Time series analysis in the time domain and resampling methods for studies of functional magnetic resonance brain imaging

Abstract

Although functional magnetic resonance imaging (fMRI) methods yield rich temporal and spatial data for even a single subject, universally accepted data analysis techniques have not been developed that use all the potential information from fMRI of the brain. Specifically, temporal correlations and confounds are a problem in assessing change within pixels. Spatial correlations across pixels are a problem in determining regions of activation and in correcting for multiple significance tests. We propose methods that address these issues in the analysis of task-related changes in mean signal intensity for individual subjects. Our approach to temporally based problems within pixels is to employ a model based on autoregressive-moving average (ARMA or 'Box-Jenkins') time series methods, which we call CARMA (Contrasts and ARMA). To adjust for performing multiple significance tests across pixels, taking into account between-pixel correlations, we propose adjustment of P values with 'resampling methods.' Our objective is to produce two- or three-dimensional brain maps that provide, at each pixel in the map, an estimated P value with absolute meaning. That is, each P value approximates the probability of having obtained by chance the observed signal effect at that pixel, given that the null hypothesis is true. Simulated and real data examples are provided.