Three-dimensional finite element modeling of ligaments: technical aspects

Deciphering the "Art" in Modeling and Simulation of the Knee Joint: Assessing Model Calibration Workflows and Outcomes

Model reproducibility is a point of emphasis for the National Institutes of Health (NIH) and in science, broadly. As the use of computational modeling in biomechanics and orthopedics grows, so does the need to assess the reproducibility of modeling workflows and simulation predictions. The long-term goal of the KneeHub project is to understand the influence of potentially subjective decisions, thus the modeler's "art", on the reproducibility and predictive uncertainty of computational knee joint models. In this paper, we report on the model calibration phase of this project, during which five teams calibrated computational knee joint models of the same specimens from the same specimen-specific joint mechanics dataset. We investigated model calibration approaches and decisions, and compared calibration workflows and model outcomes among the teams. The selection of the calibration targets used in the calibration workflow differed greatly between the teams and was influenced by modeling decisions related to the representation of structures, and considerations for computational cost and implementation of optimization. While calibration improved model performance, differences in the postcalibration ligament properties and predicted kinematics were quantified and discussed in the context of modeling decisions. Even for teams with demonstrated expertise, model calibration is difficult to foresee and plan in detail, and the results of this study underscore the importance of identification and standardization of best practices for data sharing and calibration.

Modelling for design and evaluation of industrial exoskeletons: A systematic review

Industrial exoskeletons are developed to relieve workers' physical demands in the workplace and to alleviate ergonomic issues associated with work-related musculoskeletal disorders. As a safe and economical alternative to empirical/experimental methods, modelling is considered as a powerful tool for design and evaluation of industrial exoskeletons. This systematic review aims to provide a comprehensive understanding of the current literature on the design and evaluation of industrial exoskeletons through modelling. A systematic study was conducted by general keyword searches of five electronic databases over the last two decades (2003-2022). Out of the 701 records initially retrieved, 33 eligible articles were included and analyzed in the final review, presenting a variety of model inputs, model development, and model outputs used in the modelling. This systematic review study revealed that existing modelling methods can evaluate the biomechanical and physiological effects of industrial exoskeletons and provide some design parameters. However, the modelling method is currently unable to cover some of the main evaluation metrics supported by experimental assessments, such as task performance, user experience/discomfort, change in metabolic costs etc. Standard guidelines for model construction and implementation, as well as validation of human-exoskeleton interactions, remain to be established.

Contribution of Elastic and Collagen Fibers to the Mechanical Behavior of Bovine Nuchal Ligament

Ligamentum nuchae is a highly elastic tissue commonly used to study the structure and mechanics of elastin. This study combines imaging, mechanical testing, and constitutive modeling to examine the structural organization of elastic and collagen fibers and their contributions to the nonlinear stress-strain behavior of the tissue. Rectangular samples of bovine ligamentum nuchae cut in both longitudinal and transverse directions were tested in uniaxial tension. Purified elastin samples were also obtained and tested. It was observed that the stress-stretch response of purified elastin tissue follows a similar curve as the intact tissue initially, but the intact tissue shows a significant stiffening behavior for stretches above 1.29 with collagen engagement. Multiphoton and histology images confirm the elastin-dominated bulk of ligamentum nuchae interspersed with small bundles of collagen fibrils and sporadic collagen-rich regions with cellular components and ground substance. A transversely isotropic constitutive model that considers the longitudinal organization of elastic and collagen fibers was developed to describe the mechanical behavior of both intact and purified elastin tissue under uniaxial tension. These findings shed light on the unique structural and mechanical roles of elastic and collagen fibers in tissue mechanics and may aid in future use of ligamentum nuchae in tissue grafting.

A comparison of intervertebral ligament properties utilized in a thoracic spine functional unit through kinematic evaluation

Ligament properties in the literature are variable, yet scarce, but needed to calibrate computational models for spine clinical research applications. A comparison of ligament stiffness properties and their effect on the kinematic behavior of a thoracic functional spinal unit (FSU) is examined in this paper. Six unique ligament property sets were utilized within a volumetric T7-T8 finite element (FE) model developed using computer-aided design (CAD) spinal geometry. A 7.5 Nm moment was applied along three anatomical planes both with and without costovertebral (CV) joints present. Range of Motion (RoM) was assessed for each property set and compared to published experimental data. Intact and serial ligament removal procedures were implemented in accordance with experimental protocol. The variance in both kinematic behavior and comparability with experimental data among property sets emphasizes the role nonlinear characterization plays in determining proper kinematic behavior in spinal FE models. Additionally, a decrease in RoM variation among property sets was exhibited when the model setup incorporated the CV joint. With proper assessment of the source and size of each ligament, the material properties considered here could be expanded and justified for implementation into thoracic spine clinical studies.

Knee instability caused by altered graft mechanical properties after anterior cruciate ligament reconstruction: the early onset of osteoarthritis?

Anterior cruciate ligament (ACL) rupture is a very common knee joint injury. Torn ACLs are currently reconstructed using tendon autografts. However, half of the patients develop osteoarthritis (OA) within 10 to 14 years postoperatively. Proposedly, this is caused by altered knee kine(ma)tics originating from changes in graft mechanical properties during the in vivo remodeling response. Therefore, the main aim was to use subject-specific finite element knee models and investigate the influence of decreasing graft stiffness and/or increasing graft laxity on knee kine(ma)tics and cartilage loading. In this research, 4 subject-specific knee geometries were used, and the material properties of the ACL were altered to either match currently used grafts or mimic in vivo graft remodeling, i.e., decreasing graft stiffness and/or increasing graft laxity. The results confirm that the in vivo graft remodeling process increases the knee range of motion, up to >300 percent, and relocates the cartilage contact pressures, up to 4.3 mm. The effect of remodeling-induced graft mechanical properties on knee stability exceeded that of graft mechanical properties at the time of surgery. This indicates that altered mechanical properties of ACL grafts, caused by in vivo remodeling, can initiate the early onset of osteoarthritis, as observed in many patients clinically.

A Critical Comparison of Comparators Used to Demonstrate Credibility of Physics-Based Numerical Spine Models

The ability of new medical devices and technology to demonstrate safety and effectiveness, and consequently acquire regulatory approval, has been dependent on benchtop, in vitro, and in vivo evidence and experimentation. Regulatory agencies have recently begun accepting computational models and simulations as credible evidence for virtual clinical trials and medical device development. However, it is crucial that any computational model undergo rigorous verification and validation activities to attain credibility for its context of use before it can be accepted for regulatory submission. Several recently published numerical models of the human spine were considered for their implementation of various comparators as a means of model validation. The comparators used in each published model were examined and classified as either an engineering or natural comparator. Further, a method of scoring the comparators was developed based on guidelines from ASME V&V40 and the draft guidance from the US FDA, and used to evaluate the pertinence of each comparator in model validation. Thus, this review article aimed to score the various comparators used to validate numerical models of the spine in order to examine the comparator's ability to lend credibility towards computational models of the spine for specific contexts of use.

Using a finite element model of the thumb to study Trapeziometacarpal joint contact during lateral pinch

BACKGROUND

Finite element (FE) analysis is widely used in different fields of orthopaedic surgery, however, its application to the trapeziometacarpal joint has been limited due to the small size, complex biconcave-convex joint geometry, and complex musculature. The goal of this study was to improve upon existing models by creating a muscle-driven FE thumb model and use the model to simulate the biomechanical effect of hand therapy exercises and ligament reconstructive surgeries.

METHODS

Bone and cartilage geometry were based on a CT dataset of a subject performing a static lateral pinch task. A previously validated musculoskeletal model was utilized to extract electromyography (EMG)-driven muscle forces. Five ligaments with biomechanical significance were modeled as springs using literature values and attached according to their anatomical landmarks.

FINDINGS

The biomechanical consequence of various interventions was proxied as a change in the maximum cartilage stress. The result shows tightening the dorsal ligament complex (dorsal radial ligament, dorsal central ligament, posterior oblique ligament) is the most effective, achieving a stress reduction of 4.8%. Five exercises used in hand therapies were modeled, among which thenar eminence strengthening showed the most prominent stress reduction of 4.0%. Four ligament reconstructive surgeries were modeled, with Eaton-Littler reconstruction showed the most significant stress reduction of 25.0%.

INTERPRETATION

Among the routinely utilized treatment options for early thumb osteoarthritis, we found that three methods: dorsal ligament imbrication, thenar eminence exercise, and the Eaton-Littler method may confer biomechanical advantages cartilage loading. These advantages align with the clinically observed favorable outcomes.

The stress and strain pattern in the ligaments of the acromioclavicular joint using a quasi-static model

BACKGROUND

The precise role of the acromioclavicular and coracoclavicular ligaments during shoulder motion is unclear. We evaluate changes in the stress-strain distribution of the acromioclavicular joint's ligaments during different shoulder passive motion positions.

METHODS

A 3D acromioclavicular joint model was reconstructed. A constitutive hyperelastic model was used for the ligaments. The kinematics of the shoulder girdle was taken to simulate shoulder abduction (Motion 1) and horizontal adduction (Motion 2). A computer-generated quasi-static and non-linear finite element model was used to predict the 3D stress-strain distribution pattern of the acromioclavicular ligament and the coracoclavicular ligament complex.

FINDINGS

In motion 1, from 20 to 90° the peak von Mises stress was found in the conoid (4.14 MPa) and the anteroinferior bundle (2.46 MPa), while from 90 to 120° it was found in the conoid and the trapezoid. However, there were no significant differences between the mean stress values between anteroinferior bundle and trapezoid throughout the motion (p = 0.98). In Motion 2, from 20 to 80° the maximum equivalent elastic strain was found in the anteroinferior bundle (0.68 mm/mm) and the conoid (0.57 mm/mm), while from 80 to 100° it was higher in the conoid (0.88 mm/mm) than in the anteroinferior bundle (0.77 mm/mm).

INTERPRETATION

The coracoclavicular ligament complex demonstrated a high stress-strain concentration during simulated passive shoulder abduction. Additionally, it was shown that the acromioclavicular ligament plays an important role in joint restraint during passive horizontal adduction, changing the primary role with the trapezoid and conoid at different motion intervals.

Mechanical Model and FEM Simulations for Efforts on Biceps and Triceps Muscles under Vertical Load: Mathematical Formulation of Results

Although isometric contractions in human muscles have been analyzed several times, there are no FEA models that allow us to use the same modeled joint (the elbow under our case) in different conditions. Most elbow joints use 3D elements for meshing. Representing the muscles in the joint is quite useful when the study is focused on the muscle itself, knowing stress distribution on muscle, and checking damage in muscle in a detailed manner (tendon–muscle insertion, for example). However, this technique is not useful for studying muscle behavior at different positions of the joint. This study, based on the mechanical model of the elbow joint, proposes a methodology for modelling muscles that will be studied in different positions by meshing them with 1D elements. Furthermore, the methodology allows us to calculate biceps and triceps efforts under load for different angles of elbow joint aperture. The simulation results have been mathematically modelled to obtain general formulations for these efforts, depending on the load and the aperture angle.

Anteroinferior bundle of the acromioclavicular ligament plays a substantial role in the joint function during shoulder elevation and horizontal adduction: a finite element model

Background

Postoperative acromioclavicular (AC) ligament deficiency has been identified as a common cause of failure after isolated coracoclavicular reconstruction. The two-bundle arrangement of the acromioclavicular ligament has recently been reported in histological and anatomical research. In addition, a clear structural advantage of the superoposterior bundle (SPB) over the less consistent anteroinferior bundle (AIB) was also found. However, the current understanding of the function of the acromioclavicular ligament in joint stability is based on uniaxial bone loading experiments and sequential ligament sectioning. Consequently, these rigid biomechanics models do not reproduce the coupled physiological kinematics, neither in the normal joint nor in the postoperative condition. Therefore, our goal was to build a quasi-static finite element model to study the function of the acromioclavicular ligament based on its biomechanical performance patterns using the benefits of computational models.

Methods

A three-dimensional bone model is reconstructed using images from a healthy shoulder. The ligament structures were modeled according to the architecture and dimensions of the bone. The kinematics conditions for the shoulder girdle were determined after the osseous axes aligned to simulate the shoulder elevation in the coronal plane and horizontal adduction. Three patterns evaluated ligament function. The peak von Mises stress values were recorded using a clock model that identified the stress distribution. In addition, the variation in length and displacement of the ligament during shoulder motion were compared using a two-tailed hypotheses test. P values < 0.01 were considered statistically significant.

Results

The peak von Mises stress was consistently observed in the AIB at 2:30 in coronal elevation (4.06 MPa) and horizontal adduction (2.32 MPa). Except in the position 2:00, statistically significant higher deformations were identified in the two bundles during shoulder elevation. The highest ligament displacement was observed on the Y- and Z-axes.

Conclusions

The AIB has the primary role in restricting the acromioclavicular joint during shoulder motion, even though the two bundles of the AC ligament have a complementary mode of action. During horizontal adduction, the SPB appears to prevent anterior and superior translation.

Supplementary Information

The online version contains supplementary material available at 10.1186/s13018-022-02966-0.

Biomechanical modeling of spinal ligaments: finite element analysis of L4-L5 spinal segment

The complex mechanical structure of spine is usually simplified in finite element (FE) modes. In this study, different 3D models of L4-L5 spinal segment distinguished by their ligament modelling were developed (1D truss, 2D shell and 3D space truss elements). All models could be considered validated with respect to range of motion and intradiscal pressure, although their ligament stresses/forces were substantially different. The models with 2D shell and 3D space truss ligaments showed the stress distribution and identified the potential failure/injury locations in ligaments. The model with 3D space truss ligaments showed the stress/force direction (representing collagen fiber directions).

The effect of exercise on the protein profile of rat knee joint intra- and extra-articular ligaments

Injuries to the intra-articular anterior cruciate ligament (ACL) and the extra-articular medial collateral ligament (MCL) result in significant knee joint instability, pain, and immobility. Moderate endurance-type exercise can increase ligament strength but little is known on the effect of short-term regular bouts of high-intensity exercise on the extracellular matrix (ECM) structure of knee ligaments. Therefore, this study aimed to identify the effect of short-term regular bouts high exercise on the proteome of the rat ACL and MCL using mass spectrometry. Sprague-Dawley male rats (n = 6) were split into control and exercise groups, and subjected to high-intensity training for four 4 weeks followed by proteomic analyses of the ACL and MCL. Knee joint health status was assessed using OARSI and a validated histological scoring system. Histopathological analyses demonstrated no significant changes in either in cruciate, collateral ligaments, or cartilage between the control and exercised knee joints. However, significant proteins were found to be more abundant in the exercised ACL compared to ACL control group but not between the exercised MCL and control MCL groups. The significant abundant proteins in ACL exercise groups were mostly cytoskeletal, ribosomal and enzymes with several abundant matrisomal proteins such as collagen proteins and proteoglycans being found in this group. In conclusion, our results indicate that short-term regular bouts of high-intensity exercise have an impact on the intra-articular ACL but not extra-articular MCL ECM protein expression.

Multiaxial validation of a finite element model of the intervertebral disc with multigenerational fibers to establish residual strain

Finite element models of the intervertebral disc are used to address research questions that cannot be tested through typical experimentation. A disc model requires complex geometry and tissue properties to be accurately defined to mimic the physiological disc. The physiological disc possesses residual strain in the annulus fibrosus (AF) due to osmotic swelling and due to inherently pre-strained fibers. We developed a disc model with residual contributions due to swelling-only, and a multigeneration model with residual contributions due to both swelling and AF fiber pre-strain and validated it against organ-scale uniaxial, quasi-static and multiaxial, dynamic mechanical tests. In addition, we demonstrated the models' ability to mimic the opening angle observed following radial incision of bovine discs. Both models were validated against organ-scale experimental data. While the swelling only model responses were within the experimental 95% confidence interval, the multigeneration model offered outcomes closer to the experimental mean and had a bovine model opening angle within one SD of the experimental mean. The better outcomes for the multigeneration model, which allowed for the inclusion of inherently pre-strained fibers in AF, is likely due to its uniform fiber contribution throughout the AF. We conclude that the residual contribution of pre-strained fibers in the AF should be included to best simulate the physiological disc and its behaviors.

Automatic modelling of human musculoskeletal ligaments - Framework overview and model quality evaluation

BACKGROUND

Accurate segmentation of connective soft tissues in medical images is very challenging, hampering the generation of geometric models for bio-mechanical computations. Alternatively, one could predict ligament insertion sites and then approximate the shapes, based on anatomical knowledge and morphological studies.

OBJECTIVE

In this work, we describe an integrated framework for automatic modelling of human musculoskeletal ligaments.

METHOD

We combine statistical shape modelling with geometric algorithms to automatically identify insertion sites, based on which geometric surface/volume meshes are created. As clinical use case, the framework has been applied to generate models of the forearm interosseous membrane. Ligament insertion sites in the statistical model were defined according to anatomical predictions following a published approach.

RESULTS

For evaluation we compared the generated sites, as well as the ligament shapes, to data obtained from a cadaveric study, involving five forearms with 15 ligaments. Our framework permitted the creation of models approximating ligaments' shapes with good fidelity. However, we found that the statistical model trained with the state-of-the-art prediction of the insertion sites was not always reliable. Average mean square errors as well as Hausdorff distances of the meshes could increase by an order of magnitude, as compared to employing known insertion locations of the cadaveric study. Using those, an average mean square error of 0.59 mm and an average Hausdorff distance of less than 7 mm resulted, for all ligaments.

CONCLUSIONS

The presented approach for automatic generation of ligament shapes from insertion points appears to be feasible but the detection of the insertion sites with a SSM is too inaccurate, thus making a patient-specific approach necessary.

Sensitivity analysis of biomechanical effect in vertebral body of two different augmenters

BACKGROUND

Transvertebral Bone Graft and Augmentation (TBGA) has achieved good clinical effects in the treatment of osteoporotic vertebral compression fractures (OVCFs). This study aimed to investigate the postoperatively biomechanical effects of TBGA and compare the biomechanical sensitivity of two different augmenters: a cylindrical enhancement device (CED) and bone cement.

METHODS

Finite element models of the spine segment T11-L3 were created, including one model based on normal segment and the other three with L1 augmentation for pathological conditions. Three treatments were simulated including CED implant treatment A, CED implant treatment B, and bone cement treatment. The stress distribution and maximum displacement of the four models under different treatments were analyzed. A method of linear fitting of dummy variables was used to analyze the sensitivity of biomechanical parameters to the degree of osteoporosis (DO) and load.

FINDINGS

The reduction of stress with increasing DO in augmented and adjacent vertebral bodies under bone cement augmentation was less than that under CED augmentation. The stress of augmented vertebral body and the adjacent vertebral body was most sensitive to extension and rotation loading conditions. As DO increasing, the bone cement augmentation significantly increased the stress level on the upper and lower endplates.

INTERPRETATION

When the degree of osteoporosis increased, CED outperforms bone cement in terms of the stress reduction in augmented vertebral and adjacent vertebral, which could be beneficial for avoiding re-fracture. Using TBGA to treat OVCFs, especially with Plan B method, the condition of the pathological spine is closer to the original status in terms of the sensitivity to stress and the spinal range of motion. The TBGA treatment is sensitive to lateral bending and torsion, therefore patients should be advised to avoid high-risk motions like lateral bending and rotation.

A COMPARATIVE ANALYSIS OF THE EFFECTS OF TWO AUGMENTERS ON THE SENSITIVITY OF VERTEBRAL BIOMECHANICAL BEHAVIOR IN VERTEBROPLASTY

The treatment of osteoporotic vertebral compression fractures (OVCFS) by transvertebral bone graft and augmentation (TBGA) has achieved satisfactory clinical results, but its biomechanical effects are not clear. The purpose of this study was to investigate the biomechanical effects of TBGA and compare the biomechanical sensitivity of the augmenter used in TBGA — a cylindrical enhancement device (CED) with bone cement. The finite element (FE) model of healthy segments T11-L3 (M1) was built, and two other models with L1 augmentation (M2, M3) were established to simulate CED and bone cement treatment, respectively. The stress and displacement distribution of the three models under five physiological loads were calculated and analyzed by the FE method. Based on the results, the sensitivities of biomechanical parameters to the degree of osteoporosis (DO) and loads were analyzed by linear fitting method using dummy variables. With the increase of DO, the CED is superior to bone cement in preventing the fractures of the augmented vertebral and the adjacent vertebral under the set loading conditions. Simulating TBGA method, the model 2 with L1 reconstructed was closer to the normal T11-L3 model in terms of sensitivity of stress and displacement under different loading conditions.

Performance evaluation of surgical techniques for treatment of scapholunate instability in a type II wrist

We investigated the performance of three tenodesis techniques, modified Brunelli, Corella, and scapholunate axis (SLAM) methods in repairing scapholunate interosseous ligament (SLIL) disruption for a type II wrist using finite element-based virtual surgery and compared the results with those of a previous investigation for a type I wrist. In addition, a comparison of the carpal mechanics of type I and type II wrists was undertaken in order to elucidate the difference between the two types. For the type II wrist, following simulated SLIL disruption, the Corella reconstruction technique provided a superior outcome, restoring dorsal gap, volar gap, and SL angle to within 3.5%, 7.1%, and 8.4%, respectively, of the intact wrist. Moreover, application of the ligament reconstruction techniques did not significantly alter the motion pattern of the type II and type I wrists. For the type I wrist, SLIL disruption resulted in no contact between scaphoid-lunate cartilage articulation, whereas for the type II wrist, some contact was maintained. We conclude that the Corella ligamentous reconstruction technique is best able to restore SL gap, angle, and stability following SL ligament injury for both type II and type I wrists and is able to do so without altering wrist kinematics. Our findings also support the view that type I wrists exhibit row behaviour and type II wrists column behaviour. In addition, our analysis suggests that the extra articulation between the lunate and hamate in a type II wrist may help improve stability following SL ligament injury.

Contributions of elastic fibers, collagen, and extracellular matrix to the multiaxial mechanics of ligament

Elastin is a biopolymer known to provide resilience to extensible biologic tissues through elastic recoil of its highly crosslinked molecular network. Recent studies have demonstrated that elastic fibers in ligament provide significant resistance to tensile and especially shear stress. We hypothesized that the biomechanics of elastic fibers in ligament could be described as transversely isotropic with both fiber and matrix components in a multi-material mixture. Similarly, we hypothesized that material coefficients derived using the experimental tensile response could be used to predict the experimental shear response. Experimental data for uniaxial and transverse tensile testing of control tissues, and those enzymatically digested to disrupt elastin, were used as inputs to a material coefficient optimization algorithm. An additive decomposition of the strain energy was used to model the total stress as the sum of contributions from collagen fibers, elastic fibers, elastic matrix, and ground substance matrix. Matrices were modeled as isotropic Veronda-Westmann hyperelastic materials, whereas fiber families were modeled as piecewise exponential-linear hyperelastic materials. Optimizations provided excellent fits to the tensile experimental data for each treatment case and material model. Given the disparity in magnitude of stresses between longitudinal and transverse/shear tests and agreement between models and experiments, the hypothesized transversely isotropic material of elastin symmetry was supported. In addition, the coefficients derived from uniaxial and transverse tensile experiments provided reasonable predictions of the experimental behavior during shear deformation. The magnitudes of coefficients representing stress, nonlinearity, and stiffness supported the experimental evidence that elastic fibers dominate the low strain tensile and shear response of ligament. These findings demonstrate that the additive decomposition modeling strategy can represent each discrete fiber and matrix constituent and their relative contribution to the material response of the tissue. These experimental data and the validated constitutive model provide essential inputs and a framework to refine existing computational models of ligament and tendon mechanics by explicitly representing the mechanical contributions of elastic fibers.

FEBio: History and Advances

The principal goal of the FEBio project is to provide an advanced finite element tool for the biomechanics and biophysics communities that allows researchers to model mechanics, transport, and electrokinetic phenomena for biological systems accurately and efficiently. In addition, because FEBio is geared toward the research community, the code is designed such that new features can be added easily, thus making it an ideal tool for testing novel computational methods. Finally, because the success of a code is determined by its user base, integral goals of the FEBio project have been to offer support and outreach to our community; to provide mechanisms for dissemination of results, models, and data; and to encourage interaction between users. This review presents the history of the FEBio project, from its initial developments through its current funding period. We also present a glimpse into the future of FEBio.

Evaluation of the performance of three tenodesis techniques for the treatment of scapholunate instability: flexion-extension and radial-ulnar deviation

Chronic scapholunate ligament (SL) injuries are difficult to treat and can lead to wrist dysfunction. Whilst several tendon reconstruction techniques have been employed in the management of SL instability, SL gap reappearance after surgery has been reported. Using a finite element model and cadaveric study data, we investigated the performance of the Corella, scapholunate axis (SLAM) and modified Brunelli tenodesis (MBT) techniques. Scapholunate dorsal and volar gap and angle were obtained following virtual surgery undertaken using each of the three reconstruction methods with the wrist positioned in flexion, extension, ulnar deviation and radial deviation, in addition to the ulnar-deviated clenched fist and neutral positions. From the study, it was found that, following simulated scapholunate interosseous ligament rupture, the Corella technique was better able to restore the SL gap and angle close to the intact ligament for all wrist positions investigated, followed by SLAM and MBT. The results suggest that for the tendon reconstruction techniques, the use of multiple junction points between scaphoid and lunate may be of benefit.

Graphical abstract

A Combined Experimental and Computational Approach to Subject-Specific Analysis of Knee Joint Laxity

Modeling complex knee biomechanics is a continual challenge, which has resulted in many models of varying levels of quality, complexity, and validation. Beyond modeling healthy knees, accurately mimicking pathologic knee mechanics, such as after cruciate rupture or meniscectomy, is difficult. Experimental tests of knee laxity can provide important information about ligament engagement and overall contributions to knee stability for development of subject-specific models to accurately simulate knee motion and loading. Our objective was to provide combined experimental tests and finite-element (FE) models of natural knee laxity that are subject-specific, have one-to-one experiment to model calibration, simulate ligament engagement in agreement with literature, and are adaptable for a variety of biomechanical investigations (e.g., cartilage contact, ligament strain, in vivo kinematics). Calibration involved perturbing ligament stiffness, initial ligament strain, and attachment location until model-predicted kinematics and ligament engagement matched experimental reports. Errors between model-predicted and experimental kinematics averaged <2 deg during varus-valgus (VV) rotations, <6 deg during internal-external (IE) rotations, and <3 mm of translation during anterior-posterior (AP) displacements. Engagement of the individual ligaments agreed with literature descriptions. These results demonstrate the ability of our constraint models to be customized for multiple individuals and simultaneously call attention to the need to verify that ligament engagement is in good general agreement with literature. To facilitate further investigations of subject-specific or population based knee joint biomechanics, data collected during the experimental and modeling phases of this study are available for download by the research community.

Mechanobiological modelling of tendons: Review and future opportunities

Tendons are adapted to carry large, repeated loads and are clinically important for the maintenance of musculoskeletal health in an increasing, actively ageing population, as well as in elite athletes. Tendons are known to adapt to mechanical loading. Also, their healing and disease processes are highly sensitive to mechanical load. Computational modelling approaches developed to capture this mechanobiological adaptation in tendons and other tissues have successfully addressed many important scientific and clinical issues. The aim of this review is to identify techniques and approaches that could be further developed to address tendon-related problems. Biomechanical models are identified that capture the multi-level aspects of tendon mechanics. Continuum whole tendon models, both phenomenological and microstructurally motivated, are important to estimate forces during locomotion activities. Fibril-level microstructural models are documented that can use these estimated forces to detail local mechanical parameters relevant to cell mechanotransduction. Cell-level models able to predict the response to such parameters are also described. A selection of updatable mechanobiological models is presented. These use mechanical signals, often continuum tissue level, along with rules for tissue change and have been applied successfully in many tissues to predict in vivo and in vitro outcomes. Signals may include scalars derived from the stress or strain tensors, or in poroelasticity also fluid velocity, while adaptation may be represented by changes to elastic modulus, permeability, fibril density or orientation. So far, only simple analytical approaches have been applied to tendon mechanobiology. With the development of sophisticated computational mechanobiological models in parallel with reporting more quantitative data from in vivo or clinical mechanobiological studies, for example, appropriate imaging, biochemical and histological data, this field offers huge potential for future development towards clinical applications.

3-D computer modelling of malunited posterior malleolar fractures: effect of fragment size and offset on ankle stability, contact pressure and pattern

BACKGROUND

The positioning of the fracture fragment of a posterior malleolus fracture is critical to healing and a successful outcome as malunion of a posterior malleolar fracture, a condition seen in clinical practice, can affect the dynamics of the ankle joint, cause posterolateral rotational subluxation of the talus and ultimately lead to destruction of the joint. Current consensus is to employ anatomic reduction with internal fixation when the fragment size is larger than 25 to 33% of the tibial plafond.

METHODS

A 3-dimensional finite element (FE) model of ankle was developed in order to investigate the effect of fragment size (6-15 mm) and offset (1-4 mm) of a malunited posterior malleolus on tibiotalar joint contact area, pressure, motion of joint and ligament forces. Three positions of the joint were simulated; neutral position, 20° dorsiflexion and 30° plantarflexion.

RESULTS

Compared to the intact joint our model predicted that contact area was greater in all malunion scenarios considered. In general, the joint contact area was affected more by section length than section offset. In addition fibula contact area played a role in all the malunion cases.

CONCLUSIONS

We found no evidence to support the current consensus of fixing posterior malleolus fractures of greater than 25% of the tibial plafond. Our model predicted joint instability only with the highest level of fracture in a loaded limb at an extreme position of dorsiflexion. No increase of peak contact pressure as a result of malunion was predicted but contact pattern was modified. The results of our study support the view that in cases of posterior malleolar fracture, posttraumatic osteoarthritis occurs as a result of load on areas of cartilage not used to loading rather than an increase in contact pressure. Ankle repositioning resulted in increased force in two ankle ligaments. Our finding could explain commonly reported clinical observations.

Computational model-based probabilistic analysis of in vivo material properties for ligament stiffness using the laxity test and computed tomography

The objective of this paper was to evaluate in vivo material properties in order to address technical aspects of computational modeling of ligaments in the tibiofemoral joint using a probabilistic method. The laxity test was applied to the anterior-posterior drawer under 30° and 90° of flexion with a series of stress radiographs, a Telos device, and computed tomography. Ligament stiffness was investigated using sensitivity analysis based on the Monte-Carlo method with a subject-specific finite element model generated from in vivo computed tomography and magnetic resonance imaging data, subjected to laxity test conditions. The material properties of ligament stiffness and initial ligament strain in a subject-specific finite element model were optimized to minimize the differences between the movements of the tibia and femur in the finite element model and the computed tomography images in the laxity test. The posterior cruciate ligament was the most significant factor in flexion and posterior drawer, while the anterior cruciate ligament primarily was the most significant factor for the anterior drawer. The optimized material properties model predictions in simulation and the laxity test were more accurate than predictions based on the initial material properties in subject-specific computed tomography measurement. Thus, this study establishes a standard for future designs in allograft, xenograft, and artificial ligaments for anterior cruciate ligament and posterior cruciate ligament injuries.

Effect of Anconeus Muscle Blocking on Elbow Kinematics: Electromyographic, Inertial Sensors and Finite Element Study

The specific contribution of the anconeus muscle to elbow function is still uncertain. This study aimed to investigate the effect on elbow kinematics and kinetics of blocking anconeus using lidocaine. Ten healthy volunteers performed experimental trials involving flexion–extension and supination–pronation movements in horizontal and sagittal planes. Inertial sensors and surface electromyography were used to record elbow kinematics and kinetics and electrical activity from the anconeus, biceps and triceps brachii before and after blocking anconeus. Moreover, a finite element model of the elbow was created to further investigate the contribution of anconeus to elbow kinematics. The electrical activity results from the trials before blocking clearly indicated that activity of anconeus was increased during extension, suggesting that it behaves as an extensor. However, blocking anconeus had no effect on the elbow kinematics and kinetics, including the angular velocity, net torque and power of the joint. The electrical activity of the biceps and triceps brachii did not alter significantly following anconeus blocking. These results suggest that anconeus is a weak extensor, and the relative small contribution of anconeus to extension before blocking was compensated by triceps brachii. The finite element results indicated that anconeus does not contribute significantly to elbow kinematics.

The influence of the human TMJ eminence inclination on predicted masticatory muscle forces

Aim of this paper was to investigate the change in masticatory muscle forces and temporomandibular joint (TMJ) reaction forces simulated by inverse dynamics when thesteepness of the anterior fossa slope was varied. We used the model by de Zee et al. (2007) created in AnyBody™. The model was equipped with 24musculotendon actuators. Mandibular movement was governed by thetrajectory of theincisal point. The TMJ was modelled as a planar constraint canted 5°medially and thecaudal inclination relative to the occlusal plane was varied from 10° to 70°. Our models showed that for the two simulated movements (empty chewing and unilateral clenching) the joint reaction forces were smallest for the eminence inclination of 30° and 40° and highest for 70°. The muscle forces were relatively insensitive to change of the eminence inclination for the angles between 20° and 50°. This did not hold for the pterygoid muscle, for which the muscle forces increased continually with increasing fossa inclination. For empty chewing the muscle force reached smaller values than for clenching. During clenching, the muscle forces changed by up to 200N.

A general framework for application of prestrain to computational models of biological materials

It is often important to include prestress in computational models of biological tissues. The prestress can represent residual stresses (stresses that exist after the tissue is excised from the body) or in situ stresses (stresses that exist in vivo, in the absence of loading). A prestressed reference configuration may also be needed when modeling the reference geometry of biological tissues in vivo. This research developed a general framework for representing prestress in finite element models of biological materials. It is assumed that the material is elastic, allowing the prestress to be represented via a prestrain. For prestrain fields that are not compatible with the reference geometry, the computational framework provides an iterative algorithm for updating the prestrain until equilibrium is satisfied. The iterative framework allows for enforcement of two different constraints: elimination of distortion in order to address the incompatibility issue, and enforcing a specified in situ fiber strain field while allowing for distortion. The framework was implemented as a plugin in FEBio (www.febio.org), making it easy to maintain the software and to extend the framework if needed. Several examples illustrate the application and effectiveness of the approach, including the application of in situ strains to ligaments in the Open Knee model (simtk.org/home/openknee). A novel method for recovering the stress-free configuration from the prestrain deformation gradient is also presented. This general purpose theoretical and computational framework for applying prestrain will allow analysts to overcome the challenges in modeling this important aspect of biological tissue mechanics.

Quantitative comparison of ligament formulation and pre-strain in finite element analysis of the human lumbar spine

Data has been published that quantifies the nonlinear, anisotropic material behaviour and pre-strain behaviour of the anterior longitudinal, supraspinous (SSL), and interspinous ligaments of the human lumbar spine. Additionally, data has been published on localized material properties of the SSL. These results have been incrementally incorporated into a previously validated finite element model of the human lumbar spine. Results suggest that the effects of increased ligament model fidelity on bone strain energy were moderate and the effects on disc pressure were slight, and do not justify a change in modelling strategy for most clinical applications. There were significant effects on the ligament stresses of the ligaments that were directly modified, suggesting that these phenomena should be included in FE models where ligament stresses are the desired metric.

ACL Reconstruction Decision Support. Personalized Simulation of the Lachman Test and Custom Activities

INTRODUCTION

This article is part of the Focus Theme of Methods of Information in Medicine on "Methodologies, Models and Algorithms for Patients Rehabilitation".

OBJECTIVES

The objective of the proposed approach is to develop a clinical decision support system (DSS) that will help clinicians optimally plan the ACL reconstruction procedure in a patient specific manner.

METHODS

A full body model is developed in this study with 23 degrees of freedom and 93 muscles. The knee ligaments are modeled as non-linear spring-damper systems and a tibiofemoral contact model was utilized. The parameters of the ligaments were calibrated based on an optimization criterion. Forward dynamics were utilized during simulation for predicting the model's response to a given set of external forces, posture configuration and physiological parameters.

RESULTS

The proposed model is quantified using MRI scans and measurements of the well-known Lachman test, on several patients with a torn ACL. The clinical potential of the proposed framework is demonstrated in the context of flexion-extension, gait and jump actions. The clinician is able to modify and fine tune several parameters such as the number of bundles, insertion position on the tibia or femur and the resting length that correspond to the choices of the surgical procedure and study their effect on the biomechanical behavior of the knee.

CONCLUSION

Computational knee models can be used to predict the effect of surgical decisions and to give insight on how different parameters can affect the stability of the knee. Special focus has to be given in proper calibration and experimental validation.

Elastin governs the mechanical response of medial collateral ligament under shear and transverse tensile loading

Elastin is a highly extensible structural protein network that provides near-elastic resistance to deformation in biological tissues. In ligament, elastin is localized between and along the collagen fibers and fascicles. When ligament is stretched along the primary collagen axis, elastin supports a relatively high percentage of load. We hypothesized that elastin may also provide significant load support under elongation transverse to the primary collagen axis and shear along the collagen axis. Quasi-static transverse tensile and shear material tests were performed to quantify the mechanical contributions of elastin during deformation of porcine medial collateral ligament. Dose response studies were conducted to determine the level of elastase enzymatic degradation required to produce a maximal change in the mechanical response. Maximal changes in peak stress occurred after 3h of treatment with 2U/ml porcine pancreatic elastase. Elastin degradation resulted in a 60-70% reduction in peak stress and a 2-3× reduction in modulus for both test protocols. These results demonstrate that elastin provides significant resistance to elongation transverse to the collagen axis and shear along the collagen axis while only constituting 4% of the tissue dry weight. The magnitudes of the elastin contribution to peak transverse and shear stress were approximately 0.03 MPa, as compared to 2 MPa for axial tensile tests, suggesting that elastin provides a highly anisotropic contribution to the mechanical response of ligament and is the dominant structural protein resisting transverse and shear deformation of the tissue.

Transversely isotropic material characterization of the human anterior longitudinal ligament

The present work represents the first study to report transversely isotropic material parameters for the human anterior longitudinal ligament (ALL) in the thoraco-lumbar spine. Force-deformation data from multi-axial testing was collected from 30 cadaveric spine test specimens using an anisotropic quarter punch test technique. The experimental data was fit to a commonly used anisotropic soft tissue material model using an FEA system identification technique. The material model correlated well with the experimental response (R(2)≥0.98). The constitutive parameter values, as well as the nonlinear anisotropic stress-strain response of the ALL specimens are reported to facilitate application to biomechanical models (including finite element models) of the spine.

Material models and properties in the finite element analysis of knee ligaments: a literature review

Knee ligaments are elastic bands of soft tissue with a complex microstructure and biomechanics, which are critical to determine the kinematics as well as the stress bearing behavior of the knee joint. Their correct implementation in terms of material models and properties is therefore necessary in the development of finite element models of the knee, which has been performed for decades for the investigation of both its basic biomechanics and the development of replacement implants and repair strategies for degenerative and traumatic pathologies. Indeed, a wide range of element types and material models has been used to represent knee ligaments, ranging from elastic unidimensional elements to complex hyperelastic three-dimensional structures with anatomically realistic shapes. This paper systematically reviews literature studies, which described finite element models of the knee, and summarizes the approaches, which have been used to model the ligaments highlighting their strengths and weaknesses.

A quantitative study of the relationship between the distribution of different types of collagen and the mechanical behavior of rabbit medial collateral ligaments

The mechanical properties of ligaments are key contributors to the stability and function of musculoskeletal joints. Ligaments are generally composed of ground substance, collagen (mainly type I and III collagen), and minimal elastin fibers. However, no consensus has been reached about whether the distribution of different types of collagen correlates with the mechanical behaviors of ligaments. The main objective of this study was to determine whether the collagen type distribution is correlated with the mechanical properties of ligaments. Using axial tensile tests and picrosirius red staining-polarization observations, the mechanical behaviors and the ratios of the various types of collagen were investigated for twenty-four rabbit medial collateral ligaments from twenty-four rabbits of different ages, respectively. One-way analysis of variance was used in the comparison of the Young's modulus in the linear region of the stress-strain curves and the ratios of type I and III collagen for the specimens (the mid-substance specimens of the ligaments) with different ages. A multiple linear regression was performed using the collagen contents (the ratios of type I and III collagen) and the Young's modulus of the specimens. During the maturation of the ligaments, the type I collagen content increased, and the type III collagen content decreased. A significant and strong correlation () was identified by multiple linear regression between the collagen contents (i.e., the ratios of type I and type III collagen) and the mechanical properties of the specimens. The collagen content of ligaments might provide a new perspective for evaluating the linear modulus of global stress-strain curves for ligaments and open a new door for studying the mechanical behaviors and functions of connective tissues.

A comparison of material characterizations in frequently used constitutive models of ligaments

Longitudinal tensile and simple shear stress-strain curves of human medial collateral ligaments (MCL) were fitted by six frequently used constitutive relations of ligaments using two different fitting methods for determining which was the best fitting method and the most preferable constitutive model for describing the ligament properties. According to the results of fitting goodness, two typical constitutive models were further analyzed by FEM to investigate the effect of the variation in MCL constitutive models under some physiological loads (i.e., 4.5 Nm external tibial and 10 Nm valgus tibial torques). It was found that different fitting methods induced great variations in describing the simple shear behavior whereas no obvious difference in the longitudinal tensile behavior. The most accurate description of both the longitudinal tensile and simple shear behaviors was obtained from the constitutive model with ground substance defined by an exponential function when the parameters were fitted by the two test data, respectively. Although the distributions of maximal principal stress were almost the same, the variation in MCL constitutive models affected the highest value of the stress greatly when MCL was under the complex physiological loads.

Failure Properties and Damage of Cervical Spine Ligaments, Experiments and Modeling

Cervical spine ligaments have an important role in providing spinal cord stability and restricting excessive movements. Therefore, it is of great importance to study the mechanical properties and model the response of these ligaments. The aim of this study is to characterize the aging effects on the failure properties and model the damage of three cervical spine ligaments: the anterior and the posterior longitudinal ligament and the ligamentum flavum. A total of 46 samples of human cadaveric ligaments removed within 24–48 h after death have been tested. Uniaxial tension tests along the fiber direction were performed in physiological conditions. The results showed that aging decreased the failure properties of all three ligaments (failure load, failure elongation). Furthermore, the reported nonlinear response of cervical ligaments has been modeled with a combination of the previously reported hyperelastic and damage model. The model predicted a nonlinear response and damage region. The model fittings are in agreement with the experimental data and the quality of agreement is represented with the values of the coefficient of determination close to 1.

Comparison of stress on knee cartilage during kneeling and standing using finite element models

Kneeling is a common activity required for both occupational and cultural reasons and has been shown to be associated with an increased risk of knee disorders. While excessive contact pressure is considered to be a possible aggressor, it is not clear whether and to what extent stress on the cartilage during kneeling is different from that while standing. In this study, finite element models of the knee joint for both kneeling and standing positions were constructed. The results indicated differences in high-stress regions between kneeling and standing. And both the peak von-Mises stress and contact pressure on the cartilage were larger in kneeling. During kneeling, the contact pressure reached 4.25 MPa under a 300 N compressive load. It then increased to 4.66 MPa at 600 N and 5.15 MPa at 1000 N. Changing the Poisson's ratio of the cartilage, which represents changes in compressibility caused by different loading rates, was found to have an influence on the magnitude of stress.

Recent advances in computational mechanics of the human knee joint

Computational mechanics has been advanced in every area of orthopedic biomechanics. The objective of this paper is to provide a general review of the computational models used in the analysis of the mechanical function of the knee joint in different loading and pathological conditions. Major review articles published in related areas are summarized first. The constitutive models for soft tissues of the knee are briefly discussed to facilitate understanding the joint modeling. A detailed review of the tibiofemoral joint models is presented thereafter. The geometry reconstruction procedures as well as some critical issues in finite element modeling are also discussed. Computational modeling can be a reliable and effective method for the study of mechanical behavior of the knee joint, if the model is constructed correctly. Single-phase material models have been used to predict the instantaneous load response for the healthy knees and repaired joints, such as total and partial meniscectomies, ACL and PCL reconstructions, and joint replacements. Recently, poromechanical models accounting for fluid pressurization in soft tissues have been proposed to study the viscoelastic response of the healthy and impaired knee joints. While the constitutive modeling has been considerably advanced at the tissue level, many challenges still exist in applying a good material model to three-dimensional joint simulations. A complete model validation at the joint level seems impossible presently, because only simple data can be obtained experimentally. Therefore, model validation may be concentrated on the constitutive laws using multiple mechanical tests of the tissues. Extensive model verifications at the joint level are still crucial for the accuracy of the modeling.

Subject-specific analysis of joint contact mechanics: application to the study of osteoarthritis and surgical planning

Advances in computational mechanics, constitutive modeling, and techniques for subject-specific modeling have opened the door to patient-specific simulation of the relationships between joint mechanics and osteoarthritis (OA), as well as patient-specific preoperative planning. This article reviews the application of computational biomechanics to the simulation of joint contact mechanics as relevant to the study of OA. This review begins with background regarding OA and the mechanical causes of OA in the context of simulations of joint mechanics. The broad range of technical considerations in creating validated subject-specific whole joint models is discussed. The types of computational models available for the study of joint mechanics are reviewed. The types of constitutive models that are available for articular cartilage are reviewed, with special attention to choosing an appropriate constitutive model for the application at hand. Issues related to model generation are discussed, including acquisition of model geometry from volumetric image data and specific considerations for acquisition of computed tomography and magnetic resonance imaging data. Approaches to model validation are reviewed. The areas of parametric analysis, factorial design, and probabilistic analysis are reviewed in the context of simulations of joint contact mechanics. Following the review of technical considerations, the article details insights that have been obtained from computational models of joint mechanics for normal joints; patient populations; the study of specific aspects of joint mechanics relevant to OA, such as congruency and instability; and preoperative planning. Finally, future directions for research and application are summarized.

Design Considerations for a Prosthetic Anterior Cruciate Ligament

Anterior cruciate ligament (ACL) tearing is a common knee injury often requiring reconstruction with an autograft or an allograft. A prosthetic ligament replacement with off-the-shelf availability could potentially provide significant advantages over the current options for both patients and surgeons. Limitations of previous prosthetics include lack of biocompatibility and susceptibility to fatigue, creep, and failure of bony incorporation. This paper describes design considerations and possible improvements for the next generation prosthetic ACL. Design controls, as mandated by the FDA, are a systematic set of practices within the design and development process used to ensure that a new medical device meets the needs of the intended users. The specified requirements, called the design inputs, for a prosthetic ACL are discussed pertaining to material and structural properties, resistance to creep and fatigue, ability to support secure initial fixation, biocompatibility, and long-term osseointegration. Design innovations to satisfy the design inputs are discussed with regards to material selection, textile pattern, bone tunnel features, and short term fixation. A risk analysis is presented along with descriptions of proposed testing. Design control methodology and tissue engineering may be used to develop a next generation prosthetic ligament, solving multiple problems, simultaneously, on a holistic level, providing major improvements over earlier devices and current treatment options.

A mathematical model of the process of ligament repair: effect of cold therapy and mechanical stress

This article proposes a mathematical model that predicts the wound healing process of the ligament after a sprain, grade II. The model describes the swelling, expression of the platelet-derived growth factor (PDGF), formation and migration of fibroblasts into the injury area and the expression of collagen fibers. Additionally, the model can predict the effect of ice treatment in reducing inflammation and the action of mechanical stress in the process of remodeling of collagen fibers. The results obtained from computer simulation show a high concordance with the clinical data previously reported by other authors.

Dynamic function of coracoclavicular ligament at different shoulder abduction angles: a study using a 3-dimensional finite element model

PURPOSE

The aim of this study was to determine the acromioclavicular (AC) motion and change in length and tension of the coracoclavicular ligament during different positions of shoulder abduction using a 3-dimensional finite element model based on computed tomography images from normal human shoulders.

METHODS

The right shoulders of 10 living subjects were scanned with a high-resolution computed tomography scanner at 0°, 60°, 120°, and 180° of shoulder abduction. Several modeling programs were used to simulate AC motion. Finite element models of the conoid and trapezoid ligaments were constructed based on each footprint. The tension and length changes of each ligament during shoulder abduction were assessed.

RESULTS

The distal clavicle exhibited internal rotation with respect to the medial acromion at 0°, 60°, 120°, and full abduction (3.2° ± 2.9°, 23.2° ± 10.8°, 20.6° ± 3.7°, and 37.1° ± 3.4°, respectively). With horizontal motion, the clavicle translated posteriorly at 60° of abduction (4.4 ± 3.4 mm) and then translated anteriorly at 120° and full abduction (0.4 ± 1.6 mm and 1.9 ± 0.4 mm, respectively). The lengths of the conoid ligament gradually increased at 60° to 180° of shoulder abduction whereas those of the trapezoid ligament remained relatively consistent at 60° to 120° of abduction compared with 0° of abduction.

CONCLUSIONS

The distal clavicle had a wide range of motion during shoulder abduction, which did not support the concept of synchronous motion with the scapula. The conoid and trapezoid ligaments functioned reciprocally during shoulder abduction. With increasing shoulder abduction, the length of the conoid ligament gradually increased; meanwhile, the trapezoid ligament was relatively consistent and then lax at full abduction. In particular, the conoid ligament may act as a key restraint to prevent excessive retraction of the scapula during shoulder abduction.

CLINICAL RELEVANCE

The data in this study have the potential to suggest that conoid and trapezoid ligaments should be reconstructed separately, and rigid AC fixation in patients with AC separation is not recommended based on the findings of this study.

FINITE ELEMENT CONTACT ANALYSIS OF A HUMAN SAGITTAL KNEE JOINT

Articular cartilage is a vital component of human knee joints by providing a low-friction and wear-resistant surface in knee joints and distributing stresses to tibia. The degeneration or damage of articular cartilage will incur acute pain on the human knee joints. Hence, to understand the mechanism of normal and pathological functions of articular cartilage, it is very important to investigate the contact mechanics of the human knee joints. Experimental research has difficulties in reproducing the physiological conditions of daily activities and measuring the key factors such as contact-stress distributions inside knee joint without violating the physiological environment. On the other hand, numerical approaches such as finite element (FE) analysis provide a powerful tool in the biomechanics study of the human knee joint. This article presents a two-dimensional (2D) FE model of the human knee joints that includes the femur, tibia, patella, quadriceps, patellar tendon, and cartilages. The model is analyzed with dynamic loadings to study stress distribution in the tibia and contact area during contact with or without articular cartilage. The results obtained in this article are very helpful to find the pathological mechanism of knee joint degeneration or damage, and thus guide the therapy of knee illness and artificial joint replacement.