Multiple testing for statistical maps remains a critical and challenging problem in brain mapping. Since the false discovery rate (FDR) criterion was introduced to the neuroimaging community a decade ago, many variations have been proposed, mainly to enhance detection power. However, a fundamental geometrical property known as transformation invariance has not been adequately addressed, especially for the voxel-wise FDR. Correction of multiple testing applied after spatial transformation is not necessarily equivalent to transformation applied after correction in the original space. Without the invariance property, assigning different testing spaces will yield different results. We find that normalized residuals of linear models with Gaussian noises are uniformly distributed on a unit high-dimensional sphere, independent of t-statistics and F-statistics. By defining volumetric measure in the hyper-spherical space mapped by normalized residuals, instead of the image's Euclidean space, we can achieve invariant control of the FDR under diffeomorphic transformation. This hyper-spherical measure also reflects intrinsic "volume of randomness" in signals. Experiments with synthetic, semi-synthetic and real images demonstrate that our method significantly reduces FDR inconsistency introduced by the choice of testing spaces.

Diffusion tensor imaging is widely used in brain connectivity research. As more and more studies recruit large numbers of subjects, it is important to design registration methods which are not only theoretically rigorous, but also computationally efficient. However, the requirement of reorienting diffusion tensors complicates and considerably slows down registration procedures, due to the correlated impacts of registration forces at adjacent voxel locations. Based on the diffeomorphic Demons algorithm (Vercauteren , 2009), we propose a fast local trust region algorithm for handling inseparable registration forces for quadratic energy functions. The method guarantees that, at any time and at any voxel location, the velocity is always within its local trust region. This local regularization allows efficient calculation of the transformation update with numeric integration instead of completely solving a large linear system at every iteration. It is able to incorporate exact reorientation and regularization into the velocity optimization, and preserve the linear complexity of the diffeomorphic Demons algorithm. In an experiment with 84 diffusion tensor images involving both pair-wise and group-wise registrations, the proposed algorithm achieves better registration in comparison with other methods solving large linear systems (Yeo , 2009). At the same time, this algorithm reduces the computation time and memory demand tenfold.

Graphical models of brain functional connectivity have matured from confirming a priori hypotheses to an exploratory tool for discovering unknown connectivity. However, exploratory methods must control the error rate of "discovered" connectivity networks. Here we explore an error-rate-control method for graphical models which controls the false-discovery-rate (FDR) of the conditional-dependence relationships that a graphical model encodes. The application of this method to a group analysis of fMRI study on Parkinson's disease shows that it effectively controls the errors introduced by randomness, and yields meaningful and consistent results. The proposed approach appears promising for functional-connectivity modeling and deserves further investigation.

As dynamic connectivity is shown essential for normal brain function and is disrupted in disease, it is critical to develop models for inferring brain effective connectivity from non-invasive (e.g., fMRI) data. Increasingly, (dynamic) Bayesian network (BNs) have been suggested for this purpose due to their flexibility and suitability. However, ultimately extrapolating BN results from one subject to an entire population first requires methods meaningfully addressing inter-subject, within-group variability. Here we explore two group analysis approaches in fMRI using DBNs: one is to construct a group network based on a common structure assumption across individuals, and the other is to identify significant structure features by examining DBNs individually-trained. By investigating real fMRI data from Parkinsons disease (PD) and normal subjects performing a motor task at three progressive levels of difficulty, we noted that both methods detected statistically significant, biologically plausible connectivity between task-related region-of-interest (ROIs) that differed between the PD and normal subjects. However, the second approach was more sensitive, finding more features that were also consistent with prior neuroscience knowledge. Determining highly reproducible DBN nodes/edges across subjects seems promising for inferring altered functional connectivity within a group.

Large intersubject variability is a well-described feature of fMRI studies, making inter-group inference, of critical importance for biological interpretation, difficult. Therefore, traditional approaches involve spatially transforming the data of each subject and heavily spatially smoothing the data. Here we propose an alternate method: after first defining individually-specific regions of interest (ROIs) of each subject, we utilize local linear discriminant analysis (LLDA) to jointly optimize the individually-specific and group linear combinations of ROIs that maximally discriminates between groups characterized by either disease status or task. The proposed method was applied to fMRI data recorded from eight normal subjects performing a motor task, and it was shown to successfully detect activation in multiple cortical and subcortical structures that were not present when the data were traditionally analyzed by warping the data to a common space. We suggest that the proposed method for group fMRI data analysis may be more suitable when examining co-activation in small subcortical regions susceptible to misregistration, or examining older or neurological patient populations.

Modeling the muscle activity patterns in coordinated reaching movements from surface Electromyogram (sEMG) recordings is a key challenge in motor behavior studies. Based on Bayesian Network (BN) modeling of sEMG data, this paper presents a framework for discovering and modeling muscle networks and identifying functional muscle groupings. The learned network is further explored for the purpose of classification. We demonstrate the proposed approach on reaching movements in stroke. We found that the specific muscle triples,and, are selectively recruited during reaching movements and are differentially recruited after stroke. We call these computed muscle triplets "directed synergies" to contrast with synergies that are defined by traditional covariance methods. A BN trained on a single healthy subject completely classified and detected the affected side in all stroke subjects. The proposed approach appears a promising technique for muscle network and synergy analysis in motor control.