Assessment of Transverse Isotropy in Clinical-Level CT Images of Trabecular Bone Using the Gradient Structure Tensor

The aim of this study was to develop a GST-based methodology for accurately measuring the degree of transverse isotropy in trabecular bone. Using femoral sub-regions scanned in high-resolution peripheral QCT (HR-pQCT) and clinical-level-resolution QCT, trabecular orientation was evaluated using the mean intercept length (MIL) and the gradient structure tensor (GST) on the HR-pQCT and QCT data, respectively. The influence of local degree of transverse isotropy (DTI) and bone mineral density (BMD) was incorporated into the investigation. In addition, a power based model was derived, rendering a 1:1 relationship between GST and MIL eigenvalues. A specific DTI threshold (DTI thres) was found for each investigated size of region of interest (ROI), above which the estimate of major trabecular direction of the GST deviated no more than 30° from the gold standard MIL in 95% of the remaining ROIs (mean error: 16°). An inverse relationship between ROI size and DTI thres was found for discrete ranges of BMD. A novel methodology has been developed, where transversal isotropic measures of trabecular bone can be obtained from clinical QCT images for a given ROI size, DTI thres and power coefficient. Including DTI may improve future clinical QCT finite-element predictions of bone strength and diagnoses of bone disease.

Modelling of iron-filled magneto-active polymers with a dispersed chain-like microstructure

Magneto-active polymers are a class of smart materials commonly manufactured by mixing micron-sized iron particles in a rubber-like matrix. When cured in the presence of an externally applied magnetic field, the iron particles arrange themselves into chain-like structures that lend an overall anisotropy to the material. It has been observed through electron micrographs and X-ray tomographs that these chains are not always perfect in structure, and may have dispersion due to the conditions present during manufacturing or some undesirable material properties. We model the response of these materials to coupled magneto-mechanical loading in this paper using a probability based structure tensor that accounts for this imperfect anisotropy. The response of the matrix material is decoupled from the chain phase, though still being connected through kinematic constraints. The latter is based on the definition of a 'chain deformation gradient' and a 'chain magnetic field'. We conclude with numerical examples that demonstrate the effect of chain dispersion on the response of the material to magnetoelastic loading.

Impact of a new anisotropic rheology on simulations of Arctic sea ice

new rheology that explicitly accounts for the subcontinuum anisotropy of the sea ice cover is implemented into the Los Alamos sea ice model. This is in contrast to all models of sea ice included in global circulation models that use an isotropic rheology. The model contains one new prognostic variable, the local structure tensor, which quantifies the degree of anisotropy of the sea ice, and two parameters that set the time scale of the evolution of this tensor. The anisotropic rheology provides a subcontinuum description of the mechanical behavior of sea ice and accounts for a continuum scale stress with large shear to compression ratio and tensile stress component. Results over the Arctic of a stand-alone version of the model are presented and anisotropic model sensitivity runs are compared with a reference elasto-visco-plastic simulation. Under realistic forcing sea ice quickly becomes highly anisotropic over large length scales, as is observed from satellite imagery. The influence of the new rheology on the state and dynamics of the sea ice cover is discussed. Our reference anisotropic run reveals that the new rheology leads to a substantial change of the spatial distribution of ice thickness and ice drift relative to the reference standard visco-plastic isotropic run, with ice thickness regionally increased by more than 1 m, and ice speed reduced by up to 50%.

Modelling the rheology of sea ice as a collection of diamond-shaped floes

In polar oceans, seawater freezes to form a layer of sea ice of several metres thickness that can cover up to 8% of the Earth’s surface. The modelled sea ice cover state is described by thickness and orientational distribution of interlocking, anisotropic diamond-shaped ice floes delineated by slip lines, as supported by observation. The purpose of this study is to develop a set of equations describing the mean-field sea ice stresses that result from interactions between the ice floes and the evolution of the ice floe orientation, which are simple enough to be incorporated into a climate model. The sea ice stress caused by a deformation of the ice cover is determined by employing an existing kinematic model of ice floe motion, which enables us to calculate the forces acting on the ice floes due to crushing into and sliding past each other, and then by averaging over all possible floe orientations. We describe the orientational floe distribution with a structure tensor and propose an evolution equation for this tensor that accounts for rigid body rotation of the floes, their apparent re-orientation due to new slip line formation, and change of shape of the floes due to freezing and melting. The form of the evolution equation proposed is motivated by laboratory observations of sea ice failure under controlled conditions. Finally, we present simulations of the evolution of sea ice stress and floe orientation for several imposed flow types. Although evidence to test the simulations against is lacking, the simulations seem physically reasonable.

A continuum anisotropic model of sea-ice dynamics

We develop the essential ingredients of a new, continuum and anisotropic model of sea-ice dynamics designed for eventual use in climate simulation. These ingredients are a constitutive law for sea-ice stress, relating stress to the material properties of sea ice and to internal variables describing the sea-ice state, and equations describing the evolution of these variables. The sea-ice cover is treated as a densely flawed two-dimensional continuum consisting of a uniform field of thick ice that is uniformly permeated with narrow linear regions of thinner ice called leads. Lead orientation, thickness and width distributions are described by second-rank tensor internal variables: the structure, thickness and width tensors, whose dynamics are governed by corresponding evolution equations accounting for processes such as new lead generation and rotation as the ice cover deforms. These evolution equations contain contractions of higher-order tensor expressions that require closures. We develop a sea-ice stress constitutive law that relates sea-ice stress to the structure tensor, thickness tensor and strain rate. For the special case of empty leads (containing no ice), linear closures are adopted and we present calculations for simple shear, convergence and divergence.

Measurement of structural anisotropy in femoral trabecular bone using clinical-resolution CT images

Discrepancies in finite-element model predictions of bone strength may be attributed to the simplified modeling of bone as an isotropic structure due to the resolution limitations of clinical-level Computed Tomography (CT) data. The aim of this study is to calculate the preferential orientations of bone (the principal directions) and the extent to which bone is deposited more in one direction compared to another (degree of anisotropy). Using 100 femoral trabecular samples, the principal directions and degree of anisotropy were calculated with a Gradient Structure Tensor (GST) and a Sobel Structure Tensor (SST) using clinical-level CT. The results were compared against those calculated with the gold standard Mean-Intercept-Length (MIL) fabric tensor using micro-CT. There was no significant difference between the GST and SST in the calculation of the main principal direction (median error=28°), and the error was inversely correlated to the degree of transverse isotropy (r=−0.34, p<0.01). The degree of anisotropy measured using the structure tensors was weakly correlated with the MIL-based measurements (r=0.2, p<0.001). Combining the principal directions with the degree of anisotropy resulted in a significant increase in the correlation of the tensor distributions (r=0.79, p<0.001). Both structure tensors were robust against simulated noise, kernel sizes, and bone volume fraction. We recommend the use of the GST because of its computational efficiency and ease of implementation. This methodology has the promise to predict the structural anisotropy of bone in areas with a high degree of anisotropy, and may improve the in vivo characterization of bone.

Algorithms for super-resolution of images based on Sparse Representation and Manifolds

lmage super-resolution is defined as a class of techniques that enhance the spatial resolution of images. Super-resolution methods can be subdivided in single and multi image methods. This thesis focuses on developing algorithms based on mathematical theories for single image super­ resolution problems. lndeed, in arder to estimate an output image, we adopta mixed approach: i.e., we use both a dictionary of patches with sparsity constraints (typical of learning-based methods) and regularization terms (typical of reconstruction-based methods). Although the existing methods already per- form well, they do not take into account the geometry of the data to: regularize the solution, cluster data samples (samples are often clustered using algorithms with the Euclidean distance as a dissimilarity metric), learn dictionaries (they are often learned using PCA or K-SVD). Thus, state-of-the-art methods still suffer from shortcomings. In this work, we proposed three new methods to overcome these deficiencies. First, we developed SE-ASDS (a structure tensor based regularization term) in arder to improve the sharpness of edges. SE-ASDS achieves much better results than many state-of-the- art algorithms. Then, we proposed AGNN and GOC algorithms for determining a local subset of training samples from which a good local model can be computed for recon- structing a given input test sample, where we take into account the underlying geometry of the data. AGNN and GOC methods outperform spectral clustering, soft clustering, and geodesic distance based subset selection in most settings. Next, we proposed aSOB strategy which takes into account the geometry of the data and the dictionary size. The aSOB strategy outperforms both PCA and PGA methods. Finally, we combine all our methods in a unique algorithm, named G2SR. Our proposed G2SR algorithm shows better visual and quantitative results when compared to the results of state-of-the-art methods.

Aspects of a noncommutative scalar/tensor duality

We study the noncommutative massless Kalb-Ramond gauge field coupled to a dynamical U(1) gauge field in the adjoint representation together with a compensating vector field. We derive the Seiberg-Witten map and obtain the corresponding mapped action to first order in theta. The (emergent) gravity structure found in other situations is not present here. The off-shell dual scalar theory is derived and it does not coincide with the Seiberg-Witten mapped scalar theory. Dispersion relations are also discussed. The p-form generalization of the Seiberg-Witten map to order theta is also derived.

Fast Structure-Based Assignment of 15N HSQC Spectra of Selectively 15N-Labeled Paramagnetic Proteins

A novel strategy for fast NMR resonance assignment of N-15 HSQC spectra of proteins is presented. It requires the structure coordinates of the protein, a paramagnetic center, and one or more residue-selectively N-15-labeled samples. Comparison of sensitive undecoupled N-15 HSQC spectra recorded of paramagnetic and diamagnetic samples yields data for every cross-peak on pseudocontact shift, paramagnetic relaxation enhancement, cross-correlation between Curie-spin and dipole-dipole relaxation, and residual dipolar coupling. Comparison of these four different paramagnetic quantities with predictions from the three-dimensional structure simultaneously yields the resonance assignment and the anisotropy of the susceptibility tensor of the paramagnetic center. The method is demonstrated with the 30 kDa complex between the N-terminal domain of the epsilon subunit and the theta subunit of Escherichia Coll DNA polymerase III. The program PLATYPUS was developed to perform the assignment, provide a measure of reliability of the assignment, and determine the susceptibility tensor anisotropy.

Dynamic properties of human brain structure: learning-related changes in cortical areas and associated fiber connections.

Recent findings in neuroscience suggest that adult brain structure changes in response to environmental alterations and skill learning. Whereas much is known about structural changes after intensive practice for several months, little is known about the effects of single practice sessions on macroscopic brain structure and about progressive (dynamic) morphological alterations relative to improved task proficiency during learning for several weeks. Using T1-weighted and diffusion tensor imaging in humans, we demonstrate significant gray matter volume increases in frontal and parietal brain areas following only two sessions of practice in a complex whole-body balancing task. Gray matter volume increase in the prefrontal cortex correlated positively with subject's performance improvements during a 6 week learning period. Furthermore, we found that microstructural changes of fractional anisotropy in corresponding white matter regions followed the same temporal dynamic in relation to task performance. The results make clear how marginal alterations in our ever changing environment affect adult brain structure and elucidate the interrelated reorganization in cortical areas and associated fiber connections in correlation with improvements in task performance.

Distribution of single-particle strength due to short-range and tensor correlations

The distribution of single-particle strength in nuclear matter is calculated for a realistic nucleon-nucleon interaction. The influence of the short-range repulsion and the tensor component of the nuclear force on the spectral functions is to move approximately 13% of the total strength for all single-particle states beyond 100 MeV into the particle domain. This result is related to the abundantly observed quenching phenomena in nuclei which include the reduction of spectroscopic factors observed in (e,ep) reactions and the missing strength in low energy response functions.

Lagrangian and Hamiltonian BRST structures of the antysimmetric tensor gauge theory

We study the Becchi-Rouet-Stora-Tyutin (BRST) structure of a self-interacting antisymmetric tensor gauge field, which has an on-shell null-vector gauge transformation. The Batalin-Vilkovisky covariant general formalism is briefly reviewed, and the issue of on-shell nilpotency of the BRST transformation is elucidated. We establish the connection between the covariant and the canonical BRST formalisms for our particular theory. Finally, we point out the similarities and differences with Wittens string field theory.

Direct three-dimensional myocardial strain tensor quantification and tracking using zHARP.

Images of myocardial strain can be used to diagnose heart disease, plan and monitor treatment, and to learn about cardiac structure and function. Three-dimensional (3D) strain is typically quantified using many magnetic resonance (MR) images obtained in two or three orthogonal planes. Problems with this approach include long scan times, image misregistration, and through-plane motion. This article presents a novel method for calculating cardiac 3D strain using a stack of two or more images acquired in only one orientation. The zHARP pulse sequence encodes in-plane motion using MR tagging and out-of-plane motion using phase encoding, and has been previously shown to be capable of computing 3D displacement within a single image plane. Here, data from two adjacent image planes are combined to yield a 3D strain tensor at each pixel; stacks of zHARP images can be used to derive stacked arrays of 3D strain tensors without imaging multiple orientations and without numerical interpolation. The performance and accuracy of the method is demonstrated in vitro on a phantom and in vivo in four healthy adult human subjects.

Normal variation in fronto-occipital circuitry and cerebellar structure with an autism-associated polymorphism of CNTNAP2.

Recent genetic studies have implicated a number of candidate genes in the pathogenesis of Autism Spectrum Disorder (ASD). Polymorphisms of CNTNAP2 (contactin-associated like protein-2), a member of the neurexin family, have already been implicated as a susceptibility gene for autism by at least 3 separate studies. We investigated variation in white and grey matter morphology using structural MRI and diffusion tensor imaging. We compared volumetric differences in white and grey matter and fractional anisotropy values in control subjects characterised by genotype at rs7794745, a single nucleotide polymorphism in CNTNAP2. Homozygotes for the risk allele showed significant reductions in grey and white matter volume and fractional anisotropy in several regions that have already been implicated in ASD, including the cerebellum, fusiform gyrus, occipital and frontal cortices. Male homozygotes for the risk alleles showed greater reductions in grey matter in the right frontal pole and in FA in the right rostral fronto-occipital fasciculus compared to their female counterparts who showed greater reductions in FA of the anterior thalamic radiation. Thus a risk allele for autism results in significant cerebral morphological variation, despite the absence of overt symptoms or behavioural abnormalities. The results are consistent with accumulating evidence of CNTNAP2's function in neuronal development. The finding suggests the possibility that the heterogeneous manifestations of ASD can be aetiologically characterised into distinct subtypes through genetic-morphological analysis.

Diffusion Tensor Imaging as a Diagnostic and Research Tool: A Study on Preterm Infants

Diffusion tensor imaging (DTI) is an advanced magnetic resonance imaging (MRI) technique. DTI is based on free thermal motion (diffusion) of water molecules. The properties of diffusion can be represented using parameters such as fractional anisotropy, mean diffusivity, axial diffusivity, and radial diffusivity, which are calculated from DTI data. These parameters can be used to study the microstructure in fibrous structure such as brain white matter. The aim of this study was to investigate the reproducibility of region-of-interest (ROI) analysis and determine associations between white matter integrity and antenatal and early postnatal growth at term age using DTI. Antenatal growth was studied using both the ROI and tract-based spatial statistics (TBSS) method and postnatal growth using only the TBSS method. The infants included to this study were born below 32 gestational weeks or birth weight less than 1,501 g and imaged with a 1.5 T MRI system at term age. Total number of 132 infants met the inclusion criteria between June 2004 and December 2006. Due to exclusion criteria, a total of 76 preterm infants (ROI) and 36 preterm infants (TBSS) were accepted to this study. The ROI analysis was quite reproducible at term age. Reproducibility varied between white matter structures and diffusion parameters. Normal antenatal growth was positively associated with white matter maturation at term age. The ROI analysis showed associations only in the corpus callosum. Whereas, TBSS revealed associations in several brain white matter areas. Infants with normal antenatal growth showed more mature white matter compared to small for gestational age infants. The gestational age at birth had no significant association with white matter maturation at term age. It was observed that good early postnatal growth associated negatively with white matter maturation at term age. Growth-restricted infants seemed to have delayed brain maturation that was not fully compensated at term, despite catchup growth.