Quasi-isotropic initial triangulation of NURBS surfaces

Isotropic triangulation of NURBS surfaces provides high quality triangular meshes, where all triangles are equilateral. This isotropy increases representation quality and analysis accuracy. We introduce a new algorithm to generate quasi-isotropic triangulation on NURBS surfaces at once, with no prior meshing. The procedure consists of one front made of vertexes that advances in a divergence manner avoiding front collision. Vertexes are calculated by intersecting arcs whose radius is estimated by trapezoidal rule integration of directional derivatives. The parameter space is discretized in partitions such that the error of trapezoidal rule is controlled efficiently. A new space, called pattern space, is used to infer the direction of the arcs’ intersection. Derivatives, whose analytical computation is expensive, are estimated by NURBS surface fitting procedures, which increases the speed of the process. The resultant algorithm is robust and efficient. The mesh achieved possesses most of the triangles equilateral and with high uniformity of sizes. The performance is evaluated by measuring angles, vertex valences and size uniformity in different numerical examples

Trimming Simulation of Forming Metal Sheets IsoGeometric Models by Using NURBS Surfaces

Some metal sheets forming processes need trimming in a final stage for achieving the net- shape specification and for removing micro-cracks and irregularities. In numerical simulation, since the exact final edge location is a priori unknown in the original metal blanket, the trimming needs to be done once the forming is finished. During the forming internal stresses are generated inside the sheet. When trimming those stresses configuration is changed to achieve equilibrium as a consequence of the material removal. In this paper a novel method for simulating the trimming is presented. The part to trim is modelled using isogeometric analysis (IGA). The new surface generated is modelled with non-uniform rational B-splines (NURBS). Due to the IGA characteristics a total geometrical accuracy and an efficient residual stresses recalculation are accomplished

Atrophy computation in the spinal cord using the Boundary Shift Integral

In this work, we introduce a new pipeline based on the latest iteration of the BSI for computing atrophy in the SC and compare its results with the most popular atrophy measurements for this region, mean CSA. We demonstrated for the first time the use of BSI in the SC, as a sensitive, quantitative and objective measure of longitudinal tissue volume change. The BSI pipeline presented in this work is repeatable, reproducible and standardises a pipeline for computing SC atrophy

Fully automated grey and white matter spinal cord segmentation

Axonal loss in the spinal cord is one of the main contributing factors to irreversible clinical disability in multiple sclerosis (MS). In vivo axonal loss can be assessed indirectly by estimating a reduction in the cervical cross-sectional area (CSA) of the spinal cord over time, which is indicative of spinal cord atrophy, and such a measure may be obtained by means of image segmentation using magnetic resonance imaging (MRI). In this work, we propose a new fully automated spinal cord segmentation technique that incorporates two different multi-atlas segmentation propagation and fusion techniques: The Optimized PatchMatch Label fusion (OPAL) algorithm for localising and approximately segmenting the spinal cord, and the Similarity and Truth Estimation for Propagated Segmentations (STEPS) algorithm for segmenting white and grey matter simultaneously. In a retrospective analysis of MRI data, the proposed method facilitated CSA measurements with accuracy equivalent to the inter-rater variability, with a Dice score (DSC) of 0.967 at C2/C3 level. The segmentation performance for grey matter at C2/C3 level was close to inter-rater variability, reaching an accuracy (DSC) of 0.826 for healthy subjects and 0.835 people with clinically isolated syndrome MS

Relationship of grey and white matter abnormalities with distance from the surface of the brain in multiple sclerosis

OBJECTIVE: To assess the association between proximity to the inner (ventricular and aqueductal) and outer (pial) surfaces of the brain and the distribution of normal appearing white matter (NAWM) and grey matter (GM) abnormalities, and white matter (WM) lesions, in multiple sclerosis (MS). METHODS: 67 people with relapse-onset MS and 30 healthy controls were included in the study. Volumetric T1 images and high-resolution (1 mm(3)) magnetisation transfer ratio (MTR) images were acquired and segmented into 12 bands between the inner and outer surfaces of the brain. The first and last bands were discarded to limit partial volume effects with cerebrospinal fluid. MTR values were computed for all bands in supratentorial NAWM, cerebellar NAWM and brainstem NA tissue, and deep and cortical GM. Band WM lesion volumes were also measured. RESULTS: Proximity to the ventricular surfaces was associated with progressively lower MTR values in the MS group but not in controls in supratentorial and cerebellar NAWM, brainstem NA and in deep and cortical GM. The density of WM lesions was associated with proximity to the ventricles only in the supratentorial compartment, and no link was found with distance from the pial surfaces. CONCLUSIONS: In MS, MTR abnormalities in NAWM and GM are related to distance from the inner and outer surfaces of the brain, and this suggests that there is a common factor underlying their spatial distribution. A similar pattern was not found for WM lesions, raising the possibility that different factors promote their formation

Extremal Multicenter Black Holes: Nilpotent Orbits and Tits Satake Universality Classes

Four dimensional supergravity theories whose scalar manifold is a symmetric coset manifold U[D=4]/Hc are arranged into a finite list of Tits Satake universality classes. Stationary solutions of these theories, spherically symmetric or not, are identified with those of an euclidian three-dimensional sigma-model, whose target manifold is a Lorentzian coset U[D=3]/H* and the extremal ones are associated with H* nilpotent orbits in the K* representation emerging from the orthogonal decomposition of the algebra U[D=3] with respect to H*. It is shown that the classification of such orbits can always be reduced to the Tits-Satake projection and it is a class property of the Tits Satake universality classes. The construction procedure of Bossard et al of extremal multicenter solutions by means of a triangular hierarchy of integrable equations is completed and converted into a closed algorithm by means of a general formula that provides the transition from the symmetric to the solvable gauge. The question of the relation between H* orbits and charge orbits W of the corresponding black holes is addressed and also reduced to the corresponding question within the Tits Satake projection. It is conjectured that on the vanishing locus of the Taub-NUT current the relation between H*-orbit and W-orbit is rigid and one-to-one. All black holes emerging from multicenter solutions associated with a given H* orbit have the same W-type. For the S^3 model we provide a complete survey of its multicenter solutions associated with all of the previously classified nilpotent orbits of sl(2) x sl(2) within g[2,2]. We find a new intrinsic classification of the W-orbits of this model that might provide a paradigm for the analogous classification in all the other Tits Satake universality classes.Comment: 83 pages, LaTeX; v2: few misprints corrected and references adde