Multi-site study of additive genetic effects on fractional anisotropy of cerebral white matter: Comparing meta and megaanalytical approaches for data pooling

Combining datasets across independent studies can boost statistical power by increasing the numbers of observations and can achieve more accurate estimates of effect sizes. This is especially important for genetic studies where a large number of observations are required to obtain sufficient power to detect and replicate genetic effects. There is a need to develop and evaluate methods for joint-analytical analyses of rich datasets collected in imaging genetics studies. The ENIGMA-DTI consortium is developing and evaluating approaches for obtaining pooled estimates of heritability through meta-and mega-genetic analytical approaches, to estimate the general additive genetic contributions to the intersubject variance in fractional anisotropy (FA) measured from diffusion tensor imaging (DTI). We used the ENIGMA-DTI data harmonization protocol for uniform processing of DTI data from multiple sites. We evaluated this protocol in five family-based cohorts providing data from a total of 2248 children and adults (ages: 9-85) collected with various imaging protocols. We used the imaging genetics analysis tool, SOLAR-Eclipse, to combine twin and family data from Dutch, Australian and Mexican-American cohorts into one large "mega-family". We showed that heritability estimates may vary from one cohort to another. We used two meta-analytical (the sample-size and standard-error weighted) approaches and a mega-genetic analysis to calculate heritability estimates across-population. We performed leave-one-out analysis of the joint estimates of heritability, removing a different cohort each time to understand the estimate variability. Overall, meta- and mega-genetic analyses of heritability produced robust estimates of heritability.

White matter integrity measured by fractional anisotropy correlates poorly with actual individual fiber anisotropy

Fractional anisotropy (FA), a very widely used measure of fiber integrity based on diffusion tensor imaging (DTI), is a problematic concept as it is influenced by several quantities including the number of dominant fiber directions within each voxel, each fiber's anisotropy, and partial volume effects from neighboring gray matter. High-angular resolution diffusion imaging (HARDI) can resolve more complex diffusion geometries than standard DTI, including fibers crossing or mixing. The tensor distribution function (TDF) can be used to reconstruct multiple underlying fibers per voxel, representing the diffusion profile as a probabilistic mixture of tensors. Here we found that DTIderived mean diffusivity (MD) correlates well with actual individual fiber MD, but DTI-derived FA correlates poorly with actual individual fiber anisotropy, and may be suboptimal when used to detect disease processes that affect myelination. Analysis of the TDFs revealed that almost 40% of voxels in the white matter had more than one dominant fiber present. To more accurately assess fiber integrity in these cases, we here propose the differential diffusivity (DD), which measures the average anisotropy based on all dominant directions in each voxel.

A novel measure of fractional anisotropy based on the tensor distribution function

Fractional anisotropy (FA), a very widely used measure of fiber integrity based on diffusion tensor imaging (DTI), is a problematic concept as it is influenced by several quantities including the number of dominant fiber directions within each voxel, each fiber's anisotropy, and partial volume effects from neighboring gray matter. With High-angular resolution diffusion imaging (HARDI) and the tensor distribution function (TDF), one can reconstruct multiple underlying fibers per voxel and their individual anisotropy measures by representing the diffusion profile as a probabilistic mixture of tensors. We found that FA, when compared with TDF-derived anisotropy measures, correlates poorly with individual fiber anisotropy, and may sub-optimally detect disease processes that affect myelination. By contrast, mean diffusivity (MD) as defined in standard DTI appears to be more accurate. Overall, we argue that novel measures derived from the TDF approach may yield more sensitive and accurate information than DTI-derived measures.

Changes in white matter connectivity following therapy for anomia post stroke

Background. The majority of studies investigating the neural mechanisms underlying treatment-induced recovery in aphasia have focused on the cortical regions associated with language processing. However, the integrity of the white matter connecting these regions may also be crucial to understanding treatment mechanisms. Objective. This study investigated the integrity of the arcuate fasciculus (AF) and uncinate fasciculus (UF) before and after treatment for anomia in people with aphasia. Method. Eight people with aphasia received 12 treatment sessions to improve naming; alternating between phonologically-based and semantic-based tasks, with high angular resolution diffusion imaging conducted pre and post treatment. The mean generalized fractional anisotropy (GFA), a measure of fiber integrity, and number of fibers in the AF and UF were compared pre and post treatment, as well as with a group of 14 healthy older controls. Results. Pre treatment, participants with aphasia had significantly fewer fibers and lower mean GFA in the left AF compared with controls. Post treatment, mean GFA increased in the left AF to be statistically equivalent to controls. Additionally, mean GFA in the left AF pre and post treatment positively correlated with maintenance of the phonologically based treatment. No differences were found in the right AF, or the UF in either hemisphere, between participants with aphasia and controls, and no changes were observed in these tracts following treatment. Conclusions. Anomia treatments may improve the integrity of the white matter connecting cortical language regions. These preliminary results add to the understanding of the mechanisms underlying treatment outcomes in people with aphasia post stroke.

How does angular resolution affect diffusion imaging measures?

A key question in diffusion imaging is how many diffusion-weighted images suffice to provide adequate signal-to-noise ratio (SNR) for studies of fiber integrity. Motion, physiological effects, and scan duration all affect the achievable SNR in real brain images, making theoretical studies and simulations only partially useful. We therefore scanned 50 healthy adults with 105-gradient high-angular resolution diffusion imaging (HARDI) at 4T. From gradient image subsets of varying size (6 ≤ N ≤ 94) that optimized a spherical angular distribution energy, we created SNR plots (versus gradient numbers) for seven common diffusion anisotropy indices: fractional and relative anisotropy (FA, RA), mean diffusivity (MD), volume ratio (VR), geodesic anisotropy (GA), its hyperbolic tangent (tGA), and generalized fractional anisotropy (GFA). SNR, defined in a region of interest in the corpus callosum, was near-maximal with 58, 66, and 62 gradients for MD, FA, and RA, respectively, and with about 55 gradients for GA and tGA. For VR and GFA, SNR increased rapidly with more gradients. SNR was optimized when the ratio of diffusion-sensitized to non-sensitized images was 9.13 for GA and tGA, 10.57 for FA, 9.17 for RA, and 26 for MD and VR. In orientation density functions modeling the HARDI signal as a continuous mixture of tensors, the diffusion profile reconstruction accuracy rose rapidly with additional gradients. These plots may help in making trade-off decisions when designing diffusion imaging protocols.

Comparison of fractional and geodesic anisotropy in diffusion tensor images of 90 monozygotic and dizygotic twins

We used diffusion tensor magnetic resonance imaging (DTI) to reveal the extent of genetic effects on brain fiber microstructure, based on tensor-derived measures, in 22 pairs of monozygotic (MZ) twins and 23 pairs of dizygotic (DZ) twins (90 scans). After Log-Euclidean denoising to remove rank-deficient tensors, DTI volumes were fluidly registered by high-dimensional mapping of co-registered MP-RAGE scans to a geometrically-centered mean neuroanatomical template. After tensor reorientation using the strain of the 3D fluid transformation, we computed two widely used scalar measures of fiber integrity: fractional anisotropy (FA), and geodesic anisotropy (GA), which measures the geodesic distance between tensors in the symmetric positive-definite tensor manifold. Spatial maps of intraclass correlations (r) between MZ and DZ twins were compared to compute maps of Falconer's heritability statistics, i.e. the proportion of population variance explainable by genetic differences among individuals. Cumulative distribution plots (CDF) of effect sizes showed that the manifold measure, GA, comparably the Euclidean measure, FA, in detecting genetic correlations. While maps were relatively noisy, the CDFs showed promise for detecting genetic influences on brain fiber integrity as the current sample expands.

Analytical solutions for the multi-term time-space Caputo-Riesz fractional advection-diffusion equations on a finite domain

Generalized fractional partial differential equations have now found wide application for describing important physical phenomena, such as subdiffusive and superdiffusive processes. However, studies of generalized multi-term time and space fractional partial differential equations are still under development. In this paper, the multi-term time-space Caputo-Riesz fractional advection diffusion equations (MT-TSCR-FADE) with Dirichlet nonhomogeneous boundary conditions are considered. The multi-term time-fractional derivatives are defined in the Caputo sense, whose orders belong to the intervals [0, 1], [1, 2] and [0, 2], respectively. These are called respectively the multi-term time-fractional diffusion terms, the multi-term time-fractional wave terms and the multi-term time-fractional mixed diffusion-wave terms. The space fractional derivatives are defined as Riesz fractional derivatives. Analytical solutions of three types of the MT-TSCR-FADE are derived with Dirichlet boundary conditions. By using Luchko's Theorem (Acta Math. Vietnam., 1999), we proposed some new techniques, such as a spectral representation of the fractional Laplacian operator and the equivalent relationship between fractional Laplacian operator and Riesz fractional derivative, that enabled the derivation of the analytical solutions for the multi-term time-space Caputo-Riesz fractional advection-diffusion equations. © 2012.

Hierarchical clustering of the genetic connectivity matrix reveals the network topology of gene action on brain microstructure: An N=531 twin study

Genetic correlation (rg) analysis determines how much of the correlation between two measures is due to common genetic influences. In an analysis of 4 Tesla diffusion tensor images (DTI) from 531 healthy young adult twins and their siblings, we generalized the concept of genetic correlation to determine common genetic influences on white matter integrity, measured by fractional anisotropy (FA), at all points of the brain, yielding an NxN genetic correlation matrix rg(x,y) between FA values at all pairs of voxels in the brain. With hierarchical clustering, we identified brain regions with relatively homogeneous genetic determinants, to boost the power to identify causal single nucleotide polymorphisms (SNP). We applied genome-wide association (GWA) to assess associations between 529,497 SNPs and FA in clusters defined by hubs of the clustered genetic correlation matrix. We identified a network of genes, with a scale-free topology, that influences white matter integrity over multiple brain regions.

Diffusion tensor of water in model articular cartilage

We used Monte Carlo simulations of Brownian dynamics of water to study anisotropic water diffusion in an idealised model of articular cartilage. The main aim was to use the simulations as a tool for translation of the fractional anisotropy of the water diffusion tensor in cartilage into quantitative characteristics of its collagen fibre network. The key finding was a linear empirical relationship between the collagen volume fraction and the fractional anisotropy of the diffusion tensor. Fractional anisotropy of the diffusion tensor is potentially a robust indicator of the microstructure of the tissue because, in the first approximation, it is invariant to the inclusion of proteoglycans or chemical exchange between free and collagen-bound water in the model. We discuss potential applications of Monte Carlo diffusion-tensor simulations for quantitative biophysical interpretation of MRI diffusion-tensor images of cartilage. Extension of the model to include collagen fibre disorder is also discussed.

Langevin dynamics modeling of the water diffusion tensor in partially aligned collagen networks

In this work, a Langevin dynamics model of the diffusion of water in articular cartilage was developed. Numerical simulations of the translational dynamics of water molecules and their interaction with collagen fibers were used to study the quantitative relationship between the organization of the collagen fiber network and the diffusion tensor of water in model cartilage. Langevin dynamics was used to simulate water diffusion in both ordered and partially disordered cartilage models. In addition, an analytical approach was developed to estimate the diffusion tensor for a network comprising a given distribution of fiber orientations. The key findings are that (1) an approximately linear relationship was observed between collagen volume fraction and the fractional anisotropy of the diffusion tensor in fiber networks of a given degree of alignment, (2) for any given fiber volume fraction, fractional anisotropy follows a fiber alignment dependency similar to the square of the second Legendre polynomial of cos(θ), with the minimum anisotropy occurring at approximately the magic angle (θMA), and (3) a decrease in the principal eigenvalue and an increase in the transverse eigenvalues is observed as the fiber orientation angle θ progresses from 0◦ to 90◦. The corresponding diffusion ellipsoids are prolate for θ < θMA, spherical for θ ≈ θMA, and oblate for θ > θMA. Expansion of the model to include discrimination between the combined effects of alignment disorder and collagen fiber volume fraction on the diffusion tensor is discussed.

Diffusion tensor of water in partially aligned fibre networks

Monte Carlo simulations were used to investigate the relationship between the morphological characteristics and the diffusion tensor (DT) of partially aligned networks of cylindrical fibres. The orientation distributions of the fibres in each network were approximately uniform within a cone of a given semi-angle (θ0). This semi-angle was used to control the degree of alignment of the fibres. The networks studied ranged from perfectly aligned (θ0 = 0) to completely disordered (θ0 = 90°). Our results are qualitatively consistent with previous numerical models in the overall behaviour of the DT. However, we report a non-linear relationship between the fractional anisotropy (FA) of the DT and collagen volume fraction, which is different to the findings from previous work. We discuss our results in the context of diffusion tensor imaging of articular cartilage. We also demonstrate how appropriate diffusion models have the potential to enable quantitative interpretation of the experimentally measured diffusion-tensor FA in terms of collagen fibre alignment distributions.

Genetic and environmental influences on neuroimaging phenotypes: A meta-analytical perspective on twin imaging studies

Because brain structure and function are affected in neurological and psychiatric disorders, it is important to disentangle the sources of variation in these phenotypes. Over the past 15 years, twin studies have found evidence for both genetic and environmental influences on neuroimaging phenotypes, but considerable variation across studies makes it difficult to draw clear conclusions about the relative magnitude of these influences. Here we performed the first meta-analysis of structural MRI data from 48 studies on >1,250 twin pairs, and diffusion tensor imaging data from 10 studies on 444 twin pairs. The proportion of total variance accounted for by genes (A), shared environment (C), and unshared environment (E), was calculated by averaging A, C, and E estimates across studies from independent twin cohorts and weighting by sample size. The results indicated that additive genetic estimates were significantly different from zero for all metaanalyzed phenotypes, with the exception of fractional anisotropy (FA) of the callosal splenium, and cortical thickness (CT) of the uncus, left parahippocampal gyrus, and insula. For many phenotypes there was also a significant influence of C. We now have good estimates of heritability for many regional and lobar CT measures, in addition to the global volumes. Confidence intervals are wide and number of individuals small for many of the other phenotypes. In conclusion, while our meta-analysis shows that imaging measures are strongly influenced by genes, and that novel phenotypes such as CT measures, FA measures, and brain activation measures look especially promising, replication across independent samples and demographic groups is necessary.

Relationship of a variant in the NTRK1 gene to white matter microstructure in young adults

The NTRK1 gene (also known as TRKA) encodes a high-affinity receptor for NGF, a neurotrophin involved in nervous system development and myelination. NTRK1 has been implicated in neurological function via links between the T allele at rs6336 (NTRK1-T) and schizophrenia risk. A variant in the neurotrophin gene, BDNF, was previously associated with white matter integrity in young adults, highlighting the importantce of neurotrophins to white matter development. We hypothesized that NTRK1-T would relate to lower fractional anisotropy in healthy adults. We scanned 391 healthy adult human twins and their siblings (mean age: 23.6 ± 2.2 years; 31 NTRK1-T carriers, 360 non-carriers) using 105-gradient diffusion tensor imaging at 4 tesla. We evaluated in brain white matter how NTRK1-T and NTRK1 rs4661063 allele A (rs4661063-A, which is in moderate linkage disequilibrium with rs6336) related to voxelwise fractional anisotropy-acommondiffusion tensor imaging measure of white matter microstructure. We used mixed-model regression to control for family relatedness, age, and sex. The sample was split in half to test reproducibility of results. The false discovery rate method corrected for voxelwise multiple comparisons. NTRK1-T and rs4661063-A correlated with lower white matter fractional anisotropy, independent of age and sex (multiple-comparisons corrected: false discovery rate critical p=0.038 forNTRK1-Tand0.013 for rs4661063-A). In each half-sample, theNTRK1-T effectwasreplicated in the cingulum, corpus callosum, superior and inferior longitudinal fasciculi, inferior fronto-occipital fasciculus, superior corona radiata, and uncinate fasciculus. Our results suggest that NTRK1-T is important for developing white matter microstructure.

Common Alzheimer's disease risk variant within the CLU gene affects white matter microstructure in young adults

There is a strong genetic risk for late-onset Alzheimer's disease (AD), but so far few gene variants have been identified that reliably contribute to that risk. A newly confirmed genetic risk allele C of the clusterin (CLU) gene variant rs11136000 is carried by ~88% of Caucasians. The C allele confers a 1.16 greater odds of developing late-onset AD than the T allele. AD patients have reductions in regional white matter integrity. We evaluated whether the CLU risk variant was similarly associated with lower white matter integrity in healthy young humans. Evidence of early brain differences would offer a target for intervention decades before symptom onset. We scanned 398 healthy young adults (mean age, 23.6 ± 2.2 years) with diffusion tensor imaging, a variation of magnetic resonance imaging sensitive to white matter integrity in the living brain. We assessed genetic associations using mixed-model regression at each point in the brain to map the profile of these associations with white matter integrity. Each C allele copy of the CLUvariant was associated with lower fractional anisotropy-a widely accepted measure of white matter integrity-in multiple brain regions, including several known to degenerate in AD. These regions included the splenium of the corpus callosum, the fornix, cingulum, and superior and inferior longitudinal fasciculi in both brain hemispheres. Young healthy carriers of the CLU gene risk variant showed a distinct profile of lower white matter integrity that may increase vulnerability to developing AD later in life.