Surface area and cortical thickness descriptors reveal different attributes of the structural human brain networks.

Recently, a related morphometry-based connection concept has been introduced using local mean cortical thickness and volume to study the underlying complex architecture of the brain networks. In this article, the surface area is employed as a morphometric descriptor to study the concurrent changes between brain structures and to build binarized connectivity graphs. The statistical similarity in surface area between pair of regions was measured by computing the partial correlation coefficient across 186 normal subjects of the Cuban Human Brain Mapping Project. We demonstrated that connectivity matrices obtained follow a small-world behavior for two different parcellations of the brain gray matter. The properties of the connectivity matrices were compared to the matrices obtained using the mean cortical thickness for the same cortical parcellations. The topology of the cortical thickness and surface area networks were statistically different, demonstrating that both capture distinct properties of the interaction or different aspects of the same interaction (mechanical, anatomical, chemical, etc.) between brain structures. This finding could be explained by the fact that each descriptor is driven by distinct cellular mechanisms as result of a distinct genetic origin. To our knowledge, this is the first time that surface area is used to study the morphological connectivity of brain networks.

Approximate average head models for EEG source imaging.

We examine the performance of approximate models (AM) of the head in solving the EEG inverse problem. The AM are needed when the individual's MRI is not available. We simulate the electric potential distribution generated by cortical sources for a large sample of 305 subjects, and solve the inverse problem with AM. Statistical comparisons are carried out with the distribution of the localization errors. We propose several new AM. These are the average of many individual realistic MRI-based models, such as surface-based models or lead fields. We demonstrate that the lead fields of the AM should be calculated considering source moments not constrained to be normal to the cortex. We also show that the imperfect anatomical correspondence between all cortices is the most important cause of localization errors. Our average models perform better than a random individual model or the usual average model in the MNI space. We also show that a classification based on race and gender or head size before averaging does not significantly improve the results. Our average models are slightly better than an existing AM with shape guided by measured individual electrode positions, and have the advantage of not requiring such measurements. Among the studied models, the Average Lead Field seems the most convenient tool in large and systematical clinical and research studies demanding EEG source localization, when MRI are unavailable. This AM does not need a strict alignment between head models, and can therefore be easily achieved for any type of head modeling approach.

Model driven EEG/fMRI fusion of brain oscillations.

This article reviews progress and challenges in model driven EEG/fMRI fusion with a focus on brain oscillations. Fusion is the combination of both imaging modalities based on a cascade of forward models from ensemble of post-synaptic potentials (ePSP) to net primary current densities (nPCD) to EEG; and from ePSP to vasomotor feed forward signal (VFFSS) to BOLD. In absence of a model, data driven fusion creates maps of correlations between EEG and BOLD or between estimates of nPCD and VFFS. A consistent finding has been that of positive correlations between EEG alpha power and BOLD in both frontal cortices and thalamus and of negative ones for the occipital region. For model driven fusion we formulate a neural mass EEG/fMRI model coupled to a metabolic hemodynamic model. For exploratory simulations we show that the Local Linearization (LL) method for integrating stochastic differential equations is appropriate for highly nonlinear dynamics. It has been successfully applied to small and medium sized networks, reproducing the described EEG/BOLD correlations. A new LL-algebraic method allows simulations with hundreds of thousands of neural populations, with connectivities and conduction delays estimated from diffusion weighted MRI. For parameter and state estimation, Kalman filtering combined with the LL method estimates the innovations or prediction errors. From these the likelihood of models given data are obtained. The LL-innovation estimation method has been already applied to small and medium scale models. With improved Bayesian computations the practical estimation of very large scale EEG/fMRI models shall soon be possible.

Inferring multiple maxima in intravoxel white matter fiber distribution.

A new methodology is introduced that characterizes the intravoxel orientation distribution function (ODF) based on a single-fiber model of the diffusion MRI signal. Using a Bayesian framework the probability of finding a fiber in a specific orientation is obtained. The proposed ODF estimation relies on a cigar-like diffusion tensor model, the methodology is thus denominated Bayesian cigar-like diffusion tensor (BCDT). This work makes two major contributions: 1) the study of single-fiber models in detecting fibers with different volume fractions in a voxel, and 2) the introduction of the Nth-root correction to improve the detection of fibers with smaller volume fractions, where N is the number of diffusion MRI measurements. It is demonstrated that the incomplete signal modeling fails to reconstruct the relative fiber volume fractions, especially when the intravoxel diffusion profiles have dissimilar contributions to the diffusion MRI signal. In this situation the fibers with smaller contributions are hardly detectable. The BCDT method proposed here reduces this effect by introducing the Nth-root correction, making multiple fibers estimable. The performance of the new methodology is illustrated using synthetic and real data, as well as the data from a phantom of intersecting capillaries.

A Bayesian framework to identify principal intravoxel diffusion profiles based on diffusion-weighted MR imaging.

In this paper we introduce a new method to characterize the intravoxel anisotropy based on diffusion-weighted imaging (DWI). The proposed solution, under a fully Bayesian formalism, deals with the problem of joint Bayesian Model selection and parameter estimation to reconstruct the principal diffusion profiles or primary fiber orientations in a voxel. We develop an efficient stochastic algorithm based on the reversible jump Markov chain Monte Carlo (RJMCMC) method in order to perform the Bayesian computation. RJMCMC is a good choice for this problem because of its ability to jump between models of different dimensionality. This methodology provides posterior estimates of the parameters of interest (fiber orientation, diffusivities etc) unconditional of the model assumed. It also gives an empirical posterior distribution of the number of primary nerve fiber orientations given the DWI data. Different probability maps can be assessed using this methodology: 1) the intravoxel fiber orientation map (or orientational distribution function) that gives the probability of finding a fiber in a particular spatial orientation; 2) a three-dimensional map of the probability of finding a particular number of fibers in each voxel; 3) a three-dimensional MaxPro (maximum probability) map that provides the most probable number of fibers for each voxel. In order to study the performance and reliability of the presented approach, we tested it on synthetic data; an ex-vivo phantom of intersecting capillaries; and DWI data from a human subject.

Studying the human brain anatomical network via diffusion-weighted MRI and Graph Theory.

Our goal is to study the human brain anatomical network. For this, the anatomical connection probabilities (ACP) between 90 cortical and subcortical brain gray matter areas are estimated from diffusion-weighted Magnetic Resonance Imaging (DW-MRI) techniques. The ACP between any two areas gives the probability that those areas are connected at least by a single nervous fiber. Then, the brain is modeled as a non-directed weighted graph with continuous arc weights given by the ACP matrix. Based on this approach, complex networks properties such as small-world attributes, efficiency, degree distribution, vulnerability, betweenness centrality and motifs composition are studied. The analysis was carried out for 20 right-handed healthy subjects (mean age: 31.10, S.D.: 7.43). According to the results, all networks have small-world and broad-scale characteristics. Additionally, human brain anatomical networks present bigger local efficiency and smaller global efficiency than the corresponding random networks. In a vulnerability and betweenness centrality analysis, the most indispensable and critical anatomical areas were identified: putamens, precuneus, insulas, superior parietals and superior frontals. Interestingly, some areas have a negative vulnerability (e.g. superior temporal poles, pallidums, supramarginals and hechls), which suggest that even at the cost of losing in global anatomical efficiency, these structures were maintained through the evolutionary processes due to their important functions. Finally, symmetrical characteristic building blocks (motifs) of size 3 and 4 were calculated, obtaining that motifs of size 4 are the expanded version of motif of size 3. These results are in agreement with previous anatomical studies in the cat and macaque cerebral cortex.