5,525 research outputs found

    Phase-field boundary conditions for the voxel finite cell method: surface-free stress analysis of CT-based bone structures

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    The voxel finite cell method employs unfitted finite element meshes and voxel quadrature rules to seamlessly transfer CT data into patient-specific bone discretizations. The method, however, still requires the explicit parametrization of boundary surfaces to impose traction and displacement boundary conditions, which constitutes a potential roadblock to automation. We explore a phase-field based formulation for imposing traction and displacement constraints in a diffuse sense. Its essential component is a diffuse geometry model generated from metastable phase-field solutions of the Allen-Cahn problem that assumes the imaging data as initial condition. Phase-field approximations of the boundary and its gradient are then employed to transfer all boundary terms in the variational formulation into volumetric terms. We show that in the context of the voxel finite cell method, diffuse boundary conditions achieve the same accuracy as boundary conditions defined over explicit sharp surfaces, if the inherent length scales, i.e., the interface width of the phase-field, the voxel spacing and the mesh size, are properly related. We demonstrate the flexibility of the new method by analyzing stresses in a human femur and a vertebral body

    3D Reality-Based Survey and Retopology for Structural Analysis of Cultural Heritage

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    Cultural heritage’s structural changes and damages can influence the mechanical behaviour of artefacts and buildings. The use of finite element methods (FEM) for mechanical analysis is largely used in modelling stress behaviour. The workflow involves the use of CAD 3D models and the use of non-uniform rational B-spline (NURBS) surfaces. For cultural heritage objects, altered by the time elapsed since their creation, the representation created with the CAD model may introduce an extreme level of approximation, leading to wrong simulation results. The focus of this work is to present an alternative method intending to generate the most accurate 3D representation of a real artefact from highly accurate 3D reality-based models, simplifying the original models to make them suitable for finite element analysis (FEA) software. The approach proposed, and tested on three different case studies, was based on the intelligent use of retopology procedures to create a simplified model to be converted to a mathematical one made by NURBS surfaces, which is also suitable for being processed by volumetric meshes typically embedded in standard FEM packages. This allowed us to obtain FEA results that were closer to the actual mechanical behaviour of the analysed heritage asset

    Enabling technology for non-rigid registration during image-guided neurosurgery

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    In the context of image processing, non-rigid registration is an operation that attempts to align two or more images using spatially varying transformations. Non-rigid registration finds application in medical image processing to account for the deformations in the soft tissues of the imaged organs. During image-guided neurosurgery, non-rigid registration has the potential to assist in locating critical brain structures and improve identification of the tumor boundary. Robust non-rigid registration methods combine estimation of tissue displacement based on image intensities with the spatial regularization using biomechanical models of brain deformation. In practice, the use of such registration methods during neurosurgery is complicated by a number of issues: construction of the biomechanical model used in the registration from the image data, high computational demands of the application, and difficulties in assessing the registration results. In this dissertation we develop methods and tools that address some of these challenges, and provide components essential for the intra-operative application of a previously validated physics-based non-rigid registration method.;First, we study the problem of image-to-mesh conversion, which is required for constructing biomechanical model of the brain used during registration. We develop and analyze a number of methods suitable for solving this problem, and evaluate them using application-specific quantitative metrics. Second, we develop a high-performance implementation of the non-rigid registration algorithm and study the use of geographically distributed Grid resources for speculative registration computations. Using the high-performance implementation running on the remote computing resources we are able to deliver the results of registration within the time constraints of the neurosurgery. Finally, we present a method that estimates local alignment error between the two images of the same subject. We assess the utility of this method using multiple sources of ground truth to evaluate its potential to support speculative computations of non-rigid registration

    Unified Heat Kernel Regression for Diffusion, Kernel Smoothing and Wavelets on Manifolds and Its Application to Mandible Growth Modeling in CT Images

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    We present a novel kernel regression framework for smoothing scalar surface data using the Laplace-Beltrami eigenfunctions. Starting with the heat kernel constructed from the eigenfunctions, we formulate a new bivariate kernel regression framework as a weighted eigenfunction expansion with the heat kernel as the weights. The new kernel regression is mathematically equivalent to isotropic heat diffusion, kernel smoothing and recently popular diffusion wavelets. Unlike many previous partial differential equation based approaches involving diffusion, our approach represents the solution of diffusion analytically, reducing numerical inaccuracy and slow convergence. The numerical implementation is validated on a unit sphere using spherical harmonics. As an illustration, we have applied the method in characterizing the localized growth pattern of mandible surfaces obtained in CT images from subjects between ages 0 and 20 years by regressing the length of displacement vectors with respect to the template surface.Comment: Accepted in Medical Image Analysi

    Statistical Shape Modelling and Segmentation of the Respiratory Airway

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    The human respiratory airway consists of the upper (nasal cavity, pharynx) and the lower (trachea, bronchi) respiratory tracts. Accurate segmentation of these two airway tracts can lead to better diagnosis and interpretation of airway-specific diseases, and lead to improvement in the localization of abnormal metabolic or pathological sites found within and/or surrounding the respiratory regions. Due to the complexity and the variability displayed in the anatomical structure of the upper respiratory airway along with the challenges in distinguishing the nasal cavity from non-respiratory regions such as the paranasal sinuses, it is difficult for existing algorithms to accurately segment the upper airway without manual intervention. This thesis presents an implicit non-parametric framework for constructing a statistical shape model (SSM) of the upper and lower respiratory tract, capable of distinct shape generation and be adapted for segmentation. An SSM of the nasal cavity was successfully constructed using 50 nasal CT scans. The performance of the SSM was evaluated for compactness, specificity and generality. An averaged distance error of 1.47 mm was measured for the generality assessment. The constructed SSM was further adapted with a modified locally constrained random walk algorithm to segment the nasal cavity. The proposed algorithm was evaluated on 30 CT images and outperformed comparative state-of-the-art and conventional algorithms. For the lower airway, a separate algorithm was proposed to automatically segment the trachea and bronchi, and was designed to tolerate the image characteristics inherent in low-contrast CT images. The algorithm was evaluated on 20 clinical low-contrast CT from PET-CT patient studies and demonstrated better performance (87.1±2.8 DSC and distance error of 0.37±0.08 mm) in segmentation results against comparative state-of-the-art algorithms
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