Mathematical and Statistical Analysis Techniques for in vivo Imaging Studies

由于疾病或正常大脑中各种通路的激活而产生的脑功能活动图像的变化，只有在量化成像方法基础上的生理和生化过程的速率时，才能明确地解释。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），量化是通过描述示踪剂和被追踪分子代谢途径中生化反应速率的数学模型来进行的。选择最佳的动力学模型是至关重要的，因为使用不适当的模型可能导致量化的重大错误和可能的结果误解。一旦选择了模型，就需要高效、稳健且对测量误差的假设最小的数值程序来准确地估计参数。此外，还需要强有力的统计检验，以便检验实验组之间的显著差异。这个项目的目标是发展更好的技术来处理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)在参数估计和统计假设检验的稳健最小方差自适应（MVA）方法的发展方面完成了工作。MVA方法不是在数据分析之前选择一个特定的估计量或测试统计量，而是通过从一个大的候选组中选择单个最佳（最小方差）估计量或特定数据的测试统计量来适应每个数据集。与参数方法不同，MVA方法不需要对潜在总体的统计概率分布进行先验假设。(2)继续研究水的扩散限制和组织的动力学异质性对O-15标记水和PET测定脑血流量（CBF）的影响，这些影响必须包括在PET测量的视野中。目前用于测量脑血流的动力学模型没有考虑到这两种效应。我们之前用目前使用的动力学模型量化了动力学非均质性导致CBF低估的程度，并开发了一种考虑非均质性并避免CBF低估的替代动力学模型。然而，由于模型参数的高度非线性，用标准非线性最小二乘算法估计参数缺乏鲁棒性，且计算量大。我们已经开发了一种替代算法，既高效又健壮。模拟研究的初步结果表明，该算法提供了混合组织中加权平均血流量和灰质血流量的准确估计。发表：Turkheimer F， Pettigrew K, Sokoloff L, Schmidt K（1999）“参数估计和假设检验的最小方差自适应技术”，《统计学报》28(4):931-956。李建军，李建军，李建军，李建军（2000），“神经影像数据的自适应检验统计量的选择”，《神经影像》12(2):219-229。Schmidt KC（2000）“可以通过对所有隔室的总和进行光谱分析来分析的线性隔室系统的识别”，载于《PET脑生理成像》。A Gjedde, SB Hansen, GM Knudsen, OB Paulson, Eds。学术出版社（出版中）。

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) Work concluded on the development of a robust minimum variance adaptive (MVA) method for parameter estimation and statistical hypothesis testing. Rather than choosing a specific estimator or test statistic prior to the data analysis, the MVA method adapts to each data set by choosing from a large candidate group the single best (minimum variance) estimator or test statistic for the particular data. Unlike parametric methods, the MVA method requires no prior assumptions about the statistical probability distribution of the underlying population. (2) Examination of the effects of the diffusion limitation of water, and of kinetic heterogeneity of tissues necessarily included in field of view of PET measurements, on determinations of cerebral blood flow (CBF) with O-15 labeled water and PET continued. The kinetic model currently used for measurement of CBF does not take either effect into account. 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. Due to the high degree of nonlinearity of the model in its parameters, however, estimation of the parameters with standard nonlinear least squares algorithms lacks robustness and is computationally intensive. We have developed an alternative algorithm that is both efficient and robust. Preliminary results from simulation studies indicate that the algorithm provides accurate estimates of weighted average blood flow and gray matter blood flow in a mixed tissue. Publications: Turkheimer F, Pettigrew K, Sokoloff L, Schmidt K (1999) "A minimum variance adaptive technique for parameter estimation and hypothesis testing," Commun Statist - Simula 28(4): 931-956.Turkheimer F, Pettigrew K, Sokoloff L, Smith CB, Schmidt K (2000) "Selection of an adaptive test statistic for use with multiple comparison analyses of neuroimaging data," Neuroimage 12(2): 219-229.Schmidt KC (2000) "Identification of linear compartmental systems that can be analyzed by spectral analysis of the sum of all compartments", in Physiological Imaging of the Brain with PET. A Gjedde, SB Hansen, GM Knudsen, OB Paulson, Eds. Academic Press (In press).