Mathematical and Statistical Analysis Techniques for in Vivo Imaging Studies

近年来，我们改进了用L-1-C-11亮氨酸和PET估计脑蛋白合成（rCPS）速率的动力学模型分析方法。由于rCPS在不同的生理条件下变化不大，因此动力学分析测定rCPS必须达到尽可能高的准确性。

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.