The geometry of the knee in the sagittal plane

A geometric model of the tibio-femoral joint in the sagittal plane has been developed which demonstrates the relationship between the geometry of the cruciate ligaments and the geometry of the articular surfaces. The cruciate ligaments are represented as two inextensible fibres which, with the femur and the tibia, are analysed as a crossed four-bar linkage. The directions of the ligaments at each position of flexion are calculated. The instant centre, where the flexion axis crosses the parasagittal plane through the joint, lies at the intersection of the cruciates. It moves relative to each of the bones during flexion and extension. The successive positions of the flexion axis relative to a fixed femur and to a fixed tibia are deduced. The shapes of articular surfaces which would allow the bones to flex and extend while maintaining the ligaments each at constant length are calculated and are found to agree closely with the shapes of the natural articular surfaces. The calculated movements of the contact point between the femur and the tibia during flexion also agree well with measurements made on cadaver specimens. The outcome is a geometric simulation of the tibio-femoral joint in the sagittal plane which illustrates the central role played by the cruciate ligaments in the kinematics of the knee and which can be used for the analysis of ligament and contact forces.     

Three-dimensional contact dynamic model of the human knee joint during walking

It is well known that the geometry of the articular surface has a major role in determining the position of articular contact and the lines of action for the contact forces. The contact force calculation of the knee joint under the effect of sliding and rolling is one of the most challenging issues in this field. We present a 3-D human knee joint model including sliding and rolling motions and major ligaments to calculate the lateral and medial condyle contact forces from the recovered total internal reaction force using inverse dynamic contact modeling and the Least-Square method. As results, it is believed that the patella, muscles and tendon affect a lot for the internal reaction forces at the initial heel contact stage. With increasing flexion angles during gait, the decreasing contact area is progressively shifted to the posterior direction on the tibia plateau. In addition, the medial side contact force is larger than the lateral side contact force in the knee joint during normal human walking. The total internal forces of the knee joint are reasonabe compared to previous studies.     

A model of human knee ligaments in the sagittal plane. Part 1: Response to passive flexion.

The development of a mathematical model of the knee ligaments in the sagittal plane is presented. Essential features of the model are (a) the representation of selected cruciate ligament fibres as isometric links in a kinematic mechanism that controls passive knee flexion and (b) the mapping of all other ligament fibres between attachments on the tibia and femur. Fibres slacken and tighten as the ligament attachment areas on the bones move relative to each other. The model is used to study the shape and fibre length changes of the cruciate and collateral ligaments in response to passive flexion/extension of the knee. The model ligament shape and fibre length changes compare well qualitatively with experimental results reported in the literature. The results suggest that when designing and implanting a ligament replacement with the aim of reproducing the natural fibre strain patterns, the surgeon must not only implant through the natural attachment areas but must also maintain the natural fibre mapping and render all fibres just tight at the appropriate flexion angle.     

Mechanics of the passive knee joint. Part 2: interaction between the ligaments and the articular surfaces in guiding the joint motion

The aim of this study was to examine how the interaction between ligament tensions and contact forces guides the knee joint through its specific pattern of passive motion. A computer model was built based on cadaver data. The passive motion and the ligament lengthening and force patterns predicted by the model were verified with data from the literature. The contribution of each ligament and contact force was measured in terms of the rotational moment that it produced about the tibial medial plateau and the anterior-posterior (AP) force that it exerted on the tibia. The high tension of the anterior cruciate ligament (ACL) and the geometric constraints of the anterior horns of the menisci were found to be key features that stabilized the knee at full extension. The mutual effect of the cruciates was found as the reason for the screw-home mechanism at early flexion. Past 300, the AP component of contact force on the convex geometry of the lateral tibial plateau and tension of the lateral collateral ligament (LCL) were identified as elements that control the joint motion. From 60 degrees to 90 degrees, reduction in the tension of the ACL was determined as a reason for continuation of the tibial anterior translation. From 90 degrees to 120 degrees, increase in the tension of the posterior cruciate ligament and the AP component of the contact force on the convex geometry of the lateral tibial plateau pushed the tibia more anteriorly. This anterior translation was limited by the constraining effects of the ACL tension and the AP component of the contact force on the medial meniscus. The important guiding role observed for the LCL suggests that it should not be overlooked in knee models.     

A model of human knee ligaments in the sagittal plane. Part 2: Fibre recruitment under load.

A mathematical model of the knee ligaments in the sagittal plane is used to study the forces in the cruciate and collateral ligaments produced by anterior/posterior tibial translation. The model is based on ligament fibre functional architecture. Geometric analysis of the deformed configurations of the model ligaments provides the additional compatibility conditions necessary for calculation of the statically indeterminate distributions of strain and stress within the ligaments and the sharing of load between ligaments. The investigation quantifies the process of ligament fibre recruitment, which occurs when fibres made slack by passive flexion/extension of the knee stretch and change their spatial positions in order to resist applied loads. The calculated ligament forces are in reasonable agreement with experimental results reported in the literature. The model explains some subtleties of ligament function not incorporated in models that represent the ligaments by a small number of lines.     

A dynamic model of simulating stress distribution in the distal femur after total knee replacement

The aim of this study has been to develop a dynamic model of the knee joint after total knee replacement (TKR) to analyse the stress distribution in the distal femur during daily activities. Using MSC/ADAMS and MSC/MARC software, a dynamic model of an implanted knee joint has been developed. This model consists of the components of the knee prosthesis as well as the bones and ligaments of the knee. The femur, tibia, fibula, and patella have been modelled as mixed cortico-cancellous bone. The distal part of femur has been modelled as a flexible body with springs used to simulate the ligaments positioned at their anatomical insertion points. With this dynamic model a gait cycle was simulated. Stress shielding was identified in the distal femur after TKR, which is consistent with other investigators' results. Interestingly, higher stresses were found in the bone adjacent to the femoral component peg. This dynamic model can now be used to analyse the stress distribution in the distal femur with different load conditions. This will help to improve implant designs and will allow comparison of prostheses from different manufacturers.     

Muscle-ligament interactions at the human knee (I)

A three-dimensional dynamic model of the knee was developed to study the interactions between the articulating surfaces of the bones and the geometrical and mechanical properties of the ligaments. The contact-surface geometry of the distal femur, proximal tibia, and patella was modeled by fitting polynomials to each of the eight articular surfaces. Twelve elastic elements were used to describe the function of the ligamentous and capsular structures of the knee. The origin and insertion sites of each model ligament were obtained from cadaveric data reported for an average-size knee. The response of the model to both anterior-posterior drawer and axial rotation suggests that the geometrical and mechanical properties of the model ligaments approximate the behavior of real ligaments in the intact knee. Comparison of the model’s response with experimental data obtained from cadaveric knee extension indicate further that the three-dimensional model reproduces the response of the real knee during movement.     

Muscle-ligament interactions at the human knee (II)

In part I of this paper, a three-dimensional model of the human knee joint was incorporated into a detailed human musculoskeletal lower extremity model. The model was used to determine the muscle, ligament, and articular contact forces transmitted at the knee as humans extend/flex in an isometric state. Part II investigates the sensitivity of the model calculations to changes in the parameters which describe the mechanical behavior of cartilage and the ligaments of the knee. The ligament function in the real knee was most sensitive to changes in ligament reference lengths or strains, less sensitive to changes in cartilage stiffness, and least sensitive to changes in ligament stiffness.     

A spatial model of the knee for the preoperative planning of knee surgery

A model on the spatial mechanical behaviour of the passive knee is presented. The femoral articular surfaces were represented by generalized, sagittally elliptical, toroidal surfaces. The medial and lateral tibial articular surfaces were represented by a dished spherical surface and the lower hemihyperbolic region of a torus respectively. Anatomical articular cartilage, knee ligaments and the posterior capsule were represented by spring-like deformable elements with non-linear load versus deflection characteristics. All the forces that act on the femur relative to the tibia were represented by three orthogonal forces and three associated moments. Spatial, articulation-dependent femorotibial kinematic constraint equations of the passive knee were formulated in an analytically explicit manner, based on the natural coordinates of the articular surfaces. The constraint equations were solved algebraically in closed form. Equations were derived that describe spatial femoro-tibial motion, ligament length, ligament strain, ligament-based elastic potential energy and the quasi-static equilibrium of the passive knee. Software was written, simulations on the motion characteristics and load versus deflection characteristics of the knee were carried out and graphical results were presented. The simulation of planar flexion/extension was almost spontaneous. The time taken to simulate spatial six-degree-of-freedom femoro-tibial motion was less than 2.5 min. The models were found to be capable of representing real-life passive knees to a high degree of satisfaction. It has been demonstrated that the models can provide knee surgeons with additional information on major aspects of the preoperative planning of knee surgery. The models can be used to enhance the preoperative planning of ligament reconstruction, articular surfaces related surgery, osteotomy and patellar tendon transfer surgery.     

An optimal control model for determining articular contact forces at the human knee during rising from a static squat position

A two-dimensional dynamic model of the knee joint was incorporated into a four-segment, eight-muscle model of the human body to determine the muscle, ligament, and articular contact forces transmitted at the knee as humans stand up from a static squatting position. Our optimal control model predicted peak tibiofemoral contact forces 8 times as high as body weight. Furthermore, ligament forces, especially those in the anterior-cruciate, were nearly body weight as knee flexion approached 90 degrees. Ligament and tibiofemoral contact loads were dominated by the forces exerted by muscles during the movement.     

Knee joint forces: prediction, measurement, and significance

Knee forces are highly significant in osteoarthritis and in the survival and function of knee arthroplasty. A large number of studies have attempted to estimate forces around the knee during various activities. Several approaches have been used to relate knee kinematics and external forces to internal joint contact forces, the most popular being inverse dynamics, forward dynamics, and static body analyses. Knee forces have also been measured in vivo after knee arthroplasty, which serves as valuable validation of computational predictions. This review summarizes the results of published studies that measured knee forces for various activities. The efficacy of various methods to alter knee force distribution, such as gait modification, orthotics, walking aids, and custom treadmills are analyzed. Current gaps in our knowledge are identified and directions for future research in this area are outlined.     

The variation in the orientations and moment arms of the knee extensor and flexor muscle tendons with increasing muscle force: a mathematical analysis

The orientations and moment arms of the knee extensor and flexor muscle tendons are evaluated with increasing values of muscle force during simulated isometric exercises. A four-bar linkage model of the knee in the sagittal plane was used to define the motion of the joint in the unloaded state during 0-120 degrees flexion. The cruciate and collateral ligaments were represented by arrays of elastic fibres, which were recruited sequentially under load or remained buckled when slack. A bi-articular model of the patello-femoral joint was used. Simple straight-line representation was used for the lines of action of the forces transmitted by the model muscle tendons. The effects of tissue deformation with increasing muscle force were considered. During quadriceps contraction resisted by an external flexing load, the maximum change in moment arm of the patellar tendon was found to be 2 per cent at 0 degree flexion when the quadriceps force was increased tenfold, from 250 to 2500 N. The corresponding maximum change in orientation of the tendon was 3 degrees at 120 degrees flexion. During hamstrings contraction resisted by an external extending load, the maximum change in moment arm of the hamstrings tendon was 8 per cent at 60 degrees flexion when the hamstrings force was increased tenfold, from 100 to 1000 N. During gastrocnemious contraction, the corresponding maximum change for the gastrocnemious tendon was 3 per cent at 0 degree. The orientations of the flexor muscle tendons in this range of force either remained constant or changed by 1 degree or less at any flexion angle. The general trend at any flexion angle was that, as the muscle force was increased, the moment arms and the orientations approached nearly constant values, showing asymptotic behaviour. It is concluded that experimental simulations of knee muscle action with low values of the externally applied load, of the order of 50 N, can provide reliable estimates of the relationships between muscle forces and external loads during activity.     

Three-dimensional dynamic model of the knee

A three-dimensional dynamic model of the knee was developed to study the interactions between the articulating surfaces of the bones and the geometrical and mechanical properties of the ligaments. The contact-surface geometry of the distal femur, proximal tibia, and patella was modeled by fitting polynomials to each of the eight articular surfaces. Twelve elastic elements were used to describe the function of the ligamentous and capsular structures of the knee. The origin and insertion sites of each model ligament were obtained from cadaveric data reported for an average-size knee. The response of the model to both anterior-posterior drawer and axial rotation suggests that the geometrical and mechanical properties of the model ligaments approximate the behavior of real ligaments in the intact knee. Comparison of the model’s response with experimental data obtained from cadaveric knee extension indicate further that the three-dimensional model reproduces the response of the real knee during movement.     

Analysis of muscle activity during gait cycle using fuzzy rule-based reasoning

The purpose of this study was to determine the patterns of muscle activation as outcome measures of the ground reaction forces during normal walking tasks using optical motion analysis capture system, instrumented treadmill and electromyography (EMG), respectively. The recognition of the muscle patterns during gait dynamics offers insight into the control of skeletal position, joint stiffness, vibrations of the soft tissue packages, stability during ground contact, and propulsion for the movement task. Sixteen able-bodied participants were recruited to walk on a dual-belt instrumented treadmill with embedded force plates. A fuzzy rule-based reasoning algorithm for recognizing the activation patterns of the lower extremity muscles during normal walking maneuvers within the seven gait phases was developed. The resulting recognition will enable the determination of alterations in the locomotor control system, contribute to suggest symptoms of a neurological disease, disease severity, and also indications of improvements in response to therapeutic interventions.     

Knee and hip joint forces--sensitivity to the degrees of freedom classification at the knee

Previous research has demonstrated that the number of degrees of freedom (DOF) modelled at a given joint affects the antagonistic muscle activity predicted by inverse dynamics optimization techniques. This higher level of muscle activity in turn results in greater joint contact forces. For instance, modelling the knee as a 3 DOF joint has been shown to result in higher hip and knee joint forces commensurate with a higher level of muscular activity than when the knee is modelled with 1 DOF. In this study, a previously described musculoskeletal model of the lower limb was used to evaluate the sensitivity of the knee and hip joint contact forces to the DOF at the knee during vertical jumping in both a 1 and a 3 DOF knee model. The 3 DOF knee was found to predict higher tibiofemoral and hip joint contact forces and lower patellofemoral joint contact forces. The magnitude of the difference in hip contact force was at least as significant as that found in previous research exploring the effect of subject-specific hip geometry on hip contact force. This study therefore demonstrates a key sensitivity of knee and hip joint contact force calculations to the DOF at the knee. Finally, it is argued that the results of this study highlight an important physiological question with practical implications for the loading of the structures of the knee; that is, the relative interaction of muscular, ligamentous, and articular structures in creating moment equilibrium at the knee.     

The effect of cartilage deformation on the laxity of the knee joint

In this paper, deformation of the articular cartilage layers is incorporated into an existing two-dimensional quasi-static model of the knee joint. The new model relates the applied force and the joint displacement, as measured in the Lachmann drawer test, and allows the effect of cartilage deformation on the knee joint laxity to be determined. The new model augments the previous knee model by calculating the tibio-femoral contact force subject to an approximate 'thin-layer' constitutive equation, and a method is described for finding the configuration of the knee under a specified load, in terms of a displacement from a zero-load reference configuration. The results show that inclusion of deformable cartilage layers can cause a reduction of between 10 and 35 per cent in the force required to produce a given tibial displacement, over the range of flexion angles considered. The presence of cartilage deformation was found to be an important modifier of the loading response but is secondary to the effect of ligamentous extension. The flexion angle dependence of passive joint laxity is much more strongly influenced by fibre recruitment in the ligaments than by cartilage deformation.     

Computer simulation of the human leg subjected to impact loading

One of the most important tasks in clinical practice is to determine accurately the forces and displacements of the various anatomical structural components of the human leg, especially when subjected to impact loading. This paper therefore develops a computer simulation which describes the biodynamic response of the human lower extremity for realistic activities such as kicking by foot etc. Firstly, the paper derives the nonlinear equations of motion and nonlinear constraint equation governing the sagittal plane response of the human leg subjected to impact loading. The equations are then solved using numerical techniques and the results are presented. Special attention is given to the ligament, contact and muscle group forces, the location of contact points, anterior-posterior displacements and the motion trajectories of the femur and the tibia.     

Influence of the varus-valgus instability on the contact of the femoro-tibial joint

The varus-valgus instability of the knee joint is mainly due to ruptured or lax collateral ligaments. The purpose of this investigation was to study the influence of the varus-valgus instability on the contact pressures of the femoro-tibial joint. Six fresh knee specimens of human cadavers were tested to measure the contact pressure on the tibia plateau of the knee joint at varus or valgus alignment under various loads and at full extension. Pressure transducers and Bourdon tube pressure gauges were used simultaneously for recording pressure. At neutral alignment of the knee with the menisci intact, the peak pressure increased linearly with forces up to 4 MPa. With increasing varus alignment, the peak contact pressure on the medial plateau not covered by the menisci increased up to a maximum of 7.3 MPa at 5 degrees varus, and at 5 degrees valgus, the peak pressure on the lateral plateau was 7.8 MPa. After total meniscectomy, the contact pressure increased up to a maximum of 7.4 MPa at a force of 2700 N. With increasing varus alignment, the contact pressure on the medial plateau increased to 8.1 MPa at 5 degrees varus and on the lateral plateau 9.2 MPa at 5 degrees valgus.     

Glenohumeral contact forces

Glenohumeral contact forces have only been calculated previously either for simple abduction or for athletic activities. The objective of this study was to determine the glenohumeral contact forces for tasks which are demanding of the shoulder but which would commonly be performed by older people. The functional tasks chosen were using the arms to stand up from and sit down into a chair, walking with a cane, lifting a 5 kg box to shoulder height with both hands, and lifting a 10 kg suitcase. The trunk angles, arm angles and hand loads of six healthy subjects, average age 55 years, were recorded. This information was input into a biomechanical computer model which optimized the muscle force distribution by minimizing the sum of squared muscle stresses subject to constraints on the maximum muscle forces and maintaining the direction of the resultant force within the glenoid fossa. Average contact forces ranged from 1.3 to 2.4 times body weight (930-1720 N), the highest force being for lifting a suitcase. This latter value would be even higher if lifting either a greater load or to a greater height. Thus, contact forces at the shoulder should not be underestimated. This study provides functionally relevant contact forces which can be used for mechanical testing or finite element modelling of shoulder prostheses.     

Morphology of the stifle in agouti (Dasyprocta prymnolopha,Wagler 1831)

The agouti (Dasyprocta prymnolopha, Wagler 1831) is a wild rodent of great zootechnical potential, a fact that enables anatomical and morphological studies to support management actions with this animal. In this perspective, this study aimed to describe the anatomy and histology of the agouti stifle joint. Four adult agoutis were used, two females and two males. The animals were submitted to dissection and identification of the structures of the stifle joint. For light microscopy study, samples of the patellar ligament, cranial and caudal cruciate ligaments, medial and lateral collateral ligaments were used. Agouti has a highly congruent patellofemoral joint; elongated patella; medial and lateral fabellae at the proximal insertion of the gastrocnemius muscle; medial and lateral meniscus with lunula; in addition to the presence of the following ligament structures: patellar ligament, cranial and caudal cruciate ligaments, medial and lateral collateral ligaments, meniscofemoral ligament, caudal meniscal ligament of the medial meniscus, and medial and lateral cranial ligaments. The patellar ligament presents bundles of parallel collagen fibers with a straight path and coated fibroblasts; collateral and cruciate ligaments had loose and dense connective tissue, coated fibroblasts and collagen bundle undulations, the latter most expressive in the caudal cruciate ligament. Thus, except for the shape and angulation of the stifle, which allows specific movements, the agouti stifle has structures analogous to that of other rodents and domestic animals.