Mesh considerations for finite element blast modelling in biomechanics

Finite element (FE) modelling is a popular tool for studying human body response to blast exposure. However, blast modelling is a complex problem owing to more numerous fluid–structure interactions (FSIs) and the high–frequency loading that accompanies blast exposures. This study investigates FE mesh design for blast modelling using a sphere in a closed-ended shock tube meshed with varying element sizes using both tetrahedral and hexahedral elements. FSI was consistent for sphere-to-fluid element ratios between 0.25 and 4, and acceleration response was similar for both element types (R² = 0.997). Tetrahedral elements were found to become increasingly volatile following shock loading, causing higher pressures and stresses than predicted with the hexahedral elements. Deviatoric stress response was dependent on the sphere mesh size (p < 0.001), while the pressure response was dependent on the shock tube mesh size (p < 0.001). The results of this study highlight the necessity for mesh sensitivity analysis in blast models.     

Effect of meniscus replacement fixation technique on restoration of knee contact mechanics and stability

The menisci are important biomechanical components of the knee. We developed and validated a finite element model of meniscal replacement to assess the effect of surgical fixation technique on contact behavior and knee stability. The geometry of femoral and tibial articular cartilage and menisci was segmented from magnetic resonance images of a normal cadaver knee using MIMICS (Materialise, Leuven, Belgium). A finite element mesh was generated using HyperWorks (Altair Inc, Santa Ana, CA). A finite element solver (Abaqus v6.9, Simulia, Providence, RI) was used to compute contact area and stresses under axial loading and to assess stability (reaction force generated during anteroposterior translation of the femur). The natural and surgical attachments of the meniscal horns and peripheral rim were simulated using springs. After total meniscectomy, femoral contact area decreased by 26% with a concomitant increase in average contact stresses (36%) and peak contact stresses (33%). Replacing the meniscus without suturing the horns did little to restore femoral contact area. Suturing the horns increased contact area and reduced peak contact stresses. Increasing suture stiffness correlated with increased meniscal contact stresses as a greater proportion of tibiofemoral load was transferred to the meniscus. A small incremental benefit was seen of simulated bone plug fixation over the suture construct with the highest stiffness (50 N/mm). Suturing the rim did little to change contact conditions. The nominal anteroposterior stiffness reduced by 3.1 N/mm after meniscectomy. In contrast to contact area and stress, stiffness of the horn fixation sutures had a smaller effect on anteroposterior stability. On the other hand suturing the rim of the meniscus affected anteroposterior stability to a much larger degree. This model emphasizes the importance of the meniscus in knee biomechanics. Appropriate meniscal replacement fixation techniques are likely to be critical to the clinical success of meniscal replacement. While contact conditions are mainly sensitive to meniscus horn fixation, the stability of the knee under anteroposterior shear loads appeared to be more sensitive to meniscal rim fixation. This model may also be useful in predicting the effect of biomaterial mechanical properties and meniscal replacement shape on knee contact conditions.     

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.     

Development and validation of a subject-specific finite element model of a human clavicle

This study aimed to develop and validate a finite element (FE) model of a human clavicle which can predict the structural response and bone fractures under both axial compression and anterior–posterior three-point bending loads. Quasi-static non-injurious axial compression and three-point bending tests were first conducted on a male clavicle followed by a dynamic three-point bending test to fracture. Then, two types of FE models of the clavicle were developed using bone material properties which were set to vary with the computed tomography image density of the bone. A volumetric solid FE model comprised solely of hexahedral elements was first developed. A solid-shell FE model was then created which modelled the trabecular bone as hexahedral elements and the cortical bone as quadrilateral shell elements. Finally, simulations were carried out using these models to evaluate the influence of variations in cortical thickness, mesh density, bone material properties and modelling approach on the biomechanical responses of the clavicle, compared with experimental data. The FE results indicate that the inclusion of density-based bone material properties can provide a more accurate reproduction of the force–displacement response and bone fracture timing than a model with uniform bone material properties. Inclusion of a variable cortical thickness distribution also slightly improves the ability of the model to predict the experimental response. The methods developed in this study will be useful for creating subject-specific FE models to better understand the biomechanics and injury mechanism of the clavicle.     

Patient-specific modelling of the foot: automated hexahedral meshing of the bones

Subject-specific finite element modelling is a powerful tool for carrying out controlled investigations of the effects of geometric and material property differences on performance and injury risk. Unfortunately, the creation of suitable meshes for these models is a challenging and time-intensive task. This paper presents an automated method of generating fully hexahedral meshes of the bones of the feet which requires only surface representations as inputs. The method is outlined and example meshes, using two human feet and the foot of a Japanese macaque, are given to demonstrate its flexibility. Mesh quality is also evaluated for the calcaneus, first metatarsal, navicular and talus. Streamlining the generation of finite element meshes of the foot will ease investigations into the patient-specific biomechanics of injury.     

Finite element modeling of the first ray of the foot: a tool for the design of interventions

Disorders of the first ray of the foot (defined as the hard and soft tissues of the first metatarsal, the sesamoids, and the phalanges of the great toe) are common, and therapeutic interventions to address these problems range from alterations in footwear to orthopedic surgery. Experimental verification of these procedures is often lacking, and thus, a computational modeling approach could provide a means to explore different interventional strategies. A three-dimensional finite element model of the first ray was developed for this purpose. A hexahedral mesh was constructed from magnetic resonance images of the right foot of a male subject. The soft tissue was assumed to be incompressible and hyperelastic, and the bones were modeled as rigid. Contact with friction between the foot and the floor or footwear was defined, and forces were applied to the base of the first metatarsal. Vertical force was extracted from experimental data, and a posterior force of 0.18 times the vertical force was assumed to represent loading at peak forefoot force in the late-stance phase of walking. The orientation of the model and joint configuration at that instant were obtained by minimizing the difference between model predicted and experimentally measured barefoot plantar pressures. The model were then oriented in a series of postures representative of push-off, and forces and joint moments were decreased to zero simultaneously. The pressure distribution underneath the first ray was obtained for each posture to illustrate changes under three case studies representing hallux limitus, surgical arthrodesis of the first ray, and a footwear intervention. Hallux limitus simulations showed that restriction of metatarsophalangeal joint dorsiflexion was directly related to increase and early occurrence of hallux pressures with severe immobility increasing the hallux pressures by as much as 223%. Modeling arthrodesis illustrated elevated hallux pressures when compared to barefoot and was dependent on fixation angles. One degree change in dorsiflexion and valgus fixation angles introduced approximate changes in peak hallux pressure by 95 and 22 kPa, respectively. Footwear simulations using flat insoles showed that using the given set of materials, reductions of at least 18% and 43% under metatarsal head and hallux, respectively, were possible.     

A framework for biomechanics simulations using four-chamber cardiac models

Computational cardiac models have been extensively used to study different cardiac biomechanics; specifically, finite-element analysis has been one of the tools used to study the internal stresses and strains in the cardiac wall during the cardiac cycle. Cubic-Hermite finite element meshes have been used for simulating cardiac biomechanics due to their convergence characteristics and their ability to capture smooth geometries compactly–fewer elements are needed to build the cardiac geometry–compared to linear tetrahedral meshes. Such meshes have previously been used only with simple ventricular geometries with non-physiological boundary conditions due to challenges associated with creating cubic-Hermite meshes of the complex heart geometry. However, it is critical to accurately capture the different geometric characteristics of the heart and apply physiologically equivalent boundary conditions to replicate the in vivo heart motion. In this work, we created a four-chamber cardiac model utilizing cubic-Hermite elements and simulated a full cardiac cycle by coupling the 3D finite element model with a lumped circulation model. The myocardial fiber-orientations were interpolated within the mesh using the Log-Euclidean method to overcome the singularity associated with interpolation of orthogonal matrices. Physiologically equivalent rigid body constraints were applied to the nodes along the valve plane and the accuracy of the resulting simulations were validated using open source clinical data. We then simulated a complete cardiac cycle of a healthy heart and a heart with acute myocardial infarction. We compared the pumping functionality of the heart for both cases by calculating the ventricular work. We observed a 20% reduction in acute work done by the heart immediately after myocardial infarction. The myocardial wall displacements obtained from the four-chamber model are comparable to actual patient data, without requiring complicated non-physiological boundary conditions usually required in truncated ventricular heart models.     

Gaussian curvature analysis allows for automatic block placement in multi-block hexahedral meshing

Musculoskeletal finite element analysis (FEA) has been essential to research in orthopaedic biomechanics. The generation of a volumetric mesh is often the most challenging step in a FEA. Hexahedral meshing tools that are based on a multi-block approach rely on the manual placement of building blocks for their mesh generation scheme. We hypothesise that Gaussian curvature analysis could be used to automatically develop a building block structure for multi-block hexahedral mesh generation. The Automated Building Block Algorithm incorporates principles from differential geometry, combinatorics, statistical analysis and computer science to automatically generate a building block structure to represent a given surface without prior information. We have applied this algorithm to 29 bones of varying geometries and successfully generated a usable mesh in all cases. This work represents a significant advancement in automating the definition of building blocks.     

Comparison of Minimalist Footwear Strategies for Simulating Barefoot Running: A Randomized Crossover Study

Possible benefits of barefoot running have been widely discussed in recent years. Uncertainty exists about which footwear strategy adequately simulates barefoot running kinematics. The objective of this study was to investigate the effects of athletic footwear with different minimalist strategies on running kinematics. Thirty-five distance runners (22 males, 13 females, 27.9 ± 6.2 years, 179.2 ± 8.4 cm, 73.4 ± 12.1 kg, 24.9 ± 10.9 km.week^-1) performed a treadmill protocol at three running velocities (2.22, 2.78 and 3.33 m.s^-1) using four footwear conditions: barefoot, uncushioned minimalist shoes, cushioned minimalist shoes, and standard running shoes. 3D kinematic analysis was performed to determine ankle and knee angles at initial foot-ground contact, rate of rear-foot strikes, stride frequency and step length. Ankle angle at foot strike, step length and stride frequency were significantly influenced by footwear conditions (p<0.001) at all running velocities. Posthoc pairwise comparisons showed significant differences (p<0.001) between running barefoot and all shod situations as well as between the uncushioned minimalistic shoe and both cushioned shoe conditions. The rate of rear-foot strikes was lowest during barefoot running (58.6% at 3.33 m.s^-1), followed by running with uncushioned minimalist shoes (62.9%), cushioned minimalist (88.6%) and standard shoes (94.3%). Aside from showing the influence of shod conditions on running kinematics, this study helps to elucidate differences between footwear marked as minimalist shoes and their ability to mimic barefoot running adequately. These findings have implications on the use of footwear applied in future research debating the topic of barefoot or minimalist shoe running.     

Gaussian curvature analysis allows for automatic block placement in multi-block hexahedral meshing

Musculoskeletal finite element analysis (FEA) has been essential to research in orthopaedic biomechanics. The generation of a volumetric mesh is often the most challenging step in a FEA. Hexahedral meshing tools that are based on a multi-block approach rely on the manual placement of building blocks for their mesh generation scheme. We hypothesise that Gaussian curvature analysis could be used to automatically develop a building block structure for multi-block hexahedral mesh generation. The Automated Building Block Algorithm incorporates principles from differential geometry, combinatorics, statistical analysis and computer science to automatically generate a building block structure to represent a given surface without prior information. We have applied this algorithm to 29 bones of varying geometries and successfully generated a usable mesh in all cases. This work represents a significant advancement in automating the definition of building blocks.     

Foot structure and knee joint kinetics during walking with and without wedged footwear insoles

The relationship between static foot structure characteristics and knee joint biomechanics during walking, or the biomechanical response to wedged insoles are currently unknown. In this study, 3D foot scanning, dual X-ray absorptiometry and gait analysis methods were used to determine structural parameters of the foot and assess their relation to knee joint loading and biomechanical response to wedged insoles in 30 patients with knee osteoarthritis. In multiple linear regression models, foot fat content, height of the medial longitudinal arch and static hind foot angle were not associated with the magnitude of the knee adduction moment (R² = 0.24, p = 0.060), knee adduction angular impulse (R² = 0.21, p = 0.099) or 3D resultant knee moment (R² = 0.23, p = 0.073) during gait. Furthermore, these foot structure parameters were not associated with the patients’ biomechanical response to medial or lateral wedge footwear insoles (all p < 0.01). These findings suggest that static foot structure is not associated with gait mechanics at the knee, and that static foot structure alone cannot be utilized to predict an individual’s biomechanical response to wedged footwear insoles in patients with knee osteoarthritis.     

A simple field method to identify foot strike pattern during running

Identifying foot strike patterns in running is an important issue for sport clinicians, coaches and footwear industrials. Current methods allow the monitoring of either many steps in laboratory conditions or only a few steps in the field. Because measuring running biomechanics during actual practice is critical, our purpose is to validate a method aiming at identifying foot strike patterns during continuous field measurements. Based on heel and metatarsal accelerations, this method requires two uniaxial accelerometers. The time between heel and metatarsal acceleration peaks (THM) was compared to the foot strike angle in the sagittal plane (α_foot) obtained by 2D video analysis for various conditions of speed, slope, footwear, foot strike and state of fatigue. Acceleration and kinematic measurements were performed at 1000 Hz and 120 Hz, respectively, during 2-min treadmill running bouts. Significant correlations were observed between THM and α_foot for 14 out of 15 conditions. The overall correlation coefficient was r=0.916 (P<0.0001, n=288). The THM method is thus highly reliable for a wide range of speeds and slopes, and for all types of foot strike except for extreme forefoot strike during which the heel rarely or never strikes the ground, and for different footwears and states of fatigue. We proposed a classification based on THM: FFS<−5.49 ms<MFS<15.2 ms<RFS. With only a few precautions being necessary to ensure appropriate use of this method, it is reliable for distinguishing rearfoot and non-rearfoot strikers in situ.     

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.     

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.     

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).     

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).     

Growing multiblock structures: a semi-automated approach to block placement for multiblock hexahedral meshing

Finite element (FE) analysis is a cornerstone of orthopaedic biomechanics research. Three-dimensional medical imaging provides sufficient resolution for the subject-specific FE models to be generated from these data-sets. FE model development requires discretisation of a three-dimensional domain, which can be the most time-consuming component of a FE study. Hexahedral meshing tools based on the multiblock method currently rely on the manual placement of building blocks for mesh generation. We hypothesise that angular analysis of the geometric centreline for a three-dimensional surface could be used to automatically generate building block structures for the multiblock hexahedral mesh generation. Our algorithm uses a set of user-defined points and parameters to automatically generate a multiblock structure based on a surface's geometric centreline. This significantly reduces the time required for model development. We have applied this algorithm to 47 bones of varying geometries and successfully generated a FE mesh in all cases. This work represents significant advancement in automatically generating multiblock structures for a wide range of geometries.     

An eFTD-VP framework for efficiently generating patient-specific anatomically detailed facial soft tissue FE mesh for craniomaxillofacial surgery simulation

Accurate surgical planning and prediction of craniomaxillofacial surgery outcome requires simulation of soft tissue changes following osteotomy. This can only be achieved by using an anatomically detailed facial soft tissue model. The current state-of-the-art of model generation is not appropriate to clinical applications due to the time-intensive nature of manual segmentation and volumetric mesh generation. The conventional patient-specific finite element (FE) mesh generation methods are to deform a template FE mesh to match the shape of a patient based on registration. However, these methods commonly produce element distortion. Additionally, the mesh density for patients depends on that of the template model. It could not be adjusted to conduct mesh density sensitivity analysis. In this study, we propose a new framework of patient-specific facial soft tissue FE mesh generation. The goal of the developed method is to efficiently generate a high-quality patient-specific hexahedral FE mesh with adjustable mesh density while preserving the accuracy in anatomical structure correspondence. Our FE mesh is generated by eFace template deformation followed by volumetric parametrization. First, the patient-specific anatomically detailed facial soft tissue model (including skin, mucosa, and muscles) is generated by deforming an eFace template model. The adaptation of the eFace template model is achieved by using a hybrid landmark-based morphing and dense surface fitting approach followed by a thin-plate spline interpolation. Then, high-quality hexahedral mesh is constructed by using volumetric parameterization. The user can control the resolution of hexahedron mesh to best reflect clinicians’ need. Our approach was validated using 30 patient models and 4 visible human datasets. The generated patient-specific FE mesh showed high surface matching accuracy, element quality, and internal structure matching accuracy. They can be directly and effectively used for clinical simulation of facial soft tissue change.