein Synthesis (rCPS) with L-1-C-11 leucine and PET. Because rCPS tends to change only modestly under different physiological conditions, it is essential that kinetic analyses for determination of rCPS achieve the highest possible accuracy. Quantification with PET tracers utilize compartmental models that generally assume that tissue regions in which activity is measured are homogeneous with respect to all relevant physiological parameters. The kinetic model of the L-1-C-11 leucine PET method was originally applied to region-of-interest (ROI) data and included the assumption that tissue in each ROI is homogeneous with respect to concentrations of amino acids, blood flow, rates of transport and metabolism of amino acids, and rates of incorporation into protein (Schmidt et al 2005). Due to the limited spatial resolution of PET, however, most regions contain a kinetically heterogeneous mixture of tissue components; this may bias estimation results. We have been successively refining our analyses to minimize effects of tissue heterogeneity on estimates of the kinetic parameters and rCPS. Firstly, based on the premise that a substantial reduction in the volume of the tissue region examined should reduce the impact of tissue heterogeneity, we developed a method to apply the homogeneous tissue model to the analysis of PET data at the voxel level (Tomasi et al, 2009). We found that voxel-level estimates of rCPS averaged over a ROI were substantially less biased than estimates based on direct fitting of the ROI time-activity curve with a homogeneous tissue model. Model fits of the tissue time-activity curves showed that the effects of tissue heterogeneity had been reduced, but not entirely eliminated. We then developed a second approach that explicitly takes heterogeneity within a tissue ROI into account, spectral analysis with an iterative filter (SAIF). When optimized for and applied to ROI-level data, SAIF-ROI produced low bias, low variance estimates of rCPS (Veronese et al, 2010). It performed comparably to the voxel-level method of Tomasi et al when countrates are normal, but at low countrates it performed better. Although SAIF allows for heterogeneity in the tissue under analysis, it does require an assumed constraint on the relationship among the kinetic parameters within the heterogeneous tissue in order to estimate rCPS. This has the most impact when kinetics of the various tissues within the ROI are most dissimilar. Under the premise that the dissimilarity among the tissues would be less at the voxel level, we extended the SAIF method and optimized it for analysis of voxel-level data (Veronese et al, 2012). In normal countrate studies rCPS estimated with SAIF-voxel was approximately 5-15% higher than with SAIF-ROI analysis; intersubject variability was comparable. Based on simulation studies we conclude that the difference is predominantely due to underestimation of rCPS with SAIF-ROI, i.e., the performance SAIF-voxel is better. We are currently comparing performance of SAIF-voxel with that of the voxelwise estimation method of Tomasi et al in normal and low countrate studies.