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.

Nonlinear analysis for the pre- and post-yield behaviour of a hybrid structure by a higher-order element with the refined plastic hinge approach

Efficient and accurate geometric and material nonlinear analysis of the structures under ultimate loads is a backbone to the success of integrated analysis and design, performance-based design approach and progressive collapse analysis. This paper presents the advanced computational technique of a higher-order element formulation with the refined plastic hinge approach which can evaluate the concrete and steel-concrete structure prone to the nonlinear material effects (i.e. gradual yielding, full plasticity, strain-hardening effect when subjected to the interaction between axial and bending actions, and load redistribution) as well as the nonlinear geometric effects (i.e. second-order P-d effect and P-D effect, its associate strength and stiffness degradation). Further, this paper also presents the cross-section analysis useful to formulate the refined plastic hinge approach.

The impact of nonlinear pedagogy on physical education teacher education students’ intrinsic motivation

Background: Providing motivationally supportive physical education experiences for learners is crucial since empirical evidence in sport and physical education research has associated intrinsic motivation with positive educational outcomes. Self-determination theory (SDT) provides a valuable framework for examining motivationally supportive physical education experiences through satisfaction of three basic psychological needs: autonomy, competence and relatedness. However, the capacity of the prescriptive teaching philosophy of the dominant traditional physical education teaching approach to effectively satisfy the psychological needs of students to engage in physical education has been questioned. The constraints-led approach (CLA) has been proposed as a viable alternative teaching approach that can effectively support students’ self-motivated engagement in physical education. Purpose: We sought to investigate whether adopting the learning design and delivery of the CLA, guided by key pedagogical principles of nonlinear pedagogy (NLP), would address basic psychological needs of learners, resulting in higher self-reported levels of intrinsic motivation. The claim was investigated using action research. The teacher/researcher delivered two lessons aimed at developing hurdling skills: one taught using the CLA and the other using the traditional approach. Participants and Setting: The main participant for this study was the primary researcher and lead author who is a PETE educator, with extensive physical education teaching experience. A sample of 54 pre-service PETE students undertaking a compulsory second year practical unit at an Australian university was recruited for the study, consisting of an equal number of volunteers from each of two practical classes. A repeated measures experimental design was adopted, with both practical class groups experiencing both teaching approaches in a counterbalanced order. Data collection and analysis: Immediately after participation in each lesson, participants completed a questionnaire consisting of 22 items chosen from validated motivation measures of basic psychological needs and indices of intrinsic motivation, enjoyment and effort. All questionnaire responses were indicated on a 7-point Likert scale. A two-tailed, paired-samples t-test was used to compare the groups’ motivation subscale mean scores for each teaching approach. The size of the effect for each group was calculated using Cohen’s d. To determine whether any significant differences between the subscale mean scores of the two groups was due to an order effect, a two-tailed, independent samples t test was used. Findings: Participants’ reported substantially higher levels of self-determination and intrinsic motivation during the CLA hurdles lesson compared to during the traditional hurdles lesson. Both groups reported significantly higher motivation subscale mean scores for competence, relatedness, autonomy, enjoyment and effort after experiencing the CLA than mean scores reported after experiencing the traditional approach. This significant difference was evident regardless of the order that each teaching approach was experienced. Conclusion: The theoretically based pedagogical principles of NLP that inform learning design and delivery of the CLA may provide teachers and coaches with tools to develop more functional pedagogical climates, which result in students exhibiting more intrinsically motivated behaviours during learning.

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.

Quantification of stability in an agility drill using linear and nonlinear measures of variability

This study implemented linear and nonlinear methods of measuring variability to determine differences in stability of two groups of skilled (n = 10) and unskilled (n = 10) participants performing 3m forward/backward shuttle agility drill. We also determined whether stability measures differed between the forward and backward segments of the drill. Finally, we sought to investigate whether local dynamic stability, measured using largest finite-time Lyapunov exponents, changed from distal to proximal lower extremity segments. Three-dimensional coordinates of five lower extremity markers data were recorded. Results revealed that the Lyapunov exponents were lower (P < 0.05) for skilled participants at all joint markers indicative of higher levels of local dynamic stability. Additionally, stability of motion did not differ between forward and backward segments of the drill (P > 0.05), signifying that almost the same control strategy was used in forward and backward directions by all participants, regardless of skill level. Furthermore, local dynamic stability increased from distal to proximal joints (P < 0.05) indicating that stability of proximal segments are prioritized by the neuromuscular control system. Finally, skilled participants displayed greater foot placement standard deviation values (P < 0.05), indicative of adaptation to task constraints. The results of this study provide new methods for sport scientists, coaches to characterize stability in agility drill performance.

Fourier spectral methods for fractional-in-space reaction-diffusion equations

Fractional differential equations are becoming increasingly used as a powerful modelling approach for understanding the many aspects of nonlocality and spatial heterogeneity. However, the numerical approximation of these models is demanding and imposes a number of computational constraints. In this paper, we introduce Fourier spectral methods as an attractive and easy-to-code alternative for the integration of fractional-in-space reaction-diffusion equations described by the fractional Laplacian in bounded rectangular domains ofRn. The main advantages of the proposed schemes is that they yield a fully diagonal representation of the fractional operator, with increased accuracy and efficiency when compared to low-order counterparts, and a completely straightforward extension to two and three spatial dimensions. Our approach is illustrated by solving several problems of practical interest, including the fractional Allen–Cahn, FitzHugh–Nagumo and Gray–Scott models, together with an analysis of the properties of these systems in terms of the fractional power of the underlying Laplacian operator.

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.