MATHEMATICAL AND STATISTICAL ANALYSIS TECHNIQUES FOR IN VIVO IMAGING STUDIES

只有量化了作为成像方法基础的生理和生化过程的速率，才能明确地解释疾病或正常大脑中各种通路激活所产生的大脑功能活动图像的变化。在使用放射性示踪剂的成像方式中，例如正电子发射断层扫描(PET)，通过描述示踪剂和被跟踪分子代谢途径中的生化反应速率的数学模型来进行量化。选择最好的动力学模型是至关重要的，因为使用不适当的模型可能会导致量化上的重大错误和可能对结果的曲解。一旦选择了一个模型，就需要高效、健壮、对测量误差的假设最少的数值程序来准确地估计参数。此外，还需要强大的统计检验，以便能够检查数据在试验组之间的显著差异。该项目的目标是开发更好的技术来解决这些相互关联的数学和统计问题；本年度在以下领域取得了进展：(1)我们扩大了先前的研究，以确定满足应用光谱分析方法所需条件的分室系统。用谱方法确定被研究系统的最佳动力学模型，并估计系统参数。由于PET扫描仪的空间分辨率不足以获得运动和结构上均一的组织区域的测量结果，因此在使用PET进行脑成像研究时，它们尤其重要。因此，描述数据所需的组件总数通常是未知的。目前的光谱方法并不适用于所有的线性隔室系统，在应用光谱技术之前，必须确定所有可能用于描述被分析数据的候选隔室系统满足光谱分析条件。(2)我们已经开始了一项研究，以考察水的扩散限制对用O-15标记水和PET测定脑血流量(CBF)的影响。目前用于测量CBF的动力学模型既没有考虑水的扩散限制，也没有考虑由于PET扫描仪的空间分辨率有限而必须包括在每次测量视野中的组织的动力学异质性。我们以前已经用目前使用的动力学模型量化了动力学异质性导致CBF低估的程度，并开发了一个替代的动力学模型，该模型考虑了异质性，避免了CBF低估。我们现在已经开始量化由于水的扩散限制而低估CBF的程度，并探索在动力学模型中包括修正的可能性。(3)用于参数估计和统计假设检验的稳健最小方差自适应(MVA)方法的发展取得了进一步进展。MVA方法为感兴趣的参数选择具有最小可能不确定性的估计器或检验统计量，即最小可能方差。它是自适应的，因为在数据分析之前没有选择特定的估计器或检验统计量。取而代之的是，考虑了一大组可能的估计器或检验统计量，并且该过程通过选择对被分析的数据集最好的单一估计器或检验统计量来进行调整。与参数方法不同，MVA方法不需要关于潜在总体的统计概率分布的先验假设。发表：特克海默F，索科洛夫L，贝托尔多A，卢西尼亚尼G，瑞维奇M，Jaggi JL，Schmidt K(1998)谱分析中分量和参数分布的估计。大脑血液流动Metab 18：1211-1222 Schmidt K(1999)可以通过对所有隔室的PET输出数据进行频谱分析来分析哪些线性隔室系统？J大脑血流Metab 19：560-569.图克海默F，小矮人K，索科洛夫L，施密特K.一种用于参数估计和假设检验的最小方差自适应技术.《统计通讯--模拟和计算》，印刷中(1999年5月5日接受)。

Changes in images of brain functional activity that are produced by disease or by activation of various pathways in the normal brain can only be unambiguously interpreted if the rates of the physiological and biochemical processes that underlie the imaging method are quantified. In imaging modalities that use radioactive tracers, e.g. positron emission tomography (PET), quantification is carried out by means of a mathematical model that describes the rates of the biochemical reactions in the metabolic pathway of the tracer and traced molecules. Selection of the best kinetic model is critical as the use of an inappropriate model can lead to substantial errors in quantification and possible misinterpretation of results. Once a model is selected, numerical procedures that are efficient, robust, and require minimal assumptions about the errors in the measurements are required to estimate accurately the parameters. Additionally, powerful statistical tests are needed so that the data can be examined for significant differences among experimental groups. The objective of this project is to develop better techniques for addressing these interrelated mathematical and statistical issues; advances in the current year were made in the following areas:(1) We have extended a previous study to identify compartmental systems that meet the conditions necessary for application of spectral methods. Spectral methods are used to determine the best kinetic model for a system under study and estimate the system parameters. They are particularly important for use in brain imaging studies with PET because the spatial resolution of the PET scanner is insufficient to obtain measurements in kinetically and structurally homogeneous tissue regions. The total number of components necessary to describe the data is, therefore, usually unknown. Current spectral methods do not apply to all linear compartmental systems, and it is essential to establish that all possible candidate compartmental systems that may be used for describing the data under analysis meet the spectral analytic conditions prior to application of the spectral technique.(2) We have initiated a study to examine the effects of the diffusion limitation of water on determinations of cerebral blood flow (CBF) with O-15 labeled water and PET. The kinetic model currently used for measurement of CBF does not take into account either the diffusion limitation of water or the kinetic heterogeneity of the tissues necessarily included in the field of view of each measurement due to the limited spatial resolution of the PET scanner. We have previously quantified the extent to which kinetic heterogeneity leads to an underestimation of CBF with the kinetic model currently in use, and developed an alternative kinetic model that takes into account the heterogeneity and avoids the CBF underestimation. We have now begun to quantify the extent of the underestimations of CBF due to the diffusion limitation of water and to explore the possibility of including corrections in the kinetic model.(3) Further progress was made in the development of a robust minimum variance adaptive (MVA) method for parameter estimation and statistical hypothesis testing. The MVA method selects an estimator for the parameter of interest or a test statistic that possesses the minimum possible uncertainty, i.e. the minimum possible variance. It is adaptive in the sense that the specific estimator or test statistic is not chosen prior to the data analysis. Instead, a large group of possible estimators or test statistics is considered, and the procedure adapts by choosing the single estimator or test statistic that is best for the data set under analysis. Unlike parametric methods, the MVA method requires no prior assumptions about the statistical probability distribution of the underlying population. Publications:Turkheimer F, Sokoloff L, Bertoldo A, Lucignani G, Reivich M, Jaggi JL, Schmidt K (1998) Estimation of component and parameter distributions in spectral analysis. J Cereb Blood Flow Metab 18:1211-1222.Schmidt K (1999) Which linear compartmental systems can be analyzed by spectral analysis of PET output data summed over all compartments? J Cereb Blood Flow Metab 19:560-569.Turkheimer F, Pettigrew K, Sokoloff L, Schmidt K. A minimum variance adaptive technique for parameter estimation and hypothesis testing. Communications in Statistics - Simulation and Computation, In press (accepted 5 May 1999).