Iterated Residual Graph Convolutional Neural Network for Personalized Three-Dimensional Reconstruction of Left Myocardium from Cardiac MR Images.

Three-dimensional reconstruction of the left myocardium is of great significance for the diagnosis and treatment of cardiac diseases. This paper proposes a personalized 3D reconstruction algorithm for the left myocardium using cardiac MR images by incorporating a residual graph convolutional neural network. The accuracy of the mesh, reconstructed using the model-based algorithm, is largely affected by the similarity between the target object and the average model. The initial triangular mesh is obtained directly from the segmentation result of the left myocardium. The mesh is then deformed using an iterated residual graph convolutional neural network. A vertex feature learning module is also built to assist the mesh deformation by adopting an encoder-decoder neural network to represent the skeleton of the left myocardium at different receptive fields. In this way, the shape and local relationships of the left myocardium are used to guide the mesh deformation. Qualitative and quantitative comparative experiments were conducted on cardiac MR images, and the results verified the rationale and competitiveness of the proposed method compared to related state-of-the-art approaches.

Deep Neural Network for 3D Shape Classification Based on Mesh Feature.

Virtual reality, driverless cars, and robotics all make extensive use of 3D shape classification. One of the most popular ways to represent 3D data is with polygonal meshes. In particular, triangular mesh is frequently employed. A triangular mesh has more features than 3D data formats such as voxels, multi-views, and point clouds. The current challenge is to fully utilize and extract useful information from mesh data. In this paper, a 3D shape classification network based on triangular mesh and graph convolutional neural networks was suggested. The triangular face of this model was viewed as a unit. By obtaining an adjacency matrix from mesh data, graph convolutional neural networks can be utilized to process mesh data. The studies were performed on the ModelNet40 dataset with an accuracy of 91.0%, demonstrating that the classification network in this research may produce effective results.

TEAM: Triangular-mEsh Adaptive and Multiscale proton spot generation method.

BACKGROUND: Proton therapy is preferred for its dose conformality to spare normal tissues and organs-at-risk (OAR) via Bragg peaks with negligible exit dose. However, proton dose conformality can be further optimized: (1) the spot placement is based on the structured (e.g., Cartesian) grid, which may not offer conformal shaping to complex tumor targets; (2) the spot sampling pattern is uniform, which may be insufficient at the tumor boundary to provide the sharp dose falloff, and at the same time may be redundant at the tumor interior to provide the uniform dose coverage, for example, due to multiple Coulomb scattering (MCS); and (3) the lateral spot penumbra increases with respect to the depth due to MCS, which blurs the lateral dose falloff. On the other hand, while (1) the deliverable spots are subject to the minimum-monitor-unit (MMU) constraint, and (2) the dose rate is proportional to the MMU threshold, the current spot sampling method is sensitive to the MMU threshold and can fail to provide satisfactory plan quality for a large MMU threshold (i.e., high-dose-rate delivery). PURPOSE: This work will develop a novel Triangular-mEsh-based Adaptive and Multiscale (TEAM) proton spot generation method to address these issues for optimizing proton dose conformality and plan delivery efficiency. METHODS: Compared to the standard clinically-used spot placement method, three key elements of TEAM are as follows: (1) a triangular mesh instead of a structured grid: the triangular mesh is geometrically more conformal to complex target shapes and therefore more efficient and accurate for dose shaping inside and around the target; (2) adaptive sampling instead of uniform sampling: the adaptive sampling consists of relatively dense sampling at the tumor boundary to create the sharp dose falloff, which is more accurate, and coarse sampling at the tumor interior to uniformly cover the target, which is more efficient; and (3) depth-dependent sampling instead of depth-independent sampling: the depth-dependent sampling is used to compensate for MCS, that is, with increasingly dense sampling at the tumor boundary to improve dose shaping accuracy, and increasingly coarse sampling at the tumor interior to improve dose shaping efficiency, as the depth increases. In the TEAM method the spot locations are generated for each energy layer and layer-by-layer in the multiscale fashion; and then the spot weights are derived by solving the IMPT problem of dose-volume planning objectives, MMU constraints, and robustness optimization with respect to range and setup uncertainties. RESULTS: Compared to the standard clinically-used spot placement method UNIFORM, TEAM achieved (1) better plan quality using <60% number of spots of UNIFORM; (2) better robustness to the number of spots; (3) better robustness to a large MMU threshold. Furthermore, TEAM provided better plan quality with fewer spots than other adaptive methods (Cartesian-grid or triangular-mesh). CONCLUSIONS: A novel triangular-mesh-based proton spot placement method called TEAM is proposed, and it is demonstrated to improve plan quality, robustness to the number of spots, and robustness to the MMU threshold, compared to the clinically-used spot placement method and other adaptive methods.

Anatomy-guided multi-resolution image reconstruction in PET.

Objective. In this paper, we propose positron emission tomography image reconstruction using a multi-resolution triangular mesh. The mesh can be adapted based on patient specific anatomical information that can be in the form of a computed tomography or magnetic resonance imaging image in the hybrid imaging systems. The triangular mesh can be adapted to high resolution in localized anatomical regions of interest (ROI) and made coarser in other regions, leading to an imaging model with high resolution in the ROI with clearly reduced number of degrees of freedom compared to a conventional uniformly dense imaging model.Approach.We compare maximum likelihood expectation maximization reconstructions with the multi-resolution model to reconstructions using a uniformly dense mesh, a sparse mesh and regular rectangular pixel mesh. Two simulated cases are used in the comparison, with the first one using the NEMA image quality phantom and the second the XCAT human phantom.Main results.When compared to the results with the uniform imaging models, the locally refined multi-resolution mesh retains the accuracy of the dense mesh reconstruction in the ROI while being faster to compute than the reconstructions with the uniformly dense mesh. The locally dense multi-resolution model leads also to more accurate reconstruction than the pixel-based mesh or the sparse triangular mesh.Significance.The findings suggest that triangular multi-resolution mesh, which can be made patient and application specific, is a potential alternative for pixel-based reconstruction.

Techniques for element formulation and quadtree-based triangular mesh generation for strain-based finite elements.

Finite elements are often formulated by imposing sufficient conditions to ensure convergence and good accuracy. This work demonstrates a new technique to impose compatibility and equilibrium conditions for membrane finite elements that are formulated based on the strain approach.•The compatibility and equilibrium conditions are imposed onto the initial formulations (or test functions) by using corrective coefficients (c1, c2 , and c3 ).•The technique is found to be capable of producing alternate or similar forms for the test functions. Performances of the resultant (or final) formulations are shown by solving three benchmark problems. Additionally, a new technique to formulate strain-based triangular transition elements (denoted as SB-TTE) is introduced.•The new technique introduces another node (the fourth node) at one of the sides of a strain-based triangular element (mid-node, which is needed for the quadtree-based triangular mesh generation) without adding a degree of freedom.

SPHERICAL TRANSFORMER FOR QUALITY ASSESSMENT OF PEDIATRIC CORTICAL SURFACES.

Brain cortical surfaces, which have an intrinsic spherical topology, are typically represented by triangular meshes and mapped onto a spherical manifold in neuroimaging analysis. Inspired by the strong capability of feature learning in Convolutional Neural Networks (CNNs), spherical CNNs have been developed accordingly and achieved many successes in cortical surface analysis. Motivated by the recent success of the transformer, in this paper, for the first of time, we extend the transformer into the spherical space and propose the spherical transformer, which can better learn contextual and structural features than spherical CNNs. We applied the spherical transformer in the important task of automatic quality assessment of infant cortical surfaces, which is a necessary procedure to identify problematic cases due to extremely low tissue contrast and strong motion effects in pediatric brain MRI studies. Experiments on 1,860 infant cortical surfaces validated its superior effectiveness and efficiency in comparison with spherical CNNs.

Triangular mesh reduction of digitized maxillectomy defects for prosthetic rehabilitation: A 3D deviation study.

OBJECTIVES: To evaluate the effect of triangular mesh reduction on the trueness of digitized complete-arch dentate and edentulous maxillectomy defects models. MATERIAL AND METHODS: Twenty gypsum maxillectomy defect models (dentate and edentulous group: n = 10) were digitized using the Trios 3 intraoral scanner, scanning the teeth, mucosa and maxillectomy defect. These datasets (reference, R0) were saved as standard tessellation language (STL) files, and triangular mesh reduction was performed using the Meshmixer reduction tool. Digital test-datasets with file sizes reduced by 50%(R1), 75%(R2), and 90%(R3) were generated (each: n = 20). Each test-dataset was compared to the R0 file using a 3D evaluation software (GOM Inspect), applying automated pre-alignment followed by a best-fit alignment, and root mean square (RMS) 3-dimensional (3D) deviations were calculated. Statistical analyses were performed, at a level of significance of α=0.05. RESULTS: The number of triangles, and STL file size were synchronized with each other and inversely proportional to the amount of mesh reduction. The resulting mean percentages of the STL file sizes were 50.00% for R1, 24.93% for R2, and 10.00% for R3. There were no 3D deviations at 50% triangular mesh reduction. The 3D deviations increased with the amount of mesh reduction: at 75% reduction the median deviations were lower (dentate:0.0016 mm, IQR:0.0015-0.0018; edentulous:0.0016 mm, IQR:0.0015-0.0016), than at 90% (dentate:0.004 mm, IQR:0.0038-0.0041; edentulous:0.003 mm, IQR:0.0036-0.0039). A statistically significant increase in 3D deviations was observed with higher degrees of mesh reduction (p<0.001). CONCLUSIONS: Triangular mesh reduction results in a significant increase in 3D deviations if the reduction is more than 75%. CLINICAL SIGNIFICANCE: Digital models of patients with maxillectomy defects can be saved with a mesh reduction of 50% without affecting the trueness. The use of a 50% mesh reduction decreases the required storage capacity by 50%.

Role of molecular turnover in dynamic deformation of a three-dimensional cellular membrane.

In cells, the molecular constituents of membranes are dynamically turned over by transportation from one membrane to another. This molecular turnover causes the membrane to shrink or expand by sensing the stress state within the cell, changing its morphology. At present, little is known as to how this turnover regulates the dynamic deformation of cellular membranes. In this study, we propose a new physical model by which molecular turnover is coupled with three-dimensional membrane deformation to explore mechanosensing roles of turnover in cellular membrane deformations. In particular, as an example of microscopic machinery, based on a coarse-graining description, we suppose that molecular turnover depends on the local membrane strain. Using the proposed model, we demonstrate computational simulations of a single vesicle. The results show that molecular turnover adaptively facilitates vesicle deformation, owing to its stress dependence; while the vesicle drastically expands in the case with low bending rigidity, it shrinks in that with high bending rigidity. Moreover, localized active tension on the membrane causes cellular migration by driving the directional transport of molecules within the cell. These results illustrate the use of the proposed model as well as the role of turnover in the dynamic deformations of cellular membranes.

DRACO-STEM: An Automatic Tool to Generate High-Quality 3D Meshes of Shoot Apical Meristem Tissue at Cell Resolution.

Context: The shoot apical meristem (SAM), origin of all aerial organs of the plant, is a restricted niche of stem cells whose growth is regulated by a complex network of genetic, hormonal and mechanical interactions. Studying the development of this area at cell level using 3D microscopy time-lapse imaging is a newly emerging key to understand the processes controlling plant morphogenesis. Computational models have been proposed to simulate those mechanisms, however their validation on real-life data is an essential step that requires an adequate representation of the growing tissue to be carried out. Achievements: The tool we introduce is a two-stage computational pipeline that generates a complete 3D triangular mesh of the tissue volume based on a segmented tissue image stack. DRACO (Dual Reconstruction by Adjacency Complex Optimization) is designed to retrieve the underlying 3D topological structure of the tissue and compute its dual geometry, while STEM (SAM Tissue Enhanced Mesh) returns a faithful triangular mesh optimized along several quality criteria (intrinsic quality, tissue reconstruction, visual adequacy). Quantitative evaluation tools measuring the performance of the method along those different dimensions are also provided. The resulting meshes can be used as input and validation for biomechanical simulations. Availability: DRACO-STEM is supplied as a package of the open-source multi-platform plant modeling library OpenAlea (http://openalea.github.io/) implemented in Python, and is freely distributed on GitHub (https://github.com/VirtualPlants/draco-stem) along with guidelines for installation and use.

3D Reconstruction of human bones based on dictionary learning.

An effective method for reconstructing a 3D model of human bones from computed tomography (CT) image data based on dictionary learning is proposed. In this study, the dictionary comprises the vertices of triangular meshes, and the sparse coefficient matrix indicates the connectivity information. For better reconstruction performance, we proposed a balance coefficient between the approximation and regularisation terms and a method for optimisation. Moreover, we applied a local updating strategy and a mesh-optimisation method to update the dictionary and the sparse matrix, respectively. The two updating steps are iterated alternately until the objective function converges. Thus, a reconstructed mesh could be obtained with high accuracy and regularisation. The experimental results show that the proposed method has the potential to obtain high precision and high-quality triangular meshes for rapid prototyping, medical diagnosis, and tissue engineering.

How round is a protein? Exploring protein structures for globularity using conformal mapping.

We present a new algorithm that automatically computes a measure of the geometric difference between the surface of a protein and a round sphere. The algorithm takes as input two triangulated genus zero surfaces representing the protein and the round sphere, respectively, and constructs a discrete conformal map f between these surfaces. The conformal map is chosen to minimize a symmetric elastic energy E S (f) that measures the distance of f from an isometry. We illustrate our approach on a set of basic sample problems and then on a dataset of diverse protein structures. We show first that E S (f) is able to quantify the roundness of the Platonic solids and that for these surfaces it replicates well traditional measures of roundness such as the sphericity. We then demonstrate that the symmetric elastic energy E S (f) captures both global and local differences between two surfaces, showing that our method identifies the presence of protruding regions in protein structures and quantifies how these regions make the shape of a protein deviate from globularity. Based on these results, we show that E S (f) serves as a probe of the limits of the application of conformal mapping to parametrize protein shapes. We identify limitations of the method and discuss its extension to achieving automatic registration of protein structures based on their surface geometry.