Assumptions and validations of statistical tests for functional neuroimaging

Cerebral achromatopsia: colour blindness despite wavelength processing

Cortical colour blindness is caused by brain damage to the ventro-medial occipital and temporal lobes. A possible explanation is that the pathway responsible for transmitting information about wavelength and its subsequent elaboration as colour has been destroyed at the cortical level. However, several signs of chromatic processing persist in an achromatopsic subject who, despite his inability to tell colours apart, can still detect chromatic borders, perceive shape from colour, and discriminate the direction in which a striped pattern moves when the determination of direction requires the viewer to 'know' which stripes have a particular colour. Perhaps only the information about wavelength that leads to conscious awareness of colour has been destroyed. It is unclear whether incomplete achromatopsia is merely a less severe form of the disorder or whether it is qualitatively different, perhaps reflecting impaired colour constancy. In monkeys, removing cortical area V4 impairs performance on colour constancy tasks but, invariably, impairs several other aspects of visual perception. If the lesion that causes total achromatopsia in human subjects corresponds to area V4 in monkeys, it is an unsolved puzzle that a totally achromatopsic subject paradoxically demonstrates certain characteristics of colour constancy, unless his residual performance reflects the much underrated retinal contribution to colour constancy.

Statistical limitations in functional neuroimaging. I. Non-inferential methods and statistical models

Functional neuroimaging (FNI) provides experimental access to the intact living brain making it possible to study higher cognitive functions in humans. In this review and in a companion paper in this issue, we discuss some common methods used to analyse FNI data. The emphasis in both papers is on assumptions and limitations of the methods reviewed. There are several methods available to analyse FNI data indicating that none is optimal for all purposes. In order to make optimal use of the methods available it is important to know the limits of applicability. For the interpretation of FNI results it is also important to take into account the assumptions, approximations and inherent limitations of the methods used. This paper gives a brief overview over some non-inferential descriptive methods and common statistical models used in FNI. Issues relating to the complex problem of model selection are discussed. In general, proper model selection is a necessary prerequisite for the validity of the subsequent statistical inference. The non-inferential section describes methods that, combined with inspection of parameter estimates and other simple measures, can aid in the process of model selection and verification of assumptions. The section on statistical models covers approaches to global normalization and some aspects of univariate, multivariate, and Bayesian models. Finally, approaches to functional connectivity and effective connectivity are discussed. In the companion paper we review issues related to signal detection and statistical inference.

Statistical limitations in functional neuroimaging. II. Signal detection and statistical inference

The field of functional neuroimaging (FNI) methodology has developed into a mature but evolving area of knowledge and its applications have been extensive. A general problem in the analysis of FNI data is finding a signal embedded in noise. This is sometimes called signal detection. Signal detection theory focuses in general on issues relating to the optimization of conditions for separating the signal from noise. When methods from probability theory and mathematical statistics are directly applied in this procedure it is also called statistical inference. In this paper we briefly discuss some aspects of signal detection theory relevant to FNI and, in addition, some common approaches to statistical inference used in FNI. Low-pass filtering in relation to functional-anatomical variability and some effects of filtering on signal detection of interest to FNI are discussed. Also, some general aspects of hypothesis testing and statistical inference are discussed. This includes the need for characterizing the signal in data when the null hypothesis is rejected, the problem of multiple comparisons that is central to FNI data analysis, omnibus tests and some issues related to statistical power in the context of FNI. In turn, random field, scale space, non-parametric and Monte Carlo approaches are reviewed, representing the most common approaches to statistical inference used in FNI. Complementary to these issues an overview and discussion of non-inferential descriptive methods, common statistical models and the problem of model selection is given in a companion paper. In general, model selection is an important prelude to subsequent statistical inference. The emphasis in both papers is on the assumptions and inherent limitations of the methods presented. Most of the methods described here generally serve their purposes well when the inherent assumptions and limitations are taken into account. Significant differences in results between different methods are most apparent in extreme parameter ranges, for example at low effective degrees of freedom or at small spatial autocorrelation. In such situations or in situations when assumptions and approximations are seriously violated it is of central importance to choose the most suitable method in order to obtain valid results.

Analysis of brain activation patterns using a 3-D scale-space primal sketch

A fundamental problem in brain imaging concerns how to define functional areas consisting of neurons that are activated together as populations. We propose that this issue can be ideally addressed by a computer vision tool referred to as the scale-space primal sketch. This concept has the attractive properties that it allows for automatic and simultaneous extraction of the spatial extent and the significance of regions with locally high activity. In addition, a hierarchical nested tree structure of activated regions and subregions is obtained. The subject in this article is to show how the scale-space primal sketch can be used for automatic determination of the spatial extent and the significance of rCBF changes. Experiments show the result of applying this approach to functional PET data, including a preliminary comparison with two more traditional clustering techniques. Compared to previous approaches, the method overcomes the limitations of performing the analysis at a single scale or assuming specific models of the data.

Global, voxel, and cluster tests, by theory and permutation, for a difference between two groups of structural MR images of the brain

We describe almost entirely automated procedures for estimation of global, voxel, and cluster-level statistics to test the null hypothesis of zero neuroanatomical difference between two groups of structural magnetic resonance imaging (MRI) data. Theoretical distributions under the null hypothesis are available for 1) global tissue class volumes; 2) standardized linear model [analysis of variance (ANOVA and ANCOVA)] coefficients estimated at each voxel; and 3) an area of spatially connected clusters generated by applying an arbitrary threshold to a two-dimensional (2-D) map of normal statistics at voxel level. We describe novel methods for economically ascertaining probability distributions under the null hypothesis, with fewer assumptions, by permutation of the observed data. Nominal Type I error control by permutation testing is generally excellent; whereas theoretical distributions may be over conservative. Permutation has the additional advantage that it can be used to test any statistic of interest, such as the sum of suprathreshold voxel statistics in a cluster (or cluster mass), regardless of its theoretical tractability under the null hypothesis. These issues are illustrated by application to MRI data acquired from 18 adolescents with hyperkinetic disorder and 16 control subjects matched for age and gender.

Shape and roughness activate different somatosensory areas in the human brain

Somatosensory stimuli are known to activate the postcentral gyrus, and neurons there fire when the skin is in contact with objects. Also neurons in the lateral fissure, the parietal operculum, fire when rough surfaces are felt. However the localization of somatosensory association areas in humans is largely unknown and differences in functional contributions between somatosensory association areas has not been previously demonstrated. For these reasons the regional cerebral blood flow was measured with 15O-butanol and positron-emission tomography in two groups of young volunteers discriminating the lengths, shapes, and roughness of objects with their right hand. Roughness discrimination activated the lateral parietal opercular cortex significantly more than did length or shape discrimination. A Boolean intersection of the cluster images showing the statistical significant increases of length and shape discrimination demonstrated that shape and length discrimination activated the same cortical field lining the anterior part of the intraparietal sulcus (IPA). Shape and length discrimination activated IPA significantly more than did roughness discriminaton. These findings demonstrate a separation in functional contributions of lateral parietal opercular cortex and IPA. The results indicate different cortical processing streams for the somatosensory submodalities microgeometry and macrogeometry.