Statistical Methods for the Analysis of Functional Magnetic Resonance Imaging Data

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Proposal: DMS 9505007 PI(s): William Eddy, Chris Genovese Institution: Carnegie Mellon University Title: Statisitcal Methods for the Analysis of Functional Magnetic Resonance Imaging Data Abstract: This research involves the development of new statistical methods for the analysis and interpretation of functional Magnetic Resonance Imaging (fMRI) data. Such data can be viewed as the realization of a spatio-temporal process with a very complicated distributional structure. Models in current use are grossly simplified for both mathematical and computational expediency. The statistical challenges in constructing more realistic models are difficult and manifold. Many revolve around understanding the nature of the noise in the measurements and its effect on successfully detecting regions of neural activation. Noise in the data shows significant spatial and temporal correlations that depend strongly on how the data are collected. Outliers are common, and there are strong sources of systematic variation such as the subject's respiratory and cardiac cycles. Variances in the images depend nonlinearly on the means, and the observed absolute levels of activation tend to shift between sessions because of subject movement. Moreover, all of these difficulties occur for data collected from a single subject; the situation becomes much more complicated if comparisons across subjects are attempted. This research focusses on three general problems in the statistical analysis of fMRI data: 1. The characterization of the response to an activating stimulus in the fMRI signal and the use of this information to build more realistic models and make more precise inferences; 2. The development of robust procedures for identifying active regions that account for the complexity of the underlying spatio-temporal process; and 3. The construction of functional maps within a specified system of the brain (e.g., the visual system) and the use these maps for making predictiv e inference across subjects. Functional Magnetic Resonance Imaging (fMRI) is an exciting new technique that uses advanced technology to obtain images of the active human brain. The technique is of particular interest to cognitive neuropsychologists because of the unique perspective it offers into high-level cognitive processing in humans: areas of the brain that are activated by a stimulus or cognitive task ``light up'' in an fMRI image. This technology will thus play a critical role in understanding how the brain works; however, before this potential can be realized, significant statistical challenges in the interpretation and analysis of fMRI data must be overcome. For example, there is substantial uncertainty in the identification of neural activity from these images and in the attribution of that activity to particular cognitive processes. Moreover, there is a need for new methods of making statistical inferences of scientific interest from these large and complex sets of data. This research focusses on three broad aspects of the general problem: 1. Constructing models for the systematic components of the process that generates the data, 2. Studying and modeling the properties of the noise in the measurements so that analysis and inference can be made more precise, and 3. Developing new methods of inference for addressing interesting scientific questions with massive sets of data that arise from measurements over space and time.