They use well-established techniques and optimization schemes including Delaunay triangulation method, modified-octree technique, and advancing front technique. Tetrahedral mesh generators are a standard feature of commonly used Computer-Aided Engineering CAE packages. Today 4-noded tetrahedra and 8-noded hexahedra are the most commonly used types of finite elements. Examples include the Expectation-Maximization (EM) segmentation algorithm that has been applied in the segmentation of various anatomical structures, such as the brain and long bones (femur and tibia). This often involves statistical methods and, recently, machine learning. To improve the segmentation of medical images, anatomical prior information can be used to help delineate anatomical structures. Examples of the techniques that have been used to automate the segmentation of anatomical structures include thresholding, region growing, watershed based methods, level set approach, and edge detection algorithms (such as the contour tracing using the concept of extended boundary, Canny edge detection, Sobel edge detection and Laplacian edge detection ). The techniques available for segmentation are specific to the application, the imaging modality and anatomic structure under consideration. Consequently, there is no universal algorithm for segmenting every medical image. Adapted from Wittek et al.Īutomated image segmentation remains a challenging task due to the complexity of medical images. Image segmentation, surface generation and finite element mesh generation often require direct involvement of the analyst and, therefore, are labor intensive. From a medical image to patient-specific computational biomechanics model using finite element method (neurosurgery simulation example). If we assume that the total volume of the tetrahedron is V and the volume for each subtetrahedron is V i, where i = 1 to 4, then volume ratios V i V = ξ i are denoted as the natural coordinates of the tetrahedron. Similarly, we can identify three additional tetrahedrons P– P 2– P 3– P 4, P– P 3– P 1– P 4, and P– P 1– P 2– P 3. Note that in this case, P– P 1– P 2 forms the base, and as such, the points are considered to be on the same vertical layer, with only P 4 forming a new layer at the vertex. We can visualize from Fig. 3.7(left) that P– P 1– P 2– P 4 forms a subtetrahedron. To establish the natural coordinates, we drop a line from P 4 to somewhere within the tetrahedron, and call this point P. Right: An 8-node, 3D hexahedral solid element in a global coordinate system mapped onto a cubical element in the natural coordinate system, and vice versa. Left: A tetrahedron which is divided into four subtetrahedrons, where the volume ratio is used to define its natural coordinate system.
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