GPU accelerated algorithms for computing matrix function vector products with applications to exponential integrators and fractional diffusion

The efficient computation of matrix function vector products has become an important area of research in recent times, driven in particular by two important applications: the numerical solution of fractional partial differential equations and the integration of large systems of ordinary differential equations. In this work we consider a problem that combines these two applications, in the form of a numerical solution algorithm for fractional reaction diffusion equations that after spatial discretisation, is advanced in time using the exponential Euler method. We focus on the efficient implementation of the algorithm on Graphics Processing Units (GPU), as we wish to make use of the increased computational power available with this hardware. We compute the matrix function vector products using the contour integration method in [N. Hale, N. Higham, and L. Trefethen. Computing Aα, log(A), and related matrix functions by contour integrals. SIAM J. Numer. Anal., 46(5):2505–2523, 2008]. Multiple levels of preconditioning are applied to reduce the GPU memory footprint and to further accelerate convergence. We also derive an error bound for the convergence of the contour integral method that allows us to pre-determine the appropriate number of quadrature points. Results are presented that demonstrate the effectiveness of the method for large two-dimensional problems, showing a speedup of more than an order of magnitude compared to a CPU-only implementation.

Molecular recognition of 2,4,6-trinitrotoluene by 6-aminohexanethiol and surface-enhanced Raman scattering sensor

2,4,6-trinitrotoluene (TNT) is one of the most commonly used nitro aromatic explosives in landmine, military and mining industry. This article demonstrates rapid and selective identification of TNT by surface-enhanced Raman spectroscopy (SERS) using 6-aminohexanethiol (AHT) as a new recognition molecule. First, Meisenheimer complex formation between AHT and TNT is confirmed by the development of pink colour and appearance of new band around 500 nm in UV-visible spectrum. Solution Raman spectroscopy study also supported the AHT:TNT complex formation by demonstrating changes in the vibrational stretching of AHT molecule between 2800-3000 cm−1. For surface enhanced Raman spectroscopy analysis, a self-assembled monolayer (SAM) of AHT is formed over the gold nanostructure (AuNS) SERS substrate in order to selectively capture TNT onto the surface. Electrochemical desorption and X-ray photoelectron studies are performed over AHT SAM modified surface to examine the presence of free amine groups with appropriate orientation for complex formation. Further, AHT and butanethiol (BT) mixed monolayer system is explored to improve the AHT:TNT complex formation efficiency. Using a 9:1 AHT:BT mixed monolayer, a very low detection limit (LOD) of 100 fM TNT was realized. The new method delivers high selectivity towards TNT over 2,4 DNT and picric acid. Finally, real sample analysis is demonstrated by the extraction and SERS detection of 302 pM of TNT from spiked.

Surface electromyography during physical exercise in water: A systematic review

Background Aquatic exercise has been widely used for rehabilitation and functional recovery due to its physical and physiological benefits. However, there is a high variability in reporting on the muscle activity from surface electromyographic (sEMG) signals. The aim of this study is to present an updated review of the literature on the state of the art of muscle activity recorded using sEMG during activities and exercise performed by humans in water. Methods A literature search was performed to identify studies of aquatic exercise movement. Results Twenty-one studies were selected for critical appraisal. Sample size, functional tasks analyzed, and muscles recorded were studied for each paper. The clinical contribution of the paper was evaluated. Conclusions Muscle activity tends to be lower in water-based compared to land-based activity; however more research is needed to understand why. Approaches from basic and applied sciences could support the understanding of relevant aspects for clinical practice.

Prediction of maximal surface electromyographically based voluntary contractions of erector spinae muscles from sonographic measurements during isometric contractions

Objectives Currently, there are no studies combining electromyography (EMG) and sonography to estimate the absolute and relative strength values of erector spinae (ES) muscles in healthy individuals. The purpose of this study was to establish whether the maximum voluntary contraction (MVC) of the ES during isometric contractions could be predicted from the changes in surface EMG as well as in fiber pennation and thickness as measured by sonography. Methods Thirty healthy adults performed 3 isometric extensions at 45° from the vertical to calculate the MVC force. Contractions at 33% and 100% of the MVC force were then used during sonographic and EMG recordings. These measurements were used to observe the architecture and function of the muscles during contraction. Statistical analysis was performed using bivariate regression and regression equations. Results The slope for each regression equation was statistically significant (P < .001) with R2 values of 0.837 and 0.986 for the right and left ES, respectively. The standard error estimate between the sonographic measurements and the regression-estimated pennation angles for the right and left ES were 0.10 and 0.02, respectively. Conclusions Erector spinae muscle activation can be predicted from the changes in fiber pennation during isometric contractions at 33% and 100% of the MVC force. These findings could be essential for developing a regression equation that could estimate the level of muscle activation from changes in the muscle architecture.

A comparison land-water environment of maximal voluntary isometric contraction during manual muscle testing through surface electromyography

Background The aim of this study was to compare through surface electromyographic (sEMG) recordings of the maximum voluntary contraction (MVC) on dry land and in water by manual muscle test (MMT). Method Sixteen healthy right-handed subjects (8 males and 8 females) participated in measurement of muscle activation of the right shoulder. The selected muscles were the cervical erector spinae, trapezius, pectoralis, anterior deltoid, middle deltoid, infraspinatus and latissimus dorsi. The MVC test conditions were random with respect to the order on the land/in water. Results For each muscle, the MVC test was performed and measured through sEMG to determine differences in muscle activation in both conditions. For all muscles except the latissimus dorsi, no significant differences were observed between land and water MVC scores (p = 0.063–0.679) and precision (%Diff = 7–10%) were observed between MVC conditions in the muscles trapezius, anterior deltoid and middle deltoid. Conclusions If the procedure for data collection is optimal, under MMT conditions it appears that comparable MVC sEMG values were achieved on land and in water and the integrity of the EMG recordings were maintained during wáter immersion.

Extending genetic linkage analysis to diffusion tensor images to map single gene effects on brain fiber architecture

We extended genetic linkage analysis - an analysis widely used in quantitative genetics - to 3D images to analyze single gene effects on brain fiber architecture. We collected 4 Tesla diffusion tensor images (DTI) and genotype data from 258 healthy adult twins and their non-twin siblings. After high-dimensional fluid registration, at each voxel we estimated the genetic linkage between the single nucleotide polymorphism (SNP), Val66Met (dbSNP number rs6265), of the BDNF gene (brain-derived neurotrophic factor) with fractional anisotropy (FA) derived from each subject's DTI scan, by fitting structural equation models (SEM) from quantitative genetics. We also examined how image filtering affects the effect sizes for genetic linkage by examining how the overall significance of voxelwise effects varied with respect to full width at half maximum (FWHM) of the Gaussian smoothing applied to the FA images. Raw FA maps with no smoothing yielded the greatest sensitivity to detect gene effects, when corrected for multiple comparisons using the false discovery rate (FDR) procedure. The BDNF polymorphism significantly contributed to the variation in FA in the posterior cingulate gyrus, where it accounted for around 90-95% of the total variance in FA. Our study generated the first maps to visualize the effect of the BDNF gene on brain fiber integrity, suggesting that common genetic variants may strongly determine white matter integrity.

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.

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.

Automated 3D mapping & shape analysis of the lateral ventricles via fluid registration of multiple surface-based atlases

We developed and validated a new method to create automated 3D parametric surface models of the lateral ventricles, designed for monitoring degenerative disease effects in clinical neuroscience studies and drug trials. First we used a set of parameterized surfaces to represent the ventricles in a manually labeled set of 9 subjects' MRIs (atlases). We fluidly registered each of these atlases and mesh models to a set of MRIs from 12 Alzheimer's disease (AD) patients and 14 matched healthy elderly subjects, and we averaged the resulting meshes for each of these images. Validation experiments on expert segmentations showed that (1) the Hausdorff labeling error rapidly decreased, and (2) the power to detect disease-related alterations monotonically improved as the number of atlases, N, was increased from 1 to 9. We then combined the segmentations with a radial mapping approach to localize ventricular shape differences in patients. In surface-based statistical maps, we detected more widespread and intense anatomical deficits as we increased the number of atlases, and we formulated a statistical stopping criterion to determine the optimal value of N. Anterior horn anomalies in Alzheimer's patients were only detected with the multi-atlas segmentation, which clearly outperformed the standard single-atlas approach.

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.

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.

Active fibers: Matching deformable tract templates to diffusion tensor images

Reliable quantitative analysis of white matter connectivity in the brain is an open problem in neuroimaging, with common solutions requiring tools for fiber tracking, tractography segmentation and estimation of intersubject correspondence. This paper proposes a novel, template matching approach to the problem. In the proposed method, a deformable fiber-bundle model is aligned directly with the subject tensor field, skipping the fiber tracking step. Furthermore, the use of a common template eliminates the need for tractography segmentation and defines intersubject shape correspondence. The method is validated using phantom DTI data and applications are presented, including automatic fiber-bundle reconstruction and tract-based morphometry. © 2009 Elsevier Inc. All rights reserved.

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.

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.