Towards a spatio-temporal analysis tool for fMRI data

NeuroImage

11, Number

5, 2000, Part 2 of 2 Parts ID

E al@

METHODS

Towards a spatio-temporal

- ANALYSIS

analysis tool for fMR1 data

P.A. De MazPre, M.M. Van Hulle Laboratory of Neuro- and Psychophysiology, Medical School, Campus Gasthuisberg, K. U.Leuven, B-3000 Leuven, Belgium Introduction Most statistical tools for functional neuroimaging. such as fMRI, are used for investigating the relationship between the experimental paradigm and changes in regional brain activity. They usually assume that the voxels in the discretiLed brain image are independently and identically distributed and, thus, that they obey univariate statistics, e.g., as is the case with SPM Ill. Furthermore, in SPM, the fMR1 signals are correlated with the known sequence of conditions by means of a general linear model. and used for constructing a statistical parameter map from which the most significant voxels arc determined. In addition. the fMRI Eignals are smoothened prior to the analysis, in order to improve their signal-to-noise ratio. However, since it is believed that cognitive functions result from interactions between different brain regions, a number of neh concepts and multivariate tools have been developed [2-41. For some of these, the active brain regions are considered to be part of a network. Here, we will introduce a still different approach by considering the spatio-temporal distribution of the recorded fMR1 signals as part of a multivariate, attractor-based dynamical system. Spatio-temporal

approach

In block design fMRI, the input conditions are given in a periodic manner. The resulting roughly periodic fMRI data set can be regarded as one originating from an attractor-based system. In non-linear system dynamics, tools are available for characterizing the complexity of such systems, such as the popular effective dimensionality [5-71. The advantage of such an approach is that we consider the spatial and temporal correlations in one pass and not in two passes as done in SPM. The idea is then to use such a tool in combination with a selection criterion for identifying the voxels that contribute the most to the definition of the attractor. We proceed in two stages: 1. we determine the effective dimensionality of the entire dataset. We have optimized the original Grassberger-Procaccia algorithm in order to be able to handle large data sets: in particular, we use 120 sample scans of the entire brain (500 MB data), which in turn are discretized into 510 K voxels. Except for a normalization over space and time, no other preprocessing, such as smoothing, is performed on the data. Typically, we obtain an effective dimensionality between 18 and 27. 2 we select with our pruning algorithm the voxels for which the corresponding fMRI signals closely approximate the effective dimensionality of the original data set. The selection of the relevant voxels is done with a genetic algorithm, and a preset selection criterion, because algorithms of this kind do not get stuck into local minima and they consider multiple valuable partial solutions from which a better partial solution can be obtained. In effect, by selecting voxels. we perform a dimensionality reduction (less voxels remain). Typically, we are able to reduce the dimensionality by a factor of severai thousands. The key advantages of the new approach are three-fold. First, due to its modular setup, different types of selection criteria can be used, e.g., signal variance, signal energy, ICA decomposition score, The whole pruning algorithm is thoroughly optimized for speed and memory-usage. Secondly, unlike SPM, the recorded fMRI signals are not smoothened and the entire fMRI signal of each voxel contributes to the analysis. In this way, the method is more sensitive in detecting small, isolated groups of active voxels. Third, the pruning phase can be combined with information about the input sequence in order to provide a clear image of the conditionand task-dependence of the recorded fMRI signals. References 1. SPM, Frackowiak R.S.J. et nl., Wellcome Dept. of Cogn. Neurology, University College London. 2. Gold, S., Christian, B., Amdt. S., Zeien. G., Cir.adlo. T.. Johnson. D.I... Flaum. M. Br Andreasen. N.C. I 19OS). HU~,I~UI K)