Hierarchical topological network analysis of anatomical human brain connectivity and differences related to sex and kinship

Modern non-invasive brain imaging technologies, such as diffusion weighted magnetic resonance imaging (DWI), enable the mapping of neural fiber tracts in the white matter, providing a basis to reconstruct a detailed map of brain structural connectivity networks. Brain connectivity networks differ from random networks in their topology, which can be measured using small worldness, modularity, and high-degree nodes (hubs). Still, little is known about how individual differences in structural brain network properties relate to age, sex, or genetic differences. Recently, some groups have reported brain network biomarkers that enable differentiation among individuals, pairs of individuals, and groups of individuals. In addition to studying new topological features, here we provide a unifying general method to investigate topological brain networks and connectivity differences between individuals, pairs of individuals, and groups of individuals at several levels of the data hierarchy, while appropriately controlling false discovery rate (FDR) errors. We apply our new method to a large dataset of high quality brain connectivity networks obtained from High Angular Resolution Diffusion Imaging (HARDI) tractography in 303 young adult twins, siblings, and unrelated people. Our proposed approach can accurately classify brain connectivity networks based on sex (93% accuracy) and kinship (88.5% accuracy). We find statistically significant differences associated with sex and kinship both in the brain connectivity networks and in derived topological metrics, such as the clustering coefficient and the communicability matrix.

Genetic clustering on the hippocampal surface for genome-wide association studies

Imaging genetics aims to discover how variants in the human genome influence brain measures derived from images. Genome-wide association scans (GWAS) can screen the genome for common differences in our DNA that relate to brain measures. In small samples, GWAS has low power as individual gene effects are weak and one must also correct for multiple comparisons across the genome and the image. Here we extend recent work on genetic clustering of images, to analyze surface-based models of anatomy using GWAS. We performed spherical harmonic analysis of hippocampal surfaces, automatically extracted from brain MRI scans of 1254 subjects. We clustered hippocampal surface regions with common genetic influences by examining genetic correlations (r(g)) between the normalized deformation values at all pairs of surface points. Using genetic correlations to cluster surface measures, we were able to boost effect sizes for genetic associations, compared to clustering with traditional phenotypic correlations using Pearson's r.

Bivariate genome-wide association study of genetically correlated neuroimaging phenotypes from DTI and MRI through a seemingly unrelated regression model

Large multisite efforts (e.g., the ENIGMA Consortium), have shown that neuroimaging traits including tract integrity (from DTI fractional anisotropy, FA) and subcortical volumes (from T1-weighted scans) are highly heritable and promising phenotypes for discovering genetic variants associated with brain structure. However, genetic correlations (rg) among measures from these different modalities for mapping the human genome to the brain remain unknown. Discovering these correlations can help map genetic and neuroanatomical pathways implicated in development and inherited risk for disease. We use structural equation models and a twin design to find rg between pairs of phenotypes extracted from DTI and MRI scans. When controlling for intracranial volume, the caudate as well as related measures from the limbic system - hippocampal volume - showed high rg with the cingulum FA. Using an unrelated sample and a Seemingly Unrelated Regression model for bivariate analysis of this connection, we show that a multivariate GWAS approach may be more promising for genetic discovery than a univariate approach applied to each trait separately.

Discovery of genes that affect human brain connectivity: A genome-wide analysis of the connectome

Human brain connectivity is disrupted in a wide range of disorders from Alzheimer's disease to autism but little is known about which specific genes affect it. Here we conducted a genome-wide association for connectivity matrices that capture information on the density of fiber connections between 70 brain regions. We scanned a large twin cohort (N=366) with 4-Tesla high angular resolution diffusion imaging (105-gradient HARDI). Using whole brain HARDI tractography, we extracted a relatively sparse 70×70 matrix representing fiber density between all pairs of cortical regions automatically labeled in co-registered anatomical scans. Additive genetic factors accounted for 1-58% of the variance in connectivity between 90 (of 122) tested nodes. We discovered genome-wide significant associations between variants and connectivity. GWAS permutations at various levels of heritability, and split-sample replication, validated our genetic findings. The resulting genes may offer new leads for mechanisms influencing aberrant connectivity and neurodegeneration. © 2012 IEEE.

Genetic influences on brain asymmetry: A DTI study of 374 twins and siblings

Brain asymmetry, or the structural and functional specialization of each brain hemisphere, has fascinated neuroscientists for over a century. Even so, genetic and environmental factors that influence brain asymmetry are largely unknown. Diffusion tensor imaging (DTI) now allows asymmetry to be studied at a microscopic scale by examining differences in fiber characteristics across hemispheres rather than differences in structure shapes and volumes. Here we analyzed 4. Tesla DTI scans from 374 healthy adults, including 60 monozygotic twin pairs, 45 same-sex dizygotic pairs, and 164 mixed-sex DZ twins and their siblings; mean age: 24.4 years ± 1.9 SD). All DTI scans were nonlinearly aligned to a geometrically-symmetric, population-based image template. We computed voxel-wise maps of significant asymmetries (left/right differences) for common diffusion measures that reflect fiber integrity (fractional and geodesic anisotropy; FA, GA and mean diffusivity, MD). In quantitative genetic models computed from all same-sex twin pairs (N=210 subjects), genetic factors accounted for 33% of the variance in asymmetry for the inferior fronto-occipital fasciculus, 37% for the anterior thalamic radiation, and 20% for the forceps major and uncinate fasciculus (all L > R). Shared environmental factors accounted for around 15% of the variance in asymmetry for the cortico-spinal tract (R > L) and about 10% for the forceps minor (L > R). Sex differences in asymmetry (men > women) were significant, and were greatest in regions with prominent FA asymmetries. These maps identify heritable DTI-derived features, and may empower genome-wide searches for genetic polymorphisms that influence brain asymmetry.

Genetics of anisotropy asymmetry: Registration and sample size effects

Brain asymmetry has been a topic of interest for neuroscientists for many years. The advent of diffusion tensor imaging (DTI) allows researchers to extend the study of asymmetry to a microscopic scale by examining fiber integrity differences across hemispheres rather than the macroscopic differences in shape or structure volumes. Even so, the power to detect these microarchitectural differences depends on the sample size and how the brain images are registered and how many subjects are studied. We fluidly registered 4 Tesla DTI scans from 180 healthy adult twins (45 identical and fraternal pairs) to a geometrically-centered population mean template. We computed voxelwise maps of significant asymmetries (left/right hemisphere differences) for common fiber anisotropy indices (FA, GA). Quantitative genetic models revealed that 47-62% of the variance in asymmetry was due to genetic differences in the population. We studied how these heritability estimates varied with the type of registration target (T1- or T2-weighted) and with sample size. All methods consistently found that genetic factors strongly determined the lateralization of fiber anisotropy, facilitating the quest for specific genes that might influence brain asymmetry and fiber integrity.

Genetics of path lengths in brain connectivity networks: HARDI-based maps in 457 adults

Brain connectivity analyses are increasingly popular for investigating organization. Many connectivity measures including path lengths are generally defined as the number of nodes traversed to connect a node in a graph to the others. Despite its name, path length is purely topological, and does not take into account the physical length of the connections. The distance of the trajectory may also be highly relevant, but is typically overlooked in connectivity analyses. Here we combined genotyping, anatomical MRI and HARDI to understand how our genes influence the cortical connections, using whole-brain tractography. We defined a new measure, based on Dijkstra's algorithm, to compute path lengths for tracts connecting pairs of cortical regions. We compiled these measures into matrices where elements represent the physical distance traveled along tracts. We then analyzed a large cohort of healthy twins and show that our path length measure is reliable, heritable, and influenced even in young adults by the Alzheimer's risk gene, CLU.

Genetic influences on sulcal patterns of the brain

We present a shape-space approach for analyzing genetic influences on the shapes of the sulcal folding patterns on the cortex. Sulci are represented as continuously parameterized functions in a shape space, and shape differences between sulci are obtained via geodesics between them. The resulting statistical shape analysis framework is used not only to construct populations averages, but also used to compute meaningful correlations within and across groups of sulcal shapes. More importantly, we present a new algorithm that extends the traditional Euclidean estimate of the intra-class correlation to the geometric shape space, thereby allowing us to study heritability of sulcal shape traits for a population of 193 twin pairs. This new methodology reveals strong genetic influences on the sulcal geometry of the cortex.

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.

Tensor-based analysis of genetic influences on brain integrity using DTI in 100 twins

Information from the full diffusion tensor (DT) was used to compute voxel-wise genetic contributions to brain fiber microstructure. First, we designed a new multivariate intraclass correlation formula in the log-Euclidean framework. We then analyzed used the full multivariate structure of the tensor in a multivariate version of a voxel-wise maximum-likelihood structural equation model (SEM) that computes the variance contributions in the DTs from genetic (A), common environmental (C) and unique environmental (E) factors. Our algorithm was tested on DT images from 25 identical and 25 fraternal twin pairs. After linear and fluid registration to a mean template, we computed the intraclass correlation and Falconer's heritability statistic for several scalar DT-derived measures and for the full multivariate tensors. Covariance matrices were found from the DTs, and inputted into SEM. Analyzing the full DT enhanced the detection of A and C effects. This approach should empower imaging genetics studies that use DTI.

The multivariate A/C/E model and the genetics of fiber architecture

We present a new algorithm to compute the voxel-wise genetic contribution to brain fiber microstructure using diffusion tensor imaging (DTI) in a dataset of 25 monozygotic (MZ) twins and 25 dizygotic (DZ) twin pairs (100 subjects total). First, the structural and DT scans were linearly co-registered. Structural MR scans were nonlinearly mapped via a 3D fluid transformation to a geometrically centered mean template, and the deformation fields were applied to the DTI volumes. After tensor re-orientation to realign them to the anatomy, we computed several scalar and multivariate DT-derived measures including the geodesic anisotropy (GA), the tensor eigenvalues and the full diffusion tensors. A covariance-weighted distance was measured between twins in the Log-Euclidean framework [2], and used as input to a maximum-likelihood based algorithm to compute the contributions from genetics (A), common environmental factors (C) and unique environmental ones (E) to fiber architecture. Quanititative genetic studies can take advantage of the full information in the diffusion tensor, using covariance weighted distances and statistics on the tensor manifold.

Multivariate variance-components analysis in DTI

Twin studies are a major research direction in imaging genetics, a new field, which combines algorithms from quantitative genetics and neuroimaging to assess genetic effects on the brain. In twin imaging studies, it is common to estimate the intraclass correlation (ICC), which measures the resemblance between twin pairs for a given phenotype. In this paper, we extend the commonly used Pearson correlation to a more appropriate definition, which uses restricted maximum likelihood methods (REML). We computed proportion of phenotypic variance due to additive (A) genetic factors, common (C) and unique (E) environmental factors using a new definition of the variance components in the diffusion tensor-valued signals. We applied our analysis to a dataset of Diffusion Tensor Images (DTI) from 25 identical and 25 fraternal twin pairs. Differences between the REML and Pearson estimators were plotted for different sample sizes, showing that the REML approach avoids severe biases when samples are smaller. Measures of genetic effects were computed for scalar and multivariate diffusion tensor derived measures including the geodesic anisotropy (tGA) and the full diffusion tensors (DT), revealing voxel-wise genetic contributions to brain fiber microstructure.

Best individual template selection from deformation tensor minimization

We study the influence of the choice of template in tensor-based morphometry. Using 3D brain MR images from 10 monozygotic twin pairs, we defined a tensor-based distance in the log-Euclidean framework [1] between each image pair in the study. Relative to this metric, twin pairs were found to be closer to each other on average than random pairings, consistent with evidence that brain structure is under strong genetic control. We also computed the intraclass correlation and associated permutation p-value at each voxel for the determinant of the Jacobian matrix of the transformation. The cumulative distribution function (cdf) of the p-values was found at each voxel for each of the templates and compared to the null distribution. Surprisingly, there was very little difference between CDFs of statistics computed from analyses using different templates. As the brain with least log-Euclidean deformation cost, the mean template defined here avoids the blurring caused by creating a synthetic image from a population, and when selected from a large population, avoids bias by being geometrically centered, in a metric that is sensitive enough to anatomical similarity that it can even detect genetic affinity among anatomies.

Genetic architecture of subcortical brain regions: Common and region-specific genetic contributions

Understanding the aetiology of patterns of variation within and covariation across brain regions is key to advancing our understanding of the functional, anatomical and developmental networks of the brain. Here we applied multivariate twin modelling and principal component analysis (PCA) to investigate the genetic architecture of the size of seven subcortical regions (caudate nucleus, thalamus, putamen, pallidum, hippocampus, amygdala and nucleus accumbens) in a genetically informative sample of adolescents and young adults (N=1038; mean age=21.6±3.2years; including 148 monozygotic and 202 dizygotic twin pairs) from the Queensland Twin IMaging (QTIM) study. Our multivariate twin modelling identified a common genetic factor that accounts for all the heritability of intracranial volume (0.88) and a substantial proportion of the heritability of all subcortical structures, particularly those of the thalamus (0.71 out of 0.88), pallidum (0.52 out of 0.75) and putamen (0.43 out of 0.89). In addition, we also found substantial region-specific genetic contributions to the heritability of the hippocampus (0.39 out of 0.79), caudate nucleus (0.46 out of 0.78), amygdala (0.25 out of 0.45) and nucleus accumbens (0.28 out of 0.52). This provides further insight into the extent and organization of subcortical genetic architecture, which includes developmental and general growth pathways, as well as the functional specialization and maturation trajectories that influence each subcortical region. This multivariate twin study identifies a common genetic factor that accounts for all the heritability of intracranial volume (0.88) and a substantial proportion of the heritability of all subcortical structures, particularly those of the thalamus (0.71 out of 0.88), pallidum (0.52 out of 0.75) and putamen (0.43 out of 0.89). In parallel, it also describes substantial region-specific genetic contributions to the heritability of the hippocampus (0.39 out of 0.79), caudate nucleus (0.46 out of 0.78), amygdala (0.25 out of 0.45) and nucleus accumbens (0.28 out of 0.52).

A comprehensive neuropsychiatric study of elderly twins: The Older Australian Twins Study

The Older Australian Twins Study (OATS) was recently initiated to investigate genetic and environmental factors and their associations and interactions in healthy brain ageing and ageing-related neurocognitive disorders. The study extends the classic MZ-DZ design to include one or two equivalently aged siblings for each twin pair and utilizes the rich resources of the Australian Twin Registry. The study has a number of distinguishing features including comprehensive psychiatric, neuropsychological, cardiovascular, metabolic, and neuroimaging assessments, a longitudinal design and links with a brain donor program. The study measures many behavioral and environmental factors, but in particular lifetime physical and mental activity, physical and psychological trauma, loss of parent early in life, later losses and life events, early-life socioeconomic environment, alcohol and drug use, occupational exposure, and nutrition. It also includes comprehensive cardiovascular assessment, blood biochemistry, genetics and proteomics. The socio-demographic and health data on the first 172 pairs of twins participating in this study are presented. Prevalence of mild cognitive impairment is 12.8% and of dementia 1.5% in the sample. The target sample size is 1000, with at least 400 pairs of twins aged 65-90 years. The cohort will be assessed every two years, with in-depth assessments being repeated. OATS offers an excellent opportunity for collaboration with other similar studies as well as researchers who share the same interests.