Brain fiber architecture, genetics, and intelligence: a high angular resolution diffusion imaging (HARDI) study

We developed an analysis pipeline enabling population studies of HARDI data, and applied it to map genetic influences on fiber architecture in 90 twin subjects. We applied tensor-driven 3D fluid registration to HARDI, resampling the spherical fiber orientation distribution functions (ODFs) in appropriate Riemannian manifolds, after ODF regularization and sharpening. Fitting structural equation models (SEM) from quantitative genetics, we evaluated genetic influences on the Jensen-Shannon divergence (JSD), a novel measure of fiber spatial coherence, and on the generalized fiber anisotropy (GFA) a measure of fiber integrity. With random-effects regression, we mapped regions where diffusion profiles were highly correlated with subjects' intelligence quotient (IQ). Fiber complexity was predominantly under genetic control, and higher in more highly anisotropic regions; the proportion of genetic versus environmental control varied spatially. Our methods show promise for discovering genes affecting fiber connectivity in the brain.

Mapping genetic influences on brain fiber architecture with high angular resolution diffusion imaging (HARDI)

We report the first 3D maps of genetic effects on brain fiber complexity. We analyzed HARDI brain imaging data from 90 young adult twins using an information-theoretic measure, the Jensen-Shannon divergence (JSD), to gauge the regional complexity of the white matter fiber orientation distribution functions (ODF). HARDI data were fluidly registered using Karcher means and ODF square-roots for interpol ation; each subject's JSD map was computed from the spatial coherence of the ODFs in each voxel's neighborhood. We evaluated the genetic influences on generalized fiber anisotropy (GFA) and complexity (JSD) using structural equation models (SEM). At each voxel, genetic and environmental components of data variation were estimated, and their goodness of fit tested by permutation. Color-coded maps revealed that the optimal models varied for different brain regions. Fiber complexity was predominantly under genetic control, and was higher in more highly anisotropic regions. These methods show promise for discovering factors affecting fiber connectivity in the brain.

Sex differences in the human connectome: 4-Tesla high angular resolution diffusion imaging (HARDI) tractography in 234 young adult twins

Cortical connectivity is associated with cognitive and behavioral traits that are thought to vary between sexes. Using high-angular resolution diffusion imaging at 4 Tesla, we scanned 234 young adult twins and siblings (mean age: 23.4 2.0 SD years) with 94 diffusion-encoding directions. We applied a novel Hough transform method to extract fiber tracts throughout the entire brain, based on fields of constant solid angle orientation distribution functions (ODFs). Cortical surfaces were generated from each subject's 3D T1-weighted structural MRI scan, and tracts were aligned to the anatomy. Network analysis revealed the proportions of fibers interconnecting 5 key subregions of the frontal cortex, including connections between hemispheres. We found significant sex differences (147 women/87 men) in the proportions of fibers connecting contralateral superior frontal cortices. Interhemispheric connectivity was greater in women, in line with long-standing theories of hemispheric specialization. These findings may be relevant for ongoing studies of the human connectome.

Development of insula connectivity between ages 12 and 30 revealed by high angular resolution diffusion imaging

The insula, hidden deep within the Sylvian fissures, has proven difficult to study from a connectivity perspective. Most of our current information on the anatomical connectivity of the insula comes from studies of nonhuman primates and post mortem human dissections. To date, only two neuroimaging studies have successfully examined the connectivity of the insula. Here we examine how the connectivity of the insula develops between ages 12 and 30, in 307 young adolescent and adult subjects scanned with 4-Tesla high angular resolution diffusion imaging (HARDI). The density of fiber connections between the insula and the frontal and parietal cortex decreased with age, but the connection density between the insula and the temporal cortex generally increased with age. This trajectory is in line with well-known patterns of cortical development in these regions. In addition, males and females showed different developmental trajectories for the connection between the left insula and the left precentral gyrus. The insula plays many different roles, some of them affected in neuropsychiatric disorders; this information on the insula's connectivity may help efforts to elucidate mechanisms of brain disorders in which it is implicated.

Analyzing multi-fiber reconstruction in high angular resolution diffusion imaging using the tensor distribution function

High-angular resolution diffusion imaging (HARDI) can reconstruct fiber pathways in the brain with extraordinary detail, identifying anatomical features and connections not seen with conventional MRI. HARDI overcomes several limitations of standard diffusion tensor imaging, which fails to model diffusion correctly in regions where fibers cross or mix. As HARDI can accurately resolve sharp signal peaks in angular space where fibers cross, we studied how many gradients are required in practice to compute accurate orientation density functions, to better understand the tradeoff between longer scanning times and more angular precision. We computed orientation density functions analytically from tensor distribution functions (TDFs) which model the HARDI signal at each point as a unit-mass probability density on the 6D manifold of symmetric positive definite tensors. In simulated two-fiber systems with varying Rician noise, we assessed how many diffusionsensitized gradients were sufficient to (1) accurately resolve the diffusion profile, and (2) measure the exponential isotropy (EI), a TDF-derived measure of fiber integrity that exploits the full multidirectional HARDI signal. At lower SNR, the reconstruction accuracy, measured using the Kullback-Leibler divergence, rapidly increased with additional gradients, and EI estimation accuracy plateaued at around 70 gradients.

Visualization tools for high angular resolution diffusion imaging

There is a major effort in medical imaging to develop algorithms to extract information from DTI and HARDI, which provide detailed information on brain integrity and connectivity. As the images have recently advanced to provide extraordinarily high angular resolution and spatial detail, including an entire manifold of information at each point in the 3D images, there has been no readily available means to view the results. This impedes developments in HARDI research, which need some method to check the plausibility and validity of image processing operations on HARDI data or to appreciate data features or invariants that might serve as a basis for new directions in image segmentation, registration, and statistics. We present a set of tools to provide interactive display of HARDI data, including both a local rendering application and an off-screen renderer that works with a web-based viewer. Visualizations are presented after registration and averaging of HARDI data from 90 human subjects, revealing important details for which there would be no direct way to appreciate using conventional display of scalar images.

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.

Development of brain structural connectivity between ages 12 and 30: A 4-Tesla diffusion imaging study in 439 adolescents and adults

Understanding how the brain matures in healthy individuals is critical for evaluating deviations from normal development in psychiatric and neurodevelopmental disorders. The brain's anatomical networks are profoundly re-modeled between childhood and adulthood, and diffusion tractography offers unprecedented power to reconstruct these networks and neural pathways in vivo. Here we tracked changes in structural connectivity and network efficiency in 439 right-handed individuals aged 12 to 30 (211 female/126 male adults, mean age=23.6, SD=2.19; 31 female/24 male 12 year olds, mean age=12.3, SD=0.18; and 25 female/22 male 16 year olds, mean age=16.2, SD=0.37). All participants were scanned with high angular resolution diffusion imaging (HARDI) at 4 T. After we performed whole brain tractography, 70 cortical gyral-based regions of interest were extracted from each participant's co-registered anatomical scans. The proportion of fiber connections between all pairs of cortical regions, or nodes, was found to create symmetric fiber density matrices, reflecting the structural brain network. From those 70 × 70 matrices we computed graph theory metrics characterizing structural connectivity. Several key global and nodal metrics changed across development, showing increased network integration, with some connections pruned and others strengthened. The increases and decreases in fiber density, however, were not distributed proportionally across the brain. The frontal cortex had a disproportionate number of decreases in fiber density while the temporal cortex had a disproportionate number of increases in fiber density. This large-scale analysis of the developing structural connectome offers a foundation to develop statistical criteria for aberrant brain connectivity as the human brain matures.

Investigating brain connectivity heritability in a twin study using diffusion imaging data

Heritability of brain anatomical connectivity has been studied with diffusion-weighted imaging (DWI) mainly by modeling each voxel's diffusion pattern as a tensor (e.g., to compute fractional anisotropy), but this method cannot accurately represent the many crossing connections present in the brain. We hypothesized that different brain networks (i.e., their component fibers) might have different heritability and we investigated brain connectivity using High Angular Resolution Diffusion Imaging (HARDI) in a cohort of twins comprising 328 subjects that included 70 pairs of monozygotic and 91 pairs of dizygotic twins. Water diffusion was modeled in each voxel with a Fiber Orientation Distribution (FOD) function to study heritability for multiple fiber orientations in each voxel. Precision was estimated in a test-retest experiment on a sub-cohort of 39 subjects. This was taken into account when computing heritability of FOD peaks using an ACE model on the monozygotic and dizygotic twins. Our results confirmed the overall heritability of the major white matter tracts but also identified differences in heritability between connectivity networks. Inter-hemispheric connections tended to be more heritable than intra-hemispheric and cortico-spinal connections. The highly heritable tracts were found to connect particular cortical regions, such as medial frontal cortices, postcentral, paracentral gyri, and the right hippocampus.

NOVEL PHANTOMS AND POST-PROCESSING FOR DIFFUSION SPECTRUM IMAGING

High Angular Resolution Diffusion Imaging (HARDI) techniques, including Diffusion Spectrum Imaging (DSI), have been proposed to resolve crossing and other complex fiber architecture in the human brain white matter. In these methods, directional information of diffusion is inferred from the peaks in the orientation distribution function (ODF). Extensive studies using histology on macaque brain, cat cerebellum, rat hippocampus and optic tracts, and bovine tongue are qualitatively in agreement with the DSI-derived ODFs and tractography. However, there are only two studies in the literature which validated the DSI results using physical phantoms and both these studies were not performed on a clinical MRI scanner. Also, the limited studies which optimized DSI in a clinical setting, did not involve a comparison against physical phantoms. Finally, there is lack of consensus on the necessary pre- and post-processing steps in DSI; and ground truth diffusion fiber phantoms are not yet standardized. Therefore, the aims of this dissertation were to design and construct novel diffusion phantoms, employ post-processing techniques in order to systematically validate and optimize (DSI)-derived fiber ODFs in the crossing regions on a clinical 3T MR scanner, and develop user-friendly software for DSI data reconstruction and analysis. Phantoms with a fixed crossing fiber configuration of two crossing fibers at 90° and 45° respectively along with a phantom with three crossing fibers at 60°, using novel hollow plastic capillaries and novel placeholders, were constructed. T2-weighted MRI results on these phantoms demonstrated high SNR, homogeneous signal, and absence of air bubbles. Also, a technique to deconvolve the response function of an individual peak from the overall ODF was implemented, in addition to other DSI post-processing steps. This technique greatly improved the angular resolution of the otherwise unresolvable peaks in a crossing fiber ODF. The effects of DSI acquisition parameters and SNR on the resultant angular accuracy of DSI on the clinical scanner were studied and quantified using the developed phantoms. With a high angular direction sampling and reasonable levels of SNR, quantification of a crossing region in the 90°, 45° and 60° phantoms resulted in a successful detection of angular information with mean ± SD of 86.93°±2.65°, 44.61°±1.6° and 60.03°±2.21° respectively, while simultaneously enhancing the ODFs in regions containing single fibers. For the applicability of these validated methodologies in DSI, improvement in ODFs and fiber tracking from known crossing fiber regions in normal human subjects were demonstrated; and an in-house software package in MATLAB which streamlines the data reconstruction and post-processing for DSI, with easy to use graphical user interface was developed. In conclusion, the phantoms developed in this dissertation offer a means of providing ground truth for validation of reconstruction and tractography algorithms of various diffusion models (including DSI). Also, the deconvolution methodology (when applied as an additional DSI post-processing step) significantly improved the angular accuracy of the ODFs obtained from DSI, and should be applicable to ODFs obtained from the other high angular resolution diffusion imaging techniques.

Fluid registration of diffusion tensor images using information theory

We apply an information-theoretic cost metric, the symmetrized Kullback-Leibler (sKL) divergence, or $J$-divergence, to fluid registration of diffusion tensor images. The difference between diffusion tensors is quantified based on the sKL-divergence of their associated probability density functions (PDFs). Three-dimensional DTI data from 34 subjects were fluidly registered to an optimized target image. To allow large image deformations but preserve image topology, we regularized the flow with a large-deformation diffeomorphic mapping based on the kinematics of a Navier-Stokes fluid. A driving force was developed to minimize the $J$-divergence between the deforming source and target diffusion functions, while reorienting the flowing tensors to preserve fiber topography. In initial experiments, we showed that the sKL-divergence based on full diffusion PDFs is adaptable to higher-order diffusion models, such as high angular resolution diffusion imaging (HARDI). The sKL-divergence was sensitive to subtle differences between two diffusivity profiles, showing promise for nonlinear registration applications and multisubject statistical analysis of HARDI data.

Left versus right hemisphere differences in brain connectivity: 4-Tesla HARDI tractography in 569 twins

Diffusion imaging can map anatomical connectivity in the living brain, offering new insights into fundamental questions such as how the left and right brain hemispheres differ. Anatomical brain asymmetries are related to speech and language abilities, but less is known about left/right hemisphere differences in brain wiring. To assess this, we scanned 457 young adults (age 23.4±2.0 SD years) and 112 adolescents (age 12-16) with 4-Tesla 105-gradient high-angular resolution diffusion imaging. We extracted fiber tracts throughout the brain with a Hough transform method. A 70×70 connectivity matrix was created, for each subject, based on the proportion of fibers intersecting 70 cortical regions. We identified significant differences in the proportions of fibers intersecting left and right hemisphere cortical regions. The degree of asymmetry in the connectivity matrices varied with age, as did the asymmetry in network topology measures such as the small-world effect.

Changes in anatomical brain connectivity between ages 12 and 30: A HARDI study of 467 adolescents and adults

Graph theory can be applied to matrices that represent the brain's anatomical connections, to better understand global properties of anatomical networks, such as their clustering, efficiency and "small-world" topology. Network analysis is popular in adult studies of connectivity, but only one study - in just 30 subjects - has examined how network measures change as the brain develops over this period. Here we assessed the developmental trajectory of graph theory metrics of structural brain connectivity in a cross-sectional study of 467 subjects, aged 12 to 30. We computed network measures from 70×70 connectivity matrices of fiber density generated using whole-brain tractography in 4-Tesla 105-gradient high angular resolution diffusion images (HARDI). We assessed global efficiency and modularity, and both age and age 2 effects were identified. HARDI-based connectivity maps are sensitive to the remodeling and refinement of structural brain connections as the human brain develops.

Heritability of white matter fiber tract shapes: A HARDI study of 198 twins

Genetic analysis of diffusion tensor images (DTI) shows great promise in revealing specific genetic variants that affect brain integrity and connectivity. Most genetic studies of DTI analyze voxel-based diffusivity indices in the image space (such as 3D maps of fractional anisotropy) and overlook tract geometry. Here we propose an automated workflow to cluster fibers using a white matter probabilistic atlas and perform genetic analysis on the shape characteristics of fiber tracts. We apply our approach to large study of 4-Tesla high angular resolution diffusion imaging (HARDI) data from 198 healthy, young adult twins (age: 20-30). Illustrative results show heritability for the shapes of several major tracts, as color-coded maps.

Information-theoretic analysis of brain white matter fiber orientation distribution functions

We propose a new information-theoretic metric, the symmetric Kullback-Leibler divergence (sKL-divergence), to measure the difference between two water diffusivity profiles in high angular resolution diffusion imaging (HARDI). Water diffusivity profiles are modeled as probability density functions on the unit sphere, and the sKL-divergence is computed from a spherical harmonic series, which greatly reduces computational complexity. Adjustment of the orientation of diffusivity functions is essential when the image is being warped, so we propose a fast algorithm to determine the principal direction of diffusivity functions using principal component analysis (PCA). We compare sKL-divergence with other inner-product based cost functions using synthetic samples and real HARDI data, and show that the sKL-divergence is highly sensitive in detecting small differences between two diffusivity profiles and therefore shows promise for applications in the nonlinear registration and multisubject statistical analysis of HARDI data.