Mesh deformation with exact surface reconstruction using a reduced radial basis function approach

This paper presents a novel reduced radial basis function approach with exact surface reconstruction. The new approach combines two well proven mesh deformation algorithms in a three step approach. In a first pre-processing step an explicit reduction of radial basis function points is performed using a k-d tree. In the second step the classic radial basis function interpolation is used to propagate the deformation field. In a last post-processing step an exact surface reconstruction is achieved using an efficient Delaunay graph mapping approach. The new mesh deformation approach is compared to the two original approaches by investigating a 2D viscous mesh test case. The applicability of the new approach to 3D is shown via an aeroelastic relevant wing test case

Capture and Modeling of Non-Linear Heterogeneous Soft Tissue

This paper introduces a data-driven representation and modeling technique for simulating non-linear heterogeneous soft tissue. It simplifies the construction of convincing deformable models by avoiding complex selection and tuning of physical material parameters, yet retaining the richness of non-linear heterogeneous behavior. We acquire a set of example deformations of a real object, and represent each of them as a spatially varying stress-strain relationship in a finite-element model. We then model the material by non-linear interpolation of these stress-strain relationships in strain-space. Our method relies on a simple-to-build capture system and an efficient run-time simulation algorithm based on incremental loading, making it suitable for interactive computer graphics applications. We present the results of our approach for several non-linear materials and biological soft tissue, with accurate agreement of our model to the measured data.Engineering and Applied Science

Real-time simulation of surgery by Proper Generalized Decomposition techniques

La simulación quirúrgica por ordenador en tiempo real se ha convertido en una alternativa muy atractiva a los simuladores quirúrgicos tradicionales. Entre otras ventajas, los simuladores por ordenador consiguen ahorros importantes de tiempo y de costes de mantenimiento, y permiten que los estudiantes practiquen sus habilidades quirúrgicas en un entorno seguro tantas veces como sea necesario. Sin embargo, a pesar de las capacidades de los ordenadores actuales, la cirugía computacional sigue siendo un campo de investigación exigente. Uno de sus mayores retos es la alta velocidad a la que se tienen que resolver complejos problemas de mecánica de medios continuos para que los interfaces hápticos puedan proporcionar un sentido del tacto realista (en general, se necesitan velocidades de respuesta de 500-1000 Hz).Esta tesis presenta algunos métodos numéricos novedosos para la simulación interactiva de dos procedimientos quirúrgicos habituales: el corte y el rasgado (o desgarro) de tejidos blandos. El marco común de los métodos presentados es el uso de la Descomposición Propia Generalizada (PGD en inglés) para la generación de vademécums computacionales, esto es, metasoluciones generales de problemas paramétricos de altas dimensiones que se pueden evaluar a velocidades de respuesta compatibles con entornos hápticos.En el caso del corte, los vademécums computacionales se utilizan de forma conjunta con técnicas basadas en XFEM, mientras que la carga de cálculo se distribuye entre una etapa off-line (previa a la ejecución interactiva) y otra on-line (en tiempo de ejecución). Durante la fase off-line, para el órgano en cuestión se precalculan tanto un vademécum computacional para cualquier posición de una carga, como los desplazamientos producidos por un conjunto de cortes. Así, durante la etapa on-line, los resultados precalculados se combinan de la forma más adecuada para obtener en tiempo real la respuesta a las acciones dirigidas por el usuario. En cuanto al rasgado, a partir de una ecuación paramétrica basada en mecánica del daño continuo, se obtiene un vademécum computacional. La complejidad del modelo se reduce mediante técnicas de Descomposición Ortogonal Propia (POD en inglés), y el vademécum se incorpora a una formulación incremental explícita que se puede interpretar como una especie de integrador temporal.A modo de ejemplo, el método para el corte se aplica a la simulación de un procedimiento quirúrgico refractivo de la córnea conocido como queratotomía radial, mientras que el método para el rasgado se centra en la simulación de la colecistectomía laparoscópica (la extirpación de la vesícula biliar mediante laparoscopia). En ambos casos, los métodos implementados ofrecen excelentes resultados en términos de velocidades de respuesta y producen simulaciones muy realistas desde los puntos de vista visual y háptico.The real-time computer-based simulation of surgery has proven to be an appealing alternative to traditional surgical simulators. Amongst other advantages, computer-based simulators provide considerable savings on time and maintenance costs, and allow trainees to practice their surgical skills in a safe environment as often as necessary. However, in spite of the current computer capabilities, computational surgery continues to be a challenging field of research. One of its major issues is the high speed at which complex problems in continuum mechanics have to be solved so that haptic interfaces can render a realistic sense of touch (generally, feedback rates of 500–1 000 Hz are required). This thesis introduces some novel numerical methods for the interactive simulation of two usual surgical procedures: cutting and tearing of soft tissues. The common framework of the presented methods is the use of the Proper Generalised Decomposition (PGD) for the generation of computational vademecums, i. e. general meta-solutions of parametric high-dimensional problems that can be evaluated at feedback rates compatible with haptic environments. In the case of cutting, computational vademecums are used jointly with XFEM-based techniques, and the computing workload is distributed into an off-line and an on-line stage. During the off-line stage, both a computational vademecum for any position of a load and the displacements produced by a set of cuts are pre-computed for the organ under consideration. Thus, during the on-line stage, the pre-computed results are properly combined together to obtain in real-time the response to the actions driven by the user. Concerning tearing, a computational vademecum is obtained from a parametric equation based on continuum damage mechanics. The complexity of the model is reduced by Proper Orthogonal Decomposition (POD) techniques, and the vademecum is incorporated into an explicit incremental formulation that can be viewed as a sort of time integrator. By way of example, the cutting method is applied to the simulation of a corneal refractive surgical procedure known as radial keratotomy, whereas the tearing method focuses on the simulation of laparoscopic cholecystectomy (i. e. the removal of the gallbladder). In both cases, the implemented methods offer excellent performances in terms of feedback rates, and produce.<br /

Computational methods in cardiovascular mechanics

The introduction of computational models in cardiovascular sciences has been progressively bringing new and unique tools for the investigation of the physiopathology. Together with the dramatic improvement of imaging and measuring devices on one side, and of computational architectures on the other one, mathematical and numerical models have provided a new, clearly noninvasive, approach for understanding not only basic mechanisms but also patient-specific conditions, and for supporting the design and the development of new therapeutic options. The terminology in silico is, nowadays, commonly accepted for indicating this new source of knowledge added to traditional in vitro and in vivo investigations. The advantages of in silico methodologies are basically the low cost in terms of infrastructures and facilities, the reduced invasiveness and, in general, the intrinsic predictive capabilities based on the use of mathematical models. The disadvantages are generally identified in the distance between the real cases and their virtual counterpart required by the conceptual modeling that can be detrimental for the reliability of numerical simulations.Comment: 54 pages, Book Chapte

Guided Medical Data Segmentation Using Structure-Aligned Planar Contours

Segmentation of 3D/4D biological images is a critical step for a wide range of applications such as treatment planning, quantitative analysis, virtual simulations, and rendering visualizations. Automatic segmentation methods are becoming more reliable, but many experts still rely on manual intervention which makes segmentation a time and resource intensive bottleneck. Marking boundary contours in 3D images can be difficult when images are often noisy or the delineation of biological tissue is unclear. Non-parallel contours can be more accurate and reduce the amount of marking necessary, but require extra effort to ensure boundary consistency and maintain spatial orientation. This dissertation focuses three problems that pertain to drawing non-parallel contour networks and generating a segmentation surface from those networks. First a guided structure-aligned segmentation system is detailed that utilizes prior structure knowledge from past segmentations of similar data. It employs a contouring protocol to aid in navigating the volume data and support using arbitrarily-oriented contouring planes placed to capture or follow the global structure shape. A user study is provided to test how well novices perform segmentation using this system. The following two problems then aim to improve different aspects of this system. A new deformation approach to reconstruction is discussed which deforms previous segmentation meshes to fit protocol drawn contours from new data instances in order to obtain accurate segmentations that have the correct topology and general shape and preserves fine details. The focus is on the problem of finding a correspondence between a mesh and a set of contours describing a similar shape. And finally, a new robust algorithm that resolves inconsistencies in contour networks is detailed. Inconsistent contours are faster and less demanding to draw, and they allow the segmenter to focus on drawing boundaries and not maintaining consistency. However, inconsistency is detrimental to most reconstruction algorithms, so the network must be fixed as a post process after drawing

On the Real-Time Performance, Robustness and Accuracy of Medical Image Non-Rigid Registration

Three critical issues about medical image non-rigid registration are performance, robustness and accuracy. A registration method, which is capable of responding timely with an accurate alignment, robust against the variation of the image intensity and the missing data, is desirable for its clinical use. This work addresses all three of these issues. Unacceptable execution time of Non-rigid registration (NRR) often presents a major obstacle to its routine clinical use. We present a hybrid data partitioning method to parallelize a NRR method on a cooperative architecture, which enables us to get closer to the goal: accelerating using architecture rather than designing a parallel algorithm from scratch. to further accelerate the performance for the GPU part, a GPU optimization tool is provided to automatically optimize GPU execution configuration.;Missing data and variation of the intensity are two severe challenges for the robustness of the registration method. A novel point-based NRR method is presented to resolve mapping function (deformation field) with the point correspondence missing. The novelty of this method lies in incorporating a finite element biomechanical model into an Expectation and Maximization (EM) framework to resolve the correspondence and mapping function simultaneously. This method is extended to deal with the deformation induced by tumor resection, which imposes another challenge, i.e. incomplete intra-operative MRI. The registration is formulated as a three variable (Correspondence, Deformation Field, and Resection Region) functional minimization problem and resolved by a Nested Expectation and Maximization framework. The experimental results show the effectiveness of this method in correcting the deformation in the vicinity of the tumor. to deal with the variation of the intensity, two different methods are developed depending on the specific application. For the mono-modality registration on delayed enhanced cardiac MRI and cine MRI, a hybrid registration method is designed by unifying both intensity- and feature point-based metrics into one cost function. The experiment on the moving propagation of suspicious myocardial infarction shows effectiveness of this hybrid method. For the multi-modality registration on MRI and CT, a Mutual Information (MI)-based NRR is developed by modeling the underlying deformation as a Free-Form Deformation (FFD). MI is sensitive to the variation of the intensity due to equidistant bins. We overcome this disadvantage by designing a Top-to-Down K-means clustering method to naturally group similar intensities into one bin. The experiment shows this method can increase the accuracy of the MI-based registration.;In image registration, a finite element biomechanical model is usually employed to simulate the underlying movement of the soft tissue. We develop a multi-tissue mesh generation method to build a heterogeneous biomechanical model to realistically simulate the underlying movement of the brain. We focus on the following four critical mesh properties: tissue-dependent resolution, fidelity to tissue boundaries, smoothness of mesh surfaces, and element quality. Each mesh property can be controlled on a tissue level. The experiments on comparing the homogeneous model with the heterogeneous model demonstrate the effectiveness of the heterogeneous model in improving the registration accuracy

Free vibration analysis of composite plates based on a variable separation method

International audienceThis work deals with the free vibration analysis of laminated composite plates through a variable separationapproach. The displacement field is approximated as a sum of separated functions of the in-plane coordinatesx, y and the transverse coordinate z. This choice yields to a non-linear problem that can be solved by an iterativeprocess. That consists of solving a 2D and 1D eigenvalue problem successively. In the thickness direction, afourth-order expansion in each layer is considered. For the in-plane description, classical Finite Element methodis used.A wide range of numerical tests involving several representative laminated and sandwich plates is addressedto show the accuracy of the present LayerWise (LW) method. Different slenderness ratios and boundary conditionsare also considered. By comparing with exact or 3D FEM solutions, it is shown that it can provideaccurate results less costly than classical LW computations