Scaffolding skeletons using spherical Voronoi diagrams

International audienceGiven a skeleton made of line segments we describe how to obtain a coarse mesh (or scaffold) of a surface surrounding it. We emphasize in this abstract the key result that allows us to complete the approach in [3] that could not treat skeletons with loops

Scaffolding skeletons using spherical Voronoi diagrams: feasibility, regularity and symmetry

International audienceGiven a skeleton made of line segments we describe how to obtain a coarse quad mesh of a surface that encloses tightly the skeleton and follows its structure-the scaffold. We formalize as an Integer Linear Program the problem of constructing an optimal scaffold that minimizes the total number of quads on the mesh. We prove the feasibility of the Integer Linear Program for any skeleton. In particular we can generate these scaffolds for skeletons with cycles. We additionally show how to obtain regular scaffolds, i.e. with the same number of quad patches around each line segment, and symmetric scaffolds that respect the symmetries of the skeleton. An application to polygonization of skeleton-based implicit surfaces is also presented

Higher-order block-structured hex meshing of tubular structures

Numerical simulations of the cardiovascular system are growing in popularity due to the increasing availability of computational power, and their proven contribution to the understanding of pathodynamics and validation of medical devices with in-silico trials as a potential future breakthrough. Such simulations are performed on volumetric meshes reconstructed from patient-specific imaging data. These meshes are most often unstructured, and result in a brutally large amount of elements, significantly increasing the computational complexity of the simulations, whilst potentially adversely affecting their accuracy. To reduce such complexity, we introduce a new approach for fully automatic generation of higher-order, structured hexahedral meshes of tubular structures, with a focus on healthy blood vessels. The structures are modeled as skeleton-based convolution surfaces. From the same skeleton, the topology is captured by a block-structure, and the geometry by a higher-order surface mesh. Grading may be induced to obtain tailored refinement, thus resolving, e.g., boundary layers. The volumetric meshing is then performed via transfinite mappings. The resulting meshes are of arbitrary order, their elements are of good quality, while the spatial resolution may be as coarse as needed, greatly reducing computing time. Their suitability for practical applications is showcased by a simulation of physiological blood flow modelled by a generalised Newtonian fluid in the human aorta

Solid NURBS Conforming Scaffolding for Isogeometric Analysis

This work introduces a scaffolding framework to compactly parametrise solid structures with conforming NURBS elements for isogeometric analysis. A novel formulation introduces a topological, geometrical and parametric subdivision of the space in a minimal plurality of conforming vectorial elements. These determine a multi-compartmental scaffolding for arbitrary branching patterns. A solid smoothing paradigm is devised for the conforming scaffolding achieving higher than positional geometrical and parametric continuity. Results are shown for synthetic shapes of varying complexity, for modular CAD geometries, for branching structures from tessellated meshes and for organic biological structures from imaging data. Representative simulations demonstrate the validity of the introduced scaffolding framework with scalable performance and groundbreaking applications for isogeometric analysis

Automated CAD Model Generation for Structural Optimisation

Computer-aided design (CAD) models play a crucial role in the design, manufacturing and maintenance of products. Therefore, the mesh-based finite element descriptions common in structural optimisation must be first translated into CAD models. Currently, this translation either can be performed semi-manually or fails to reserve the structural optimality found by the structural optimisation due to the intrinsic difference in geometric representation between finite element mesh and CAD model. This thesis propose a fully automated and topologically accurate approach to synthesise structurally sound parametric CAD models from topology-optimised finite element models to fill the long-existing gap between structural optimisation and CAD systems. This approach successfully preserves the optimal structural performance during the mesh-CAD conversion. The solution provided in this thesis is to first convert the topology-optimised structure into a spatial frame structure and then to regenerate it in a CAD system using standard constructive solid geometry (CSG) operations. The obtained parametric CAD models are compact, that is, have as few as possible geometric parameters, which makes them ideal for editing and further processing within a CAD system. The critical task of converting the topology-optimised structure into an optimal spatial frame structure is accomplished in several steps. The first step is to generate a one-voxel-wide voxel chain model from the topology-optimised voxel model using a topology-preserving skeletonisation algorithm from digital topology. The undirected graph defined by the voxel chain model yields a spatial frame structure after processing it with the proposed graph algorithms. Subsequently, the cross-sections and layout of the frame members are optimised to recover its optimality, which may have been compromised during the conversion process. At last, the obtained frame structure is generated in a CAD system by repeatedly combining primitive solids, like cylinders and spheres, using boolean operations. The resulting solid model is a boundary representation (B-Rep) consisting of trimmed non-uniform rational B-spline (NURBS) curves and surfaces. The numerical studies in this thesis clarify that the converted spatial frame structures are with equivalent structural performance. Moreover, CAD models generated from the spatial frame structures have significantly fewer geometric degree of freedom compared to the topology-optimised structures. Though the numerical studies use topology-optimised structures as input and compact CSG models as output, this thesis also provides the way to extend the proposed generation process to taking other optimised meshes and producing outputs of various geometric representations. This offers a wide range of possible applications and brings new thoughts to industrial design and manufacturing.Chinese Scholarship Counci

Caractérisation géométrique par la logique floue et simulation de la résorption cellulairement assistée de substituts poreux pour tissus osseux par microtomographie à rayons X

The objective of this thesis is to provide an improved characterization of porous scaffolds. A more focused objective is to provide a computational model simulating the cell mediated resorption process of resorbable bone substitutes. The thesis is structured in three scientific manuscripts. The first manuscript used fuzzy-based image treatment methods to analyse images generated by micro-computed tomography. From the literature, it is known that the fuzzy-based method helps to improve the accuracy of the characterization, in particular for scaffolds featuring a relatively small pore size. In addition, a new algorithm was introduced to determine both pore and interconnection sizes. The surface area of bone substitutes was quantified by using marching cube algorithm. Besides, the so-called Lattice Boltzmann method was used to characterize the permeability of the investigated scaffolds. Scaffolds made of [béta]-tricalcium phosphate ([béta]-Ca[subscript 3](PO[subscript 4])[subscript 2]) and presenting a constant porosity and four variable pore sizes were examined. The average pore size (diameter) of the four bone substitute groups (denominated with a letter from group A to D) was measured to be 170.3«1.7, 217.3«5.2, 415.8«18.8 and 972.3«10.9 [micro]m. Despite this significant change in pore size, the pore interconnection size only increased slightly, in the range of 61.7 to 85.2 [micro]m. The average porosity of the four groups was 52.3«1.5 %. The surface density of scaffolds decreased from 11.5 to 3.3 mm[superscript -1], when the pore size increased. The results revealed that the permeability of scaffolds is in the same order of magnitude and increased from 1.1?10[superscript -10] to 4.1?10[superscript -10] m[superscript 2] with increasing the pore size. The second manuscript was devoted to the use of subvoxelization algorithm and high-resolution scanner, in an attempt to further improve the accuracy of the results, in particular, of the small pore scaffolds. As expected, an increase of the image resolution from 15 to 7.5 [micro]m significantly eased the segmentation process and hence improved scaffold characterization. Subvoxelization also improved the results specifically in terms of interconnection sizes. Specifically, much smaller interconnection sizes were yielded after applying the subvoxelization process. For example, the mean interconnection size of small pore size groups, group A and B, dropped from 63 to 20 and 30 [micro]m, respectively. Furthermore, due to more details obtained from subvoxelization and high-resolution scanning, additional effects so called"boundary effects" were observed. The boundary effects can yield misleading results in terms of interconnection sizes. The means to reduce these effects were proposed. The third manuscript focused on the simulation and understanding of cell mediated resorption of bone graft substitutes. A computer model was developed to simulate the resorption process of four bone substitute groups. [mu]CT data and new"image processing" tools such as labelling and skeletonization were combined in an algorithm to perform the steps of resorption simulation algorithm. The proposed algorithm was verified by comparing simulation results with the analytical results of a simple geometry and biological in vivo data of bone substitutes. A correlation coefficient between the simulation results and both analytical and experimental data, was found to be larger than 0.9. Local resorption process revealed faster resorption in external region specifically at earlier resorption time. This finding is in agreement with the in vivo results. Two definitions were introduced to estimate the resorption rate; volume resorption rate and linear resorption rate. The volume resorption rate was proportional to accessible surface and decreased when the pore size increased, while the linear resorption rate was proportional to thickness of material and increased with increasing the pore size. In addition, the simulation results revealed no effect of resorption direction on resorption behaviour of substitutes. However, the resorption rate of small pore size samples was decreased with increasing the minimum interconnection size required for cell ingrowth, to 100 [micro]m. This thesis combined novel"image processing" tools and subvoxelization method to improve the characterization of porous bone substitutes used in the bone repair process. The improved characterization allowed a more accurate simulation process. The simulation data were consistent with previously obtained biological data of the same group and allows understanding the local resorption process. The available tools and results are expected to help with the design of optimal substitute for bone repair."--Résumé abrégé par UMI

Application of computational method in designing a unit cell of bone tissue engineering scaffold: a review

The design of a scaffold of bone tissue engineering plays an important role in ensuring cell viability and cell growth. Therefore, it is a necessity to produce an ideal scaffold by predicting and simulating the properties of the scaffold. Hence, the computational method should be adopted since it has a huge potential to be used in the implementation of the scaffold of bone tissue engineering. To explore the field of computational method in the area of bone tissue engineering, this paper provides an overview of the usage of a computational method in designing a unit cell of bone tissue engineering scaffold. In order to design a unit cell of the scaffold, we discussed two categories of unit cells that can be used to design a feasible scaffold, which are non-parametric and parametric designs. These designs were later described and being categorised into multiple types according to their characteristics, such as circular structures and Triply Periodic Minimal Surface (TPMS) structures. The advantages and disadvantages of these designs were discussed. Moreover, this paper also represents some software that was used in simulating and designing the bone tissue scaffold. The challenges and future work recommendations had also been included in this paper

An Adjectival Interface for procedural content generation

Includes abstract.Includes bibliographical references.In this thesis, a new interface for the generation of procedural content is proposed, in which the user describes the content that they wish to create by using adjectives. Procedural models are typically controlled by complex parameters and often require expert technical knowledge. Since people communicate with each other using language, an adjectival interface to the creation of procedural content is a natural step towards addressing the needs of non-technical and non-expert users. The key problem addressed is that of establishing a mapping between adjectival descriptors, and the parameters employed by procedural models. We show how this can be represented as a mapping between two multi-dimensional spaces, adjective space and parameter space, and approximate the mapping by applying novel function approximation techniques to points of correspondence between the two spaces. These corresponding point pairs are established through a training phase, in which random procedural content is generated and then described, allowing one to map from parameter space to adjective space. Since we ultimately seek a means of mapping from adjective space to parameter space, particle swarm optimisation is employed to select a point in parameter space that best matches any given point in adjective space. The overall result, is a system in which the user can specify adjectives that are then used to create appropriate procedural content, by mapping the adjectives to a suitable set of procedural parameters and employing the standard procedural technique using those parameters as inputs. In this way, none of the control offered by procedural modelling is sacrificed â although the adjectival interface is simpler, it can at any point be stripped away to reveal the standard procedural model and give users access to the full set of procedural parameters. As such, the adjectival interface can be used for rapid prototyping to create an approximation of the content desired, after which the procedural parameters can be used to fine-tune the result. The adjectival interface also serves as a means of intermediate bridging, affording users a more comfortable interface until they are fully conversant with the technicalities of the underlying procedural parameters. Finally, the adjectival interface is compared and contrasted to an interface that allows for direct specification of the procedural parameters. Through user experiments, it is found that the adjectival interface presented in this thesis is not only easier to use and understand, but also that it produces content which more accurately reflects usersâ intentions

Large bichromatic point sets admit empty monochromatic 4-gons

We consider a variation of a problem stated by Erd˝os and Szekeres in 1935 about the existence of a number fES(k) such that any set S of at least fES(k) points in general position in the plane has a subset of k points that are the vertices of a convex k-gon. In our setting the points of S are colored, and we say that a (not necessarily convex) spanned polygon is monochromatic if all its vertices have the same color. Moreover, a polygon is called empty if it does not contain any points of S in its interior. We show that any bichromatic set of n ≥ 5044 points in R2 in general position determines at least one empty, monochromatic quadrilateral (and thus linearly many).Postprint (published version