KINETIC MODELING/MATHEMATICAL ANALYSIS OF PHYSIOLOGICAL & BIOCHEMICAL PROCESSES

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Quantification of physiological and biochemical processes in vivo by use of radioactive tracers requires an appropriate mathematical model to describe the rates of the biochemical reactions in the metabolic pathway of the tracer and traced molecules. Efficient numerical techniques to estimate accurately the parameters of the kinetic model and powerful statistical tests to examine the data for significant differences in rates among different experimental groups are also required. The Laboratory's ongoing modeling effort addresses these interrelated mathematical and statistical issues; advances in the current year were made in the following specific areas: (1) A robust minimum variance adaptive (MVA) method for parameter estimation and statistical hypothesis testing developed in the Laboratory was extended to include a multivariate testing procedure. 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. (2) A new technique was developed to estimate the uncertainty in the components detected by spectral analysis of time series data. Spectral methods, because they do not require the a priori postulation of a kinetic model, but rather are used a posteriori to determine the number of components necessary to describe the data, are particularly important tools for use in studies with positron emission tomography in which the spatial resolution is insufficient to obtain measurements in kinetically and structurally homogeneous tissue regions.