Introduction

The aim of this paper is to give an overview of the existing methods based on the General Linear Model (GLM) to assess activity in an fMRI study, resulting in a statistical parametric map. The successive steps of every method are: modelling the response at each voxel by a GLM, then testing a hypothesis (about the parameters of the model) and representing the observed statistic map thresholded at a given level according to the point distribution of the statistic (uncorrected levels) or according to the field distribution of the statistic (corrected levels for local maxima) ¹. The GLM model used can refer to a single subject, one group of subjects or more groups of subjects which can represent different subjects (e.g. male, female) or the same subjects (e.g. placebo, drug A, drug B in a cross-over design). Note that the modelling part is univariate, i.e. is separated for each voxel², and is in fact usually separated for each subject. The paradigm applied is usually well balanced (e.g. the same number of ``OFF'' and ``ON'' scans in a block-design). The simplest approach uses only a $t$-test, and Friston et.al [7] embedded this analysis in a General Linear model to be able to take into account covariates in the analysis. Autocorrelation in fMRI time series requires some changes necessitating also the use of GLM [1,16,17]. Multi-subject fMRI experiment can also be expressed in a GLM framework with different forms according to the approach taken: fixed or random subject analysis. Estimation can be improved using spatial consideration (smoothing) in order to regain some quality of the estimation (spatially smoothed autocorrelation ³). In the context of multi-subject analysis a similar spatial consideration is investigated by Worsley [18] to ``diminish between-subject variability". Section 2 redescribes the classical single subject analysis, for an ON and OFF (block-design) experiment in its simplest approach. Then the multi-subjects (section 3) approaches are explained with fixed-effect and random-effect analyses, and alternatives such as ``conjunction analysis'' [5] and ``variance ratio smoothing'' [18]. One group and two groups analyses are summarised in section 4. These procedures were related to t distributed statistics; section 5 returns to GLM, to redescribe them briefly under general hypothesis testing. It takes also into account time-series autocorrelation, and investigates the case of more than two groups which involves F distributed statistics. The repeated measures aspect of fMRI experiments can also be illustrated in a multivariate model. This point is discussed in the last section of this article introducing also a multivariable multivariate general linear model written to be able to take into account spatial correlation aspects in the model. This last model will be fully described in a later paper.