Patient-specific computational haemodynamics: generation of structured and conformal hexahedral meshes from triangulated surfaces of vascular bifurcations

Measuring the blood flow is still limited by current imaging technologies and is generally overcome using computational fluid dynamics (CFD) which, because of the complex geometry of blood vessels, has widely relied on tetrahedral meshes. Hexahedral meshes offer more accurate results with lower-density meshes and faster computation as compared to tetrahedral meshes, but their use is limited by the far more complex mesh generation. We present a robust methodology for conformal and structured hexahedral mesh generation - applicable to complex arterial geometries as bifurcating vessels - starting from triangulated surfaces. Cutting planes are used to slice the lumen surface and to construct longitudinal Bezier splines. Afterwards, an isoparametric transformation is used to map a parametrically defined quadrilateral surface mesh into the vessel volume, resulting in stacks of sections which can then be used for sweeping. Being robust and open source based, this methodology may improve the current standard in patient-specific mesh generation and enhance the reliability of CFD to patient-specific haemodynamics.     

Tetrahedral vs. polyhedral mesh size evaluation on flow velocity and wall shear stress for cerebral hemodynamic simulation

Haemodynamic factors, in particular wall shear stresses (WSSs) may have significant impact on growth and rupture of cerebral aneurysms. Without a means to measure WSS reliably in vivo, computational fluid dynamic (CFD) simulations are frequently employed to visualise and quantify blood flow from patient-specific computational models. With increasing interest in integrating these CFD simulations into pretreatment planning, a better understanding of the validity of the calculations in respect to computation parameters such as volume element type, mesh size and mesh composition is needed. In this study, CFD results for the two most common aneurysm types (saccular and terminal) are compared for polyhedral- vs. tetrahedral-based meshes and discussed regarding future clinical applications. For this purpose, a set of models were constructed for each aneurysm with spatially varying surface and volume mesh configurations (mesh size range: 5119-258, 481 volume elements). WSS distribution on the model wall and point-based velocity measurements were compared for each configuration model. Our results indicate a benefit of polyhedral meshes in respect to convergence speed and more homogeneous WSS patterns. Computational variations of WSS values and blood velocities are between 0.84 and 6.3% from the most simple mesh (tetrahedral elements only) and the most advanced mesh design investigated (polyhedral mesh with boundary layer).     

Requirements for mesh resolution in 3D computational hemodynamics

Computational techniques are widely used for studying large artery hemodynamics. Current trends favor analyzing flow in more anatomically realistic arteries. A significant obstacle to such analyses is generation of computational meshes that accurately resolve both the complex geometry and the physiologically relevant flow features. Here we examine, for a single arterial geometry, how velocity and wall shear stress patterns depend on mesh characteristics. A well-validated Navier-Stokes solver was used to simulate flow in an anatomically realistic human right coronary artery (RCA) using unstructured high-order tetrahedral finite element meshes. Velocities, wall shear stresses (WSS), and wall shear stress gradients were computed on a conventional "high-resolution" mesh series (60,000 to 160,000 velocity nodes) generated with a commercial meshing package. Similar calculations were then performed in a series of meshes generated through an adaptive mesh refinement (AMR) methodology. Mesh-independent velocity fields were not very difficult to obtain for both the conventional and adaptive mesh series. However, wall shear stress fields, and, in particular, wall shear stress gradient fields, were much more difficult to accurately resolve. The conventional (nonadaptive) mesh series did not show a consistent trend towards mesh-independence of WSS results. For the adaptive series, it required approximately 190,000 velocity nodes to reach an r.m.s. error in normalized WSS of less than 10 percent. Achieving mesh-independence in computed WSS fields requires a surprisingly large number of nodes, and is best approached through a systematic solution-adaptive mesh refinement technique. Calculations of WSS, and particularly WSS gradients, show appreciable errors even on meshes that appear to produce mesh-independent velocity fields.     

Subject specific finite element mesh generation of the pelvis from biplanar x-ray images: application to 120 clinical cases

Several Finite Element (FE) models of the pelvis have been developed to comprehensively assess the onset of pathologies and for clinical and industrial applications. However, because of the difficulties associated with the creation of subject-specific FE mesh from CT scan and MR images, most of the existing models rely on the data of one given individual. Moreover, although several fast and robust methods have been developed for automatically generating tetrahedral meshes of arbitrary geometries, hexahedral meshes are still preferred today because of their distinct advantages but their generation remains an open challenge. Recently, approaches have been proposed for fast 3D reconstruction of bones based on X-ray imaging. In this study, we adapted such an approach for the fast and automatic generation of all-hexahedral subject-specific FE models of the pelvis based on the elastic registration of a generic mesh to the subject-specific target in conjunction with element regularity and quality correction. The technique was successfully tested on a database of 120 3D reconstructions of pelvises from biplanar X-ray images. For each patient, a full hexahedral subject-specific FE mesh was generated with an accurate surface representation.     

Characterisation of the haemodynamics of the superior mesenteric artery

In contrast to its prevalence in the surrounding vasculature, occurrence of primary atherosclerotic disease in the superior mesenteric artery (SMA) is rare (Glagov et al., 1988. Hemodynamics and atherosclerosis, Insights and perspectives gained from studies of human arteries. Archives of Pathology and Laboratory Medicine 112(10), 1018-1031; Hansen et al., 2004. Mesenteric artery disease in the elderly. Journal of Vascular Surgery 40(1), 45-52). We hypothesise that this sparing might be attributed to more favourable haemodynamic characteristics in the SMA than in other vessels locally. Dynamic magnetic resonance imaging (MRI) images established that the SMA is highly mobile (Jeays, 2006. Investigation of blood flow in the superior mesenteric artery and its potential influence on atheroma and gut ischaemia. Ph.D. Thesis, University of Sheffield), and thus that an analysis based on rigid geometry might be inappropriate. This paper describes an efficient methodology for the construction of a patient-specific, time-dependent model of an arterial segment and reports the results of a haemodynamic characterisation of the SMA for one individual. A transient computational fluid dynamic (CFD) model was constructed by morphing a parametric mesh constructed from simple geometric primitives. This process has the merit that it is easy to control the element size distribution mapped onto the original geometric primitives. It is robust in operation, and is ideally suited to the generation of dynamic CFD meshes of arterial systems that are free from major pathology. Flow boundary conditions were determined based on phase contrast MRI velocity measurements. Comparative studies with rigid walls and with moving walls, based on the transient data, indicated that, despite the significant motion of the SMA (radial dilation of the order of 10% and translation of the order of the radius), the maximum (spatially and temporally-resolved) wall shear stresses changed by no more than 21.6% of a global norm, and the average change was less than 2.1%.     

Automatic preparation,calibration, and simulation of deformable objects

Many simulation environments – particularly those intended for medical simulation – require solid objects to deform at interactive rates, with deformation properties that correspond to real materials. Furthermore, new objects may be created frequently (for example, each time a new patient's data is processed), prohibiting manual intervention in the model preparation process. This paper provides a pipeline for rapid preparation of deformable objects with no manual intervention, specifically focusing on mesh generation (preparing solid meshes from surface models), automated calibration of models to finite element reference analyses (including a novel approach to reducing the complexity of calibrating nonhomogeneous objects), and automated skinning of meshes for interactive simulation.     

The mesh-matching algorithm: an automatic 3D mesh generator for finite element structures

Several authors have employed finite element analysis for stress and strain analysis in orthopaedic biomechanics. Unfortunately, the definition of three-dimensional models is time consuming (mainly because of the manual 3D meshing process) and consequently the number of analyses to be performed is limited. The authors have investigated a new patient-specific method allowing automatically 3D mesh generation for structures as complex as bone for example. This method, called the mesh-matching (M-M) algorithm, generated automatically customized 3D meshes of anatomical structures from an already existing model. The M-M algorithm has been used to generate FE models of 10 proximal human femora from an initial one which had been experimentally validated. The automatically generated meshes seemed to demonstrate satisfying results.     

A Three-Dimensional Finite Element Scheme to Investigate the Apparent Mechanical Properties of Trabecular Bone

A computational technique is described for investigating the apparent mechanical properties of trabecular bone based on tissue geometry obtained from the marching cubes volume rendering scheme. Using this scheme, a 3D representation of the trabecular bone was extracted from two-dimensional cross-sections of the tissue originating from a quantitative serial sectioning procedure. Surface information consists of node coordinates and polygon connectivity in a 3D space. A custom, adaptive mesh generation technique using a normal offset was used to prepare 3D finite element volume meshes (4-node tetrahedral elements) of variable mesh density from the extracted surface geometry. Nine target mesh resolutions (32 μm to 107 μm) were examined for a (1.5 mmx 1.5 mmx 2 mm) volume of trabecular bone. A mesh density of 50,000 elements/mm(3) of bone tissue was found to be adequate for convergence of apparent (bulk) modulus for 1% uniaxial compression. For this convergent case, the maximum local normal compressive tissue stress was 400 MPa which was six hundred-fold greater than the computed apparent stress. Variation in the apparent modulus was less than 5% when Poisson's ratio values were varied between 0.1 and 0.4. Poisson's ratio values greater than 0.4 had a more marked effect on the apparent modulus. Based upon these results, approximately 1 million, 4-node tetrahedral elements are required to analyze a continuum scale model of trabecular bone (5 mm cube).     

The effects of different mesh generation methods on computational fluid dynamic analysis and power loss assessment in total cavopulmonary connection

The flow field and energetic efficiency of total cavopulmonary connection (TCPC) models have been studied by both in vitro experiment and computational fluid dynamics (CFD). All the previous CFD studies have employed the structured mesh generation method to create the TCPC simulation model. In this study, a realistic TCPC model with complete anatomical features was numerically simulated using both structured and unstructured mesh generation methods. The flow fields and energy losses were compared in these two meshes. Two different energy loss calculation methods, the control volume and viscous dissipation methods, were investigated. The energy losses were also compared to the in vitro experimental results. The results demonstrated that: (1) the flow fields in the structured model were qualitatively similar to the unstructured model; (2) more vortices were present in the structured model than in the unstructured model; (3) both models had the least energy loss when flow was equally distributed to the left and right pulmonary arteries, while high losses occurred for extreme pulmonary arterial flow splits; (4) the energy loss results calculated using the same method were significantly different for different meshes; and (5) the energy loss results calculated using different methods were significantly different for the same mesh.     

Finite-element modeling of the hemodynamics of stented aneurysms

BACKGROUND: Computational fluid dynamics (CFD) simulations are used to analyze the wall shear stress distribution and flow streamlines near the throat of a stented basilar side-wall aneurysm. Previous studies of stented aneurysm flows used low mesh resolution, did not include mesh convergence analyses, and depended upon conformal meshing techniques that apply only to very artificial stent geometries. METHOD OF APPROACH: We utilize general-purpose computer assisted design and unstructured mesh generation tools that apply in principle to stents and vasculature of arbitrary complexity. A mesh convergence analysis for stented steady flow is performed, varying node spacing near the stent. Physiologically realistic pulsatile simulations are then performed using the converged mesh. RESULTS: Artifact-free resolution of the wall shear stress field on stent wires requires a node spacing of approximately 1/3 wire radius. Large-scale flow features tied to the velocity field are, however, captured at coarser resolution (nodes spaced by about one wire radius or more). CONCLUSIONS: Results are consistent with previous work, but our methods yield more detailed insights into the complex flow dynamics. However, routine applications of CFD to anatomically realistic cases still depend upon further development of dedicated algorithms, most crucially to handle geometry definition and mesh generation for complicated stent deployments.     

Improving the local solution accuracy of large-scale digital image-based finite element analyses

Digital image-based finite element modeling (DIBFEM) has become a widely utilized approach for efficiently meshing complex biological structures such as trabecular bone. While DIBFEM can provide accurate predictions of apparent mechanical properties, its application to simulate local phenomena such as tissue failure or adaptation has been limited by high local solution errors at digital model boundaries. Furthermore, refinement of digital meshes does not necessarily reduce local maximum errors. The purpose of this study was to evaluate the potential to reduce local mean and maximum solution errors in digital meshes using a post-processing filtration method. The effectiveness of a three-dimensional, boundary-specific filtering algorithm was found to be mesh size dependent. Mean absolute and maximum errors were reduced for meshes with more than five elements through the diameter of a cantilever beam considered representative of a single trabecula. Furthermore, mesh refinement consistently decreased errors for filtered solutions but not necessarily for non-filtered solutions. Models with more than five elements through the beam diameter yielded absolute mean errors of less than 15% for both Von Mises stress and maximum principal strain. When applied to a high-resolution model of trabecular bone microstructure, boundary filtering produced a more continuous solution distribution and reduced the predicted maximum stress by 30%. Boundary-specific filtering provides a simple means of improving local solution accuracy while retaining the model generation and numerical storage efficiency of the DIBFEM technique.     

Dynamic Lung Modeling and Tumor Tracking Using Deformable Image Registration and Geometric Smoothing

A greyscale-based fully automatic deformable image registration algorithm, based on an optical flow method together with geometric smoothing, is developed for dynamic lung modeling and tumor tracking. In our computational processing pipeline, the input data is a set of 4D CT images with 10 phases. The triangle mesh of the lung model is directly extracted from the more stable exhale phase (Phase 5). In addition, we represent the lung surface model in 3D volumetric format by applying a signed distance function and then generate tetrahedral meshes. Our registration algorithm works for both triangle and tetrahedral meshes. In CT images, the intensity value reflects the local tissue density. For each grid point, we calculate the displacement from the static image (Phase 5) to match with the moving image (other phases) by using merely intensity values of the CT images. The optical flow computation is followed by a regularization of the deformation field using geometric smoothing. Lung volume change and the maximum lung tissue movement are used to evaluate the accuracy of the application. Our testing results suggest that the application of deformable registration algorithm is an effective way for delineating and tracking tumor motion in image-guided radiotherapy.     

A semi-automated method for hexahedral mesh construction of human vertebrae from CT scans

Generation of finite element (FE) meshes of vertebrae from computed tomography (CT) scans is labour intensive due to their geometric complexity. As such, techniques that simplify creation of meshes of vertebrae are needed to make FE analysis feasible for large studies and clinical applications. Techniques to obtain a geometric representation of bone contours from CT scans of vertebrae and construct a hexahedral mesh from the contours were developed. An automated edge detection technique was developed to identify surface contours of the vertebrae, followed by atlas based B-spline curve fitting to construct curves from the edge points. The method was automatic and robust to missing data, with a controllable degree of smoothing and interpolation. Parametric mapping was then used to generate nodes for each CT slice, which were connected between slices to obtain a hexahedral mesh. This method could be adapted for modelling a variety of orthopaedic structures.     

蛋白质分子表面高质量网格构建技术的研究进展

分子表面即分子边界,在一定程度上蕴含了分子的生物化学属性信息,对分子表面进行分析将有助于理解分子对接、识别和相互作用等问题。由于蛋白质分子表面的构造相对复杂,尤其是分子表面的网格化,因此寻求高效的算法构建高质量的蛋白质分子表面网格对生成光滑的分子表面、分子可视化及分子模拟都有着重要的意义。本文主要根据现有定义的蛋白质分子表面,针对近年来几种高质量分子表面网格构建的新技术进行了阐述,同时介绍了几款蛋白质分子表面可视化软件,并对它们的性能进行了简单的分析。     

Adaptive generation of multimaterial grids from imaging data for biomedical Lagrangian fluid–structure simulations

Spatial discretization of complex imaging- derived fluid–solid geometries, such as the cardiac environment, is a critical but often overlooked challenge in biomechanical computations. This is particularly true in problems with Lagrangian interfaces, where the fluid and solid phases share a common interface geometrically. For simplicity and better accuracy, it is also highly desirable for the two phases to have a matching surface mesh at the interface between them. We outline a method for solving this problem, and illustrate the approach with a 3D fluid–solid mesh of the mouse heart. An MRI dataset of a perfusion-fixed mouse heart with 50μm isotropic resolution was semi-automatically segmented using a customized multimaterial connected-threshold approach that divided the volume into non-overlapping regions of blood, tissue, and background. Subsequently a multimaterial marching cubes algorithm was applied to the segmented data to produce two detailed, compatible isosurfaces, one for blood and one for tissue. Both isosurfaces were simultaneously smoothed with a multimaterial smoothing algorithm that exactly conserves the volume for each phase. Using these two isosurfaces, we developed and applied novel automated meshing algorithms to generate anisotropic hybrid meshes on arbitrary biological geometries with the number of layers and the desired element anisotropy for each phase as the only input parameters. Since our meshes adapt to the local feature sizes and include boundary layer prisms, they are more efficient and accurate than non-adaptive, isotropic meshes, and the fluid–structure interaction computations will tend to have relative error equilibrated over the whole mesh.     

Orbital and maxillofacial computer aided surgery: patient-specific finite element models to predict surgical outcomes

This paper addresses an important issue raised for the clinical relevance of Computer-Assisted Surgical applications, namely the methodology used to automatically build patient-specific finite element (FE) models of anatomical structures. From this perspective, a method is proposed, based on a technique called the mesh-matching method, followed by a process that corrects mesh irregularities. The mesh-matching algorithm generates patient-specific volume meshes from an existing generic model. The mesh regularization process is based on the Jacobian matrix transform related to the FE reference element and the current element.This method for generating patient-specific FE models is first applied to computer-assisted maxillofacial surgery, and more precisely, to the FE elastic modelling of patient facial soft tissues. For each patient, the planned bone osteotomies (mandible, maxilla, chin) are used as boundary conditions to deform the FE face model, in order to predict the aesthetic outcome of the surgery. Seven FE patient-specific models were successfully generated by our method. For one patient, the prediction of the FE model is qualitatively compared with the patient's post-operative appearance, measured from a computer tomography scan. Then, our methodology is applied to computer-assisted orbital surgery. It is, therefore, evaluated for the generation of 11 patient-specific FE poroelastic models of the orbital soft tissues. These models are used to predict the consequences of the surgical decompression of the orbit. More precisely, an average law is extrapolated from the simulations carried out for each patient model. This law links the size of the osteotomy (i.e. the surgical gesture) and the backward displacement of the eyeball (the consequence of the surgical gesture).     

Comparison of hexahedral and tetrahedral elements in finite element analysis of the foot and footwear

Finite element analysis has been widely used in the field of foot and footwear biomechanics to determine plantar pressures as well as stresses and strains within soft tissue and footwear materials. When dealing with anatomical structures such as the foot, hexahedral mesh generation accounts for most of the model development time due to geometric complexities imposed by branching and embedded structures. Tetrahedral meshing, which can be more easily automated, has been the approach of choice to date in foot and footwear biomechanics. Here we use the nonlinear finite element program Abaqus (Simulia, Providence, RI) to examine the advantages and disadvantages of tetrahedral and hexahedral elements under compression and shear loading, material incompressibility, and frictional contact conditions, which are commonly seen in foot and footwear biomechanics. This study demonstrated that for a range of simulation conditions, hybrid hexahedral elements (Abaqus C3D8H) consistently performed well while hybrid linear tetrahedral elements (Abaqus C3D4H) performed poorly. On the other hand, enhanced quadratic tetrahedral elements with improved stress visualization (Abaqus C3D10I) performed as well as the hybrid hexahedral elements in terms of contact pressure and contact shear stress predictions. Although the enhanced quadratic tetrahedral element simulations were computationally expensive compared to hexahedral element simulations in both barefoot and footwear conditions, the enhanced quadratic tetrahedral element formulation seems to be very promising for foot and footwear applications as a result of decreased labor and expedited model development, all related to facilitated mesh generation.     

Three-dimensional geometric modeling of membrane-bound organelles in ventricular myocytes: bridging the gap between microscopic imaging and mathematical simulation

A general framework of image-based geometric processing is presented to bridge the gap between three-dimensional (3D) imaging that provides structural details of a biological system and mathematical simulation where high-quality surface or volumetric meshes are required. A 3D density map is processed in the order of image pre-processing (contrast enhancement and anisotropic filtering), feature extraction (boundary segmentation and skeletonization), and high-quality and realistic surface (triangular) and volumetric (tetrahedral) mesh generation. While the tool-chain described is applicable to general types of 3D imaging data, the performance is demonstrated specifically on membrane-bound organelles in ventricular myocytes that are imaged and reconstructed with electron microscopic (EM) tomography and two-photon microscopy (T-PM). Of particular interest in this study are two types of membrane-bound Ca²⁺-handling organelles, namely, transverse tubules (T-tubules) and junctional sarcoplasmic reticulum (jSR), both of which play an important role in regulating the excitation–contraction (E–C) coupling through dynamic Ca²⁺ mobilization in cardiomyocytes.     

Beyond heuristics: CFD-based novel multiparameter scale-up for geometrically disparate bioreactors demonstrated at industrial 2kL–10kL scales

The timely delivery of the most up-to-date medicines and drug products is essential for patients throughout the world. Successful scaling of the bioreactors used within the biopharmaceutical industry plays a large part in the quality and time to market of these products. Scale and topology differences between vessels add a large degree of complication and uncertainty within the scaling process. Currently, this approach is primarily achieved through extensive experimentation and facile empirical correlations, which can be costly and time consuming while providing limited information. The work undertaken in the current study demonstrates a more robust and complete approach using computational fluid dynamics (CFD) to provide potent multiparameter scalability, which only requires geometric and material properties before a comprehensive and detailed solution can be generated. The CFD model output parameters that can be applied in the scale-up include mass transfer rates, mixing times, shear rates, gas hold-up values, and bubble residence times. The authors examined three bioreactors with variable geometries and were able to validate them based on single-phase and multiphase experiments. Furthermore, leveraging the resulting CFD output information enabled the authors to successfully scale-up from a known 2kL to a novel and disparate 5kL single-use bioreactor in the first attempted cell culture. This multiparameter scaling approach promises to ultimately lead to a reduction in the time to market providing patients with earlier access to the most groundbreaking medicines.