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  1. Free, publicly-accessible full text available July 1, 2023
  2. Faithful, accurate, and successful cardiac biomechanics and electrophysiological simulations require patient-specific geometric models of the heart. Since the cardiac geometry consists of highly-curved boundaries, the use of high-order meshes with curved elements would ensure that the various curves and features present in the cardiac geometry are well-captured and preserved in the corresponding mesh. Most other existing mesh generation techniques require computer-aided design files to represent the geometric boundary, which are often not available for biomedical applications. Unlike such methods, our technique takes a high-order surface mesh, generated from patient medical images, as input and generates a high-order volume mesh directly from the curved surface mesh. In this paper, we use our direct high-order curvilinear tetrahedral mesh generation method [1] to generate several second-order cardiac meshes. Our meshes include the left ventricle myocardia of a healthy heart and hearts with dilated and hypertrophic cardiomyopathy. We show that our high-order cardiac meshes do not contain inverted elements and are of sufficiently high quality for use in cardiac finite element simulations.
    Free, publicly-accessible full text available December 1, 2022
  3. Computational modeling and simulation of real-world problems, e.g., various applications in the automotive, aerospace, and biomedical industries, often involve geometric objects which are bounded by curved surfaces. The geometric modeling of such objects can be performed via high-order meshes. Such a mesh, when paired with a high-order partial differential equation (PDE) solver, can realize more accurate solution results with a decreased number of mesh elements (in comparison to a low-order mesh). There are several types of high-order mesh generation approaches, such as direct methods, a posteriori methods, and isogeometric analysis (IGA)-based spline modeling approaches. In this paper, we propose a direct, high-order, curvilinear tetrahedral mesh generation method using an advancing front technique. After generating the mesh, we apply mesh optimization to improve the quality and to take advantage of the degrees of freedom available in the initially straight-sided quadratic elements. Our method aims to generate high-quality tetrahedral mesh elements from various types of boundary representations including the cases where no computer-aided design files are available. Such a method is essential, for example, for generating meshes for various biomedical models where the boundary representation is obtained from medical images instead of CAD files. We present several numerical examples of second-order tetrahedralmore »meshes generated using our method based on input triangular surface meshes.« less
  4. Cardiac Cine Magnetic Resonance (CMR) Imaging has made a significant paradigm shift in medical imaging technology, thanks to its capability of acquiring high spatial and temporal resolution images of different structures within the heart that can be used for reconstructing patient-specific ventricular computational models. In this work, we describe the development of dynamic patient-specific right ventricle (RV) models associated with normal subjects and abnormal RV patients to be subsequently used to assess RV function based on motion and kinematic analysis. We first constructed static RV models using segmentation masks of cardiac chambers generated from our accurate, memory-efficient deep neural architecture - CondenseUNet - featuring both a learned group structure and a regularized weight-pruner to estimate the motion of the right ventricle. In our study, we use a deep learning-based deformable network that takes 3D input volumes and outputs a motion field which is then used to generate isosurface meshes of the cardiac geometry at all cardiac frames by propagating the end-diastole (ED) isosurface mesh using the reconstructed motion field. The proposed model was trained and tested on the Automated Cardiac Diagnosis Challenge (ACDC) dataset featuring 150 cine cardiac MRI patient datasets. The isosurface meshes generated using the proposed pipeline weremore »compared to those obtained using motion propagation via traditional non-rigid registration based on several performance metrics, including Dice score and mean absolute distance (MAD).« less
    Free, publicly-accessible full text available November 1, 2022
  5. Sherwin, Spencer J. ; Moxey, David ; Peiró, Joaquim (Ed.)
  6. In this paper, we propose a novel method of generating high-order curvilinear triangular meshes using an advancing front approach. Our method relies on a direct approach to generate meshes on geometries with curved boundaries. Our advancing front method yields high-quality triangular elements in each iteration which omits the need for post-processing steps. We present several numerical examples of second-order curvilinear triangular meshes of patient-specific anatomical models generated using our technique on boundary meshes obtained from biomedical images.
  7. One challenge in the generation of high-order meshes is that mesh tangling can occur as a consequence of moving the new boundary nodes to the true curved boundary. In this paper, we propose a new optimization-based method that uses signed angles to untangle invalid second- and third-order triangular meshes. Our proposed method consists of two passes. In the first pass, we loop over each high-order interior edge node and minimize an objective function based on the signed angles of the pair of triangles that share the node. In the second pass, we loop over face nodes and move them to the mean of the high-order nodes of the triangle to which the face node belongs. We present several numerical examples in two dimensions with second- and third-order elements that demonstrate the capabilities of our method for untangling invalid meshes.