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.     

Graded meshes in bio-thermal problems with transmission-line modeling method

In this study, the transmission-line modeling (TLM) applied to bio-thermal problems was improved by incorporating several novel computational techniques, which include application of graded meshes which resulted in 9 times faster in computational time and uses only a fraction (16%) of the computational resources used by regular meshes in analyzing heat flow through heterogeneous media. Graded meshes, unlike regular meshes, allow heat sources to be modeled in all segments of the mesh. A new boundary condition that considers thermal properties and thus resulting in a more realistic modeling of complex problems is introduced. Also, a new way of calculating an error parameter is introduced. The calculated temperatures between nodes were compared against the results obtained from the literature and agreed within less than 1% difference. It is reasonable, therefore, to conclude that the improved TLM model described herein has great potential in heat transfer of biological systems.     

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.     

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.     

Towards accurate numerical method for monodomain models using a realistic heart geometry

The simulation of cardiac electrophysiological waves are known to require extremely fine meshes, limiting the applicability of current numerical models to simplified geometries and ionic models. In this work, an accurate numerical method based on a time-dependent anisotropic remeshing strategy is presented for simulating three-dimensional cardiac electrophysiological waves. The proposed numerical method greatly reduces the number of elements and enhances the accuracy of the prediction of the electrical wave fronts. Illustrations of the performance and the accuracy of the proposed method are presented using a realistic heart geometry. Qualitative and quantitative results show that the proposed methodology is far superior to the uniform mesh methods commonly used in cardiac electrophysiology.     

IVUS-based computational modeling and planar biaxial artery material properties for human coronary plaque vulnerability assessment

Image-based computational modeling has been introduced for vulnerable atherosclerotic plaques to identify critical mechanical conditions which may be used for better plaque assessment and rupture predictions. In vivo patient-specific coronary plaque models are lagging due to limitations on non-invasive image resolution, flow data, and vessel material properties. A framework is proposed to combine intravascular ultrasound (IVUS) imaging, biaxial mechanical testing and computational modeling with fluid-structure interactions and anisotropic material properties to acquire better and more complete plaque data and make more accurate plaque vulnerability assessment and predictions. Impact of pre-shrink-stretch process, vessel curvature and high blood pressure on stress, strain, flow velocity and flow maximum principal shear stress was investigated.     

Anisotropic adaptive finite element method for modelling blood flow

In this study, we present an adaptive anisotropic finite element method (FEM) and demonstrate how computational efficiency can be increased when applying the method to the simulation of blood flow in the cardiovascular system. We use the SUPG formulation for the transient 3D incompressible Navier–Stokes equations which are discretised by linear finite elements for both the pressure and the velocity field.

Given the pulsatile nature of the flow in blood vessels we have pursued adaptivity based on the average flow over a cardiac cycle. Error indicators are derived to define an anisotropic mesh metric field. Mesh modification algorithms are used to anisotropically adapt the mesh according to the desired size field. We demonstrate the efficiency of the method by first applying it to pulsatile flow in a straight cylindrical vessel and then to a porcine aorta with a stenosis bypassed by a graft. We demonstrate that the use of an anisotropic adaptive FEM can result in an order of magnitude reduction in computing time with no loss of accuracy compared to analyses obtained with uniform meshes.     

2D/3D hybrid structural model of vocal folds

The spatial dimensionality of the vocal fold vibration is a common challenge in creating parsimonious models of vocal fold vibration. The ideal model is one that is accurate, with the lowest possible computational expense. Inclusion of full 3D flow and structural vibration typically requires massive amounts of computation, whereas reduction of either the flow or the structure to two dimensions eliminates certain aspects of physical reality, thus making the resulting models less accurate. Previous 2D models of the vocal fold structure have utilized a plane strain formulation, which is shown to be an erroneous modeling approach since it ignores influential stress components. We herein present a 2D/3D hybrid vocal fold model that preserves three-dimensional effects of length and longitudinal shear stresses, while taking advantage of a two-dimensional computational domain. The resulting model exhibits static and dynamic responses comparable to a 3D model, and retains the computational advantage of a two-dimensional model.     

Computational framework to model and design surgical meshes for hernia repair

Surgical procedures for hernia surgery are usually performed using prosthetic meshes. In spite of all the improvements in these biomaterials, the perfect match between the prosthesis and the implant site has not been achieved. Thus, new designs of surgical meshes are still being developed. Previous to implantation in humans, the validity of the meshes has to be addressed, and to date experimental studies have been the gold standard in testing and validating new implants. Nevertheless, these procedures involve long periods of time and are expensive. Thus, a computational framework for the simulation of prosthesis and surgical procedures may overcome some disadvantages of the experimental methods. The computational framework includes two computational models for designing and validating the behaviour of new meshes, respectively. Firstly, the beam model, which reproduces the exact geometry of the mesh, is set to design the weave and determine the stiffness of the surgical prosthesis. However, this implies a high computational cost whereas the membrane model, defined within the framework of the large deformation hyperelasticity, is a relatively inexpensive computational tool, which also enables a prosthesis to be included in more complex geometries such as human or animal bodies.     

The layer-oriented approach to declarative languages for biological modeling

We present a new approach to modeling languages for computational biology, which we call the layer-oriented approach. The approach stems from the observation that many diverse biological phenomena are described using a small set of mathematical formalisms (e.g. differential equations), while at the same time different domains and subdomains of computational biology require that models are structured according to the accepted terminology and classification of that domain. Our approach uses distinct semantic layers to represent the domain-specific biological concepts and the underlying mathematical formalisms. Additional functionality can be transparently added to the language by adding more layers. This approach is specifically concerned with declarative languages, and throughout the paper we note some of the limitations inherent to declarative approaches. The layer-oriented approach is a way to specify explicitly how high-level biological modeling concepts are mapped to a computational representation, while abstracting away details of particular programming languages and simulation environments. To illustrate this process, we define an example language for describing models of ionic currents, and use a general mathematical notation for semantic transformations to show how to generate model simulation code for various simulation environments. We use the example language to describe a Purkinje neuron model and demonstrate how the layer-oriented approach can be used for solving several practical issues of computational neuroscience model development. We discuss the advantages and limitations of the approach in comparison with other modeling language efforts in the domain of computational biology and outline some principles for extensible, flexible modeling language design. We conclude by describing in detail the semantic transformations defined for our language.     

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.     

Anisotropic adaptive finite element method for modelling blood flow

In this study, we present an adaptive anisotropic finite element method (FEM) and demonstrate how computational efficiency can be increased when applying the method to the simulation of blood flow in the cardiovascular system. We use the SUPG formulation for the transient 3D incompressible Navier-Stokes equations which are discretised by linear finite elements for both the pressure and the velocity field. Given the pulsatile nature of the flow in blood vessels we have pursued adaptivity based on the average flow over a cardiac cycle. Error indicators are derived to define an anisotropic mesh metric field. Mesh modification algorithms are used to anisotropically adapt the mesh according to the desired size field. We demonstrate the efficiency of the method by first applying it to pulsatile flow in a straight cylindrical vessel and then to a porcine aorta with a stenosis bypassed by a graft. We demonstrate that the use of an anisotropic adaptive FEM can result in an order of magnitude reduction in computing time with no loss of accuracy compared to analyses obtained with uniform meshes.     

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.     

Using in vivo Cine and 3D multi-contrast MRI to determine human atherosclerotic carotid artery material properties and circumferential shrinkage rate and their impact on stress/strain predictions

In vivo magnetic resonance image (MRI)-based computational models have been introduced to calculate atherosclerotic plaque stress and strain conditions for possible rupture predictions. However, patient-specific vessel material properties are lacking in those models, which affects the accuracy of their stress/strain predictions. A noninvasive approach of combining in vivo Cine MRI, multicontrast 3D MRI, and computational modeling was introduced to quantify patient-specific carotid artery material properties and the circumferential shrinkage rate between vessel in vivo and zero-pressure geometries. In vivo Cine and 3D multicontrast MRI carotid plaque data were acquired from 12 patients after informed consent. For each patient, one nearly-circular slice and an iterative procedure were used to quantify parameter values in the modified Mooney-Rivlin model for the vessel and the vessel circumferential shrinkage rate. A sample artery slice with and without a lipid core and three material parameter sets representing stiff, median, and soft materials from our patient data were used to demonstrate the effect of material stiffness and circumferential shrinkage process on stress/strain predictions. Parameter values of the Mooney-Rivlin models for the 12 patients were quantified. The effective Young's modulus (YM, unit: kPa) values varied from 137 (soft), 431 (median), to 1435 (stiff), and corresponding circumferential shrinkages were 32%, 12.6%, and 6%, respectively. Using the sample slice without the lipid core, the maximum plaque stress values (unit: kPa) from the soft and median materials were 153.3 and 96.2, which are 67.7% and 5% higher than that (91.4) from the stiff material, while the maximum plaque strain values from the soft and median materials were 0.71 and 0.293, which are about 700% and 230% higher than that (0.089) from the stiff material, respectively. Without circumferential shrinkages, the maximum plaque stress values (unit: kPa) from the soft, median, and stiff models were inflated to 330.7, 159.2, and 103.6, which were 116%, 65%, and 13% higher than those from models with proper shrinkage. The effective Young's modulus from the 12 human carotid arteries studied varied from 137 kPa to 1435 kPa. The vessel circumferential shrinkage to the zero-pressure condition varied from 6% to 32%. The inclusion of proper shrinkage in models based on in vivo geometry is necessary to avoid over-estimating the stresses and strains by up 100%. Material stiffness had a greater impact on strain (up to 700%) than on stress (up to 70%) predictions. Accurate patient-specific material properties and circumferential shrinkage could considerably improve the accuracy of in vivo MRI-based computational stress/strain predictions.     

Model reduction using a posteriori analysis

Mathematical models in biology and physiology are often represented by large systems of non-linear ordinary differential equations. In many cases, an observed behaviour may be written as a linear functional of the solution of this system of equations. A technique is presented in this study for automatically identifying key terms in the system of equations that are responsible for a given linear functional of the solution. This technique is underpinned by ideas drawn from a posteriori error analysis. This concept has been used in finite element analysis to identify regions of the computational domain and components of the solution where a fine computational mesh should be used to ensure accuracy of the numerical solution. We use this concept to identify regions of the computational domain and components of the solution where accurate representation of the mathematical model is required for accuracy of the functional of interest. The technique presented is demonstrated by application to a model problem, and then to automatically deduce known results from a cell-level cardiac electrophysiology model.     

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.     

Automatic 4D Reconstruction of Patient-Specific Cardiac Mesh with 1-to-1 Vertex Correspondence from Segmented Contours Lines

We propose an automatic algorithm for the reconstruction of patient-specific cardiac mesh models with 1-to-1 vertex correspondence. In this framework, a series of 3D meshes depicting the endocardial surface of the heart at each time step is constructed, based on a set of border delineated magnetic resonance imaging (MRI) data of the whole cardiac cycle. The key contribution in this work involves a novel reconstruction technique to generate a 4D (i.e., spatial–temporal) model of the heart with 1-to-1 vertex mapping throughout the time frames. The reconstructed 3D model from the first time step is used as a base template model and then deformed to fit the segmented contours from the subsequent time steps. A method to determine a tree-based connectivity relationship is proposed to ensure robust mapping during mesh deformation. The novel feature is the ability to handle intra- and inter-frame 2D topology changes of the contours, which manifests as a series of merging and splitting of contours when the images are viewed either in a spatial or temporal sequence. Our algorithm has been tested on five acquisitions of cardiac MRI and can successfully reconstruct the full 4D heart model in around 30 minutes per subject. The generated 4D heart model conforms very well with the input segmented contours and the mesh element shape is of reasonably good quality. The work is important in the support of downstream computational simulation activities.     

Assessment of factors influencing finite element vertebral model predictions

This study aimed to establish model construction and configuration procedures for future vertebral finite element analysis by studying convergence, sensitivity, and accuracy behaviors of semiautomatically generated models and comparing the results with manually generated models. During a previous study, six porcine vertebral bodies were imaged using a microcomputed tomography scanner and tested in axial compression to establish their stiffness and failure strength. Finite element models were built using a manual meshing method. In this study, the experimental agreement of those models was compared with that of semiautomatically generated models of the same six vertebrae. Both manually and semiautomatically generated models were assigned gray-scale-based, element-specific material properties. The convergence of the semiautomatically generated models was analyzed for the complete models along with material property and architecture control cases. A sensitivity study was also undertaken to test the reaction of the models to changes in material property values, architecture, and boundary conditions. In control cases, the element-specific material properties reduce the convergence of the models in comparison to homogeneous models. However, the full vertebral models showed strong convergence characteristics. The sensitivity study revealed a significant reaction to changes in architecture, boundary conditions, and load position, while the sensitivity to changes in material property values was proportional. The semiautomatically generated models produced stiffness and strength predictions of similar accuracy to the manually generated models with much shorter image segmentation and meshing times. Semiautomatic methods can provide a more rapid alternative to manual mesh generation techniques and produce vertebral models of similar accuracy. The representation of the boundary conditions, load position, and surrounding environment is crucial to the accurate prediction of the vertebral response. At present, an element size of 2x2x2 mm(3) appears sufficient since the error at this size is dominated by factors, such as the load position, which will not be improved by increasing the mesh resolution. Higher resolution meshes may be appropriate in the future as models are made more sophisticated and computational processing time is reduced.     

A generalized finite difference method for modeling cardiac electrical activation on arbitrary, irregular computational meshes

A generalized finite difference (GFD) method is presented that can be used to solve the bi-domain equations modeling cardiac electrical activity. Classical finite difference methods have been applied by many researchers to the bi-domain equations. However, these methods suffer from the limitation of requiring computational meshes that are structured and orthogonal. Finite element or finite volume methods enable the bi-domain equations to be solved on unstructured meshes, although implementations of such methods do not always cater for meshes with varying element topology. The GFD method solves the bi-domain equations on arbitrary and irregular computational meshes without any need to specify element basis functions. The method is useful as it can be easily applied to activation problems using existing meshes that have originally been created for use by finite element or finite difference methods. In addition, the GFD method employs an innovative approach to enforcing nodal and non-nodal boundary conditions. The GFD method performs effectively for a range of two and three-dimensional test problems and when computing bi-domain electrical activation moving through a fully anisotropic three-dimensional model of canine ventricles.     

Self-expanding stent modelling and radial force accuracy

Computational simulations using finite element analysis are a tool commonly used to analyse stent designs, deployment geometries and interactions between stent struts and arterial tissue. Such studies require large computational models and efforts are often made to simplify models in order to reduce computational time while maintaining reasonable accuracy. The objective of the study is focused on computational modelling and specifically aims to investigate how different methods of modelling stent–artery interactions can affect the results, computational time taken and computational size of the model. Various different models, each with increasing levels of complexity, are used to simulate this analysis, representing the many assumptions and simplifications used in other similar studies in order to determine what level of simplification will still allow for an accurate representation of stent radial force and resulting stress concentrations on the inner lining of the vessel during self-expanding stent deployment. The main conclusions of the study are that methods used in stent crimping impact on the resulting predicted radial force of the stent; that accurate representation of stent–artery interactions can only be made when modelling the full length of the stent due to the incorporation of end effects; and that modelling self-contact of the stent struts greatly impacts on the resulting stress concentrations within the stent, but that the effect of this on the unloading behaviour and resulting radial force of the stent is negligible.