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.     

The Biomechanical Effects of Sagittal Split Ramus Osteotomy on Temporomandibular Joint

Abstract

The aim of this study was to evaluate the stress distributions and deformations of the temporomandibular joint (TMJ) during different periods before and after sagittal split ramus osteotomy (SSRO). A three-dimensional finite element model of the mandible and TMJ was established, based on the preoperative CT of a patient with mandibular prognathism. Numerical SSRO was performed and the models of three postoperative periods were established. Contact elements were used to simulate the interaction between the articular discs and the articular cartilages. Nonlinear cable elements were used to simulate the disc attachments and the ligaments. Muscle forces and boundary conditions corresponding to the central occlusion were applied on all the models. The results showed that the stress distributions of the patient’s TMJs were not the same as those of asymptomatic subjects. The stress distributions and deformations of the disc, condylar and temporal cartilage were changed at different periods after SSRO. The biomechanical parameters of TMJ were improved after SSRO. And the postoperative results showed that appropriate functional training could help to avoid TMJ diseases. Therefore SSRO could improve the stress distributions of the TMJ and relieve the symptoms of temporomandibular disorder (TMD).     

Prediction of the articular eminence shape in a patient with unilateral hypoplasia of the right mandibular ramus before and after distraction osteogenesis—A simulation study

The aim of this work was to predict the shape of the articular eminence in a patient with unilateral hypoplasia of the right mandibular ramus before and after distraction osteogenesis (DO). Using a patient-specific musculoskeletal model of the mandible the hypothesis that the observed differences in this patient in the left and right articular eminence inclinations were consistent with minimisation of joint loads was tested. Moreover, a prediction was made of the final shape of the articular eminence after DO when the expected remodelling has reached a steady state. The individual muscle forces and the average TMJ loading were computed for each combination of articular eminence angles both before and after DO. This exhaustive parameter study provides a full overview of average TMJ loading depending on the angles of the articular eminences. Before DO the parameter study resulted in different articular eminence inclinations between left and right sides consistent with patient data obtained from CT scans, indicating that in this patient the articular eminence shapes result from minimisation of joint loads. The simulation model predicts development of almost equal articular eminence shapes after DO. The same tendency was observed in cone beam CT scans (NewTom) of the patient taken 6.5 years after surgery.     

Prediction of biomechanical parameters in the lumbar spine during static sagittal plane lifting.

A combined approach involving optimization and the finite element technique was used to predict biomechanical parameters in the lumbar spine during static lifting in the sagittal plane. Forces in muscle fascicles of the lumbar region were first predicted using an optimization-based force model including the entire lumbar spine. These muscle forces as well as the distributed upper body weight and the lifted load were then applied to a three-dimensional finite element model of the thoracolumbar spine and rib cage to predict deformation, the intradiskal pressure, strains, stresses, and load transfer paths in the spine. The predicted intradiskal pressures in the L3-4 disk at the most deviated from the in vivo measurements by 8.2 percent for the four lifting cases analyzed. The lumbosacral joint flexed, while the other lumbar joints extended for all of the four lifting cases studied (rotation of a joint is the relative rotation between its two vertebral bodies). High stresses were predicted in the posterolateral regions of the endplates and at the junctions of the pedicles and vertebral bodies. High interlaminar shear stresses were found in the posterolateral regions of the lumbar disks. While the facet joints of the upper two lumbar segments did not transmit any load, the facet joints of the lower two lumbar segments experienced significant loads. The ligaments of all lumbar motion segments except the lumbosacral junction provided only marginal moments. The limitations of the current model and possible improvements are discussed.     

A new method to investigate in vivo knee behavior using a finite element model of the lower limb

Several finite element models have been developed for estimating the mechanical response of joint internal structures, where direct or indirect in vivo measurement is difficult or impossible. The quality of the predictions made by those models is largely dependent on the quality of the experimental data (e.g. load/displacement) used to drive them. Also numerical problems have been described in the literature when using implicit finite element techniques to simulate problems that involve contacts and large displacements. In this study, a unique strategy was developed combining high accuracy in vivo three-dimensional kinematics and a lower limb finite element model based on explicit finite element techniques. The method presents an analytical technique applied to a dynamic loading condition (impact during hopping on one leg). The validation of the lower limb model focused on the response of the whole model and the knee joint in particular to the imposed 3D femoral in vivo kinematics and ground reaction forces. The approach outlined in this study introduces a generic tool for the study of in vivo knee joint behavior.     

Load transfer across the scapula during humeral abduction

Stress analysis in the individual parts of the scapula under normal physiological conditions is necessary to understand the load transfer mechanism, its relation with morphology of bone and to analyse the deviations in stress patterns due to implantation of the glenoid. The purpose of this study was to obtain stress distribution in the scapula during abduction of the arm and to obtain a qualitative estimate of the function of coracoacromial ligament. An accurate three-dimensional (3D) finite element (FE) model of the natural scapula has been developed for this purpose, using computed tomography data and shell-solid modelling approach. The model was experimentally validated. A musculoskeletal shoulder model of forces that calculates all muscle, ligament and joint reaction forces, in six load cases (30-180 degrees) during unloaded humeral abduction was used as applied loading conditions for the 3D FE model. High tensile and compressive stresses (15-60 MPa) were generated in the thick bony ridges of the scapula, like the scapular spine, lateral border, glenoid and acromion. High compressive stresses (45-58 MPa) were evoked in the glenoid and at the connection of glenoid-scapular spine-infraspinous fossa. The stresses in the infraspinous fossa and supraspinous fossa were low (0.05-15 MPa). These results indicated that the transfer of major muscle and joint reaction take place predominantly through the thick bony ridges, whereas the fossa area act more as attachment sites of large muscles. During humeral abduction, coracoacromial ligament was stretched, and presumably will be under tension.     

Stresses at the meniscofemoral joint: elastostatic investigations on the applicability of interface elements

Stress distributions at the meniscofemoral joint were analysed and the applicability of nonlinear interface elements in a finite element model (FEM) were tested. Centred and 70% off-centre load cases with a complete, a partially removed or a totally removed medial meniscus were evaluated in two dimensions. Interface width was assumed to increase linearly from almost zero to 1 mm at the inner and outer border of the femoral condyles. Maximum interface forces were found at the centre of the condyles, decreasing to zero at the peripherical and intercondylar femoral border. Simulation data concerning a removed medial meniscus or medial 70% off-centre load with complete meniscus indicated higher medial contact forces in the first case. A decrease in the elastic modulus of the articular surface tissues caused two small force transfer peaks (femoral centre and intercondylar border), which were strongly influenced by the predefined gap width.     

Role of the acetabular labrum in load support across the hip joint

The relatively high incidence of labral tears among patients presenting with hip pain suggests that the acetabular labrum is often subjected to injurious loading in vivo. However, it is unclear whether the labrum participates in load transfer across the joint during activities of daily living. This study examined the role of the acetabular labrum in load transfer for hips with normal acetabular geometry and acetabular dysplasia using subject-specific finite element analysis. Models were generated from volumetric CT data and analyzed with and without the labrum during activities of daily living. The labrum in the dysplastic model supported 4-11% of the total load transferred across the joint, while the labrum in the normal model supported only 1-2% of the total load. Despite the increased load transferred to the acetabular cartilage in simulations without the labrum, there were minimal differences in cartilage contact stresses. This was because the load supported by the cartilage correlated with the cartilage contact area. A higher percentage of load was transferred to the labrum in the dysplastic model because the femoral head achieved equilibrium near the lateral edge of the acetabulum. The results of this study suggest that the labrum plays a larger role in load transfer and joint stability in hips with acetabular dysplasia than in hips with normal acetabular geometry.     

Validation of a musculo-skeletal model of the mandible and its application to mandibular distraction osteogenesis

Mandibular distraction osteogenesis will lead to a change in muscle coordination and load transfer to the temporomandibular joints (TMJ). The objective of this work is to present and validate a rigid-body musculo-skeletal model of the mandible based on inverse dynamics for calculation of the muscle activations, muscle forces and TMJ reaction forces for different types of clenching tasks and dynamic tasks. This approach is validated on a symmetric mandible model and an application will be presented where the TMJ reaction forces during unilateral clenching are estimated for a virtual distraction patient with a shortened left ramus. The mandible model consists of 2 rigid segments and has 4 degrees-of-freedom. The model was equipped with 24 hill-type musculotendon actuators. During the validation experiment one subject was asked to do several tasks while measuring EMG activity, bite force and kinematics. The bite force and kinematics were used as input for the simulations of the same tasks after which the estimated muscle activities were compared with the measured muscle activities. This resulted in an average correlation coefficient of 0.580 and an average of the Mean Absolute Error of 0.109. The virtual distraction model showed a large difference in the TMJ reaction forces between left and right compared with the symmetric model for the same loading case. The present work is a step in the direction of building patient-specific mandible models, which can assess the mechanical effects on the TMJ before mandibular distraction osteogenesis surgery.     

Role of gastrocnemius-soleus muscle in forefoot force transmission at heel rise - A 3D finite element analysis

The functions of the gastrocnemius-soleus (G-S) complex and other plantar flexor muscles are to stabilize and control major bony joints, as well as to provide primary coordination of the foot during the stance phase of gait. Geometric positioning of the foot and transferring of plantar loads can be adversely affected when muscular control is abnormal (e.g., equinus contracture). Although manipulation of the G-S muscle complex by surgical intervention (e.g., tendo-Achilles lengthening) is believed to be effective in restoring normal plantar load transfer in the foot, there is lack of quantitative data supporting that notion. Thus, the objective of this study is to formulate a three-dimensional musculoskeletal finite element model of the foot to quantify the precise role of the G-S complex in terms of biomechanical response of the foot. The model established corresponds to a muscle-demanding posture during heel rise, with simulated activation of major extrinsic plantar flexors. In the baseline (reference) case, required muscle forces were determined from what would be necessary to generate the targeted resultant ground reaction forces. The predicted plantar load transfer through the forefoot plantar surface, as indicated by plantar pressure distribution, was verified by comparison with experimental observations. This baseline model served as a reference for subsequent parametric analysis, where muscle forces applied by the G-S complex were decreased in a step-wise manner. Adaptive changes of the foot mechanism, in terms of internal joint configurations and plantar stress distributions, in response to altered muscular loads were analyzed. Movements of the ankle and metatarsophalangeal joints, as well as forefoot plantar pressure peaks and pressure distribution under the metatarsal heads (MTHs), were all found to be extremely sensitive to reduction in the muscle load in the G-S complex. A 40% reduction in G-S muscle stabilization can result in dorsal-directed rotations of 8.81° at the ankle, and a decreased metatarsophalangeal joint extension of 4.65°. The resulting peak pressure reductions at individual MTHs, however, may be site-specific and possibly dependent on foot structure, such as intrinsic alignment of the metatarsals. The relationships between muscular control, internal joint movements, and plantar load distributions are envisaged to have important clinical implications on tendo-Achilles lengthening procedures, and to provide surgeons with an understanding of the underlying mechanism for relieving forefoot pressure in diabetic patients suffering from ankle equinus contracture.     

Proximal Femoral Density Patterns are Consistent with Bicentric Joint Loads

We developed an alternate method for density-based load estimation and applied it to estimate hip joint load distributions for two femora. Two-dimensional finite element models were constructed from single energy quantitative computed tomography (QCT) data. Load estimation was performed using five loading regions on the femoral head. Within each loading region, individual nodal loads, normal to the local surface, were supplied as input to the load estimation. An optimization procedure independently adjusted individual nodal load magnitudes in each region, and the magnitudes of muscle forces on the greater trochanter, such that the applied tissue stimulus approached the reference stimulus throughout the model. Dominant estimated load resultant directions were generally consistent with published experimental data for loads during gait. The estimated loads also suggested that loads near the extremes of the articulating surface may be important (even required) for development and maintenance of normal bone architecture. Estimated load distributions within nearly all regions predicted bicentric loading patterns, which are consistent with observations of hip joint incongruity. Remodeling simulations with the estimated loads predicted density distributions with features qualitatively similar to the QCT data sets. This study illustrates how applications of density-based bone load estimation can improve understanding of dominant loading patterns in other bones and joints. The prediction of bicentric loading suggests a very fine level of local adaptation to details of joint loading.     

Proximal Femoral Density Patterns are Consistent with Bicentric Joint Loads

We developed an alternate method for density-based load estimation and applied it to estimate hip joint load distributions for two femora. Two-dimensional finite element models were constructed from single energy quantitative computed tomography (QCT) data. Load estimation was performed using five loading regions on the femoral head. Within each loading region, individual nodal loads, normal to the local surface, were supplied as input to the load estimation. An optimization procedure independently adjusted individual nodal load magnitudes in each region, and the magnitudes of muscle forces on the greater trochanter, such that the applied tissue stimulus approached the reference stimulus throughout the model. Dominant estimated load resultant directions were generally consistent with published experimental data for loads during gait. The estimated loads also suggested that loads near the extremes of the articulating surface may be important (even required) for development and maintenance of normal bone architecture. Estimated load distributions within nearly all regions predicted bicentric loading patterns, which are consistent with observations of hip joint incongruity. Remodeling simulations with the estimated loads predicted density distributions with features qualitatively similar to the QCT data sets. This study illustrates how applications of density-based bone load estimation can improve understanding of dominant loading patterns in other bones and joints. The prediction of bicentric loading suggests a very fine level of local adaptation to details of joint loading.     

Design and calibration of load sensing orthopaedic implants

Contact forces and moments act on orthopaedic implants such as joint replacements. The three forces and three moment components can be measured by six internal strain gauges and wireless telemetric data transmission. The accuracy of instrumented implants is restricted by their small size, varying modes of load transfer, and the accuracy of calibration. Aims of this study were to test with finite element studies design features to improve the accuracy, to develop simple but accurate calibration arrangements, and to select the best mathematical method for calculating the calibration constants. Several instrumented implants, and commercial and test transducers were calibrated using different loading setups and mathematical methods. It was found that the arrangement of flexible elements such as bellows or notches between the areas of load transfer and the central sensor locations is most effective to improve the accuracy. Increasing the rigidity of the implant areas, which are fixed in bones or articulate against joint surfaces, is less effective. Simple but accurate calibration of the six force and moment components can be achieved by applying eccentric forces instead of central forces and pure moments. Three different methods for calculating the measuring constants proved to be equally well suited. Employing these improvements makes it possible to keep the average measuring errors of many instrumented implants below 1-2% of the calibration ranges, including cross talk. Additional errors caused by noise of the transmitted signals can be reduced by filtering if this is permitted by the sampling rate and the required frequency content of the loads.     

Role of trunk muscles in generating follower load in the lumbar spine of neutral standing posture

Recently, experimental results have demonstrated that the load carrying capacity of the human spine substantially increases under the follower load condition. Thus, it is essential to prove that a follower load can be generated in vivo by activating the appropriate muscles in order to demonstrate the possibility that the stability of the spinal column could be maintained through a follower load mechanism. The aim of this study was to analyze the coordination of the trunk muscles in order to understand the role of the muscles in generating the follower load. A three-dimensional finite element model of the lumbar spine was developed from T12 to S1 and 117 pairs of trunk muscles (58 pairs of superficial muscles and 59 pairs of deep muscles) were considered. The follower load concept was mathematically represented as an optimization problem. The muscle forces required to generate the follower load were predicted by solving the optimization problem. The corresponding displacements and rotations at all nodes were estimated along with the follower forces, shear forces, and joint moments acting on those nodes. In addition, the muscle forces and the corresponding responses were investigated when the activations of the deep muscles or the superficial muscles were restricted to 75% of the maximum activation, respectively. Significantly larger numbers of deep muscles were involved in the generation of the follower load than the number of superficial muscles, regardless of the restriction on muscle activation. The shear force and the resultant joint moment are more influenced by the change in muscle activation in the superficial muscles. A larger number of deep trunk muscles were activated in order to maintain the spinal posture in the lumbar spine. In addition, the deep muscles have a larger capability to reduce the shear force and the resultant joint moment with respect to the perturbation of the external load or muscle fatigue compared to the superficial muscles.     

Effect of load position on muscle forces, internal loads and stability of the human spine in upright postures

A novel kinematics-based approach coupled with a non-linear finite element model was used to investigate the effect of changes in the load position and posture on muscle activity, internal loads and stability margin of the human spine in upright standing postures. In addition to 397 N gravity, external loads of 195 and 380 N were considered at different lever arms and heights. Muscle forces, internal loads and stability margin substantially increased as loads displaced anteriorly away from the body. Under same load magnitude and location, adopting a kyphotic posture as compared with a lordotic one increased muscle forces, internal loads and stability margin. An increase in the height of a load held at a fixed lever arm substantially diminished system stability thus requiring additional muscle activations to maintain the same margin of stability. Results suggest the importance of the load position and lumbar posture in spinal biomechanics during various manual material handling operations.     

Modeling the biomechanics of the mandible: a three-dimensional finite element study.

Three-dimensional finite element models of a partially edentulated human mandible were generated to calculate the mechanical response to simulated isometric biting and mastication loads. The level of mesh refinement was established via a convergence test and showed that a model with over 30,000 degrees of freedom was required to obtain analysis accuracy. The functional loading cases included muscle loading based on an algorithm that assigns muscle forces in accordance with muscle cross-sectional area, while maintaining static equilibrium. Results were found for isometric application of unilateral and bilateral bite and mastication loading, and two different sets of displacement boundary conditions were imposed at the condyles. The mechanical response is shown in terms of displacements, principal strains, and a new measure called the 'mechanical intensity scalar'. For each load case studied, there was substantial bending in the molar region of the corpus and high tensile strains in the anterior portion of the ramus.     

Finite element analysis of a hemi-pelvis: the effect of inclusion of cartilage layer on acetabular stresses and strain

An appropriate method of application of the hip-joint force and stress analysis of the pelvic bone, in particular the acetabulum, is necessary to investigate the changes in load transfer due to implantation and to calculate the reference stimulus for bone remodelling simulations. The purpose of the study is to develop a realistic 3D finite element (FE) model of the hemi-pelvis and to assess stress and strain distribution during a gait cycle. The FE modelling approach of the pelvic bone was based on CT scan data and image segmentation of cortical and cancellous bone boundaries. Application of hip-joint force through an anatomical femoral head having a cartilage layer was found to be more appropriate than a perfectly spherical head, thereby leading to more accurate stress–strain distribution in the acetabulum. Within the acetabulum, equivalent strains varied between 0.1% and 0.7% strain in the cancellous bone. High compressive (15–30 MPa) and low tensile (0–5 MPa) stresses were generated within the acetabulum. The hip-joint force is predominantly transferred from the acetabulum through the lateral cortex to the sacroiliac joint and the pubic symphysis. The study is useful to understand the load transfer within the acetabulum and for further investigations on acetabular prosthesis.     

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.     

Biomechanical consequences of subtalar joint arthroereisis in treating posterior tibial tendon dysfunction: a theoretical analysis using finite element analysis

Subtalar joint arthroereisis (SJA) has been introduced to control the hyperpronation in cases of flatfoot. The objective of this study is to evaluate the biomechanical consequence of SJA to restore the internal stress and load transfer to the intact state from the attenuated biomechanical condition induced by posterior tibial tendon dysfunction (PTTD). A three-dimensional finite element model of the foot and ankle complex was constructed based on clinical images of a healthy female (age 28 years, height 165 cm, body mass 54 kg). The boundary and loading condition during walking was acquired from the gait experiment of the model subject. Five sets of simulations (conditions) were completed: intact condition, mild PTTD, severe PTTD, mild PTTD with SJA, severe PTTD with SJA. The maximum von Mises stress of the metatarsal shafts and the load transfer along the midfoot during stance were analyzed. Generally, SJA deteriorated the joint force of the medial cuneonavicular and calcaneocuboid joints during late stance, while that of the metatarsocuneiform joints during early stance were over-corrected. Only the calcaneocuboid joint force at 45% stance demonstrated a trend of improvement. Besides, SJA exaggerated the increased stress of the metatarsals compared to the PTTD conditions, except that of the first metatarsal. Our study did not support the hypothesis that SJA can restore the internal load transfer and midfoot stress. SJA cannot compensate the salvage of midfoot stability attributed by PTTD and could be biomechanically insufficient to restore the biomechanical environment. Additional procedures such as orthotic intervention may be necessary.     

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.