Modeling Inter-Subject Variability in fMRI Activation Location: A Bayesian Hierarchical Spatial Model

• Published in: Biometrics Vol. 65; no. 4; pp. 1041 - 1051
• Main Authors: Xu, Lei, Johnson, Timothy D., Nichols, Thomas E., Nee, Derek E.
• Format: Journal Article
• Language: English
• Published: Malden, USA Blackwell Publishing Inc 01.12.2009; Wiley-Blackwell; Blackwell Publishing Ltd
• Subjects: A priori knowledge; Bayes Theorem; Bayesian analysis; Bayesian hierarchical model; Bioinformatics; Biometric Methodology; Biometrics; biometry; Biometry - methods; Brain Mapping - statistics & numerical data; Covariance matrices; Data models; Functional brain mapping; Graphics; Humans; image analysis; Magnetic resonance imaging; Magnetic Resonance Imaging - statistics & numerical data; Markov chain; Markov Chains; Mathematical models; Memory interference; Models, Statistical; Monte Carlo Method; Multi-subject fMRI data analysis; Multilevel models; NMR; Nuclear magnetic resonance; Population distributions; Reversible jump Markov chain Monte Carlo; Spatial mixture model; Spatial models
• ISSN: 0006-341X; 1541-0420; 1541-0420
• DOI: 10.1111/j.1541-0420.2008.01190.x

The aim of this article is to develop a spatial model for multi-subject fMRI data. There has been extensive work on univariate modeling of each voxel for single and multi-subject data, some work on spatial modeling of single-subject data, and some recent work on spatial modeling of multi-subject data. However, there has been no work on spatial models that explicitly account for inter-subject variability in activation locations. In this article, we use the idea of activation centers and model the inter-subject variability in activation locations directly. Our model is specified in a Bayesian hierarchical framework which allows us to draw inferences at all levels: the population level, the individual level, and the voxel level. We use Gaussian mixtures for the probability that an individual has a particular activation. This helps answer an important question that is not addressed by any of the previous methods: What proportion of subjects had a significant activity in a given region. Our approach incorporates the unknown number of mixture components into the model as a parameter whose posterior distribution is estimated by reversible jump Markov chain Monte Carlo. We demonstrate our method with a fMRI study of resolving proactive interference and show dramatically better precision of localization with our method relative to the standard mass-univariate method. Although we are motivated by fMRI data, this model could easily be modified to handle other types of imaging data.