Modeling mechanical strains and stresses in soft tissues of the shoulder during load carriage based on load-bearing open MRI

Shoulder strain is a major limiting factor associated with load carriage. Despite advances in backpack designs, there are still reports of shoulder discomfort, loss of sensorimotor functions, and brachial plexus syndrome. The current study is aimed at characterizing mechanical loading conditions (strains and stresses) that develop within the shoulder's soft tissues when carrying a backpack. Open MRI scans were used for reconstructing a three-dimensional geometrical model of an unloaded shoulder and for measuring the soft tissue deformations caused by a 25-kg backpack; subsequently, a subject-specific finite element (FE) model for nonlinear, large-deformation stress-strain analyses was developed. Skin pressure distributions under the backpack strap were used as reference data and for verifying the numerical solutions. The parameters of the model were adjusted to fit the calculated tissue deformations to those obtained by MRI. The MRI scans revealed significant compression of the soft tissues of the shoulder, with substantial deformations in the area of the subclavian muscle and the brachial plexus. The maximal pressure values exerted by a 25-kg load were substantial and reached ～90 kPa. In the muscle surrounding the brachial plexus, the model predicted maximal compressive strain of 0.14 and maximal tensile strain of 0.13, which might be injurious for the underlying neural tissue. In conclusion, the FE model provided some insights regarding the potential mechanisms underlying brachial plexus injuries related to load carriage. The large tissue deformations and pressure hotspots that were observed are likely to result in tissue damage, which may hamper neural function if sustained for long time exposures.     

Validation and application of an intervertebral disc finite element model utilizing independently constructed tissue-level constitutive formulations that are nonlinear,anisotropic, and time-dependent

Finite element (FE) models are advantageous in the study of intervertebral disc mechanics as the stress–strain distributions can be determined throughout the tissue and the applied loading and material properties can be controlled and modified. However, the complicated nature of the disc presents a challenge in developing an accurate and predictive disc model, which has led to limitations in FE geometry, material constitutive models and properties, and model validation. The objective of this study was to develop a new FE model of the intervertebral disc, to validate the model?s nonlinear and time-dependent responses without tuning or calibration, and to evaluate the effect of changes in nucleus pulposus (NP), cartilaginous endplate (CEP), and annulus fibrosus (AF) material properties on the disc mechanical response. The new FE disc model utilized an analytically-based geometry. The model was created from the mean shape of human L4/L5 discs, measured from high-resolution 3D MR images and averaged using signed distance functions. Structural hyperelastic constitutive models were used in conjunction with biphasic-swelling theory to obtain material properties from recent tissue tests in confined compression and uniaxial tension. The FE disc model predictions fit within the experimental range (mean±95% confidence interval) of the disc?s nonlinear response for compressive slow loading ramp, creep, and stress-relaxation simulations. Changes in NP and CEP properties affected the neutral-zone displacement but had little effect on the final stiffness during slow-ramp compression loading. These results highlight the need to validate FE models using the disc?s full nonlinear response in multiple loading scenarios.     

Three-dimensional finite element analysis of the foot during standing--a material sensitivity study

Information on the internal stresses/strains in the human foot and the pressure distribution at the plantar support interface under loading is useful in enhancing knowledge on the biomechanics of the ankle-foot complex. While techniques for plantar pressure measurements are well established, direct measurement of the internal stresses/strains is difficult. A three-dimensional (3D) finite element model of the human foot and ankle was developed using the actual geometry of the foot skeleton and soft tissues, which were obtained from 3D reconstruction of MR images. Except the phalanges that were fused, the interaction among the metatarsals, cuneiforms, cuboid, navicular, talus, calcaneus, tibia and fibula were defined as contact surfaces, which allow relative articulating movement. The plantar fascia and 72 major ligaments were simulated using tension-only truss elements by connecting the corresponding attachment points on the bone surfaces. The bony and ligamentous structures were embedded in a volume of soft tissues. The encapsulated soft tissue was defined as hyperelastic, while the bony and ligamentous structures were assumed to be linearly elastic. The effects of soft tissue stiffening on the stress distribution of the plantar surface and bony structures during balanced standing were investigated. Increases of soft tissue stiffness from 2 and up to 5 times the normal values were used to approximate the pathologically stiffened tissue behaviour with increasing stages of diabetic neuropathy. The results showed that a five-fold increase in soft tissue stiffness led to about 35% and 33% increase in the peak plantar pressure at the forefoot and rearfoot regions, respectively. This corresponded to about 47% decrease in the total contact area between the plantar foot and the horizontal support surface. Peak bone stress was found at the third metatarsal in all calculated cases with a minimal increase of about 7% with soft tissue stiffening.     

Strategies towards rapid generation of forefoot model incorporating realistic geometry of metatarsals encapsulated into lumped soft tissues for personalized finite element analysis

Use of finite element (FE) foot model as a clinical diagnostics tool is likely to improve the specificity of foot injury predictions in the diabetic population. Here we proposed a novel workflow for rapid construction of foot FE model incorporating realistic geometry of metatarsals encapsulated into lumped forefoot’s soft tissues. Custom algorithms were implemented to perform unsupervised segmentation and mesh generation to directly convert CT data into a usable FE model. The automatically generated model provided higher efficiency and comparable numerical accuracy when compared to the model constructed using a traditional solid-based mesh process. The entire procedure uses MATLAB as the main platform, and makes the present approach attractive for creating personalized foot models to be used in clinical studies.     

Digital image correlation and finite element modelling as a method to determine mechanical properties of human soft tissue in vivo

The mechanical properties of human soft tissue are crucial for impact biomechanics, rehabilitation engineering, and surgical simulation. Validation of these constitutive models using human data remains challenging and often requires the use of non-invasive imaging and inverse finite element (FE) analysis. Post-processing data from imaging methods such as tagged magnetic resonance imaging (MRI) can be challenging. Digital image correlation (DIC), however, is a relatively straightforward imaging method. DIC has been used in the past to study the planar and superficial properties of soft tissue and excised soft tissue layers. However, DIC has not been used to non-invasive study of the bulk properties of human soft tissue in vivo. Thus, the goal of this study was to assess the use of DIC in combination with FE modelling to determine the bulk material properties of human soft tissue. Indentation experiments were performed on a silicone gel soft tissue phantom. A two camera DIC setup was then used to record the 3D surface deformation. The experiment was then simulated using a FE model. The gel was modelled as Neo-Hookean hyperelastic, and the material parameters were determined by minimising the error between the experimental and FE data. The iterative FE analysis determined material parameters (μ=1.80 kPa, K=2999 kPa) that were in close agreement with parameters derived independently from regression to uniaxial compression tests (μ=1.71 kPa, K=2857 kPa). Furthermore the FE model was capable of reproducing the experimental indentor force as well as the surface deformation found (R²=0.81). It was therefore concluded that a two camera DIC configuration combined with FE modelling can be used to determine the bulk mechanical properties of materials that can be represented using hyperelastic Neo-Hookean constitutive laws.     

Determination of oral mucosal Poisson’s ratio and coefficient of friction from in-vivo contact pressure measurements

Despite their considerable importance to biomechanics, there are no existing methods available to directly measure apparent Poisson’s ratio and friction coefficient of oral mucosa. This study aimed to develop an inverse procedure to determine these two biomechanical parameters by utilizing in vivo experiment of contact pressure between partial denture and beneath mucosa through nonlinear finite element (FE) analysis and surrogate response surface (RS) modelling technique. First, the in vivo denture–mucosa contact pressure was measured by a tactile electronic sensing sheet. Second, a 3D FE model was constructed based on the patient CT images. Third, a range of apparent Poisson’s ratios and the coefficients of friction from literature was considered as the design variables in a series of FE runs for constructing a RS surrogate model. Finally, the discrepancy between computed in silico and measured in vivo results was minimized to identify the best matching Poisson’s ratio and coefficient of friction. The established non-invasive methodology was demonstrated effective to identify such biomechanical parameters of oral mucosa and can be potentially used for determining the biomaterial properties of other soft biological tissues.     

Computer aided stress analysis of long bones utilizing computed tomography

A computer aided analysis method has been developed which utilizes computed tomography (CT) and a finite element (FE) computer program to determine the stress-displacement pattern in a long bone section. The CT data file provides the geometry, the apparent density and the elastic properties for the three-dimensional FE model. A developed pre-processor generates the FE model of a human diaphyseal tibia section which is then analyzed by the SAP IV finite element program. The results obtained are sorted and displayed by a developed post-processor and compared with stresses and deformations from the literature. The model generation method was verified by applying it to a model of simple geometry and boundary conditions, then comparing the results with the analytical solution of the same problem. The convergence behavior of nodal displacements was tested as a function of mesh refinement. This method provides an automatic, versatile, non-invasive and accurate tool of long bone modeling for finite element stress analysis.     

Strains and stresses in sub-dermal tissues of the buttocks are greater in paraplegics than in healthy during sitting

A pressure-related deep tissue injury (DTI) is a severe pressure ulcer, which initiates in muscle tissue overlying a bony prominence (e.g. the ischial tuberosities, IT) and progresses outwards through fat and skin, unnoticed by the paralyzed patient. We recently showed that internal strains and stresses in muscle and fat of individuals at anatomical sites susceptible to DTI can be evaluated by integrating Open-MRI scans with subject-specific finite element (FE) analyzes (Linder-Ganz et al., Journal of Biomechanics, 2007); however, sub-dermal soft tissue strains/stresses from paraplegics are still missing in literature. We hypothesize that the pathoanatomy of the buttocks in paraplegia increases the internal soft tissue loads under the IT, making these patients inherently susceptible to DTI. We hence compared the strain and stress peaks in the gluteus muscle and fat tissues under the IT of six healthy and six paraplegic patients, using the coupled MRI-FE method. Peak principal compression, principal tension, von Mises and shear strains in the gluteus were 1.2-, 3.1-, 1.4- and 1.4-fold higher in paraplegics than in healthy, respectively (p<0.02). Likewise, peak principal compression, principal tension, von Mises and shear stresses in the gluteus were 1.9-, 2.5-, 2.1- and 1.7-fold higher for the paraplegics (p<0.05). Peak gluteal compression and shear stresses decreased by as much as 70% when the paraplegic patients moved from a sitting to a lying posture, indicating on the effectiveness of recommending such patients to lie down after prolonged periods of sitting. This is the first attempt to compare internal soft tissue loads between paraplegic and healthy subjects, using an objective standardized bioengineering method of analysis. The findings support our hypothesis that internal tissue loads are significantly higher in paraplegics, and that postural changes significantly affect these loads. The method of analysis is useful for quantifying the effectiveness of various interventions to alleviate sub-dermal tissue loads at sites susceptible to pressure ulcers and DTI, including cushions, mattresses, recommendations for posture and postural changes, etc.     

A Coupling Analysis of the Biomechanical Functions of Human Foot Complex during Locomotion

This study represents a functional analysis of the human foot complex based on in-vivo gait measurements, finite element (FE) modeling and biological coupling theory, with the objective of achieving a comprehensive understanding of the impact attenuation and energy absorption functions of the human foot complex. A simplified heel pad FE model comprising reticular fiber structure and fat cells was constructed based on the foot pad Magnetic Resonance (MR) images. The model was then used to investigate the foot pad behaviors under impact during locomotion. Three-dimensional (3D) gait measurement and a 3D FE foot model comprising 29 bones, 85 ligaments and the plantar soft tissues were used to investigate the foot arch and plantar fascia deformations in mid-stance phase. The heel pad simulation results show that the pad model with fat cells (coupling model) has much stronger capacity in impact attenuation and energy storage than the model without fat cells (structure model). Furthermore, the FE simulation reproduced the deformations of the foot arch structure and the plantar fascia extension observed in the gait measurements, which reinforces the postulation that the foot arch structure also plays an important role in energy absorption during locomotion. Finally, the coupling mechanism of the human foot functions in impact attenuation and energy absorption was proposed.     

Concept and development of an orthotropic FE model of the proximal femur

PURPOSE: In contrast to many isotropic finite-element (FE) models of the femur in literature, it was the object of our study to develop an orthotropic FE "model femur" to realistically simulate three-dimensional bone remodelling. METHODS: The three-dimensional geometry of the proximal femur was reconstructed by CT scans of a pair of cadaveric femurs at equal distances of 2mm. These three-dimensional CT models were implemented into an FE simulation tool. Well-known "density-determined" bony material properties (Young's modulus; Poisson's ratio; ultimate strength in pressure, tension and torsion; shear modulus) were assigned to each FE of the same "CT-density-characterized" volumetric group.In order to fix the principal directions of stiffness in FE areas with the same "density characterization", the cadaveric femurs were cut in 2mm slices in frontal (left femur) and sagittal plane (right femur). Each femoral slice was scanned into a computer-based image processing system. On these images, the principal directions of stiffness of cancellous and cortical bone were determined manually using the orientation of the trabecular structures and the Haversian system. Finally, these geometric data were matched with the "CT-density characterized" three-dimensional femur model. In addition, the time and density-dependent adaptive behaviour of bone remodelling was taken into account by implementation of Carter's criterion. RESULTS: In the constructed "model femur", each FE is characterized by the principal directions of the stiffness and the "CT-density-determined" material properties of cortical and cancellous bone. Thus, on the basis of anatomic data a three-dimensional FE simulation reference model of the proximal femur was realized considering orthotropic conditions of bone behaviour. CONCLUSIONS: With the orthotropic "model femur", the fundamental basis has been formed to realize realistic simulations of the dynamical processes of bone remodelling under different loading conditions or operative procedures (osteotomies, total hip replacements, etc).     

A novel methodology for generating 3D finite element models of the hip from 2D radiographs

Finite element (FE) modelling has been proposed as a tool for estimating fracture risk and patient-specific FE models are commonly based on computed tomography (CT). Here, we present a novel method to automatically create personalised 3D models from standard 2D hip radiographs. A set of geometrical parameters of the femur were determined from seven a–p hip radiographs and compared to the 3D femoral shape obtained from CT as training material; the error in reconstructing the 3D model from the 2D radiographs was assessed. Using the geometry parameters as the input, the 3D shape of another 21 femora was built and meshed, separating a cortical and trabecular compartment. The material properties were derived from the homogeneity index assessed by texture analysis of the radiographs, with focus on the principal tensile and compressive trabecular systems. The ability of these FE models to predict failure load as determined by experimental biomechanical testing was evaluated and compared to the predictive ability of DXA. The average reconstruction error of the 3D models was 1.77 mm (±1.17 mm), with the error being smallest in the femoral head and neck, and greatest in the trochanter. The correlation of the FE predicted failure load with the experimental failure load was r²=64% for the reconstruction FE model, which was significantly better (p<0.05) than that for DXA (r²=24%). This novel method for automatically constructing a patient-specific 3D finite element model from standard 2D radiographs shows encouraging results in estimating patient-specific failure loads.     

MRI-based experimentations of fingertip flat compression: Geometrical measurements and finite element inverse simulations to investigate material property parameters

Modeling human-object interactions is a necessary step in the ergonomic assessment of products. Fingertip finite element models can help investigating these interactions, if they are built based on realistic geometrical data and material properties. The aim of this study was to investigate the fingertip geometry and its mechanical response under compression, and to identify the parameters of a hyperelastic material property associated to the fingertip soft tissues.Fingertip compression tests in an MRI device were performed on 5 subjects at either 2 or 4 N and at 15° or 50°. The MRI images allowed to document both the internal and external fingertip dimensions and to build 5 subject-specific finite element models. Simulations reproducing the fingertip compression tests were run to obtain the material property parameters of the soft tissues.Results indicated that two ellipses in the sagittal and longitudinal plane could describe the external fingertip geometry. The internal geometries indicated an averaged maximal thickness of soft tissues of 6.4 ± 0.8 mm and a 4 ± 1 mm height for the phalanx bone. The averaged deflections under loading went from 1.8 ± 0.3 mm at 2 N, 50° to 3.1 ± 0.2 mm at 4 N, 15°. Finally, the following set of parameters for a second order hyperelastic law to model the fingertip soft tissues was proposed: C₀₁ = 0.59 ± 0.09 kPa and C₂₀ = 2.65 ± 0.88 kPa.These data should facilitate further efforts on fingertip finite element modeling.     

Finite element simulations of a hip joint with femoroacetabular impingement

In this study, a three-dimensional finite element (FE) model based on the specific anatomy of a patient presenting a femoroacetabular impingement of the ‘cam’-type is developed. The FE meshes of the structures of interest are obtained from arthrographic magnetic resonance images. All soft tissues are considered linear elastic and isotropic, and the bones were assumed rigid. A compression of the femur on the acetabular cavity as well as flexural movements and internal rotations are applied. Stresses and contact pressures are evaluated in this patient-specific model in order to better interpret the mechanism of aggression of the femoral and acetabular cartilages. The corresponding results are presented and discussed. The values obtained for the contact pressures are similar to those reported by other models based on idealised geometries. An FE analysis of a non-cam hip is also performed for comparison with the pathological case.     

Real-time subject-specific monitoring of internal deformations and stresses in the soft tissues of the foot: a new approach in gait analysis

No technology is presently available to provide real-time information on internal deformations and stresses in plantar soft tissues of individuals during evaluation of the gait pattern. Because internal deformations and stresses in the plantar pad are critical factors in foot injuries such as diabetic foot ulceration, this severely limits evaluation of patients. To allow such real-time subject-specific analysis, we developed a hierarchal modeling system which integrates a two-dimensional gross structural model of the foot (high-order model) with local finite element (FE) models of the plantar tissue padding the calcaneus and medial metatarsal heads (low-order models). The high-order whole-foot model provides real-time analytical evaluations of the time-dependent plantar fascia tensile forces during the stance phase. These force evaluations are transferred, together with foot-shoe local reaction forces, also measured in real time (under the calcaneus, medial metatarsals and hallux), to the low-order FE models of the plantar pad, where they serve as boundary conditions for analyses of local deformations and stresses in the plantar pad. After careful verification of our custom-made FE solver and of our foot model system with respect to previous literature and against experimental results from a synthetic foot phantom, we conducted human studies in which plantar tissue loading was evaluated in real time during treadmill gait in healthy individuals (N = 4). We concluded that internal deformations and stresses in the plantar pad during gait cannot be predicted from merely measuring the foot-shoe force reactions. Internal loading of the plantar pad is constituted by a complex interaction between the anatomical structure and mechanical behavior of the foot skeleton and soft tissues, the body characteristics, the gait pattern and footwear. Real-time FE monitoring of internal deformations and stresses in the plantar pad is therefore required to identify elevated deformation/stress exposures toward utilizing it in gait laboratories to protect feet that are susceptible to injury.     

Internal mechanical conditions in the soft tissues of a residual limb of a trans-tibial amputee

Most trans-tibial amputation (TTA) patients use a prosthesis to retain upright mobility capabilities. Unfortunately, interaction between the residual limb and the prosthetic socket causes elevated internal strains and stresses in the muscle and fat tissues in the residual limb, which may lead to deep tissue injury (DTI) and other complications. Presently, there is paucity of information on the mechanical conditions in the TTA residual limb during load-bearing. Accordingly, our aim was to characterize the mechanical conditions in the muscle flap of the residual limb of a TTA patient after donning the prosthetic socket and during load-bearing. Knowledge of internal mechanical conditions in the muscle flap can be used to identify the risk for DTI and improve the fitting of the prosthesis. We used a patient-specific modelling approach which involved an MRI scan, interface pressure measurements between the residual limb and the socket of the prosthesis and three-dimensional non-linear large-deformation finite-element (FE) modelling to quantify internal soft tissue strains and stresses in a female TTA patient during static load-bearing. Movement of the truncated tibia and fibula during load-bearing was measured by means of MRI and used as displacement boundary conditions for the FE model. Subsequently, we calculated the internal strains, strain energy density (SED) and stresses in the muscle flap under the truncated bones. Internal strains under the tibia peaked at 85%, 129% and 106% for compression, tension and shear strains, respectively. Internal strains under the fibula peaked at substantially lower values, that is, 19%, 22% and 19% for compression, tension and shear strains, respectively. Strain energy density peaked at the tibial end (104kJ/m(3)). The von Mises stresses peaked at 215kPa around the distal end of the tibia. Stresses under the fibula were at least one order of magnitude lower than the stresses under the tibia. We surmise that our present patient-specific modelling method is an important tool in understanding the etiology of DTI in the residual limbs of TTA patients.     

Three-dimensional inhomogeneous triphasic finite-element analysis of physical signals and solute transport in human intervertebral disc under axial compression

A 3D inhomogeneous finite-element model for charged hydrated soft tissues containing charged/uncharged solutes was developed and applied to analyze the mechanical, chemical, and electrical signals within the human intervertebral disc during an axial unconfined compression. The effects of tissue properties and boundary conditions on the physical signals and the transport of fluid and solute were investigated. The numerical simulation showed that, during disc compression, the fluid pressurization and the effective (von Misses) solid stress were more pronounced in the annulus fibrosus (AF) region near the interface between AF and nucleus pulposus (NP). In NP, the distributions of the fluid pressure, effective stress, and electrical potential were more uniform than those in AF. The electrical signals were very sensitive to fixed charge density. Changes in material properties of NP (water content, fixed charge density, and modulus) affected fluid pressure, electrical potential, effective stress, and solute transport in the disc. This study is important for understanding disc biomechanics, disc nutrition, and disc mechanobiology.     

Identification process based on shear wave propagation within a phantom using finite element modelling and magnetic resonance elastography

Magnetic resonance elastography (MRE), based on shear wave propagation generated by a specific driver, is a non-invasive exam performed in clinical practice to improve the liver diagnosis. The purpose was to develop a finite element (FE) identification method for the mechanical characterisation of phantom mimicking soft tissues investigated with MRE technique. Thus, a 3D FE phantom model, composed of the realistic MRE liver boundary conditions, was developed to simulate the shear wave propagation with the software ABAQUS. The assumptions of homogeneity and elasticity were applied to the FE phantom model. Different ranges of mesh size, density and Poisson's ratio were tested in order to develop the most representative FE phantom model. The simulated wave displacement was visualised with a dynamic implicit analysis. Subsequently, an identification process was performed with a cost function and an optimisation loop provided the optimal elastic properties of the phantom. The present identification process was validated on a phantom model, and the perspective will be to apply this method on abdominal tissues for the set-up of new clinical MRE protocols that could be applied for the follow-up of the effects of treatments.     

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.