A three-dimensional finite element model of the human anterior cruciate ligament: a computational analysis with experimental validation

In this study, the force and stress distribution within the anteromedial (AM) and posterolateral (PL) bundles of the anterior cruciate ligament (ACL) in response to an anterior tibial load with the knee at full extension was calculated using a validated three-dimensional finite element model (FEM) of a human ACL. The interaction between the AM and PL bundles, as well as the contact and friction caused by the ACL wrapping around the bone during knee motion, were included in the model. The AM and PL bundles of the ACL were simulated as incompressible homogeneous and isotropic hyperelastic materials. The multiple-degrees-of-freedom (DOF) knee kinematics of a cadaveric knee were first obtained using a robotic/universal force-moment sensor testing system. These data were used as the boundary conditions for the FEM of the ACL to calculate the forces in the ACL. The calculated forces were compared to the in situ force in the ACL, determined experimentally, to validate the model. The validated FEM was then used to calculate the force and stress distribution within the ACL under an anterior tibial load at full extension. The AM and PL bundles shared the force, and the stress distribution was non-uniform within both bundles with the highest stress localized near the femoral insertion site. The contact and friction caused by the ACL wrapping around the bone during knee motion played the role of transferring the force from the ACL to the bone, and had a direct effect on the force and stress distribution of the ACL. This validated model will enable the analysis of force and stress distribution in the ACL in response to more complex loading conditions and has the potential to help design improved surgical procedures following ACL injuries.     

Probabilistic finite element prediction of knee wear simulator mechanics

Computational models have recently been developed to replicate experimental conditions present in the Stanmore knee wear simulator. These finite element (FE) models, which provide a virtual platform to evaluate total knee replacement (TKR) mechanics, were validated through comparisons with experimental data for a specific implant. As with any experiment, a small amount of variability is inherently present in component alignment, loading, and environmental conditions, but this variability has not been previously incorporated in the computational models. The objectives of the current research were to assess the impact of experimental variability on predicted TKR mechanics by determining the potential envelope of joint kinematics and contact mechanics present during wear simulator loading, and to evaluate the sensitivity of the joint mechanics to the experimental parameters. In this study, 8 component alignment and 4 experimental parameters were represented as distributions and used with probabilistic methods to assess the response of the system, including interaction effects. The probabilistic FE model evaluated two levels of parameter variability (with standard deviations of component alignment parameters up to 0.5mm and 1 degrees ) and predicted a variability of up to 226% (3.44mm) in resulting anterior-posterior (AP) translation, up to 169% (4.30 degrees ) in internal-external (IE) rotation, but less than 10% (1.66MPa) in peak contact pressure. The critical alignment parameters were the tilt of the tibial insert and the IE rotational alignment of the femoral component. The observed variability in kinematics and, to a lesser extent, contact pressure, has the potential to impact wear observed experimentally.     

A dynamic finite element analysis of impulsive loading of the extension-splinted rabbit knee

A dynamic nonlinear finite element model was developed to study juxtarticular stresses in the splinted rabbit knee, an established laboratory model for creating osteoarthrosis due to impulsive loading. Plane strain finite element results were validated by comparison with corresponding experimental data. Parametric effects studied included the input tibial displacement speed, the local bone density distribution, and the modulus of cartilage and subchondral bone. While the computed resultant contact force magnitude was sensitive to a number of model parameters, the stress patterns, when normalized to a given resultant force magnitude, were not. Despite comparable force peaks, the finite element results showed approximately six-fold higher effective strain rate levels for a severely impulsive loading protocol known to induce rapid osteoarthrosis, versus those for a mildly impulsive loading protocol not usually associated with cartilage damage. A propensity for elevated shear in the deep cartilage layer near the contact periphery, observed in nearly all computed stress distributions, is consistent with previous experimental findings of fissuring at that level in the impulsively loaded rabbit knee.     

Three-dimensional finite element simulations of the mechanical response of the fingertip to static and dynamic compressions

The analysis of the mechanics of the contact interactions of fingers/handle and the stress/strain distributions in the soft tissues in the fingertip is essential to optimize design of tools to reduce many occupation-related hand disorders. In the present study, a three-dimensional (3D) finite element (FE) model for the fingertip is proposed to simulate the nonlinear and time-dependent responses of a fingertip to static and dynamic loadings. The proposed FE model incorporates the essential anatomical structures of a finger: skin layers (outer and inner skins), subcutaneous tissue, bone and nail. The soft tissues (inner skin and subcutaneous tissue) are considered to be nonlinearly viscoelastic, while the hard tissues (outer skin, bone and nail) are considered to be linearly elastic. The proposed model has been used to simulate two loading scenarios: (a) the contact interactions between the fingertip and a flat surface and (b) the indentation of the fingerpad via a sharp wedge. For case (a), the predicted force/displacement relationships and time-dependent force responses are compared with the published experimental data; for case (b), the skin surface deflection profiles were predicted and compared with the published experimental observations. Furthermore, for both cases, the time-dependent stress/strain distributions within the tissues of the fingertip were calculated. The good agreement between the model predictions and the experimental observations indicates that the present model is capable of predicting realistic time-dependent force/displacement responses and stress/strain distributions in the soft tissues for dynamic loading conditions.     

How the stiffness of meniscal attachments and meniscal material properties affect tibio-femoral contact pressure computed using a validated finite element model of the human knee joint

In an effort to prevent degeneration of articular cartilage associated with meniscectomies, both meniscal allografts and synthetic replacements are subjects of current interest and investigation. The objectives of the current study were to (1) determine whether a transversely isotropic, linearly elastic, homogeneous material model of the meniscal tissue is necessary to achieve a normal contact pressure distribution on the tibial plateau, (2) determine which material and boundary condition (attachments) parameters affect the contact pressure distribution most strongly, and (3) set tolerances on these parameters to restore the contact pressure distribution to within a specified error. To satisfy these objectives, a finite element model of the tibio-femoral joint of a human cadaveric knee (including both menisci) was used to study the contact pressure distribution on the tibial plateau. To validate the model, the contact pressure distribution on the tibial plateau was measured experimentally in the same knee used to create the model. Within physiologically reasonable bounds on five material parameters and four attachment parameters associated with a meniscal replacement, an optimization was performed under 1200 N of compressive load on the set of nine parameters to minimize the difference between the experimental and model results. The error between the experimental and model contact variables was minimized to 5.4%. The contact pressure distribution of the tibial plateau was sensitive to the circumferential modulus, axial/radial modulus, and horn stiffness, but relatively insensitive to the remaining six parameters. Consequently, both the circumferential and axial/radial moduli are important determinants of the contact pressure distribution, and hence should be matched in the design and/or selection of meniscal replacements. In addition, during surgical implantation of a meniscal replacement, the horns should be attached with high stiffness bone plugs, and the attachments of the transverse ligament and deep medial collateral ligament should be restored to minimize changes in the contact pressure distribution, and thereby possibly prevent the degradation of articular cartilage.     

Three-dimensional finite element simulations of the mechanical response of the fingertip to static and dynamic compressions

The analysis of the mechanics of the contact interactions of fingers/handle and the stress/strain distributions in the soft tissues in the fingertip is essential to optimize design of tools to reduce many occupation-related hand disorders. In the present study, a three-dimensional (3D) finite element (FE) model for the fingertip is proposed to simulate the nonlinear and time-dependent responses of a fingertip to static and dynamic loadings. The proposed FE model incorporates the essential anatomical structures of a finger: skin layers (outer and inner skins), subcutaneous tissue, bone and nail. The soft tissues (inner skin and subcutaneous tissue) are considered to be nonlinearly viscoelastic, while the hard tissues (outer skin, bone and nail) are considered to be linearly elastic. The proposed model has been used to simulate two loading scenarios: (a) the contact interactions between the fingertip and a flat surface and (b) the indentation of the fingerpad via a sharp wedge. For case (a), the predicted force/displacement relationships and time-dependent force responses are compared with the published experimental data; for case (b), the skin surface deflection profiles were predicted and compared with the published experimental observations. Furthermore, for both cases, the time-dependent stress/strain distributions within the tissues of the fingertip were calculated. The good agreement between the model predictions and the experimental observations indicates that the present model is capable of predicting realistic time-dependent force/displacement responses and stress/strain distributions in the soft tissues for dynamic loading conditions.     

Effects of femoral component placement on the balancing of a total knee at surgery

Misalignment and soft-tissue imbalance in total knee arthroplasty (TKA) can cause discomfort, pain, inadequate motion and instability that may require revision surgery. Balancing can be defined as equal collateral ligament tensions or equal medial and lateral compartmental forces during the flexion range. Our goal was to study the effects on balancing of linear femoral component misplacements (proximal, distal, anterior, posterior); and different component rotations in mechanical alignment compared to kinematic alignment throughout the flexion path. A test rig was constructed such that the position of a standard femoral component could be adjusted to simulate the linear and rotational positions. With the knee in neutral reference values of the collateral tensions were adjusted to give anatomic contact force patterns, measured with an instrumented tibial trial. The deviations in the forces for each femoral component position were then determined. Compartmental forces were significantly influenced by 2 mm linear errors in the femoral component placement. However, the errors were least for a distal error, equivalent to undercutting the distal femur. The largest errors mainly increase the lateral condyle force, occurred for proximal and posterior component errors. There were only small contact force differences between kinematic and mechanical alignment. Based on these results, surgeons should avoid overcutting the distal femur and undercutting the posterior femur. However, the 2–3 degrees varus slope of the joint line as in kinematic alignment did not have much effect on balancing, so mechanical or kinematic alignment were equivalent.     

A three-dimensional finite element analysis of the upper tibia

A three-dimensional finite element model of the proximal tibia has been developed to provide a base line for further modeling of prosthetic resurfaced tibiae. The geometry for the model was developed by digitizing coronal and transverse sections made with the milling machine, from one fresh tibia of average size. The load is equally distributed between the medial and lateral compartments over contact areas that were reported in the literature. An indentation test has been used to measure the stiffness and the ultimate strength of cancellous bone in four cadaver tibiae. These values provided the statistical basis for characterising the inhomogeneous distribution of the cancellous bone properties in the proximal tibia. All materials in the model were assumed to be linearly elastic and isotropic. Mechanical properties for the cortical bone and cartilage have been taken from the literature. Results have been compared with strain gage tests and with a two-dimensional axisymmetric finite element model both from the literature. Qualitative comparison between trabecular alignment, and the direction of the principal compressive stresses in the cancellous bone, showed a good relationship. Maximum stresses in the cancellous bone and cortical bone, under a load which occurs near stance phase during normal gait, show safety factors of approximately eight and twelve, respectively. The load sharing between the cancellous bone and the cortical bone has been plotted for the first 40 mm distally from the tibial eminence.     

The role of patient, surgical, and implant design variation in total knee replacement performance

Clinical studies demonstrate substantial variation in kinematic and functional performance within the total knee replacement (TKR) patient population. Some of this variation is due to differences in implant design, surgical technique and component alignment, while some is due to subject-specific differences in joint loading and anatomy that are inherently present within the population. Combined finite element and probabilistic methods were employed to assess the relative contributions of implant design, surgical, and subject-specific factors to overall tibiofemoral (TF) and patellofemoral (PF) joint mechanics, including kinematics, contact mechanics, joint loads, and ligament and quadriceps force during simulated squat, stance-phase gait and stepdown activities. The most influential design, surgical and subject-specific factors were femoral condyle sagittal plane radii, tibial insert superior-inferior (joint line) position and coronal plane alignment, and vertical hip load, respectively. Design factors were the primary contributors to condylar contact mechanics and TF anterior-posterior kinematics; TF ligament forces were dependent on surgical factors; and joint loads and quadriceps force were dependent on subject-specific factors. Understanding which design and surgical factors are most influential to TKR mechanics during activities of daily living, and how robust implant designs and surgical techniques must be in order to adequately accommodate subject-specific variation, will aid in directing design and surgical decisions towards optimal TKR mechanics for the population as a whole.     

Development of a statistical shape-function model of the implanted knee for real-time prediction of joint mechanics

Outcomes of total knee arthroplasty (TKA) are dependent on surgical technique, patient variability, and implant design. Non-optimal design or alignment choices may result in undesirable contact mechanics and joint kinematics, including poor joint alignment, instability, and reduced range of motion. Implant design and surgical alignment are modifiable factors with potential to improve patient outcomes, and there is a need for robust implant designs that can accommodate patient variability. Our objective was to develop a statistical shape-function model (SFM) of a posterior stabilized implanted knee to instantaneously predict joint mechanics in an efficient manner. Finite element methods were combined with Latin hypercube sampling and regression analyses to produce modeling equations relating nine implant design and six surgical alignment parameters to tibiofemoral (TF) joint mechanics outcomes during a deep knee bend. A SFM was developed and TF contact mechanics, kinematics, and soft tissue loads were instantaneously predicted from the model. Average normalized root-mean-square error predictions were between 2.79% and 9.42%, depending on the number of parameters included in the model. The statistical shape-function model generated instantaneous joint mechanics predictions using a maximum of 130 training simulations, making it ideally suited for integration into a patient-specific design and alignment optimization pipeline. Such a tool may be used to optimize kinematic function to achieve more natural motion or minimize implant wear, and may aid the engineering and clinical communities in improving patient satisfaction and surgical outcomes.     

Effects of medial collateral ligament release,limb correction,and soft tissue laxity on knee joint contact force distribution after medial opening wedge high tibial osteotomy: a computational study

In this study, the effects of medial collateral ligament (MCL) release and the limb correction strategies with pre-existing MCL laxity on tibiofemoral contact force distribution after high tibial osteotomy (HTO) were investigated. The medial and lateral contact forces of the knee were quantified during simulated standing using computational modeling techniques. MCL slackness had a primary influence on contact force distribution of the knee, while there was little effect of simulated limb correction. Anterior and middle bundle release, which involved the partial release of two-thirds of the superficial MCL, was shown to be an optimal surgical method in HTO, achieving balanced contact distribution in simulated weight-bearing standing.     

The effect of valgus/varus malalignment on load distribution in total knee replacements

Valgus or varus malpositioning of the tibial component of a total knee implant may cause increased propensity for loosening or implant wear and eventually may lead to revision surgery. The aim of this study was to determine the effect of valgus/varus malalignment on tibio-femoral mechanics during surgical trial reduction and simulated gait loading. In seven cadaver legs, posterior cruciate sparing total knee replacements were implanted and tibial inserts representing a neutral alignment and 3 degrees and 5 degrees varus and valgus alignments were sequentially inserted. Each knee with each insert was loaded in a manner representative of a trial reduction performed during knee surgery and loaded in a physiological knee simulator. Simulated gait performed on the simulator demonstrated that internal/external and adduction/abduction rotations showed statistical changes with some of the angled inserts at different points in the walking cycle. Neither medial/lateral nor anterior/posterior translations changed statistically during simulated walking. The pressure distribution and total load in the medial and lateral compartments of the tibial component changed significantly with as little as a 3 degrees variation in angulation when loaded in a manner representative of a trial reduction or with a knee simulator. These results support the need for precise surgical reconstruction of the mechanical axis of the knee and proper alignment of the tibial component. These results further demonstrate that tibial contact pressures measured during a trial reduction method may be predictive of contact mechanics at the higher loading seen in the knee simulator.     

The effect of hamstring muscle compensation for anterior laxity in the ACL-deficient knee during gait

The hamstring muscles have been recognized as an important element in compensating for the loss of stability in the ACL-deficient knee, but it is still not clear whether the hamstring muscle force can completely compensate for the loss of ACL, and the consequences of increased hamstring muscle force. A two-dimensional anatomical knee model in the sagittal plane was developed to examine the effect of various levels of hamstring muscle activation on restraining anterior tibial translation in the ACL-deficient knee during level walking. The model included the tibiofemoral and patellofemoral joints, four major ligaments, the medial capsule, and five muscle units surrounding the knee. Simulations were conducted to determine anterior tibial translation and internal joint loading at a single selected position when the knee was under a peak external flexion moment during early stance phase of gait. Incremental hamstring muscle forces were applied to the modeled normal and the ACL-deficient knees. Results of simulations showed that the ACL injury increased the anterior tibial translation by 11.8mm, while 56% of the maximal hamstring muscle force could reduce the anterior translation of the tibia to a normal level during the stance phase of gait. The consequences of increased hamstring muscle force included increased quadriceps muscle force and joint contact force.     

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.     

Detailed finite element modelling of deep needle insertions into a soft tissue phantom using a cohesive approach

Detailed finite element modelling of needle insertions into soft tissue phantoms encounters difficulties of large deformations, high friction, contact loading and material failure. This paper demonstrates the use of cohesive elements in high-resolution finite element models to overcome some of the issues associated with these factors. Experiments are presented enabling extraction of the strain energy release rate during crack formation. Using data from these experiments, cohesive elements are calibrated and then implemented in models for validation of the needle insertion process. Successful modelling enables direct comparison of finite element and experimental force–displacement plots and energy distributions. Regions of crack creation, relaxation, cutting and full penetration are identified. By closing the loop between experiments and detailed finite element modelling, a methodology is established which will enable design modifications of a soft tissue probe that steers through complex mechanical interactions with the surrounding material.     

Evaluation of a computational model used to predict the patellofemoral contact pressure distribution

One possible cause of patellofemoral pain syndrome is excessive lateral force acting on the patella. Although several treatment methods focus on decreasing the lateral force acting on the patella, the relationship between the lateral force and the patellofemoral contact pressure distribution is unclear. A computational model has been developed to determine how loading variations alter the patellofemoral force and pressure distributions for individual knees. The model allows variation in the quadriceps and patella tendon forces, and calculates the predicted contact pressure distribution using the discrete element analysis technique. To characterize the accuracy of the model, four cadaver knees were flexed on a knee simulator with three initial Q-angles, while recording the force and pressure distributions with a pressure sensor. A model of each knee was created from CT data. Using the external force applied to the knee, the geometry of the knee, and the quadriceps origin as input, the pressure distribution was calculated during flexion. Similar trends were noted for the computational and experimental results. The percentage of the total force applied to the lateral cartilage increased with the Q-angle. The maximum contact pressure increased during flexion. The maximum lateral contact pressure increased with the Q-angle for three knees. For the other knee, increasing the Q-angle decreased the maximum lateral pressure. The maximum medial contact pressure decreased as the Q-angle increased. By characterizing the influence of patellofemoral loading on the force and pressure distributions, the computational model could be used to evaluate treatment methods prescribed for patellofemoral pain.     

Modelling of global boundary effects on harmonic motion imaging of soft tissues

Biomechanical imaging techniques have been developed for soft tissue characterisation and detection of breast tumours. Harmonic motion imaging (HMI) uses a focused ultrasound technology to generate a harmonic radiation force in a localised region inside a soft tissue. The resulting dynamic response is used to map the local distribution of the mechanical properties of the tissue. In this study, a finite element (FE) model is developed to investigate the effect of global boundary conditions on the dynamic response of a soft tissue during HMI. The direct-solution steady-state dynamic analysis procedure is used to compute the harmonic displacement amplitude in FE simulations. The model is parameterised in terms of boundary conditions and viscoelastic properties, and the corresponding raster-scan displacement amplitudes are captured to examine its response. The effect of the model's global dimensions on the harmonic response is also investigated. It is observed that the dynamic response of soft tissue with high viscosity is independent of the global boundary conditions for regions remote to the boundary; thus, it can be subjected to local analysis to estimate the underlying mechanical properties. However, the dynamic response is sensitive to global boundary conditions for tissue with low viscosity or regions located near to the boundary.     

Analysis of effects of friction on the deformation behavior of soft tissues in unconfined compression tests

Frictionless specimen/platen contact in unconfined compression tests has traditionally been assumed in determining material properties of soft tissues via an analytical solution. In the present study, the suitability of this assumption was examined using a finite element method. The effect of the specimen/platen friction on the mechanical characteristics of soft tissues in unconfined compression was analyzed based on the published experimental data of three different materials (pigskin, pig brain, and human calcaneal fat). The soft tissues were considered to be nonlinear and viscoelastic; the friction coefficient at the contact interface between the specimens and platens was assumed to vary from 0.0 to 0.5. Our numerical simulations show that the tissue specimens are, due to the specimen/platen friction, not compressed in a uniform stress/strain state, as has been traditionally assumed in analytical analysis. The stress of the specimens obtained with the specimen/platen friction can be greater than those with the frictionless specimen/platen contact by more than 50%, even in well-controlled test conditions.     

In vitro forces in the normal and cruciate-deficient knee during simulated squatting motion

Three orthogonal components of the tibiofemoral and patellofemoral forces were measured simultaneously for knees with intact cruciate ligaments (nine knees), following anterior cruciate ligament resection (six knees), and subsequent posterior cruciate ligament resection (six knees). The knees were loaded using an experimental protocol that modeled static double-leg squat. The mean compressive tibial force increased with flexion angle. The mean anteroposterior tibial shear force acted posteriorly on the tibia below 50 deg flexion and anteriorly above 55 deg. Mediolateral shear forces were low compared to the other force components and tended to be directed medially on both the patella and tibia. The mean value of the ratio of the resultant tibial force divided by the quadriceps force decreased with increasing flexion angle and was between 0.6 and 0.7 above 70 deg flexion. The mean value of the ratio of the resultant tibiofemoral contact force divided by the resultant patellofemoral contact force decreased with increasing flexion and was between 0.8 and 1.0 above 55 deg flexion. Cruciate ligament resection resulted in no significant changes in the patellar contact forces. Following resection of the anterior cruciate ligament, the tibial anteroposterior shear force was directed anteriorly over all flexion angles tested. Subsequent resection of the posterior cruciate ligament resulted in an approximately 10 percent increase in the quadriceps tendon and tibial compressive force.