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Statistical Parametric Mapping |
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Karl J Friston |
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Wellcome Dept. of Imaging Neuroscience |
This chapter is about making regionally specific inferences in neuroimaging. These inferences may be about differences expressed when comparing one group of subjects to another or, within subjects, over a sequence of observations. They may pertain to structural differences (e.g. in voxel-based morphometry - Ashburner and Friston 2000) or neurophysiological indices of brain functions (e.g. fMRI). The principles of data analysis are very similar for all of these applications and constitute the subject of this chapter. We will focus on the analysis of fMRI time-series because this covers most of the issues that are likely to be encountered in other modalities. Generally, the analysis of structural images and PET scans is simpler because they do not have to deal with correlated errors, from one scan to the next.
A general issue, in data analysis, is the relationship between the neurobiological hypothesis one posits and the statistical models adopted to test that hypothesis. This chapter begins by reviewing the distinction between functional specialization and integration and how these principles serve as the motivation for most analyses of neuroimaging data. We will address the design and analysis of neuroimaging studies from both these perspectives but note that both have to be integrated for a full understanding of brain mapping results.
Statistical parametric mapping is generally used to identify functionally specialized brain regions and is the most prevalent approach to characterizing functional anatomy and disease-related changes. The alternative perspective, namely that provided by functional integration, requires a different set of [multivariate] approaches that examine the relationship between changes in activity in one brain area and another. Statistical parametric mapping is a voxel-based approach, employing classical inference, to make some comment about regionally specific responses to experimental factors. In order to assign an observed response to a particular brain structure, or cortical area, the data must conform to a known anatomical space. Before considering statistical modeling, this chapter deals briefly with how a time-series of images are realigned and mapped into some standard anatomical space (e.g. a stereotactic space). The general ideas behind statistical parametric mapping are then described and illustrated with attention to the different sorts of inferences that can be made with different experimental designs. fMRI is special, in the sense that the data lend themselves to a signal processing perspective. This can be exploited to ensure that both the design and analysis are as efficient as possible. Linear time invariant models provide the bridge between inferential models employed by statistical mapping and conventional signal processing approaches. Temporal autocorrelations in noise processes represent another important issue, specific to fMRI, and approaches to maximizing efficiency in the context of serially correlated error terms will be discussed. Nonlinear models of evoked hemodynamics will be considered here because they can be used to indicate when the assumptions behind linear models are violated. fMRI can capture data very fast (in relation to other imaging techniques), engendering the opportunity to measure event-related responses. The distinction between event and epoch-related designs will be discussed from the point of view of efficiency and the constraints provided by nonlinear characterizations. Before considering multivariate analyses we will close the discussion of inferences, about regionally specific effects, by looking at the distinction between fixed and random-effect analyses and how this relates to inferences about the subjects studied or the population from which these subjects came. The final section will deal with functional integration using models of effective connectivity and other multivariate approaches.