Algebraic relationship between the structural network's Laplacian and functional network's adjacency matrix is preserved in temporal lobe epilepsy subjects.

The relationship between anatomic and resting state functional connectivity of large-scale brain networks is a major focus of current research. In previous work, we introduced a model based on eigen decomposition of the Laplacian which predicts the functional network from the structural network in healthy brains. In this work, we apply the eigen decomposition model to two types of epilepsy; temporal lobe epilepsy associated with mesial temporal sclerosis, and MRI-normal temporal lobe epilepsy. Our findings show that the eigen relationship between function and structure holds for patients with temporal lobe epilepsy as well as normal individuals. These results suggest that the brain under TLE conditions reconfigures and rewires the fine-scale connectivity (a process which the model parameters are putatively sensitive to), in order to achieve the necessary structure-function relationship.

Functional brain connectivity is predictable from anatomic network's Laplacian eigen-structure.

How structural connectivity (SC) gives rise to functional connectivity (FC) is not fully understood. Here we mathematically derive a simple relationship between SC measured from diffusion tensor imaging, and FC from resting state fMRI. We establish that SC and FC are related via (structural) Laplacian spectra, whereby FC and SC share eigenvectors and their eigenvalues are exponentially related. This gives, for the first time, a simple and analytical relationship between the graph spectra of structural and functional networks. Laplacian eigenvectors are shown to be good predictors of functional eigenvectors and networks based on independent component analysis of functional time series. A small number of Laplacian eigenmodes are shown to be sufficient to reconstruct FC matrices, serving as basis functions. This approach is fast, and requires no time-consuming simulations. It was tested on two empirical SC/FC datasets, and was found to significantly outperform generative model simulations of coupled neural masses.

Relating Cortical Atrophy in Temporal Lobe Epilepsy with Graph Diffusion-Based Network Models.

Mesial temporal lobe epilepsy (TLE) is characterized by stereotyped origination and spread pattern of epileptogenic activity, which is reflected in stereotyped topographic distribution of neuronal atrophy on magnetic resonance imaging (MRI). Both epileptogenic activity and atrophy spread appear to follow white matter connections. We model the networked spread of activity and atrophy in TLE from first principles via two simple first order network diffusion models. Atrophy distribution is modeled as a simple consequence of the propagation of epileptogenic activity in one model, and as a progressive degenerative process in the other. We show that the network models closely reproduce the regional volumetric gray matter atrophy distribution of two epilepsy cohorts: 29 TLE subjects with medial temporal sclerosis (TLE-MTS), and 50 TLE subjects with normal appearance on MRI (TLE-no). Statistical validation at the group level suggests high correlation with measured atrophy (R = 0.586 for TLE-MTS, R = 0.283 for TLE-no). We conclude that atrophy spread model out-performs the hyperactivity spread model. These results pave the way for future clinical application of the proposed model on individual patients, including estimating future spread of atrophy, identification of seizure onset zones and surgical planning.

Network diffusion accurately models the relationship between structural and functional brain connectivity networks.

The relationship between anatomic connectivity of large-scale brain networks and their functional connectivity is of immense importance and an area of active research. Previous attempts have required complex simulations which model the dynamics of each cortical region, and explore the coupling between regions as derived by anatomic connections. While much insight is gained from these non-linear simulations, they can be computationally taxing tools for predicting functional from anatomic connectivities. Little attention has been paid to linear models. Here we show that a properly designed linear model appears to be superior to previous non-linear approaches in capturing the brain's long-range second order correlation structure that governs the relationship between anatomic and functional connectivities. We derive a linear network of brain dynamics based on graph diffusion, whereby the diffusing quantity undergoes a random walk on a graph. We test our model using subjects who underwent diffusion MRI and resting state fMRI. The network diffusion model applied to the structural networks largely predicts the correlation structures derived from their fMRI data, to a greater extent than other approaches. The utility of the proposed approach is that it can routinely be used to infer functional correlation from anatomic connectivity. And since it is linear, anatomic connectivity can also be inferred from functional data. The success of our model confirms the linearity of ensemble average signals in the brain, and implies that their long-range correlation structure may percolate within the brain via purely mechanistic processes enacted on its structural connectivity pathways.

Selective vulnerability and resilience to Alzheimer's disease tauopathy as a function of genes and the connectome.

Brain regions in Alzheimer's (AD) exhibit distinct vulnerability to the disease's hallmark pathology, with the entorhinal cortex and hippocampus succumbing early to tau tangles while others like primary sensory cortices remain resilient. The quest to understand how local/regional genetic factors, pathogenesis, and network-mediated spread of pathology together govern this selective vulnerability (SV) or resilience (SR) is ongoing. Although many risk genes in AD are known from gene association and transgenic studies, it is still not known whether and how their baseline expression signatures confer SV or SR to brain structures. Prior analyses have yielded conflicting results, pointing to a disconnect between the location of genetic risk factors and downstream tau pathology. We hypothesize that a full accounting of genes' role in mediating SV/SR would require the modeling of network-based vulnerability, whereby tau misfolds, aggregates, and propagates along fiber projections. We therefore employed an extended network diffusion model (eNDM) and tested it on tau pathology PET data from 196 AD patients from the Alzheimer's Disease Neuroimaging Initiative (ADNI). Thus the fitted eNDM model becomes a reference process from which to assess the role of innate genetic factors. Using the residual (observed - model-predicted) tau as a novel target outcome, we obtained its association with 100 top AD risk-genes, whose baseline spatial transcriptional profiles were obtained from the Allen Human Brain Atlas (AHBA). We found that while many risk genes at baseline showed a strong association with regional tau, many more showed a stronger association with residual tau. This suggests that both direct vulnerability, related to the network, as well as network-independent vulnerability, are conferred by risk genes. We then classified risk genes into four classes: network-related SV (SV-NR), network-independent SV (SV-NI), network-related SR (SR-NR), and network-independent SR (SR-NI). Each class has a distinct spatial signature and associated vulnerability to tau. Remarkably, we found from gene-ontology analyses, that genes in these classes were enriched in distinct functional processes and encompassed different functional networks. These findings offer new insights into the factors governing innate vulnerability or resilience in AD pathophysiology and may prove helpful in identifying potential intervention targets.

Network Analysis on Predicting Mean Diffusivity Change at Group Level in Temporal Lobe Epilepsy.

The two most common types of temporal lobe epilepsy are medial temporal sclerosis (TLE-MTS) epilepsy and MRI-normal temporal lobe epilepsy (TLE-no). TLE-MTS is specified by its stereotyped focus and spread pattern of neuronal damage, with pronounced neuronal loss in the hippocampus. TLE-no exhibits normal-appearing hippocampus and more widespread neuronal loss. In both cases, neuronal loss spread appears to be constrained by the white matter connections. Both varieties of epilepsy reveal pathological abnormalities in increased mean diffusivity (MD). We model MD distribution as a simple consequence of the propagation of neuronal damage. By applying this model on the structural brain connectivity network of healthy subjects, we can predict at group level the MD gray matter change in the epilepsy cohorts relative to a control group. Diffusion tensor imaging images were acquired from 10 patients with TLE-MTS, 11 patients with TLE-no, and 35 healthy subjects. Statistical validation at the group level suggests high correlation with measured neuronal loss (R = 0.56 for the TLE-MTS group and R = 0.364 for the TLE-no group). The results of this exploratory work pave the way for potential future clinical application of the proposed model on individual patients, including predicting neuronal loss spread, identification of seizure onset zones, and helping in surgical planning.

A random-effects model for group-level analysis of diffuse optical brain imaging.

Diffuse optical imaging is a non-invasive technique for measuring changes in blood oxygenation in the brain. This technique is based on the temporally and spatially resolved recording of optical absorption in tissue within the near-infrared range of light. Optical imaging can be used to study functional brain activity similar to functional MRI. However, group level comparisons of brain activity from diffuse optical data are difficult due to registration of optical sensors between subjects. In addition, optical signals are sensitive to inter-subject differences in cranial anatomy and the specific arrangement of optical sensors relative to the underlying functional region. These factors can give rise to partial volume errors and loss of sensitivity and therefore must be accounted for in combining data from multiple subjects. In this work, we describe an image reconstruction approach using a parametric Bayesian model that simultaneously reconstructs group-level images of brain activity in the context of a random-effects analysis. Using this model, we demonstrate that localization accuracy and the statistical effects size of group-level reconstructions can be improved when compared to individualized reconstructions. In this model, we use the Restricted Maximum Likelihood (ReML) method to optimize a Bayesian random-effects model.

Hierarchical Bayesian regularization of reconstructions for diffuse optical tomography using multiple priors.

Diffuse optical tomography (DOT) is a non-invasive brain imaging technique that uses low-levels of near-infrared light to measure optical absorption changes due to regional blood flow and blood oxygen saturation in the brain. By arranging light sources and detectors in a grid over the surface of the scalp, DOT studies attempt to spatially localize changes in oxy- and deoxy-hemoglobin in the brain that result from evoked brain activity during functional experiments. However, the reconstruction of accurate spatial images of hemoglobin changes from DOT data is an ill-posed linearized inverse problem, which requires model regularization to yield appropriate solutions. In this work, we describe and demonstrate the application of a parametric restricted maximum likelihood method (ReML) to incorporate multiple statistical priors into the recovery of optical images. This work is based on similar methods that have been applied to the inverse problem for magnetoencephalography (MEG). Herein, we discuss the adaptation of this model to DOT and demonstrate that this approach provides a means to objectively incorporate reconstruction constraints and demonstrate this approach through a series of simulated numerical examples.