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).
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