Analysis of FMRI Data (Alejandro Murua, organizer)

Keith Worsley (McGill University, Department of Mathematics and Statistics)
Statistical Analysis of fMRI Data: Smoothing and Degrees of Freedom

Thursday 2:00-2:30, San Rafael

Abstract:

MRI data consists of time series of 3D data (first level) repeated in different sessions on the same subject (second level), and finally repeated on different subjects chosen from a population (third level). In the statistical analysis of fMRI data, the parameter of primary interest is the effect of a contrast; of secondary interest is its standard error, and of tertiary interest is the standard error of this standard error, or equivalently, the degrees of freedom (df). In a ReML (Restricted Maximum Likelihood) analysis, we show how spatial smoothing of ratios of variances and covariances can be used to boost the effective df at each level in the analysis, without smoothing parameters of primary and secondary interest. We use some random field theory to relate the amount of smoothing to the resulting effective df. so that the amount of smoothing can be chosen in advance to achieve a target df, typically 100.


Rajesh Nandy (UCLA, Department of Psychology)
A Semi-parametric Approach to Estimate the Family-wise Error Rate in fMRI Using Resting-state Data

Thursday 2:30-3:00, San Rafael

Abstract:

One of the most important considerations in any hypothesis based fMRI data analysis is to choose the appropriate threshold to construct the activation maps, which is usually based on p-values. However, in fMRI data, there are three factors which necessitate severe corrections in the process of estimating the p-values. First, the fMRI time series at an individual voxel has strong temporal autocorrelation. The second factor is the multiple comparisons problem arising from simultaneously testing tens of thousands of voxels for activation. The third problem, which is not mentioned frequently in the context of adjusting the p-value, is the effect of inherent low frequency processes present even in resting-state data that may introduce a large number of false positives without proper adjustment. A novel and efficient semi-parametric method, using resampling of normalized spacings of order statistics, is introduced to address all the three problems mentioned above. The new method makes very few assumptions and demands minimal computational effort, unlike other existing resampling methods in fMRI. Furthermore, it will be demonstrated that no correction for temporal autocorrelation is necessary in implementing the proposed method. Results using the proposed method are compared with SPM2.


Larissa Stanberry (University of Washington, Department of Statistics)
Murua Alejandro (Department of Mathematics and Statistics, University of Montreal)
Exploring Functional Connectivity with the Potts Model

Thursday 3:00-3:30, San Rafael

Abstract:

In this work we present a clustering method based on the ferromagnetic Potts spin model as an effective tool for functional connectivity analysis. Potts model clustering is ideally suited for exploring fMRI images, since it can combine the information provided by the correlation between the voxel intensities over time with that of the intrinsic spatial neighborhood associated with the fMRI 3D representation. Potts model clustering is a kernel based method that has a number of advantages over existing clustering techniques. It makes no assumption on the within cluster distributions and requires no specification of the number of clusters. The method combines several likely clustering structures, derived from the data, into a final cluster assignment based on what we call the associated "consensus graph," with the number of clusters determined as the number of connected components in the graph. We demonstrate the effectiveness of the method through its application to a conventional periodic finger-tapping task producing functional connectivity maps that reflect motor activations associated with the paradigm. We also use the method in more complex settings to determine functional connectivity networks associated with the anterior and posterior cingulate cortices in a group of nine healthy male subjects. The resulting resting-state functional connectivity networks corroborate previous findings reported in the literature which implicate the functional components identified by our method as key regions in the default-mode brain functioning hypothesis, according to which there exists a network of brain regions firing in synchrony during rest and whose activity is suspended or altered when an explicit task is performed. We also explore the use of spatial information to increase the sensitivity of the clustering method and improve the accuracy of the resulting connectivity maps.