Semi-automatic surface and volume mesh generation for subject-specific biomedical geometries

Automatic triangulated mesh generation of pulmonary airways from segmented lung 3DCTs for computational fluid dynamics

PURPOSE

Computational fluid dynamics (CFD) of lung airflow during normal and pathophysiological breathing provides insight into regional pulmonary ventilation. By integrating CFD methods with 4D lung imaging workflows, regions of normal pulmonary function can be spared during treatment planning. To facilitate the use of CFD simulations in a clinical setup, a robust, automated, and CFD-compliant airway mesh generation technique is necessary.

METHODS

We define a CFD-compliant airway mesh to be devoid of blockages of airflow and leaks in the airway path, both of which are caused by airway meshing errors that occur when using conventional meshing techniques. We present an algorithm to create a CFD-compliant airway mesh in an automated manner. Beginning with a medial skeleton of the airway segmentation, the branches were tracked, and 3D points at which bifurcations occur were identified. Airway branches and bifurcation features were isolated to allow for automated and careful meshing that considered their anatomical nature.

RESULTS

We present the meshing results from three state-of-the-art tools and compare them with the meshes generated by our algorithm. The results show that fully CFD-compliant meshes were automatically generated for an ideal geometry and patient-specific CT scans. Using an open-source smoothed-particle hydrodynamics CFD implementation, we compared the airflow using our approach and conventionally generated airway meshes.

CONCLUSION

Our meshing algorithm was able to successfully generate a CFD-compliant mesh from pre-segmented lung CT scans, providing an automatic meshing approach that enables interventional CFD simulations to guide lung procedures such as radiotherapy or lung volume reduction surgery.

Computed Tomography-Based Preoperative Simulation System for Pedicle Screw Fixation in Spinal Surgery

BACKGROUND

A preoperative planning system facilitates improving surgical outcomes that depend on the experience of the surgeons, thanks to real-time interaction between the system and surgeons. It visualizes intermediate surgical planning results to help surgeons discuss the planning. The purpose of this study was to demonstrate the use of a newly-developed preoperative planning system for surgeons less experienced in pedicle-screw fixation in spinal surgery, especially on patients with anatomical variations.

METHODS

The marching cubes algorithm, a typical surface extraction technique, was applied to computed tomography (CT) images of vertebrae to enable three-dimensional (3D) reconstruction of a spinal mesh. Real-time processing of such data is difficult, as the surface mesh extracted from high-resolution CT data is rough, and the size of the mesh is large. To mitigate these factors, Laplacian smoothing was applied, followed by application of a quadric error metric-based mesh simplification to reduce the mesh size for the level-of-detail (LOD) image. Taubin smoothing was applied to smooth out the rough surface. On a multiplanar reconstruction (MPR) cross-sectional image or a 3D model view, the insertion position and orientation of the pedicle screw were manipulated using a mouse. The results after insertion were then visualized in each image.

RESULTS

The system was used for pre-planning pedicle-screw fixation in spinal surgery. Using any pointing device such as a mouse, surgeons can manipulate the position and angle of the screws. The pedicle screws were easy to manipulate intuitively on the MPR images, and the accuracy of screw fixation was confirmed on a trajectory view and 3D images. After surgery, CT scans were performed again, and the CT images were checked to ensure that the screws were inserted properly.

CONCLUSION

The preoperative planning system allows surgeons and students who are not familiar with pedicle-screw fixation to safely undertake surgery following preoperative planning. It also provides opportunities for screw-fixation training and simulation.

Multidimensional persistence in biomolecular data

Persistent homology has emerged as a popular technique for the topological simplification of big data, including biomolecular data. Multidimensional persistence bears considerable promise to bridge the gap between geometry and topology. However, its practical and robust construction has been a challenge. We introduce two families of multidimensional persistence, namely pseudomultidimensional persistence and multiscale multidimensional persistence. The former is generated via the repeated applications of persistent homology filtration to high-dimensional data, such as results from molecular dynamics or partial differential equations. The latter is constructed via isotropic and anisotropic scales that create new simiplicial complexes and associated topological spaces. The utility, robustness, and efficiency of the proposed topological methods are demonstrated via protein folding, protein flexibility analysis, the topological denoising of cryoelectron microscopy data, and the scale dependence of nanoparticles. Topological transition between partial folded and unfolded proteins has been observed in multidimensional persistence. The separation between noise topological signatures and molecular topological fingerprints is achieved by the Laplace-Beltrami flow. The multiscale multidimensional persistent homology reveals relative local features in Betti-0 invariants and the relatively global characteristics of Betti-1 and Betti-2 invariants.

Persistent homology analysis of protein structure, flexibility, and folding

Proteins are the most important biomolecules for living organisms. The understanding of protein structure, function, dynamics, and transport is one of the most challenging tasks in biological science. In the present work, persistent homology is, for the first time, introduced for extracting molecular topological fingerprints (MTFs) based on the persistence of molecular topological invariants. MTFs are utilized for protein characterization, identification, and classification. The method of slicing is proposed to track the geometric origin of protein topological invariants. Both all-atom and coarse-grained representations of MTFs are constructed. A new cutoff-like filtration is proposed to shed light on the optimal cutoff distance in elastic network models. On the basis of the correlation between protein compactness, rigidity, and connectivity, we propose an accumulated bar length generated from persistent topological invariants for the quantitative modeling of protein flexibility. To this end, a correlation matrix-based filtration is developed. This approach gives rise to an accurate prediction of the optimal characteristic distance used in protein B-factor analysis. Finally, MTFs are employed to characterize protein topological evolution during protein folding and quantitatively predict the protein folding stability. An excellent consistence between our persistent homology prediction and molecular dynamics simulation is found. This work reveals the topology-function relationship of proteins.

Flow-induced ATP release in patient-specific arterial geometries--a comparative study of computational models

The importance of the endothelium in the local regulation of blood flow is reflected by its influence on vascular tone by means of vasodilatory responses to many physiological stimuli. Regulatory pathways are affected by mass transport and wall shear stress (WSS), via mechanotransduction mechanisms. In the present work, we review the most relevant computational models that have been proposed to date, and introduce a general framework for modelling the responses of the endothelium to alteration in the flow, with a view to understanding the biomechanical processes involved in the pathways to endothelial dysfunction. Simulations are performed on two different patient-specific stenosed carotid artery geometries to investigate the influence of WSS and mass transport phenomena upon the agonist coupling response at the endothelium. In particular, results presented for two different models of WSS-dependent adenosine-5'-triphosphate (ATP) release reveal that existing paradigms may not account for the conditions encountered in vivo and may therefore not be adequate to model the kinetics of ATP at the endothelium.

Multiscale geometric modeling of macromolecules II: Lagrangian representation

Geometric modeling of biomolecules plays an essential role in the conceptualization of biolmolecular structure, function, dynamics, and transport. Qualitatively, geometric modeling offers a basis for molecular visualization, which is crucial for the understanding of molecular structure and interactions. Quantitatively, geometric modeling bridges the gap between molecular information, such as that from X-ray, NMR, and cryo-electron microscopy, and theoretical/mathematical models, such as molecular dynamics, the Poisson-Boltzmann equation, and the Nernst-Planck equation. In this work, we present a family of variational multiscale geometric models for macromolecular systems. Our models are able to combine multiresolution geometric modeling with multiscale electrostatic modeling in a unified variational framework. We discuss a suite of techniques for molecular surface generation, molecular surface meshing, molecular volumetric meshing, and the estimation of Hadwiger's functionals. Emphasis is given to the multiresolution representations of biomolecules and the associated multiscale electrostatic analyses as well as multiresolution curvature characterizations. The resulting fine resolution representations of a biomolecular system enable the detailed analysis of solvent-solute interaction, and ion channel dynamics, whereas our coarse resolution representations highlight the compatibility of protein-ligand bindings and possibility of protein-protein interactions.

New software developments for quality mesh generation and optimization from biomedical imaging data

In this paper we present a new software toolkit for generating and optimizing surface and volumetric meshes from three-dimensional (3D) biomedical imaging data, targeted at image-based finite element analysis of some biomedical activities in a single material domain. Our toolkit includes a series of geometric processing algorithms including surface re-meshing and quality-guaranteed tetrahedral mesh generation and optimization. All methods described have been encapsulated into a user-friendly graphical interface for easy manipulation and informative visualization of biomedical images and mesh models. Numerous examples are presented to demonstrate the effectiveness and efficiency of the described methods and toolkit.

Geometric modeling of subcellular structures, organelles, and multiprotein complexes

Recently, the structure, function, stability, and dynamics of subcellular structures, organelles, and multiprotein complexes have emerged as a leading interest in structural biology. Geometric modeling not only provides visualizations of shapes for large biomolecular complexes but also fills the gap between structural information and theoretical modeling, and enables the understanding of function, stability, and dynamics. This paper introduces a suite of computational tools for volumetric data processing, information extraction, surface mesh rendering, geometric measurement, and curvature estimation of biomolecular complexes. Particular emphasis is given to the modeling of cryo-electron microscopy data. Lagrangian-triangle meshes are employed for the surface presentation. On the basis of this representation, algorithms are developed for surface area and surface-enclosed volume calculation, and curvature estimation. Methods for volumetric meshing have also been presented. Because the technological development in computer science and mathematics has led to multiple choices at each stage of the geometric modeling, we discuss the rationales in the design and selection of various algorithms. Analytical models are designed to test the computational accuracy and convergence of proposed algorithms. Finally, we select a set of six cryo-electron microscopy data representing typical subcellular complexes to demonstrate the efficacy of the proposed algorithms in handling biomolecular surfaces and explore their capability of geometric characterization of binding targets. This paper offers a comprehensive protocol for the geometric modeling of subcellular structures, organelles, and multiprotein complexes.