A combined passive and active musculoskeletal model study to estimate L4-L5 load sharing

A number of geometrically-detailed passive finite element (FE) models of the lumbar spine have been developed and validated under in vitro loading conditions. These models are devoid of muscles and thus cannot be directly used to simulate in vivo loading conditions acting on the lumbar joint structures or spinal implants. Gravity loads and muscle forces estimated by a trunk musculoskeletal (MS) model under twelve static activities were applied to a passive FE model of the L4-L5 segment to estimate load sharing among the joint structures (disc, ligaments, and facets) under simulated in vivo loading conditions. An equivalent follower (FL), that generates IDP equal to that generated by muscle forces, was computed in each task. Results indicated that under in vivo loading conditions, the passive FE model predicted intradiscal pressures (IDPs) that closely matched those measured under the simulated tasks (R² = 0.98 and root-mean-squared-error, RMSE = 0.18 MPa). The calculated equivalent FL compared well with the resultant force of all muscle forces and gravity loads acting on the L4-L5 segment (R² = 0.99 and RMSE = 58 N). Therefore, as an alternative approach to represent in vivo loading conditions in passive FE model studies, this FL can be estimated by available in-house or commercial MS models. In clinical applications and design of implants, commonly considered in vitro loading conditions on the passive FE models do not adequately represent the in vivo loading conditions under muscle exertions. Therefore, more realistic in vivo loading conditions should instead be used.     

Cervical spine morphology and ligament property variations: A finite element study of their influence on sagittal bending characteristics

Cervical spine finite element models reported in biomechanical literature usually represent a static morphology. Not considering morphology as a model parameter limits the predictive capabilities for applications in personalized medicine, a growing trend in modern clinical practice. The objective of the study was to investigate the influence of variations in spinal morphology on the flexion-extension responses, utilizing mesh-morphing-based parametrization and metamodel-based sensitivity analysis. A C5-C6 segment was used as the baseline model. Variations of intervertebral disc height, facet joint slope, facet joint articular processes height, vertebral body anterior-posterior depth, and segment size were parametrized. In addition, material property variations of ligaments were considered for sensitivity analysis. The influence of these variations on vertebral rotation and forces in the ligaments were analyzed. The disc height, segmental size, and body depth were found to be the most influential (in the cited order) morphology variations; while among the ligament material property variations, capsular ligament and ligamentum flavum influenced vertebral rotation the most. Changes in disc height influenced forces in the posterior ligaments, indicating that changes in the anterior load-bearing column of the spine could have consequences on the posterior column. A method to identify influential morphology variations is presented in this work, which will help automation efforts in modeling to focus on variations that matter. This study underscores the importance of incorporating influential morphology parameters, easily obtained through computed tomography/magnetic resonance images, to better predict subject-specific biomechanical responses for applications in personalized medicine.     

Comparison of eight published static finite element models of the intact lumbar spine: Predictive power of models improves when combined together

Finite element (FE) model studies have made important contributions to our understanding of functional biomechanics of the lumbar spine. However, if a model is used to answer clinical and biomechanical questions over a certain population, their inherently large inter-subject variability has to be considered. Current FE model studies, however, generally account only for a single distinct spinal geometry with one set of material properties. This raises questions concerning their predictive power, their range of results and on their agreement with in vitro and in vivo values.     

Impact of material and morphological parameters on the mechanical response of the lumbar spine – A finite element sensitivity study

Finite element models are frequently used to study lumbar spinal biomechanics. Deterministic models are used to reflect a certain configuration, including the means of geometrical and material properties, while probabilistic models account for the inherent variability in the population. Because model parameters are generally uncertain, their predictive power is frequently questioned. In the present study, we determined the sensitivities of spinal forces and motions to material parameters of intervertebral discs, vertebrae, and ligaments and to lumbar morphology. We performed 1200 model simulations using a generic model of the human lumbar spine loaded under pure moments. Coefficients of determination and of variation were determined for all parameter and response combinations. Material properties of the vertebrae displayed the least impact on results, whereas those of the discs and morphology impacted most. The most affected results were the axial compression forces in the vertebral body and in several ligaments during flexion and the facet-joint forces during extension. Intervertebral rotations were considerably affected only when several parameters were varied simultaneously. Results can be used to decide which model parameters require careful consideration in deterministic models and which parameters might be omitted in probabilistic studies. Findings allow quantitative estimation of a model׳s precision.     

Implementation of reflex loops in a biomechanical finite element model

In the field of biomechanics, the offer of models which are more and more realistic requires to integrate a physiological response, in particular, the controlled muscle bracing and the reflexes. The following work aims to suggest a unique methodology which couples together a sensory and motor loop with a finite element model. Our method is applied to the study of the oscillation of the elbow in the case of a biceps brachial stretch reflex. The results obtained are promising in the purpose of the development of reactive human body models.     

A finite element model of the L4-L5 spinal motion segment: biomechanical compatibility of an interspinous device

The biomechanical compatibility of an interspinous device, used for the "dynamic stabilization" of a diseased spinal motion segment, was investigated. The behaviour of an implant made of titanium based alloy (Ti6Al4V) and that of an implant made of a super-elastic alloy (Ni-Ti) have been compared. The assessment of the biomechanical compatibility was achieved by means of the finite element method, in which suitable constitutive laws have been adopted for the annulus fibrosus and for the metal alloys. The model was aimed at simulating the healthy, the nucleotomized and the treated L4-L5 lumbar segment, subjected to compressive force and flexion-extension as well as lateral flexion moments. The computational model has shown that both the implants were able to achieve their main design purpose, which is to diminish the forces acting on the apophyseal joints. Nevertheless, the Ni-Ti implant has shown a more physiological flexural stiffness with respect to the Ti6Al4V implant, which exhibited an excessive stiffness and permanent strains (plastic strains), even under physiological loads. The computational models presented in this paper seems to be a promising tool able to predict the effectiveness of a biomedical device and to select the materials to be used for the implant manufacturing, within an engineering approach to the clinical problem of the spinal diseases.     

Validation of the AnyBody full body musculoskeletal model in computing lumbar spine loads at L4L5 level

In the panorama of available musculoskeletal modeling software, AnyBody software is a commercial tool that provides a full body musculoskeletal model which is increasingly exploited by numerous researchers worldwide. In this regard, model validation becomes essential to guarantee the suitability of the model in representing the simulated system. When focusing on lumbar spine, the previous works aimed at validating the AnyBody model in computing the intervertebral loads held several limitations, and a comprehensive validation is to be considered as lacking.The present study was aimed at extensively validating the suitability of the AnyBody model in computing lumbar spine loads at L4L5 level. The intersegmental loads were calculated during twelve specific exercise tasks designed to accurately replicate the conditions during which Wilke et al. (2001) measured in vivo the L4L5 intradiscal pressure. Motion capture data of one volunteer subject were acquired during the execution of the tasks and then imported into AnyBody to set model kinematics. Two different approaches in computing intradiscal pressure from the intersegmental load were evaluated. Lumbopelvic rhythm was compared with reference in vivo measurements to assess the accuracy of the lumbopelvic kinematics.Positive agreement was confirmed between the calculated pressures and the in vivo measurements, thus demonstrating the suitability of the AnyBody model. Specific caution needs to be taken only when considering postures characterized by large lateral displacements. Minor discrepancy was found assessing lumbopelvic rhythm. The present findings promote the AnyBody model as an appropriate tool to non-invasively evaluate the lumbar loads at L4L5 in physiological activities.     

Effect of screw position on load transfer in lumbar pedicle screws: a non-idealized finite element analysis

Angled screw insertion has been advocated to enhance fixation strength during posterior spine fixation. Stresses on a pedicle screw and surrounding vertebral bone with different screw angles were studied by finite element analysis during simulated multidirectional loading. Correlations between screw-specific vertebral geometric parameters and stresses were studied. Angulations in both the sagittal and axial planes affected stresses on the cortical and cancellous bones and the screw. Pedicle screws pointing laterally (vs. straight or medially) in the axial plane during superior screw angulation may be advantageous in terms of reducing the risk of both screw loosening and screw breakage.     

Effect of bone fragment impact velocity on biomechanical parameters related to spinal cord injury: A finite element study

Several experimental and computational studies have investigated the effect of bone fragment impact on the spinal cord during trauma. However, the effect of the impact velocity of a fragment generated by a burst fracture on the stress and strain inside the spinal cord has not been computationally investigated, even though spinal canal occlusion and peak pressure at various impact velocities were provided in experimental studies. These stresses and strains are known factors related to clinical symptoms or injuries. In this study, a fluid-structure interaction model of the spinal cord, dura mater, and cerebrospinal fluid was developed and validated. The von-Mises stress distribution in the cord, the longitudinal strain, the cord compression and cross-sectional area at the impact center, and the obliteration of the cerebrospinal fluid layer were analyzed for three pellet sizes at impact velocities ranging from 1.5 m/s to 7.5 m/s. The results indicate that stress in the cord was substantially elevated when the initial impact velocity of the pellet exceeded a threshold of 4.5 m/s. Cord compression, reduction in cross-sectional area, and obliteration of the cerebrospinal fluid increased gradually as the velocity of the pellet increased, regardless of the size of the pellet. The present study provides insight into the mechanisms underlying spinal cord injury.     

Accommodation of the human lens capsule using a finite element model based on nonlinear regionally anisotropic biomembranes

Accommodation of the eyes, the mechanism that allows humans to focus their vision on near objects, naturally diminishes with age via presbyopia. People who have undergone cataract surgery, using current surgical methods and artificial lens implants, are also left without the ability to accommodate. The process of accommodation is generally well known; however the specific mechanical details have not been adequately explained due to difficulties and consequences of performing in vivo studies. Most studies have modeled the mechanics of accommodation under assumptions of a linearly elastic, isotropic, homogenous lens and lens capsule. Recent experimental and numerical studies showed that the lens capsule exhibits nonlinear elasticity and regional anisotropy. In this paper we present a numerical model of human accommodation using a membrane theory based finite element approach, incorporating recent findings on capsular properties. This study seeks to provide a novel perspective of the mechanics of accommodation. Such findings may prove significant in seeking biomedical solutions to restoring loss of visual power.     

Development and experimental validation of a finite element model of total ankle replacement

Total ankle replacement remains a less satisfactory solution compared to other joint replacements. The goal of this study was to develop and validate a finite element model of total ankle replacement, for future testing of hypotheses related to clinical issues. To validate the finite element model, an experimental setup was specifically developed and applied on 8 cadaveric tibias. A non-cemented press fit tibial component of a mobile bearing prosthesis was inserted into the tibias. Two extreme anterior and posterior positions of the mobile bearing insert were considered, as well as a centered one. An axial force of 2 kN was applied for each insert position. Strains were measured on the bone surface using digital image correlation. Tibias were CT scanned before implantation, after implantation, and after mechanical tests and removal of the prosthesis. The finite element model replicated the experimental setup. The first CT was used to build the geometry and evaluate the mechanical properties of the tibias. The second CT was used to set the implant position. The third CT was used to assess the bone-implant interface conditions. The coefficient of determination (R-squared) between the measured and predicted strains was 0.91. Predicted bone strains were maximal around the implant keel, especially at the anterior and posterior ends. The finite element model presented here is validated for future tests using more physiological loading conditions.     

The effect of degenerative morphological changes of the intervertebral disc on the lumbar spine biomechanics: a poroelastic finite element investigation

Intervertebral disc degeneration involves changes in the spinal anatomical structures. The mechanical relevance of the following changes was investigated: disc height, endplate sclerosis, disc water content, permeability and depressurisation. A poroelastic nonlinear finite element model of the L4–L5 human spine segments was employed. Loads represented a daily cycle (500 N compression combined with flexion–extension motion for 16 h followed by 200 N compression for 8 h). In non-degenerative conditions, the model predicted a diurnal axial displacement of 1.32 mm and a peak intradiscal pressure of 0.47 MPa. Axial displacement, facet force and range of motion in flexion–extension are decreased by decreasing disc height. By decreasing the initial water content, axial displacement, facet force and fluid loss were all reduced. Endplate sclerosis did not have a significant influence on the calculated results. Depressurisation determined an increase of the disc effective stress, possibly inducing failure. Degenerative instability was not calculated in any simulations.     

Using the finite element method to model the biomechanics of the asymmetric mandible before,during and after skeletal correction by distraction osteogenesis

An approach was developed to evaluate the load transfer mechanism in the temporomandibular joint (TMJ) area before, during and after mandibular ramus elongation by distraction osteogenesis (DO). In a concerted approach using computer tomography, magnetic resonance imaging (MRI), and finite element analysis, three-dimensional numerical models based on a young male patient, with a dento-facial deformity were generated. The magnitude and direction of the muscle forces acting on the mandible were assessed using both values derived from the muscles volume and cross-section as retrieved from the MRI-scan data-sets and taken from the literature. The resistance of the soft tissue envelope towards elongation during the DO-phase was also included. The finite element analyses showed that before skeletal correction by DO the load transfer was asymmetrical with high peak stresses in the affected joint. Following ramus elongation a more symmetrical loading in TMJs was predicted. The reaction forces in the TMJs during DO were low.     

Parametric convergence sensitivity and validation of a finite element model of the human lumbar spine

The primary objective of this study was to generate a finite element model of the human lumbar spine (L1–L5), verify mesh convergence for each tissue constituent and perform an extensive validation using both kinematic/kinetic and stress/strain data. Mesh refinement was accomplished via convergence of strain energy density (SED) predictions for each spinal tissue. The converged model was validated based on range of motion, intradiscal pressure, facet force transmission, anterolateral cortical bone strain and anterior longitudinal ligament deformation predictions. Changes in mesh resolution had the biggest impact on SED predictions under axial rotation loading. Nonlinearity of the moment-rotation curves was accurately simulated and the model predictions on the aforementioned parameters were in good agreement with experimental data. The validated and converged model will be utilised to study the effects of degeneration on the lumbar spine biomechanics, as well as to investigate the mechanical underpinning of the contemporary treatment strategies.     

Development and validation of a weight-bearing finite element model for total knee replacement

Total knee arthroplasty (TKA) is a successful procedure for osteoarthritis. However, some patients (19%) do have pain after surgery. A finite element model was developed based on boundary conditions of a knee rig. A 3D-model of an anatomical full leg was generated from magnetic resonance image data and a total knee prosthesis was implanted without patella resurfacing. In the finite element model, a restarting procedure was programmed in order to hold the ground reaction force constant with an adapted quadriceps muscle force during a squat from 20° to 105° of flexion. Knee rig experimental data were used to validate the numerical model in the patellofemoral and femorotibial joint. Furthermore, sensitivity analyses of Young’s modulus of the patella cartilage, posterior cruciate ligament (PCL) stiffness, and patella tendon origin were performed. Pearson’s correlations for retropatellar contact area, pressure, patella flexion, and femorotibial ap-movement were near to 1. Lowest root mean square error for retropatellar pressure, patella flexion, and femorotibial ap-movement were found for the baseline model setup with Young’s modulus of 5 MPa for patella cartilage, a downscaled PCL stiffness of 25% compared to the literature given value and an anatomical origin of the patella tendon. The results of the conducted finite element model are comparable with the experimental results. Therefore, the finite element model developed in this study can be used for further clinical investigations and will help to better understand the clinical aspects after TKA with an unresurfaced patella.     

Development of structural and material clavicle response corridors under axial compression and three point bending loading for clavicle finite element model validation

Clavicle injuries were frequently observed in automotive side and frontal crashes. Finite element (FE) models have been developed to understand the injury mechanism, although no clavicle loading response corridors yet exist in the literature to ensure the model response biofidelity. Moreover, the typically developed structural level (e.g., force–deflection) response corridors were shown to be insufficient for verifying the injury prediction capacity of FE model, which usually is based on strain related injury criteria. Therefore, the purpose of this study is to develop both the structural (force vs deflection) and material level (strain vs force) clavicle response corridors for validating FE models for injury risk modeling. 20 Clavicles were loaded to failure under loading conditions representative of side and frontal crashes respectively, half of which in axial compression, and the other half in three point bending. Both structural and material response corridors were developed for each loading condition. FE model that can accurately predict structural response and strain level provides a more useful tool in injury risk modeling and prediction. The corridor development method in this study could also be extended to develop corridors for other components of the human body.     

An upper bound computational model for investigation of fusion effects on adjacent segment biomechanics of the lumbar spine

Abstract

Prediction of the biomechanical effects of fusion surgery on adjacent segments is a challenge in computational biomechanics of the spine. In this study, a two-segment L3-L4-L5 computational model was developed to simulate the effects of spinal fusion on adjacent segment biomechanical responses under a follower load condition. The interaction between the degenerative segment (L4-5) and the adjacent segment (L3-4) was simulated using an equivalent follower spring. The spring stiffness was calibrated using a rigid fusion of a completely degenerated disc model at the L4-5 level, resulting in an upper bound response at the adjacent (L3-4) segment. The obtained upper bound equivalent follower spring was used to simulate the upper bound biomechanical responses of fusion of the disc with different degeneration grades. It was predicted that as the disc degeneration grade at the degenerative segment decreased, the effect on the adjacent segment responses decreased accordingly after fusion. The data indicated that the upper bound computational model can be a useful computational tool for evaluation of the interaction between segments and for investigation of the biomechanical mechanisms of adjacent segment degeneration after fusion.     

A computationally efficient strategy to estimate muscle forces in a finite element musculoskeletal model of the lower limb

Concurrent multiscale simulation strategies are required in computational biomechanics to study the interdependence between body scales. However, detailed finite element models rarely include muscle recruitment due to the computational burden of both the finite element method and the optimization strategies widely used to estimate muscle forces. The aim of this study was twofold: first, to develop a computationally efficient muscle force prediction strategy based on proportional-integral-derivative (PID) controllers to track gait and chair rise experimental joint motion with a finite element musculoskeletal model of the lower limb, including a deformable knee representation with 12 degrees of freedom; and, second, to demonstrate that the inclusion of joint-level deformability affects muscle force estimation by using two different knee models and comparing muscle forces between the two solutions. The PID control strategy tracked experimental hip, knee, and ankle flexion/extension with root mean square errors below 1°, and estimated muscle, contact and ligament forces in good agreement with previous results and electromyography signals. Differences up to 11% and 20% in the vasti and biceps femoris forces, respectively, were observed between the two knee models, which might be attributed to a combination of differing joint contact geometry, ligament behavior, joint kinematics, and muscle moment arms. The tracking strategy developed in this study addressed the inevitable tradeoff between computational cost and model detail in musculoskeletal simulations and can be used with finite element musculoskeletal models to efficiently estimate the interdependence between muscle forces and tissue deformation.