Empirical Bayes estimation of pairwise maximum entropy model for nonlinear brain state dynamics.

The pairwise maximum entropy model (pMEM) has recently gained widespread attention to exploring the nonlinear characteristics of brain state dynamics observed in resting-state functional magnetic resonance imaging (rsfMRI). Despite its unique advantageous features, the practical application of pMEM for individuals is limited as it requires a much larger sample than conventional rsfMRI scans. Thus, this study proposes an empirical Bayes estimation of individual pMEM using the variational expectation-maximization algorithm (VEM-MEM). The performance of the VEM-MEM is evaluated for several simulation setups with various sample sizes and network sizes. Unlike conventional maximum likelihood estimation procedures, the VEM-MEM can reliably estimate the individual model parameters, even with small samples, by effectively incorporating the group information as the prior. As a test case, the individual rsfMRI of children with attention deficit hyperactivity disorder (ADHD) is analyzed compared to that of typically developed children using the default mode network, executive control network, and salient network, obtained from the Healthy Brain Network database. We found that the nonlinear dynamic properties uniquely established on the pMEM differ for each group. Furthermore, pMEM parameters are more sensitive to group differences and are better associated with the behavior scores of ADHD compared to the Pearson correlation-based functional connectivity. The simulation and experimental results suggest that the proposed method can reliably estimate the individual pMEM and characterize the dynamic properties of individuals by utilizing empirical information of the group brain state dynamics.

Bayesian estimation of maximum entropy model for individualized energy landscape analysis of brain state dynamics.

The pairwise maximum entropy model (MEM) for resting state functional MRI (rsfMRI) has been used to generate energy landscape of brain states and to explore nonlinear brain state dynamics. Researches using MEM, however, has mostly been restricted to fixed-effect group-level analyses, using concatenated time series across individuals, due to the need for large samples in the parameter estimation of MEM. To mitigate the small sample problem in analyzing energy landscapes for individuals, we propose a Bayesian estimation of individual MEM using variational Bayes approximation (BMEM). We evaluated the performances of BMEM with respect to sample sizes and prior information using simulation. BMEM showed advantages over conventional maximum likelihood estimation in reliably estimating model parameters for individuals with small sample data, particularly utilizing the empirical priors derived from group data. We then analyzed individual rsfMRI of the Human Connectome Project to show the usefulness of MEM in differentiating individuals and in exploring neural correlates for human behavior. MEM and its energy landscape properties showed high subject specificity comparable to that of functional connectivity. Canonical correlation analysis identified canonical variables for MEM highly associated with cognitive scores. Inter-individual variations of cognitive scores were also reflected in energy landscape properties such as energies, occupation times, and basin sizes at local minima. We conclude that BMEM provides an efficient method to characterize dynamic properties of individuals using energy landscape analysis of individual brain states.

Connectivity-based change point detection for large-size functional networks.

Recent understanding that the brain at rest does not remain in a single state but transiently visits multiple states emphasizes the importance of state changes embedded in the brain network. Due to the effectiveness of larger networks in characterizing brain states, there is an increasing need for a network-based change point detection method that is applicable to large-size networks, particularly those with longer time series. This paper presents a fast and efficient method for detecting change points in the large-size functional networks of resting-state fMRI. To detect change points, a statistic for the covariance change at each time point is tested by a local false discovery rate, estimated based on the empirical null principle using a semiparametric mixture model. We present simulations and empirical analyses of task-based and resting-state fMRI data sets with various network sizes up to 300 nodes selected from the Human Connectome Project database. We demonstrate that the proposed method is not only efficient in detecting change points in large samples of large-size networks but also is less sensitive to the window size selection and provides the consequent identification of the changed edges. The covariance-based change point detection method in this study would be very useful in exploring characteristics of dynamic states in long-term large-size resting-state brain networks.

Detecting Changes in Correlation Networks with Application to Functional Connectivity of fMRI Data.

Research questions in the human sciences often seek to answer if and when a process changes across time. In functional MRI studies, for instance, researchers may seek to assess the onset of a shift in brain state. For daily diary studies, the researcher may seek to identify when a person's psychological process shifts following treatment. The timing and presence of such a change may be meaningful in terms of understanding state changes. Currently, dynamic processes are typically quantified as static networks where edges indicate temporal relations among nodes, which may be variables reflecting emotions, behaviors, or brain activity. Here we describe three methods for detecting changes in such correlation networks from a data-driven perspective. Networks here are quantified using the lag-0 pair-wise correlation (or covariance) estimates as the representation of the dynamic relations among variables. We present three methods for change point detection: dynamic connectivity regression, max-type method, and a PCA-based method. The change point detection methods each include different ways to test if two given correlation network patterns from different segments in time are significantly different. These tests can also be used outside of the change point detection approaches to test any two given blocks of data. We compare the three methods for change point detection as well as the complementary significance testing approaches on simulated and empirical functional connectivity fMRI data examples.

Are brain networks stable during a 24-hour period?

Despite the widespread view of the brain as a large complex network, the dynamicity of the brain network over the course of a day has yet to be explored. To investigate whether the spontaneous human brain network maintains long-term stability throughout a day, we evaluated the intra-class correlation coefficient (ICC) of results from an independent component analysis (ICA), seed correlation analysis, and graph-theoretical analysis of resting state functional MRI, acquired from 12 young adults at three-hour intervals over 24 consecutive hours. According to the ICC of the usage strength of the independent network component defined by the root mean square of the temporal weights of the network components, the default mode network centered at the posterior cingulate cortex and precuneus, the superior parietal, and secondary motor networks showed a high temporal stability throughout the day (ICC>0.5). However, high intra-individual dynamicity was observed in the default mode network, including the anterior cingulate cortex and medial prefrontal cortex or posterior-anterior cingulate cortex, the hippocampal network, and the parietal and temporal networks. Seed correlation analysis showed a highly stable (ICC>0.5) extent of functionally connected regions from the posterior cingulate cortex, but poor stability from the hippocampus throughout the day. Graph-theoretical analysis using local and global network efficiency suggested that local brain networks are temporally stable but that long-range integration behaves dynamically in the course of a day. These results imply that dynamic network properties are a nature of the resting state brain network, which remains to be further researched.

Evaluation of bayesian tensor estimation using tensor coherence.

Fiber tractography, a unique and non-invasive method to estimate axonal fibers within white matter, constructs the putative streamlines from diffusion tensor MRI by interconnecting voxels according to the propagation direction defined by the diffusion tensor. This direction has uncertainties due to the properties of underlying fiber bundles, neighboring structures and image noise. Therefore, robust estimation of the diffusion direction is essential to reconstruct reliable fiber pathways. For this purpose, we propose a tensor estimation method using a Bayesian framework, which includes an a priori probability distribution based on tensor coherence indices, to utilize both the neighborhood direction information and the inertia moment as regularization terms. The reliability of the proposed tensor estimation was evaluated using Monte Carlo simulations in terms of accuracy and precision with four synthetic tensor fields at various SNRs and in vivo human data of brain and calf muscle. Proposed Bayesian estimation demonstrated the relative robustness to noise and the higher reliability compared to the simple tensor regression.

Reorganization of neural circuits in the blind on diffusion direction analysis.

The neural reorganization of the visual cortex of early blind individuals was evaluated using voxel-by-voxel analysis of diffusion tensor images with regard to the diffusion direction, diffusion anisotropy and diffusivity. Reduced anisotropy and increased diffusivity was found mainly in the visual pathways of 18 early blind individuals as opposed to 25 sighted individuals. Alteration of the diffusion direction was detected not only in the visual pathways but also in nonvisual pathways such as the u fibers of the parietal lobe, the sagittal striatum, the pulvinar and the inferior and superior longitudinal fasciculi. The alteration of regional diffusion direction, reduced anisotropy and increased diffusivity in early blind individuals imply the neural reorganization for functional adaptation to the loss of visual input during the early development period.

SENSE factors for reliable cortical thickness measurement.

The purposes of this study were to examine the effect of sensitivity encoding (SENSE) factors on cortical thickness measurements and to determine which SENSE factor to use to reliably measure cortical thickness in 3.0 T and 1.5 T T1-weighted MRI images. The 3D T1-TFE images were acquired from 11 healthy volunteers with 6 different SENSE acceleration factors from 1.0 (without SENSE acceleration) to 4.0 on a 1.5 T scanner, and 9 different SENSE factors from 1.0 to 6.0, plus a second-day 1.0 acquisition on a 3.0 T scanner. Cortical thickness was calculated for the entire cortical surface that was further subdivided into 33 regions. Repeated measures multivariate analysis of variance revealed that the main effect of SENSE factors (F=12.485, df=7, p=0.006) was a significant underestimation of cortical thickness at SENSE 5.0 (p=0.022) and 6.0 (p=0.011) at 3.0 T and at SENSE 4.0 (p<0.000) at 1.5 T. Repeated measures ANOVA showed that thickness measurements at the insula, superior temporal sulcus, the medial part of the superior frontal lobe, and cingulate cortex are highly affected by SENSE factors. SENSE factors affect thickness estimation more significantly at 1.5 T and thus 1.5 T imaging provides less reliable estimates using SENSE techniques. Faster imaging can be done without too much loss of reliability using a high SENSE factor, such as 3.0, at 3.0 T with acquisition time being inversely proportional to the SENSE factor.