Measuring brain functions : statistical tests for neuroimaging data

Abstract

This thesis is about statistical methods for functional neuroimaging data. With functional neuroimaging, here understood as PET and fMRI, the activity of the human brain can be studied in vivo. The statistical methods described in this work are used to investigate the relationships between the measured signals and the experimental conditions, and to make statistical inference about these relationships.

The signals measured with PET and fMRI are only indirectly related to the activity of the nerve cells. To be able to correctly interpret functional neuroimaging data it is therefore crucial to understand the relations between these signals and the neuronal activity. The thesis contains an in-depth discussion of this relationship with references to the literature.

To do successful experiments, not only must we know what we measure but also how to relate the measurements to the experimental conditions under which they are obtained. This is the issue of statistical modeling. The work presented here describes the most commonly used models and discusses these critically.

A novel approach to the statistical modeling of fMRI data is described. This approach is based on treating the fMRI data sets as being four dimensional. The main benefit of the suggested approach is the minimum dependency on assumptions, both regarding the temporal behavior of the signal and the properties of the noise.

Due to the randomness present in the functional neuroimaging data, statistical methods need also to be applied in inference making. Thus, when an experiment is done, some method of deciding if there are any changes due to the experimental conditions is needed. Moreover, if there are such changes, it is often desirable to know where those changes occurred. In the thesis, novel methods to do statistical inference are presented, both so-called voxel-wise and multivariate methods.

The voxel-wise methods proposed in this thesis are based on a so called Monte- Carlo approach. Two different ways of generating data sets that represent the null hypothesis are described. These methods differ in the assumptions that they make about the data. The methods are compared to other available methods and are shown to work well under most circumstances.

The thesis also contains a description of how to do hypothesis testing with multivariate linear models. Standard tests are not immediately applicable to functional neuroimaging data since the number of variables is much larger than the number of observations. A general method of generating tests in this situation is described.