Particle-based sampling and meshing of surfaces in multimaterial volumes

Marching Windows: Scalable Mesh Generation for Volumetric Data With Multiple Materials

Volumetric data abounds in medical imaging and other fields. With the improved imaging quality and the increased resolution, volumetric datasets are getting so large that the existing tools have become inadequate for processing and analyzing the data. Here we consider the problem of computing tetrahedral meshes to represent large volumetric datasets with labeled multiple materials, which are often encountered in medical imaging or microscopy optical slice tomography. Such tetrahedral meshes are a more compact and expressive geometric representation so are in demand for efficient visualization and simulation of the data, which are impossible if the original large volumetric data are used directly due to the large memory requirement. Existing methods for meshing volumetric data are not scalable for handling large datasets due to their sheer demand on excessively large run-time memory or failure to produce a tet-mesh that preserves the multi-material structure of the original volumetric data. In this article we propose a novel approach, called Marching Windows, that uses a moving window and a disk-swap strategy to reduce the run-time memory footprint, devise a new scheme that guarantees to preserve the topological structure of the original dataset, and adopt an error-guided optimization technique to improve both geometric approximation error and mesh quality. Extensive experiments show that our method is capable of processing very large volumetric datasets beyond the capability of the existing methods and producing tetrahedral meshes of high quality.

Atlas-Based Shared-Boundary Deformable Multi-Surface Models through Multi-Material and Two-Manifold Dual Contouring

This paper presents a multi-material dual “contouring” method used to convert a digital 3D voxel-based atlas of basal ganglia to a deformable discrete multi-surface model that supports surgical navigation for an intraoperative MRI-compatible surgical robot, featuring fast intraoperative deformation computation. It is vital that the final surface model maintain shared boundaries where appropriate so that even as the deep-brain model deforms to reflect intraoperative changes encoded in ioMRI, the subthalamic nucleus stays in contact with the substantia nigra, for example, while still providing a significantly sparser representation than the original volumetric atlas consisting of hundreds of millions of voxels. The dual contouring (DC) algorithm is a grid-based process used to generate surface meshes from volumetric data. The DC method enables the insertion of vertices anywhere inside the grid cube, as opposed to the marching cubes (MC) algorithm, which can insert vertices only on the grid edges. This multi-material DC method is then applied to initialize, by duality, a deformable multi-surface simplex model, which can be used for multi-surface atlas-based segmentation. We demonstrate our proposed method on synthetic and deep-brain atlas data, and a comparison of our method’s results with those of traditional DC demonstrates its effectiveness.

Deformable resection process map for intraoperative cutting guides

In this paper, we will introduce the concept of deformable resection process mapping as a time-varying geometric guide for soft tissue tumor resection procedures. The deformable resection process map (RPM) estimates the local appearance of vascular structures after cuts as a novel guide. The RPM can be directly generated from patient-specific medical images using volumetric resampling techniques. Since user input of some cutting points is the only requirement for generating the RPM, the developed software will be directly available for clinical use to preview surgical procedures and intraoperative workflow management without time-consuming setups or additional workloads. We used the CT images of the patients with hepatic cancer for the experiments. The performance of our method in the shape representation for a curved cut surface was compared with that of conventional shape modeling methods.

Development of a finite element head model for the study of impact head injury

This study is aimed at developing a high quality, validated finite element (FE) human head model for traumatic brain injuries (TBI) prediction and prevention during vehicle collisions. The geometry of the FE model was based on computed tomography (CT) and magnetic resonance imaging (MRI) scans of a volunteer close to the anthropometry of a 50th percentile male. The material and structural properties were selected based on a synthesis of current knowledge of the constitutive models for each tissue. The cerebrospinal fluid (CSF) was simulated explicitly as a hydrostatic fluid by using a surface-based fluid modeling method. The model was validated in the loading condition observed in frontal impact vehicle collision. These validations include the intracranial pressure (ICP), brain motion, impact force and intracranial acceleration response, maximum von Mises stress in the brain, and maximum principal stress in the skull. Overall results obtained in the validation indicated improved biofidelity relative to previous FE models, and the change in the maximum von Mises in the brain is mainly caused by the improvement of the CSF simulation. The model may be used for improving the current injury criteria of the brain and anthropometric test devices.

Direct volume manipulation for visualizing intraoperative liver resection process

This paper introduces a new design and application for direct volume manipulation for visualizing the intraoperative liver resection process. So far, interactive volume deformation and resection have been independently handled due to the difficulty of representing elastic behavior of volumetric objects. Our framework models global shape editing and discontinuous local deformation by merging proxy geometry encoding and displacement mapping. A local-frame-based elastic model is presented to allow stable editing of the liver shape including bending and twisting while preserving the volume. Several tests using clinical CT data have confirmed the developed software and interface can represent the intraoperative state of liver and produce local views of reference vascular structures, which provides a "road map of vessels" that are key features when approaching occluded tumors during surgery.

Lattice cleaving: a multimaterial tetrahedral meshing algorithm with guarantees

We introduce a new algorithm for generating tetrahedral meshes that conform to physical boundaries in volumetric domains consisting of multiple materials. The proposed method allows for an arbitrary number of materials, produces high-quality tetrahedral meshes with upper and lower bounds on dihedral angles, and guarantees geometric fidelity. Moreover, the method is combinatoric so its implementation enables rapid mesh construction. These meshes are structured in a way that also allows grading, to reduce element counts in regions of homogeneity. Additionally, we provide proofs showing that both element quality and geometric fidelity are bounded using this approach.

Adaptive and Unstructured Mesh Cleaving

We propose a new strategy for boundary conforming meshing that decouples the problem of building tetrahedra of proper size and shape from the problem of conforming to complex, non-manifold boundaries. This approach is motivated by the observation that while several methods exist for adaptive tetrahedral meshing, they typically have difficulty at geometric boundaries. The proposed strategy avoids this conflict by extracting the boundary conforming constraint into a secondary step. We first build a background mesh having a desired set of tetrahedral properties, and then use a generalized stenciling method to divide, or "cleave", these elements to get a set of conforming tetrahedra, while limiting the impacts cleaving has on element quality. In developing this new framework, we make several technical contributions including a new method for building graded tetrahedral meshes as well as a generalization of the isosurface stuffing and lattice cleaving algorithms to unstructured background meshes.

A pipeline for the simulation of transcranial direct current stimulation for realistic human head models using SCIRun/BioMesh3D

The current work presents a computational pipeline to simulate transcranial direct current stimulation from image based models of the head with SCIRun [15]. The pipeline contains all the steps necessary to carry out the simulations and is supported by a complete suite of open source software tools: image visualization, segmentation, mesh generation, tDCS electrode generation and efficient tDCS forward simulation.

Lattice Cleaving: Conforming Tetrahedral Meshes of Multimaterial Domains with Bounded Quality

We introduce a new algorithm for generating tetrahedral meshes that conform to physical boundaries in volumetric domains consisting of multiple materials. The proposed method allows for an arbitrary number of materials, produces high-quality tetrahedral meshes with upper and lower bounds on dihedral angles, and guarantees geometric fidelity. Moreover, the method is combinatoric so its implementation enables rapid mesh construction. These meshes are structured in a way that also allows grading, in order to reduce element counts in regions of homogeneity.

Particle systems for adaptive, isotropic meshing of CAD models

We present a particle-based approach for generating adaptive triangular surface and tetrahedral volume meshes from computer-aided design models. Input shapes are treated as a collection of smooth, parametric surface patches that can meet non-smoothly on boundaries. Our approach uses a hierarchical sampling scheme that places particles on features in order of increasing dimensionality. These particles reach a good distribution by minimizing an energy computed in 3D world space, with movements occurring in the parametric space of each surface patch. Rather than using a pre-computed measure of feature size, our system automatically adapts to both curvature as well as a notion of topological separation. It also enforces a measure of smoothness on these constraints to construct a sizing field that acts as a proxy to piecewise-smooth feature size. We evaluate our technique with comparisons against other popular triangular meshing techniques for this domain.

Mesh processing in medical-image analysis--a tutorial

Medical-image analysis requires an understanding of sophisticated scanning modalities, constructing geometric models, building meshes to represent domains, and downstream biological applications. These four steps form an image-to-mesh pipeline. For research in this field to progress, the imaging, modeling, and simulation communities will need to work together more closely.

Generating smooth surface meshes from multi-region medical images

Thanks to advances in medical imaging technologies and numerical methods, patient-specific modelling is more and more used to improve diagnosis and to estimate the outcome of surgical interventions. It requires the extraction of the domain of interest from the medical scans of the patient, as well as the discretisation of this geometry. However, extracting smooth multi-material meshes that conform to the tissue boundaries described in the segmented image is still an active field of research. We propose to solve this issue by combining an implicit surface reconstruction method with a multi-region mesh extraction scheme. The surface reconstruction algorithm is based on multi-level partition of unity implicit surfaces, which we extended to the multi-material case. The mesh generation algorithm consists in a novel multi-domain version of the marching tetrahedra. It generates multi-region meshes as a set of triangular surface patches consistently joining each other at material junctions. This paper presents this original meshing strategy, starting from boundary points extraction from the segmented data to heterogeneous implicit surface definition, multi-region surface triangulation and mesh adaptation. Results indicate that the proposed approach produces smooth and high-quality triangular meshes with a reasonable geometric accuracy. Hence, the proposed method is well suited for subsequent volume mesh generation and finite element simulations.

Smooth, volume-accurate material interface reconstruction

A new material interface reconstruction method for volume fraction data is presented. Our method is comprised of two components: first, we generate initial interface topology; then, using a combination of smoothing and volumetric forces within an active interface model, we iteratively transform the initial material interfaces into high-quality surfaces that accurately approximate the problem's volume fractions. Unlike all previous work, our new method produces material interfaces that are smooth, continuous across cell boundaries, and segment cells into regions with proper volume. These properties are critical during visualization and analysis. Generating high-quality mesh representations of material interfaces is required for accurate calculations of interface statistics, and dramatically increases the utility of material boundary visualizations.

Sampling and visualizing creases with scale-space particles

Particle systems have gained importance as a methodology for sampling implicit surfaces and segmented objects to improve mesh generation and shape analysis. We propose that particle systems have a significantly more general role in sampling structure from unsegmented data. We describe a particle system that computes samplings of crease features (i.e. ridges and valleys, as lines or surfaces) that effectively represent many anatomical structures in scanned medical data. Because structure naturally exists at a range of sizes relative to the image resolution, computer vision has developed the theory of scale-space, which considers an n-D image as an (n+1)-D stack of images at different blurring levels. Our scale-space particles move through continuous four-dimensional scale-space according to spatial constraints imposed by the crease features, a particle-image energy that draws particles towards scales of maximal feature strength, and an inter-particle energy that controls sampling density in space and scale. To make scale-space practical for large three-dimensional data, we present a spline-based interpolation across scale from a small number of pre-computed blurrings at optimally selected scales. The configuration of the particle system is visualized with tensor glyphs that display information about the local Hessian of the image, and the scale of the particle. We use scale-space particles to sample the complex three-dimensional branching structure of airways in lung CT, and the major white matter structures in brain DTI.