Aspects of Unstructured Grids and Finite-Volume Solvers for the Euler and Navier-Stokes Equations

One of the major achievements in engineering science has been the development of computer algorithms for solving nonlinear differential equations such as the Navier-Stokes equations. In the past, limited computer resources have motivated the development of efficient numerical schemes in computational fluid dynamics (CFD) utilizing structured meshes. The use of structured meshes greatly simplifies the implementation of CFD algorithms on conventional computers. Unstructured grids on the other hand offer an alternative to modeling complex geometries. Unstructured meshes have irregular connectivity and usually contain combinations of triangles, quadrilaterals, tetrahedra, and hexahedra. The generation and use of unstructured grids poses new challenges in CFD. The purpose of this note is to present recent developments in the unstructured grid generation and flow solution technology

Intersubject Regularity in the Intrinsic Shape of Human V1

Previous studies have reported considerable intersubject variability in the three-dimensional geometry of the human primary visual cortex (V1). Here we demonstrate that much of this variability is due to extrinsic geometric features of the cortical folds, and that the intrinsic shape of V1 is similar across individuals. V1 was imaged in ten ex vivo human hemispheres using high-resolution (200 μm) structural magnetic resonance imaging at high field strength (7 T). Manual tracings of the stria of Gennari were used to construct a surface representation, which was computationally flattened into the plane with minimal metric distortion. The instrinsic shape of V1 was determined from the boundary of the planar representation of the stria. An ellipse provided a simple parametric shape model that was a good approximation to the boundary of flattened V1. The aspect ration of the best-fitting ellipse was found to be consistent across subject, with a mean of 1.85 and standard deviation of 0.12. Optimal rigid alignment of size-normalized V1 produced greater overlap than that achieved by previous studies using different registration methods. A shape analysis of published macaque data indicated that the intrinsic shape of macaque V1 is also stereotyped, and similar to the human V1 shape. Previoud measurements of the functional boundary of V1 in human and macaque are in close agreement with these results

Optimized normal and distance matching for heterogeneous object modeling

This paper presents a new optimization methodology of material blending for heterogeneous object modeling by matching the material governing features for designing a heterogeneous object. The proposed method establishes point-to-point correspondence represented by a set of connecting lines between two material directrices. To blend the material features between the directrices, a heuristic optimization method developed with the objective is to maximize the sum of the inner products of the unit normals at the end points of the connecting lines and minimize the sum of the lengths of connecting lines. The geometric features with material information are matched to generate non-self-intersecting and non-twisted connecting surfaces. By subdividing the connecting lines into equal number of segments, a series of intermediate piecewise curves are generated to represent the material metamorphosis between the governing material features. Alternatively, a dynamic programming approach developed in our earlier work is presented for comparison purposes. Result and computational efficiency of the proposed heuristic method is also compared with earlier techniques in the literature. Computer interface implementation and illustrative examples are also presented in this paper

Semi-automated stereoradiographic upper limb 3D reconstructions using a combined parametric and statistical model: a preliminary study

PURPOSE: Quantitative assessment of 3D clinical indices may be crucial for elbow surgery planning. 3D parametric modeling from bi-planar radiographs was successfully proposed for spine and lower limb clinical investigation as an alternative for CT-scan. The aim of this study was to adapt this method to the upper limb with a preliminary validation. METHODS: CT-scan 3D models of humerus, radius and ulna were obtained from 20 cadaveric upper limbs and yielded parametric models made of geometric primitives. Primitives were defined by descriptor parameters (diameters, angles...) and correlations between these descriptors were found. Using these correlations, a semi-automated reconstruction method of humerus using bi-planar radiographs was achieved: a 3D personalized parametric model was built, from which clinical parameters were computed [orientation and projections on bone surface of trochlea sulcus to capitulum (CTS) axis, trochlea sulcus anterior offset and width of distal humeral epiphysis]. This method was evaluated by accuracy compared to CT-scan and reproducibility. RESULTS: Points-to-surface mean distance was 0.9 mm (2 RMS = 2.5 mm). For clinical parameters, mean differences were 0.4-1.9 mm and from 1.7° to 2.3°. All parameters except from angle formed by CTS axis and bi-epicondylar axis in transverse plane were reproducible. Reconstruction time was about 5 min. CONCLUSIONS: The presented method provides access to morphological upper limb parameters with very low level of radiation. Preliminary in vitro validation for humerus showed that it is fast and accurate enough to be used in clinical daily practice as an alternative to CT-scan for total elbow arthroplasty pre operative evaluation

Globally Optimal Surfaces By Continuous Maximal Flows

In this paper we consider the problem of computing globally minimal continuous curves and surfaces for image segmentation and 3D reconstruction. This is solved using a maximal flow approach expressed as a PDE model. Previously proposed techniques yield either grid-biased solutions (graph based approaches) or sub-optimal solutions (active contours and surfaces). The proposed algorithm simulates the flow of an ideal fluid with a spatially varying velocity constraint derived from image data. A proof is given that the algorithm gives the globally maximal flow at convergence, along with an implementation scheme. The globally minimal surface may be obtained trivially from its output. The new algorithm is applied to segmentation in 2D and 3D medical images and to 3D reconstruction from a stereo image pair. The results in 2D agree remarkably well with an existing planar minimal contour algorithm and the results in 3D segmentation and reconstruction demonstrate that the new algorithm is free from grid bias