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。本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)为参数估计和统计假设检验制定稳健的最小方差自适应方法的工作已经结束。MVA方法不是在数据分析之前选择特定的估计器或测试统计量，而是通过从大的候选组中为特定数据选择单个最佳(最小方差)估计器或测试统计量来适应每个数据集。与参数方法不同，MVA方法不需要关于潜在总体的统计概率分布的先验假设。(2)用O-15标记水和PET测量脑血流量(CBF)，继续研究水的扩散限制和PET测量视野中必须包括的组织动力学不均质性对测定脑血流(CBF)的影响。目前用于测量CBF的动力学模型没有考虑这两种影响。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。然而，由于模型参数的高度非线性，用标准的非线性最小二乘算法估计参数缺乏稳健性，计算量大。我们已经开发了一种既高效又健壮的替代算法。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：特克海默F，佩蒂格鲁K，索科洛夫L，施密特K(1999年)《一种用于参数估计和假设检验的最小方差自适应技术》，公共统计学家-Simula 28(4)：931-956.特克海默F，佩蒂格鲁K，索科洛夫L，史密斯CB，施密特K(2000年)《用于神经成像数据的多重比较分析的自适应测试统计量的选择》，NeuroImage 12(2)：219-229.施密特KC(2000)《可通过所有隔室之和的频谱分析来分析的线性隔室系统的识别》，在脑PET的生理成像中。A Gjedde，SB Hansen，GM Knudsen，OB Paulson，Eds.学术出版社(在印中)。

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).