Feature-sensitive and Adaptive Image Triangulation: A Super-pixel-based Scheme for Image Segmentation and Mesh Generation

With increasing utilization of various imaging techniques (such as CT, MRI and PET) in medical fields, it is often in great need to computationally extract the boundaries of objects of interest, a process commonly known as image segmentation. While numerous approaches have been proposed in literature on automatic/semi-automatic image segmentation, most of these approaches are based on image pixels. The number of pixels in an image can be huge, especially for 3D imaging volumes, which renders the pixel-based image segmentation process inevitably slow. On the other hand, 3D mesh generation from imaging data has become important not only for visualization and quantification but more critically for finite element based numerical simulation. Traditionally image-based mesh generation follows such a procedure as: (1) image boundary segmentation, (2) surface mesh generation from segmented boundaries, and (3) volumetric (e.g., tetrahedral) mesh generation from surface meshes. These three majors steps have been commonly treated as separate algorithms/steps and hence image information, once segmented, is not considered any more in mesh generation. In this thesis, we investigate a super-pixel based scheme that integrates both image segmentation and mesh generation into a single method, making mesh generation truly an image-incorporated approach. Our method, called image content-aware mesh generation, consists of several main steps. First, we generate a set of feature-sensitive, and adaptively distributed points from 2D grayscale images or 3D volumes. A novel image edge enhancement method via randomized shortest paths is introduced to be an optional choice to generate the features’ boundary map in mesh node generation step. Second, a Delaunay-triangulation generator (2D) or tetrahedral mesh generator (3D) is then utilized to generate a 2D triangulation or 3D tetrahedral mesh. The generated triangulation (or tetrahedralization) provides an adaptive partitioning of a given image (or volume). Each cluster of pixels within a triangle (or voxels within a tetrahedron) is called a super-pixel, which forms one of the nodes of a graph and adjacent super-pixels give an edge of the graph. A graph-cut method is then applied to the graph to define the boundary between two subsets of the graph, resulting in good boundary segmentations with high quality meshes. Thanks to the significantly reduced number of elements (super-pixels) as compared to that of pixels in an image, the super-pixel based segmentation method has tremendously improved the segmentation speed, making it feasible for real-time feature detection. In addition, the incorporation of image segmentation into mesh generation makes the generated mesh well adapted to image features, a desired property known as feature-preserving mesh generation

3D mesh processing using GAMer 2 to enable reaction-diffusion simulations in realistic cellular geometries

Recent advances in electron microscopy have enabled the imaging of single cells in 3D at nanometer length scale resolutions. An uncharted frontier for in silico biology is the ability to simulate cellular processes using these observed geometries. Enabling such simulations requires watertight meshing of electron micrograph images into 3D volume meshes, which can then form the basis of computer simulations of such processes using numerical techniques such as the Finite Element Method. In this paper, we describe the use of our recently rewritten mesh processing software, GAMer 2, to bridge the gap between poorly conditioned meshes generated from segmented micrographs and boundary marked tetrahedral meshes which are compatible with simulation. We demonstrate the application of a workflow using GAMer 2 to a series of electron micrographs of neuronal dendrite morphology explored at three different length scales and show that the resulting meshes are suitable for finite element simulations. This work is an important step towards making physical simulations of biological processes in realistic geometries routine. Innovations in algorithms to reconstruct and simulate cellular length scale phenomena based on emerging structural data will enable realistic physical models and advance discovery at the interface of geometry and cellular processes. We posit that a new frontier at the intersection of computational technologies and single cell biology is now open.Comment: 39 pages, 14 figures. High resolution figures and supplemental movies available upon reques

Patient-specific anisotropic model of human trunk based on MR data

There are many ways to generate geometrical models for numerical simulation, and most of them start with a segmentation step to extract the boundaries of the regions of interest. This paper presents an algorithm to generate a patient-specific three-dimensional geometric model, based on a tetrahedral mesh, without an initial extraction of contours from the volumetric data. Using the information directly available in the data, such as gray levels, we built a metric to drive a mesh adaptation process. The metric is used to specify the size and orientation of the tetrahedral elements everywhere in the mesh. Our method, which produces anisotropic meshes, gives good results with synthetic and real MRI data. The resulting model quality has been evaluated qualitatively and quantitatively by comparing it with an analytical solution and with a segmentation made by an expert. Results show that our method gives, in 90% of the cases, as good or better meshes as a similar isotropic method, based on the accuracy of the volume reconstruction for a given mesh size. Moreover, a comparison of the Hausdorff distances between adapted meshes of both methods and ground-truth volumes shows that our method decreases reconstruction errors faster. Copyright © 2015 John Wiley & Sons, Ltd.Natural Sciences and Engineering Research Council (NSERC) of Canada and the MEDITIS training program (´Ecole Polytechnique de Montreal and NSERC)

CAD-Based Porous Scaffold Design of Intervertebral Discs in Tissue Engineering

With the development and maturity of three-dimensional (3D) printing technology over the past decade, 3D printing has been widely investigated and applied in the field of tissue engineering to repair damaged tissues or organs, such as muscles, skin, and bones, Although a number of automated fabrication methods have been developed to create superior bio-scaffolds with specific surface properties and porosity, the major challenges still focus on how to fabricate 3D natural biodegradable scaffolds that have tailor properties such as intricate architecture, porosity, and interconnectivity in order to provide the needed structural integrity, strength, transport, and ideal microenvironment for cell- and tissue-growth. In this dissertation, a robust pipeline of fabricating bio-functional porous scaffolds of intervertebral discs based on different innovative porous design methodologies is illustrated. Firstly, a triply periodic minimal surface (TPMS) based parameterization method, which has overcome the integrity problem of traditional TPMS method, is presented in Chapter 3. Then, an implicit surface modeling (ISM) approach using tetrahedral implicit surface (TIS) is demonstrated and compared with the TPMS method in Chapter 4. In Chapter 5, we present an advanced porous design method with higher flexibility using anisotropic radial basis function (ARBF) and volumetric meshes. Based on all these advanced porous design methods, the 3D model of a bio-functional porous intervertebral disc scaffold can be easily designed and its physical model can also be manufactured through 3D printing. However, due to the unique shape of each intervertebral disc and the intricate topological relationship between the intervertebral discs and the spine, the accurate localization and segmentation of dysfunctional discs are regarded as another obstacle to fabricating porous 3D disc models. To that end, we discuss in Chapter 6 a segmentation technique of intervertebral discs from CT-scanned medical images by using deep convolutional neural networks. Additionally, some examples of applying different porous designs on the segmented intervertebral disc models are demonstrated in Chapter 6

Multi-Material Mesh Representation of Anatomical Structures for Deep Brain Stimulation Planning

The Dual Contouring algorithm (DC) is a grid-based process used to generate surface meshes from volumetric data. However, DC is unable to guarantee 2-manifold and watertight meshes due to the fact that it produces only one vertex for each grid cube. We present a modified Dual Contouring algorithm that is capable of overcoming this limitation. The proposed method decomposes an ambiguous grid cube into a set of tetrahedral cells and uses novel polygon generation rules that produce 2-manifold and watertight surface meshes with good-quality triangles. These meshes, being watertight and 2-manifold, are geometrically correct, and therefore can be used to initialize tetrahedral meshes. The 2-manifold DC method has been extended into the multi-material domain. Due to its multi-material nature, multi-material surface meshes will contain non-manifold elements along material interfaces or shared boundaries. The proposed multi-material DC algorithm can (1) generate multi-material surface meshes where each material sub-mesh is a 2-manifold and watertight mesh, (2) preserve the non-manifold elements along the material interfaces, and (3) ensure that the material interface or shared boundary between materials is consistent. The proposed method is used to generate multi-material surface meshes of deep brain anatomical structures from a digital atlas of the basal ganglia and thalamus. Although deep brain anatomical structures can be labeled as functionally separate, they are in fact continuous tracts of soft tissue in close proximity to each other. The multi-material meshes generated by the proposed DC algorithm can accurately represent the closely-packed deep brain structures as a single mesh consisting of multiple material sub-meshes. Each sub-mesh represents a distinct functional structure of the brain. Printed and/or digital atlases are important tools for medical research and surgical intervention. While these atlases can provide guidance in identifying anatomical structures, they do not take into account the wide variations in the shape and size of anatomical structures that occur from patient to patient. Accurate, patient-specific representations are especially important for surgical interventions like deep brain stimulation, where even small inaccuracies can result in dangerous complications. The last part of this research effort extends the discrete deformable 2-simplex mesh into the multi-material domain where geometry-based internal forces and image-based external forces are used in the deformation process. This multi-material deformable framework is used to segment anatomical structures of the deep brain region from Magnetic Resonance (MR) data

Heterogeneous volumetric data mapping and its medical applications

With the advance of data acquisition techniques, massive solid geometries are being collected routinely in scientific tasks, these complex and unstructured data need to be effectively correlated for various processing and analysis. Volumetric mapping solves bijective low-distortion correspondence between/among 3D geometric data, and can serve as an important preprocessing step in many tasks in compute-aided design and analysis, industrial manufacturing, medical image analysis, to name a few. This dissertation studied two important volumetric mapping problems: the mapping of heterogeneous volumes (with nonuniform inner structures/layers) and the mapping of sequential dynamic volumes. To effectively handle heterogeneous volumes, first, we studied the feature-aligned harmonic volumetric mapping. Compared to previous harmonic mapping, it supports the point, curve, and iso-surface alignment, which are important low-dimensional structures in heterogeneous volumetric data. Second, we proposed a biharmonic model for volumetric mapping. Unlike the conventional harmonic volumetric mapping that only supports positional continuity on the boundary, this new model allows us to have higher order continuity $C^1$ along the boundary surface. This suggests a potential model to solve the volumetric mapping of complex and big geometries through divide-and-conquer. We also studied the medical applications of our volumetric mapping in lung tumor respiratory motion modeling. We were building an effective digital platform for lung tumor radiotherapy based on effective volumetric CT/MRI image matching and analysis. We developed and integrated in this platform a set of geometric/image processing techniques including advanced image segmentation, finite element meshing, volumetric registration and interpolation. The lung organ/tumor and surrounding tissues are treated as a heterogeneous region and a dynamic 4D registration framework is developed for lung tumor motion modeling and tracking. Compared to the previous 3D pairwise registration, our new 4D parameterization model leads to a significantly improved registration accuracy. The constructed deforming model can hence approximate the deformation of the tissues and tumor

Numerical studies of flow in porous media using an unstructured approach

Flow and transport in porous media is relevant to many areas of engineering and science including groundwater hydrology and the recovery of oil and gas. Porous materials are characterized by the unique shape and connectivity of the internal void structures which give rise to a large range in macroscopic transport properties. Historically an inability to accurately describe the internal pore-structure has prevented detailed study of the role of pore structure on transport. In recent decades however, the combination of high resolution imaging technologies with computational modeling has seen the development of fundamental pore-scale techniques for studying flow in porous media. Image-based pore-scale modeling of transport phenomena has become an important tool for understanding the complicated relationships between pore structure and measurable macroscopic properties, including permeability and formation factor. This has commonly been achieved by a network-based approach where the pore space is idealized as a series of pores connected by throats, or by a grid-based approach where the voxels of a 3D image represent structured quadrilateral elements or nodal locations. In this work however, image-based unstructured meshing techniques are used to represent voxelised pore spaces by grids comprising entirely of tetrahedral elements. These unstructured tetrahedral grids are used in finite element models to calculate permeability and formation factor. Solutions to the Stokes equations governing creeping, or Darcy flow, are used to validate the finite element approach employed in this work, and to assess the impact of different image-based unstructured meshing strategies on predicted permeability. Testing shows that solutions to the Stokes equations by a P2P1 tetrahedral element are significantly more accurate than solutions based on a P1P1 element, while permeability is shown to be sensitive to structural changes to the pore space induced by different meshing approaches. The modeling approach is also used to investigate the relationship of an electric and hydraulic definition of tortuosity to the Carman-Kozeny equation. The results of simulations using a number of computer generated porous structures indicate that an electrical tortuosity based on computed formation factor is well correlated with the tortuosity suggested by the Carman-Kozeny equation

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

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

Large-scale Geometric Data Decomposition, Processing and Structured Mesh Generation

Mesh generation is a fundamental and critical problem in geometric data modeling and processing. In most scientific and engineering tasks that involve numerical computations and simulations on 2D/3D regions or on curved geometric objects, discretizing or approximating the geometric data using a polygonal or polyhedral meshes is always the first step of the procedure. The quality of this tessellation often dictates the subsequent computation accuracy, efficiency, and numerical stability. When compared with unstructured meshes, the structured meshes are favored in many scientific/engineering tasks due to their good properties. However, generating high-quality structured mesh remains challenging, especially for complex or large-scale geometric data. In industrial Computer-aided Design/Engineering (CAD/CAE) pipelines, the geometry processing to create a desirable structural mesh of the complex model is the most costly step. This step is semi-manual, and often takes up to several weeks to finish. Several technical challenges remains unsolved in existing structured mesh generation techniques. This dissertation studies the effective generation of structural mesh on large and complex geometric data. We study a general geometric computation paradigm to solve this problem via model partitioning and divide-and-conquer. To apply effective divide-and-conquer, we study two key technical components: the shape decomposition in the divide stage, and the structured meshing in the conquer stage. We test our algorithm on vairous data set, the results demonstrate the efficiency and effectiveness of our framework. The comparisons also show our algorithm outperforms existing partitioning methods in final meshing quality. We also show our pipeline scales up efficiently on HPC environment