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.     

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.     

Effects of nonlinear muscle elasticity on pelvic floor mechanics during vaginal childbirth

The role of the pelvic floor soft tissues during the second stage of labor, particularly the levator ani muscle, has attracted much interest recently. It has been postulated that the passage of the fetal head through the pelvis may cause excessive stretching of the levator ani muscle, which may lead to pelvic floor dysfunction and pelvic organ prolapse later in life. In order to study the complex biomechanical interactions between the levator ani muscle and the fetal head during the second stage of labor, finite element models have been developed for quantitative analysis of this process. In this study we have simulated vaginal delivery using individual-specific anatomical computer models of the pelvic floor interacting with a fetal head model with minimal restrictions placed upon its motion. Two constitutive relations were considered for the levator ani muscle (of exponential and neo-Hookean forms). For comparison purposes, the exponential relation was chosen to exhibit much greater stiffening at higher strains beyond the range of the experimental data. We demonstrated that increased nonlinearity in the elastic response of the tissues leads to considerably higher (56%) estimated force required for delivery, accompanied by a more homogeneous spatial distribution of maximum principal stretch ratio across the muscle. These results indicate that the form of constitutive relation beyond the presently available experimental data markedly affects the estimated function of the levator ani muscle during vaginal delivery, due to the large strains that occur. Further experimental data at higher strains are necessary in order to more reliably characterize the constitutive behavior required for modeling vaginal childbirth.     

A subject-specific anisotropic visco-hyperelastic finite element model of female pelvic floor stress and strain during the second stage of labor

ObjectivesTo develop an improved model representation of the biomechanics of the levator muscles during the second stage of labor and to use a sensitivity analysis to explore the pathomechanics of levator muscle injury.MethodsA subject-specific finite element model of human pelvic floor and fetal head was developed based on in vivo MRI data of a fetal head and maternal pelvis. An anisotropic visco-hyperelastic constitutive model employed material parameters estimated from biaxial tests on pelvic floor tissues. Boundary conditions reflected both anatomic constraints and the curve of Carus. A short second stage of labor, scaled to 10 min, was then simulated using a single expulsive push made in the absence of levator co-contraction.ResultsLarge levator stresses occurred near the levator hiatus reaching 9 MPa at the pubovisceral muscle enthesis. The dominant principal stresses were located at, and aligned with, the edge of the hiatus. Muscle stretch bordering the levator hiatus was inhomogeneous: the average levator stretch was 3.55 with a high of 4.64 at the pubovisceral muscle enthesis. Decreasing perineal body stiffness by 40%, 50%, and 60% led to reductions in the maximum principal stretch ratio at the pubovisceral muscle enthesis of 8%, 13%, and 18%, respectively.ConclusionsThe pubovisceral muscle enthesis and the muscle near the perineal body are the regions of greatest strain thereby placing them at highest risk for stretch-related injury. Decreasing perineal body tissue stiffness significantly reduced tissue stress and strain, and therefore injury risk, in those regions.     

The non-linear response of a muscle in transverse compression: assessment of geometry influence using a finite element model

Most recent finite element models that represent muscles are generic or subject-specific models that use complex, constitutive laws. Identification of the parameters of such complex, constitutive laws could be an important limit for subject-specific approaches. The aim of this study was to assess the possibility of modelling muscle behaviour in compression with a parametric model and a simple, constitutive law. A quasi-static compression test was performed on the muscles of dogs. A parametric finite element model was designed using a linear, elastic, constitutive law. A multi-variate analysis was performed to assess the effects of geometry on muscle response. An inverse method was used to define Young's modulus. The non-linear response of the muscles was obtained using a subject-specific geometry and a linear elastic law. Thus, a simple muscle model can be used to have a bio-faithful, biomechanical response.     

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 studies of the mechanical behaviour of the diaphragm in normal and pathological cases

The diaphragm is a muscular membrane separating the abdominal and thoracic cavities, and its motion is directly linked to respiration. In this study, using data from a 59-year-old female cadaver obtained from the Visible Human Project, the diaphragm is reconstructed and, from the corresponding solid object, a shell finite element mesh is generated and used in several analyses performed with the ABAQUS 6.7 software. These analyses consider the direction of the muscle fibres and the incompressibility of the tissue. The constitutive model for the isotropic strain energy as well as the passive and active strain energy stored in the fibres is adapted from Humphrey's model for cardiac muscles. Furthermore, numerical results for the diaphragmatic floor under pressure and active contraction in normal and pathological cases are presented.     

An approach on determining the displacements of the pelvic floor during voluntary contraction using numerical simulation and MRI

The present study was conducted in order to establish a methodology based on the finite element method to simulate the contraction of the pelvic floor (PF) muscles. In the generated finite element model, a downward pressure of 90 cm H₂O was applied, while actively contracting the PF muscles with different degrees of muscular activation (10, 50 and 100%). The finite element methodology of the active contraction behaviour proposed in this study is adequate to simulate PF muscle contraction with different degrees of muscular activation. In this case, in particular, for an activation of 100%, the numerical model was able to displace the pubovisceral muscle in a range of values very similar to the displacement found in the magnetic resonance imaging data. In the analysed case study, it would be possible to conclude that an intensity contraction of 50% would be necessary to produce enough stiffness to avoid possible urine loss.     

An approach on determining the displacements of the pelvic floor during voluntary contraction using numerical simulation and MRI

The present study was conducted in order to establish a methodology based on the finite element method to simulate the contraction of the pelvic floor (PF) muscles. In the generated finite element model, a downward pressure of 90 cm H(2)O was applied, while actively contracting the PF muscles with different degrees of muscular activation (10, 50 and 100%). The finite element methodology of the active contraction behaviour proposed in this study is adequate to simulate PF muscle contraction with different degrees of muscular activation. In this case, in particular, for an activation of 100%, the numerical model was able to displace the pubovisceral muscle in a range of values very similar to the displacement found in the magnetic resonance imaging data. In the analysed case study, it would be possible to conclude that an intensity contraction of 50% would be necessary to produce enough stiffness to avoid possible urine loss.     

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.     

Toward a biomechanical tool to evaluate rupture potential of abdominal aortic aneurysm: identification of a finite strain constitutive model and evaluation of its applicability

Knowledge of the wall stresses in an abdominal aortic aneurysm (AAA) may be helpful in evaluating the need for surgical intervention to avoid rupture. This must be preceded by the development of a more suitable finite strain constitutive model for AAA, as none currently exists. Additionally, reliable stress analysis of in vivo AAA for the purposes of clinical diagnostics requires patient-specific values of the material parameters, which are difficult to determine noninvasively. The purpose of this work, therefore, was three-fold: (1) to develop a finite strain constitutive model for AAA; (2) to estimate the variation of model parameters within a sample population; and (3) to evaluate the sensitivity of computed stress distribution in AAA due to this biologic variation. We propose here a two parameter, hyperelastic, isotropic, incompressible material model and utilize experimental data from 69 freshly excised AAA specimens to both develop the functional form of the model and estimate its material parameters. Parametric analyses were performed via repeated finite element computations to determine the effect of varying each of the two model parameters on the stress distribution in a three-dimensional AAA model. The agreement between experimental data and the proposed functional form of the constitutive law was very good (R2 > 0.9). Our finite element simulations showed that the computed AAA wall stresses changed by only 4% or less when both the parameters were varied within the 95% confidence intervals for the patient population studied. This observation indicates that in lieu of the patient-specific material parameters, which are difficult to determine the use of population mean values is sufficiently accurate for the model to be reasonably employed in a clinical setting. We believe that this is an important advancement toward the development of a computational tool for the estimation of rupture potential for individual AAA, for which there is great clinical need.     

The influence of muscles activation on the dynamical behaviour of the tympano-ossicular system of the middle ear

The human ear is a complex biomechanical system and is divided into three parts: outer, middle and inner ear. The middle ear is formed by ossicles (malleus, incus and stapes), ligaments, muscles and tendons, which transfers sound vibrations from the eardrum to the inner ear, linking with mastoid and Eustachian tube. In this work, a finite element modelling of the tympano-ossicular system of the middle ear was developed. A dynamic study based on a structural response to harmonic vibrations, for a sound pressure level (SPL) of 110, 120 and 130 dB SPL applied in the eardrum, is presented. The connection between the ossicles is made using a contact formulation. The model includes the different ligaments considering its hyperelastic behaviour. The activation of the muscles is based on the constitutive model proposed by previous work. The harmonic responses of displacement and pressure obtained on the stapes footplate, for a frequency range between 100 Hz and 10 kHz, are obtained simulating the muscle activation. The results are compared considering the passive and active states. The results are discussed and they are in accordance with audiological data published with reference to the effects of the middle ear muscles contraction.     

An approach to the mechanical constitutive modelling of arterial tissue based on homogenization and optimization

This paper is concerned with characterizing the quasistatic mechanical behaviour of arterial tissue undergoing finite deformation through hyperelastic constitutive functions. Commonly the parameters of constitutive functions are established by a process of optimization based on experimental data. Instead we construct a finite element model of a representative volume element of the material and compute its homogenized response to a range of deformations. These data are then used to provide objective functions for optimizing the parameters of two analytical models from the literature.     

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.     

Modeling the contraction of the pelvic floor muscles

We performed numerical simulation of voluntary contraction of the pelvic floor muscles to evaluate the resulting displacements of the organs and muscles. Structures were segmented in Magnetic Resonance (MR) images. Different material properties and constitutive models were attributed. The Finite Element Method was applied, and displacements were compared with dynamic MRI findings. Numerical simulation showed muscle magnitude displacement ranging from 0 to 7.9 mm, more evident in the posterior area. Accordingly, the anorectum moved more than the uterus and bladder. Dynamic MRI showed less 0.2 mm and 4.1 mm muscle dislocation in the anterior and cranial directions, respectively. Applications of this model include evaluating muscle impairment, subject-specific mesh implant planning, or effectiveness of rehabilitation.     

Mechanical properties and microstructure of intraluminal thrombus from abdominal aortic aneurysm.

Accurate estimation of the wall stress distribution in an abdominal aortic aneurysm (AAA) may prove clinically useful by predicting when a particular aneurysm will rupture. Appropriate constitutive models for both the wall and the intraluminal thrombus (ILT) found in most AAA are necessary for this task. The purpose of this work was to determine the mechanical properties of ILT within AAA and to derive a more suitable constitutive model for this material. Uniaxial tensile testing was carried out on 50 specimens, including 14 longitudinally oriented and 14 circumferentially oriented specimens from the luminal region of the ILT, and 11 longitudinally oriented and 11 circumferentially oriented specimens from the medial region. A two-parameter, large-strain, hyperelastic constitutive model was developed and used to fit the uniaxial tensile testing data for determination of the material parameters. Maximum stiffness and strength were also determined from the data for each specimen. Scanning electron microscopy (SEM) was conducted to study the regional microstructural difference. Our results indicate that the microstructure of ILT differs between the luminal, medial, and abluminal regions, with the luminal region stronger and stiffer than the medial region. In all cases, the constitutive model fit the experimental data very well (R2>0.98). No significant difference was found for either of the two material parameters between longitudinal and circumferential directions, but a significant difference in material parameters, stiffness, and strength between the laminal and medial regions was determined (p<0.01). Therefore, our results suggest that ILT is an inhomogeneous and possibly isotropic material. The two-parameter, hyperelastic, isotropic, incompressible material model derived here for ILT can be easily incorporated into finite element models for simulation of wall stress distribution in AAA.     

The Penn State Safety Floor: Part II--Reduction of fall-related peak impact forces on the femur.

The goal of this study was to develop and validate a finite element model (FEM) for use in the design of a flooring system that would provide a stable walking surface during normal locomotion but would also deform elastically under higher loads, such as those resulting from falls. The new flooring system is designed to reduce the peak force on the femoral neck during a lateral fall onto the hip. The new flooring system is passive in nature and exhibits two distinct stiffnesses. During normal activities, the floor remains essentially rigid. Upon impact, the floor collapses and becomes significantly softer. The flooring system consists of a multitude of columns supporting a continuous walking surface. The columns were designed to remain stiff up to a specific load and, after exceeding this load, to deform elastically. The flooring returns to its original shape after impact. Part I of this study presented finite element and experimental results demonstrating that the floor deflection during normal walking remained less than 2 mm. To facilitate the floor's development further, a nonlinear finite element model simulating the transient-impact response of a human hip against various floor configurations was developed. Nonlinearities included in the finite element models were: changing topology of deformable-body-to-deformable-body contact, snap-through buckling, soft tissue stiffness and damping, and large deformations. Experimental models developed for validating the finite element model included an anthropomorphic hip, an impact delivery mechanism, a data collection system, and four hand-fabricated floor tiles. The finite element model discussed in this study is shown to capture experimentally observed trends in peak femoral neck force reduction as a function of flooring design parameters. This study also indicates that a floor can be designed that deflects minimally during walking and reduces the peak force on the femoral neck during a fall-related impact by 15.2 percent.     

Constitutive model of brain tissue suitable for finite element analysis of surgical procedures.

Realistic finite element modelling and simulation of neurosurgical procedures present a formidable challenge. Appropriate, finite deformation, constitutive model of brain tissue is a prerequisite for such development. In this paper, a large deformation, linear, viscoelastic model, suitable for direct use with commercially available finite element software packages such as ABAQUS is constructed. The proposed constitutive equation is of polynomial form with time-dependent coefficients. The model requires four material constants to be identified. The material constants were evaluated based on unconfined compression experiment results. The analytical as well as numerical solutions to the unconfined compression problem are presented. The agreement between the proposed theoretical model and the experiment is good for compression levels reaching 30% and for loading velocities varying over five orders of magnitude. The numerical solution using the finite element method matched the analytical solution very closely.     

Effects of lumbo-pelvic rhythm on trunk muscle forces and disc loads during forward flexion: A combined musculoskeletal and finite element simulation study

Previous in-vivo studies suggest that the ratio of total lumbar rotation over pelvic rotation (lumbo-pelvic rhythm) during trunk sagittal movement is essential to evaluate spinal loads and discriminate between low back pain and asymptomatic population. Similarly, there is also evidence that the lumbo-pelvic rhythm is key for evaluation of realistic muscle and joint reaction forces and moments predicted by various computational musculoskeletal models. This study investigated the effects of three lumbo-pelvic rhythms defined based on in-vivo measurements on the spinal response during moderate forward flexion (60°) using a combined approach of musculoskeletal modeling of the upper body and finite element model of the lumbosacral spine. The muscle forces and joint loads predicted by the musculoskeletal model, together with the gravitational forces, were applied to the finite element model to compute the disc force and moment, intradiscal pressure, annular fibers strain, and load-sharing. The results revealed that a rhythm with high pelvic rotation and low lumbar flexion involves more global muscles and increases the role of the disc in resisting spinal loads, while its counterpart, with low pelvic rotation, recruits more local muscles and engages the ligaments to lower the disc loads. On the other hand, a normal rhythm that has balanced pelvic and lumbar rotations yields almost equal disc and ligament load-sharing and results in more balanced synergy between global and local muscles. The lumbo-pelvic rhythm has less effect on the intradiscal pressure and annular fibers strain. This work demonstrated that the spinal response during forward flexion is highly dependent on the lumbo-pelvic rhythm. It is therefore, essential to adapt this parameter instead of using the default values in musculoskeletal models for accurate prediction of muscle forces and joint reaction forces and moments. The findings provided by this work are expected to improve knowledge of spinal response during forward flexion, and are clinically relevant towards low back pain treatment and disc injury prevention.