Multi-site genetic analysis of diffusion images and voxelwise heritability analysis: A pilot project of the ENIGMA-DTI working group

The ENIGMA (Enhancing NeuroImaging Genetics through Meta-Analysis) Consortium was set up to analyze brain measures and genotypes from multiple sites across the world to improve the power to detect genetic variants that influence the brain. Diffusion tensor imaging (DTI) yields quantitative measures sensitive to brain development and degeneration, and some common genetic variants may be associated with white matter integrity or connectivity. DTI measures, such as the fractional anisotropy (FA) of water diffusion, may be useful for identifying genetic variants that influence brain microstructure. However, genome-wide association studies (GWAS) require large populations to obtain sufficient power to detect and replicate significant effects, motivating a multi-site consortium effort. As part of an ENIGMA-DTI working group, we analyzed high-resolution FA images from multiple imaging sites across North America, Australia, and Europe, to address the challenge of harmonizing imaging data collected at multiple sites. Four hundred images of healthy adults aged 18-85 from four sites were used to create a template and corresponding skeletonized FA image as a common reference space. Using twin and pedigree samples of different ethnicities, we used our common template to evaluate the heritability of tract-derived FA measures. We show that our template is reliable for integrating multiple datasets by combining results through meta-analysis and unifying the data through exploratory mega-analyses. Our results may help prioritize regions of the FA map that are consistently influenced by additive genetic factors for future genetic discovery studies. Protocols and templates are publicly available at (http://enigma.loni.ucla.edu/ongoing/dti-working-group/).

Diffusion imaging protocol effects on genetic associations

Large multi-site image-analysis studies have successfully discovered genetic variants that affect brain structure in tens of thousands of subjects scanned worldwide. Candidate genes have also associated with brain integrity, measured using fractional anisotropy in diffusion tensor images (DTI). To evaluate the heritability and robustness of DTI measures as a target for genetic analysis, we compared 417 twins and siblings scanned on the same day on the same high field scanner (4-Tesla) with two protocols: (1) 94-directions; 2mm-thick slices, (2) 27-directions; 5mm-thickness. Using mean FA in white matter ROIs and FA skeletons derived using FSL, we (1) examined differences in voxelwise means, variances, and correlations among the measures; and (2) assessed heritability with structural equation models, using the classical twin design. FA measures from the genu of the corpus callosum were highly heritable, regardless of protocol. Genome-wide analysis of the genu mean FA revealed differences across protocols in the top associations.

Automatic clustering of white matter fibers in brain diffusion mri with an application to genetics

To understand factors that affect brain connectivity and integrity, it is beneficial to automatically cluster white matter (WM) fibers into anatomically recognizable tracts. Whole brain tractography, based on diffusion-weighted MRI, generates vast sets of fibers throughout the brain; clustering them into consistent and recognizable bundles can be difficult as there are wide individual variations in the trajectory and shape of WM pathways. Here we introduce a novel automated tract clustering algorithm based on label fusion - a concept from traditional intensity-based segmentation. Streamline tractography generates many incorrect fibers, so our top-down approach extracts tracts consistent with known anatomy, by mapping multiple hand-labeled atlases into a new dataset. We fuse clustering results from different atlases, using a mean distance fusion scheme. We reliably extracted the major tracts from 105-gradient high angular resolution diffusion images (HARDI) of 198 young normal twins. To compute population statistics, we use a pointwise correspondence method to match, compare, and average WM tracts across subjects. We illustrate our method in a genetic study of white matter tract heritability in twins.

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.

Diffusion indices on magnetic resonance imaging and neuropsychological performance in amnestic mild cognitive impairment

Background: Magnetic resonance diffusion tensor imaging (DTI) shows promise in the early detection of microstructural pathophysiological changes in the brain. Objectives: To measure microstructural differences in the brains of participants with amnestic mild cognitive impairment (MCI) compared with an age-matched control group using an optimised DTI technique with fully automated image analysis tools and to investigate the correlation between diffusivity measurements and neuropsychological performance scores across groups. Methods: 34 participants (17 participants with MCI, 17 healthy elderly adults) underwent magnetic resonance imaging (MRI)-based DTI. To control for the effects of anatomical variation, diffusion images of all participants were registered to standard anatomical space. Significant statistical differences in diffusivity measurements between the two groups were determined on a pixel-by-pixel basis using gaussian random field theory. Results: Significantly raised mean diffusivity measurements (p<0.001) were observed in the left and right entorhinal cortices (BA28), posterior occipital-parietal cortex (BA18 and BA19), right parietal supramarginal gyrus (BA40) and right frontal precentral gyri (BA4 and BA6) in participants with MCI. With respect to fractional anisotropy, participants with MCI had significantly reduced measurements (p<0.001) in the limbic parahippocampal subgyral white matter, right thalamus and left posterior cingulate. Pearson's correlation coefficients calculated across all participants showed significant correlations between neuropsychological assessment scores and regional measurements of mean diffusivity and fractional anisotropy. Conclusions: DTI-based diffusivity measures may offer a sensitive method of detecting subtle microstructural brain changes associated with preclinical Alzheimer's disease.

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.

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.

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.

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.

Innovation in Road Building: Removing Obstacles for Diffusion of Novel Building Products

How can obstacles to innovation be overcome in road construction? Using a focus group methodology, and based on two prior rounds of empirical work, the analysis in this chapter generates a set of four key solutions to two main construction innovation obstacles: (1) restrictive tender assessment and (2) disagreement over who carries the risk of new product failure. The four key solutions uncovered were: 1) pre-project product certification; 2) past innovation performance assessment; 3) earlier involvement of product suppliers and road asset operators; and 4) performance-based specifications. Additional research is suggested in order to illicit deeper insights into possible solutions to construction innovation obstacles, and should emphasise furthering the theoretical interpretation of empirical phenomena.

Fractional diffusion models of cardiac electrical propagation: Role of structural heterogeneity in dispersion of repolarization

Impulse propagation in biological tissues is known to be modulated by structural heterogeneity. In cardiac muscle, improved understanding on how this heterogeneity influences electrical spread is key to advancing our interpretation of dispersion of repolarization. We propose fractional diffusion models as a novel mathematical description of structurally heterogeneous excitable media, as a means of representing the modulation of the total electric field by the secondary electrical sources associated with tissue inhomogeneities. Our results, analysed against in vivo human recordings and experimental data of different animal species, indicate that structural heterogeneity underlies relevant characteristics of cardiac electrical propagation at tissue level. These include conduction effects on action potential (AP) morphology, the shortening of AP duration along the activation pathway and the progressive modulation by premature beats of spatial patterns of dispersion of repolarization. The proposed approach may also have important implications in other research fields involving excitable complex media.

Functional localization of the human color center by decreased water displacement using diffusion-weighted fMRI

Introduction Decreased water displacement following increased neural activity has been observed using diffusion-weighted functional MRI (DfMRI) at high b-values. The physiological mechanisms underlying the diffusion signal change may be unique from the standard blood oxygenation level-dependent (BOLD) contrast and closer to the source of neural activity. Whether DfMRI reflects neural activity more directly than BOLD outside the primary cerebral regions remains unclear. Methods Colored and achromatic Mondrian visual stimuli were statistically contrasted to functionally localize the human color center Area V4 in neurologically intact adults. Spatial and temporal properties of DfMRI and BOLD activation were examined across regions of the visual cortex. Results At the individual level, DfMRI activation patterns showed greater spatial specificity to V4 than BOLD. The BOLD activation patterns were more prominent in the primary visual cortex than DfMRI, where activation was localized to the ventral temporal lobe. Temporally, the diffusion signal change in V4 and V1 both preceded the corresponding hemodynamic response, however the early diffusion signal change was more evident in V1. Conclusions DfMRI may be of use in imaging applications implementing cognitive subtraction paradigms, and where highly precise individual functional localization is required.

Preliminary investigations into the use of a functionalised polymer to reduce diffusion in Fricke gel dosimeters

Purpose A modification of the existing PVA-​FX hydrogel has been made to investigate the use of a functionalised polymer in a Fricke gel dosimetry system to decrease Fe3+ diffusion. Methods The chelating agent, xylenol orange, was chem. bonded to the gelling agent, polyvinyl alc. (PVA) to create xylenol orange functionalised PVA (XO-​PVA)​. A gel was created from the XO-​PVA (20​% w​/v) with ferrous sulfate (0.4 mM) and sulfuric acid (50 mM)​. Results This resulted in an optical d. dose sensitivity of 0.014 Gy-​1, an auto-​oxidn. rate of 0.0005 h-​1, and a diffusion rate of 0.129 mm2 h-​1; an 8​% redn. compared to the original PVA-​FX gel, which in practical terms adds approx. 1 h to the time span between irradn. and accurate read-​out. Conclusions Because this initial method of chem. bonding xylenol orange to polyvinyl alc. has inherently low conversion, the improvement on existing gel systems is minimal when compared to the drawbacks. More efficient methods of functionalising polyvinyl alc. with xylenol orange must be developed for this system to gain clin. relevance.

Bias reduction using stochastic approximation

The paper studies stochastic approximation as a technique for bias reduction. The proposed method does not require approximating the bias explicitly, nor does it rely on having independent identically distributed (i.i.d.) data. The method always removes the leading bias term, under very mild conditions, as long as auxiliary samples from distributions with given parameters are available. Expectation and variance of the bias-corrected estimate are given. Examples in sequential clinical trials (non-i.i.d. case), curved exponential models (i.i.d. case) and length-biased sampling (where the estimates are inconsistent) are used to illustrate the applications of the proposed method and its small sample properties.