A shell finite element model of the pelvic floor muscles

The pelvic floor gives support to the organs in the abdominal cavity. Using the dataset made public in (Janda et al. J. Biomech. (2003 Janda, S., van der Helm, F.C.T. and de Blok, B. 2003. Measuring morphological parameters of the pelvic floor for finite element modelling purposes. J. Biomech., 36(6): 749–757. [Crossref] , [Google Scholar]) 36(6), pp. 749–757), we have reconstructed the geometry of one of the most important parts of the pelvic floor, the levator ani, using NURB surfaces. Once the surface is triangulated, the corresponding mesh is used in a finite element analysis with shell elements.

Based on the 3D behavior of the muscle we have constructed a shell that takes into account the direction of the muscle fibers and the incompressibility of the tissue. The constitutive model for the isotropic strain energy and the passive strain energy stored in the fibers is adapted from Humphrey's model for cardiac muscles. To this the active behavior of the skeletal muscle is added.

We present preliminary results of a simulation of the levator ani muscle under pressure and with active contraction. This research aims at helping simulate the damages to the pelvic floor that can occur after childbirth.     

A shell finite element model of the pelvic floor muscles

The pelvic floor gives support to the organs in the abdominal cavity. Using the dataset made public in (Janda et al. J. Biomech. (2003) 36(6), pp. 749-757), we have reconstructed the geometry of one of the most important parts of the pelvic floor, the levator ani, using NURB surfaces. Once the surface is triangulated, the corresponding mesh is used in a finite element analysis with shell elements.Based on the 3D behavior of the muscle we have constructed a shell that takes into account the direction of the muscle fibers and the incompressibility of the tissue. The constitutive model for the isotropic strain energy and the passive strain energy stored in the fibers is adapted from Humphrey's model for cardiac muscles. To this the active behavior of the skeletal muscle is added.We present preliminary results of a simulation of the levator ani muscle under pressure and with active contraction. This research aims at helping simulate the damages to the pelvic floor that can occur after childbirth.     

Two-dimensional biomechanical finite element modeling of the pelvic floor and prolapse

Biomechanics and Modeling in Mechanobiology - We developed the pelvic floor model in physiological and pathological states to understand the changes of biomechanical axis and support that may occur...     

Achilles tendon stress is more sensitive to subject-specific geometry than subject-specific material properties: A finite element analysis

This study used subject-specific measures of three-dimensional (3D) free Achilles tendon geometry in conjunction with a finite element method to investigate the effect of variation in subject-specific geometry and subject-specific material properties on tendon stress during submaximal isometric loading. Achilles tendons of eight participants (Aged 25–35 years) were scanned with freehand 3D ultrasound at rest and during a 70% maximum voluntary isometric contraction. Ultrasound images were segmented, volume rendered and transformed into subject-specific 3D finite element meshes. The mean (±SD) lengths, volumes and cross-sectional areas of the tendons at rest were 62 ± 13 mm, 3617 ± 984 mm³ and 58 ± 11 mm² respectively. The measured tendon strain at 70% MVIC was 5.9 ± 1.3%. Subject-specific material properties were obtained using an optimisation approach that minimised the difference between measured and modelled longitudinal free tendon strain. Generic geometry was represented by the average mesh and generic material properties were taken from the literature. Local stresses were subsequently computed for combinations of subject-specific and generic geometry and material properties. For a given geometry, changing from generic to subject-specific material properties had little effect on the stress distribution in the tendon. In contrast, changing from generic to subject-specific geometry had a 26-fold greater effect on tendon stress distribution. Overall, these findings indicate that the stress distribution experienced by the living free Achilles tendon of a young and healthy population during voluntary loading are more sensitive to variation in tendon geometry than variation in tendon material properties.     

Measuring morphological parameters of the pelvic floor for finite element modelling purposes

The goal of this study was to obtain a complete data set needed for studying the complex biomechanical behaviour of the pelvic floor muscles using a computer model based on the finite element (FE) theory. The model should be able to predict the effect of surgical interventions and give insight into the function of pelvic floor muscles. Because there was a lack of any information concerning morphological parameters of the pelvic floor muscle structures, we performed an experimental measurement to uncover those morphological parameters. Geometric parameters as well as muscle parameters of the pelvic floor muscles were measured on an embalmed female cadaver. A three-dimensional (3D) geometric data set of the pelvic floor including muscle fibre directions was obtained using a palpator device. A 3D surface model based on the experimental data, needed for mathematical modelling of the pelvic floor, was created. For all parts of the diaphragma pelvis, the optimal muscle fibre length was determined by laser diffraction measurements of the sarcomere length. In addition, other muscle parameters such as physiological cross-sectional area and total muscle fibre length were determined. Apart from these measurements we obtained a data set of the pelvic floor structures based on nuclear magnetic resonance imaging (MRI) on the same cadaver specimen. The purpose of this experiment was to discover the relationship between the MRI morphology and geometrical parameters obtained from the previous measurements. The produced data set is not only important for biomechanical modelling of the pelvic floor muscles, but it also describes the geometry of muscle fibres and is useful for functional analysis of the pelvic floor in general. By the use of many reference landmarks all these morphologic data concerning fibre directions and optimal fibre length can be morphed to the geometrical data based on segmentation from MRI scans.These data can be directly used as an input for building a mathematical model based on FE theory.     

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.     

Volumetric locking free 3D finite element for modelling of anisotropic visco-hyperelastic behaviour of anterior cruciate ligament

Solids such as polymers, soft biological tissues display visco-hyperelastic, isochoric and finite deformation behaviour. The incompressibility constraint imposed severe restriction on the displacement field results in volumetric locking. Many techniques have been developed to address the issue such as reduced integration, mixed formulation, B-Bar and F-Bar methods, each of them with their own merits and demerits. In this work, we have developed a 3D finite element (hereby referred as J-Bar method) to counter volumetric locking in visco-hyperelastic solids. To validate the proposed J-Bar method, rheological characteristics of the human anterior cruciate ligament (ACL) were predicted and compared with the experimental results.     

Experiments and finite element modelling for the study of prolapse in the pelvic floor system

Pelvic prolapse affects one woman in three of all ages combined and is quite common for more than 60% of patients over 60 years of age. The treatment of this pathological problem is one of the biggest challenges to the gynaecologist today. The rate of surgical intervention failure is quite significant. The recurrence of prolapse could be related to inadequate surgical technique or the pathology or/and biomechanical deficiency of the soft tissues. The modelling and simulation of the behaviour of the pelvic cavity could be a major tool for specific evaluation of pelvic status. A first stage of this model is being developed and reported. The computer-aided design model of the organs of the pelvic floor is created using magnetic resonance image data and the ligament boundary conditions are defined. A multi-organ geometric model is thus created and studied.     

Comparison of strain measurement in the mouse forearm using subject-specific finite element models,strain gaging,and digital image correlation

Mechanical loading in bone leads to the activation of bone-forming pathways that are most likely associated with a minimum strain threshold being experienced by the osteocyte. To investigate the correlation between cellular response and mechanical stimuli, researchers must develop accurate ways to measure/compute strain both externally on the bone surface and internally at the osteocyte level. This study investigates the use of finite element (FE) models to compute bone surface strains on the mouse forearm. Strains from three FE models were compared to data collected experimentally through strain gaging and digital image correlation (DIC). Each FE model was assigned subject-specific bone properties and consisted of one-dimensional springs representing the interosseous membrane. After three-point bending was performed on the ulnae and radii, moment of inertia was determined from microCT analysis of the bone region between the supports and then used along with standard beam analyses to calculate the Young’s modulus. Non-contact strain measurements from DIC were determined to be more suitable for validating numerical results than experimental data obtained through conventional strain gaging. When comparing strain responses in the three ulnae, we observed a 3–14% difference between numerical and DIC strains while the strain gage values were 37–56% lower than numerical values. This study demonstrates a computational approach for capturing bone surface strains in the mouse forearm. Ultimately, strains from these macroscale models can be used as inputs for microscale and nanoscale FE models designed to analyze strains directly in the osteocyte lacunae.     

A subject-specific pelvic bone model and its application to cemented acetabular replacements

A subject-specific three-dimensional finite element (FE) pelvic bone model has been developed and applied to the study of bone–cement interfacial response in cemented acetabular replacements. The pelvic bone model was developed from CT scan images of a cadaveric pelvis and validated against the experiment data obtained from the same specimen at a simulated single-legged stance. The model was then implanted with a cemented acetabular cup at selected positions to simulate some typical implant conditions due to the misplacement of the cup as well as a standard cup condition. For comparison purposes, a simplified FE model with homogeneous trabecular bone material properties was also generated and similar implant conditions were examined.The results from the homogeneous model are found to underestimate significantly both the peak von Mises stress and the area of the highly stressed region in the cement near the bone–cement interface, compared with those from the subject-specific model. Non-uniform cement thickness and non-standard cup orientation seem to elevate the highly stressed region as well as the peak stress near the bone–cement interface.     

A computational study of the EN 1078 impact test for bicycle helmets using a realistic subject-specific finite element head model

Abstract

In the present study, the free fall impact test in accordance with the EN1078 standard for certification of bicycle helmets is replicated using numerical simulations. The impact scenario is simulated using an experimentally validated, patient-specific head model equipped with and without a bicycle helmet. Head accelerations and intracranial biomechanical injury metrics during the impacts are recorded. It is demonstrated that wearing the bicycle helmet during the impact reduces biomechanical injury metrics, with the biggest reduction seen in the metric for skull fracture.     

Development and validation of subject-specific finite element models for blunt trauma study

This study developed and validated finite element (FE) models of swine and human thoraxes and abdomens that had subject-specific anatomies and could accurately and efficiently predict body responses to blunt impacts. Anatomies of the rib cage, torso walls, thoracic, and abdominal organs were reconstructed from X-ray computed tomography (CT) images and extracted into geometries to build FE meshes. The rib cage was modeled as an inhomogeneous beam structure with geometry and bone material parameters determined directly from CT images. Meshes of soft components were generated by mapping structured mesh templates representative of organ topologies onto the geometries. The swine models were developed from and validated by 30 animal tests in which blunt insults were applied to swine subjects and CT images, chest wall motions, lung pressures, and pathological data were acquired. A comparison of the FE calculations of animal responses and experimental measurements showed a good agreement. The errors in calculated response time traces were within 10% for most tests. Calculated peak responses showed strong correlations with the experimental values. The stress concentration inside the ribs, lungs, and livers produced by FE simulations also compared favorably to the injury locations. A human FE model was developed from CT images from the Visible Human project and was scaled to simulate historical frontal and side post mortem human subject (PMHS) impact tests. The calculated chest deformation also showed a good agreement with the measurements. The models developed in this study can be of great value for studying blunt thoracic and abdominal trauma and for designing injury prevention techniques, equipments, and devices.     

Subject specific finite elasticity simulations of the pelvic floor

An anatomically realistic computational model of the pelvic floor and anal canal regions was used in this study to examine the mechanics of normal defecatory function within the female pelvic floor. This subject specific, MRI-based model enabled mechanical simulations to be performed and quantitatively assessed against experimental data retrieved from the same volunteer. The levator ani muscle group mesh was used as the domain over which the governing equations of finite elasticity were solved using the finite element method with a Mooney-Rivlin material law. Deformation of the levator ani was simulated during a 'bear down' maneuver in order to visualize the way this muscle group functions in an asymptomatic subject. A pressure of 4 kPa was imposed on the mesh and the computed mesh displacements were compared to those obtained from dynamic MR images with an average, experimentally consistent, downwards displacement of 27.2 mm being achieved. The RMS error for this movement was 0.7 mm equating to a percentage error of 2.6% in the supero-inferior direction and 13.7 mm or 74.5% in the antero-posterior direction.     

A subject-specific finite element musculoskeletal framework for mechanics analysis of a total knee replacement

Concurrent use of finite element (FE) and musculoskeletal (MS) modeling techniques is capable of considering the interactions between prosthetic mechanics and subject dynamics after a total knee replacement (TKR) surgery is performed. However, it still has not been performed in terms of favorable prediction accuracy and systematic experimental validation. In this study, we presented a methodology to develop a subject-specific FE-MS model of a human right lower extremity including the interactions among the subject-specific MS model, the knee joint model with ligament bundles, and the deformable FE prosthesis model. In order to evaluate its accuracy, the FE-MS model was compared with a traditional hinge-constraint MS model and experimentally verified over a gait cycle. Both models achieved good temporal agreement between the predicted muscle force and the electromyography results, though the magnitude on models is different. A higher predicted accuracy, quantified by the root-mean-square error (RMSE) and the squared Pearson correlation coefficient (r²), was found in the FE-MS model (RMSE = 177.2 N, r² = 0.90) when compared with the MS model (RMSE = 224.1 N, r² = 0.81) on the total tibiofemoral contact force. The contact mechanics, including the contact area, pressure, and stress were synchronously simulated, and the maximum contact pressure, 22.06 MPa, occurred on the medial side of the tibial insert without exceeding the yield strength of the ultra-high-molecular-weight polyethylene, 24.79 MPa. The approach outlines an accurate knee joint biomechanics analysis and provides an effective method of applying individualized prosthesis design and verification in TKR.     

Biomechanical properties of the pelvic floor muscles of continent and incontinent women using an inverse finite element analysis

Pelvic disorders can be associated with changes in the biomechanical properties in the muscle, ligaments and/or connective tissue form fascia and ligaments. In this sense, the study of their mechanical behavior is important to understand the structure and function of these biological soft tissues. The aim of this study was to establish the biomechanical properties of the pelvic floor muscles of continent and incontinent women, using an inverse finite element analysis (FEA). The numerical models, including the pubovisceral muscle and pelvic bones were built from magnetic resonance (MR) images acquired at rest. The numerical simulation of Valsalva maneuver was based on the finite element method and the material constants were determined for different constitutive models (Neo-Hookean, Mooney-Rivlin and Yeoh) using an iterative process. The material constants (MPa) for Neo-Hookean (c₁) were 0.039 ± 0.022 and 0.024 ± 0.004 for continent vs. incontinent women. For Mooney-Rivlin (c₁) the values obtained were 0.026 ± 0.010 vs. 0.016 ± 0.003, and for Yeoh (c₁) the values obtained were 0.031 ± 0.023 vs. 0.016 ± 0.002, (p < 0.05). Muscle displacements obtained in the numerical simulations of Valsalva maneuver were compared with the muscle displacements obtained through additional dynamic MRI. Incontinent women presented a higher antero-posterior displacement than the continent women. The results were also similar between MRI and numerical simulations (40.27% vs. 42.17% for Neo-Hookean, 39.87% for Mooney-Rivlin and 41.61% for Yeoh). Using an inverse FEA coupled with MR images allowed to obtain the in vivo biomechanical properties of the pelvic floor muscles, leading to a relationship between them for the continent and incontinent women in a non-invasive manner.     

Finite element analysis of blood clots based on the nonlinear visco-hyperelastic model

Mechanical thrombectomy has become the standard treatment for patients with an acute ischemic stroke. In this approach, to remove blood clots, mechanical force is applied using thrombectomy devices, in which the interaction between the clot and the device could significantly affect the clot retrieval performance. It is expected that the finite element method (FEM) could visualize the mechanical interaction by the visualization of the stress transmission from the device to the clot. This research was aimed at verifying the constitutive theory by implementing FEM based on the visco-hyperelastic theory, using a three-dimensional clot model. We used the visco-hyperelastic FEM to reproduce the mechanical behavior of blood clots, as observed in experiments. This study is focused on the mechanical responses of clots under tensile loading and unloading because in mechanical thrombectomy, elongation is assumed to occur locally on the clots during the retrieval process. Several types of cylindrical clots were created by changing the fibrinogen dose. Tensile testing revealed that the stiffness (E_0.45-value) of clots with fibrinogen could be more than three times higher than that of clots without fibrinogen. It was also found that the stiffness was not proportional to the fibrinogen dose. By fitting to the theoretical curve, it was revealed that the Mooney-Rivlin model could reproduce the hyperelastic characteristics of clots well. From the stress-relaxation data, the three-chain Maxwell model could accurately fit the experimental viscoelastic data. FEM, taking the theoretical models into account, was then carried out, and the results matched well with the experimental visco-hyperelastic characteristics of clots under tensile load, reproducing the mechanical hysteresis during unloading, the stress dependence on the strain rate, and the time-dependent stress decrease in the stress-relaxation test.     

Influence of altered geometry and material properties on tissue stress distribution under load in tendinopathic Achilles tendons – A subject-specific finite element analysis

Achilles tendon material properties and geometry are altered in Achilles tendinopathy. The purpose of this study was to determine the relative contributions of altered material properties and geometry to free Achilles tendon stress distribution during a sub-maximal contraction in tendinopathic relative to healthy tendons. Tendinopathic (n = 8) and healthy tendons (n = 8) were imaged at rest and during a sub-maximal voluntary isometric contraction using three-dimensional freehand ultrasound. Images were manually segmented and used to create subject-specific finite element models. The resting cross-sectional area of the free tendon was on average 31% greater for the tendinopathic compared to healthy tendons. Material properties for each tendon were determined using a numerical parameter optimisation approach that minimised the difference in experimentally measured longitudinal strain and the strain predicted by the finite element model under submaximal loading conditions for each tendon. The mean Young’s modulus for tendinopathic tendons was 53% lower than the corresponding control value. Finite element analyses revealed that tendinopathic tendons experience 24% less stress under the same submaximal external loading conditions compared to healthy tendons. The lower tendon stress in tendinopathy was due to a greater influence of tendon cross-sectional area, which alone reduced tendon stress by 30%, compared to a lower Young’s modulus, which alone increased tendon stress by 8%. These findings suggest that the greater tendon cross-sectional area observed in tendinopathy compensates for the substantially lower Young’s modulus, thereby protecting pathological tendon against excessive stress.     

An accurate estimation of bone density improves the accuracy of subject-specific finite element models

An experimental-numerical study was performed to investigate the relationships between computed tomography (CT)-density and ash density, and between ash density and apparent density for bone tissue, to evaluate their influence on the accuracy of subject-specific FE models of human bones. Sixty cylindrical bone specimens were examined. CT-densities were computed from CT images while apparent and ash densities were measured experimentally. The CT/ash-density and ash/apparent-density relationships were calculated. Finite element models of eight human femurs were generated considering these relationships to assess their effect on strain prediction accuracy. CT and ash density were linearly correlated (R(2)=0.997) over the whole density range but not equivalent (intercep t <0, slope >1). A constant ash/apparent-density ratio (0.598+/-0.004) was found for cortical bone. A lower ratio, with a larger dispersion, was found for trabecular bone (0.459+/-0.100), but it became less dispersed, and equal to that of cortical tissue, when testing smaller trabecular specimens (0.598+/-0.036). This suggests that an experimental error occurred in apparent-density measurements for large trabecular specimens and a constant ratio can be assumed valid for the whole density range. Introducing the obtained relationships in the FE modelling procedure improved strain prediction accuracy (R(2)=0.95, RMSE=7%). The results suggest that: (i) a correction of the densitometric calibration should be used when evaluating bone ash-density from clinical CT scans, to avoid ash-density underestimation and overestimation for low- and high-density bone tissue, respectively; (ii) the ash/apparent-density ratio can be assumed constant in human femurs and (iii) the correction improves significantly the model accuracy and should be considered in subject-specific bone modelling.