A reciprocal connection factor for assessing knee-joint function

In the knee joint, interactions between instantaneous kinetics and kinematics associated with ligamentous and articular tissues are not fully understood. These structures may be represented by the instantaneous screw axis ($) (ISA) and static force vectors ($'). Geometric changes to the joint structure affecting motion have not been fully explained, especially after surgical reconstruction and replacement procedures. The ISA offers a joint-characterisation approach, which is dependent on the combined forces of ligaments, articular contacts and muscles. The standard four-bar linkage model in the sagittal plane demonstrates that the normal contact force and the lines of action of the cruciate ligaments always intersect at the centre of rotation of the joint. A kinematic knee model in which the articular surfaces in the lateral and medial compartments as well as the isometric fascicles in the engaged ligaments may be represented as five constraints in a one-degree-of-freedom parallel spatial mechanism. This study provides a theoretical foundation to elucidate the role of each of these elements in the control of the ISA. A recourse to the principle of virtual work explained through d'Alembert's principle for reducing a dynamics problem to an instantaneous static scenario allows screws to be applied to the biomechanics of human motion. The principle of reciprocity links these approaches together to explain the transmitting load between the tibia and the femur as well as the relative motion within the knee joint. A principal clinical implication of this study is the introduction of the reciprocal connection factor to evaluate knee kinematics and kinetics in one simple term, allowing the quantitative assessment of the outcome of knee-joint treatment and rehabilitation methods.     

A constraint-based approach to modelling the mobility of the human knee joint

A model of knee mobility able to predict the range and pattern of movement in the unloaded joint was proposed by Wilson et al. (J. Biomech. 31 (1998) 1127-1136). The articular surfaces in the lateral and medial compartments and isometric fascicles in three of the knee ligaments were represented as five constraints on motion between the femur and tibia in a single degree-of-freedom parallel spatial mechanism. The path of movement of the bones during passive flexion was found by solving the forward kinematics of the mechanism using an iterative method. The present paper shows that such a mechanism-based solution approach can lead to an underestimation of the flexion range. This is due to the mechanism reaching a 'stationary configuration' and 'locking'. A new, constraint-based approach to the solution of the model joint displacement is proposed. It avoids the representation of ligaments and articular surfaces by kinematically equivalent chains of one degree-of-freedom pairs which are prone to singularities. It relies instead on a numerical solution of five non-linear constraint equations to find the relative positions of the bones at a series of flexion angles. The method is successful both in its ability to predict motion through a physiological range and in its efficiency with a solution rate forty times faster than the original algorithm. The new approach may be extended to include more complex joint surface geometry, allowing a study of the effects of articular surface shape and ligament arrangement on joint kinematics.     

A geometric model of the human ankle joint.

A two-dimensional four-bar linkage model of the ankle joint is formulated to describe dorsi/plantarflexion in unloaded conditions as observed in passive tests on ankle complex specimens. The experiments demonstrated that the human ankle joint complex behaves as a single-degree-of-freedom system during passive motion, with a moving axis of rotation. The bulk of the movement occurred at the level of the ankle. Fibres within the calcaneofibular and tibiocalcaneal ligaments remained approximately isometric. The experiments showed that passive kinematics of the ankle complex is governed only by the articular surfaces and the ligaments. It was deduced that the ankle is a single-degree-of-freedom mechanism where mobility is allowed by the sliding of the articular surfaces upon each other and the isometric rotation of two ligaments about their origins and insertions, without tissue deformation. The linkage model is formed by the tibia/fibula and talus/calcaneus bone segments and by the calcaneofibular and tibiocalcaneal ligament segments. The model predicts the path of calcaneus motion, ligament orientations, instantaneous axis of rotation, and conjugate talus surface profile as observed in the experiments. Many features of ankle kinematics such as rolling and multiaxial rotation are elucidated. The geometrical model is a necessary preliminary step to the study of ankle joint stability in response to applied loads and can be used to predict the effects of changes to the original geometry of the intact joint. Careful reconstruction of the original geometry of the ligaments is necessary after injury or during total ankle replacement.     

The interaction of muscle moment arm,knee laxity,and torque in a multi-scale musculoskeletal model of the lower limb

IntroductionMusculoskeletal modeling allows insight into the interaction of muscle force and knee joint kinematics that cannot be measured in the laboratory. However, musculoskeletal models of the lower extremity commonly use simplified representations of the knee that may limit analyses of the interaction between muscle forces and joint kinematics. The goal of this research was to demonstrate how muscle forces alter knee kinematics and consequently muscle moment arms and joint torque in a musculoskeletal model of the lower limb that includes a deformable representation of the knee.MethodsTwo musculoskeletal models of the lower limb including specimen-specific articular geometries and ligament deformability at the knee were built in a finite element framework and calibrated to match mean isometric torque data collected from 12 healthy subjects. Muscle moment arms were compared between simulations of passive knee flexion and maximum isometric knee extension and flexion. In addition, isometric torque results were compared with predictions using simplified knee models in which the deformability of the knee was removed and the kinematics at the joint were prescribed for all degrees of freedom.ResultsPeak isometric torque estimated with a deformable knee representation occurred between 45° and 60° in extension, and 45° in flexion. The maximum isometric flexion torques generated by the models with deformable ligaments were 14.6% and 17.9% larger than those generated by the models with prescribed kinematics; by contrast, the maximum isometric extension torques generated by the models were similar. The change in hamstrings moment arms during isometric flexion was greater than that of the quadriceps during isometric extension (a mean RMS difference of 9.8 mm compared to 2.9 mm, respectively).DiscussionThe large changes in the moment arms of the hamstrings, when activated in a model with deformable ligaments, resulted in changes to flexion torque. When simulating human motion, the inclusion of a deformable joint in a multi-scale musculoskeletal finite element model of the lower limb may preserve the realistic interaction of muscle force with knee kinematics and torque.     

Ligaments and articular contact guide passive knee flexion

The aim of this study was to test the hypothesis that the coupled features of passive knee flexion are guided by articular contact and by the isometric fascicles of the ACL, PCL and MCL. A three-dimensional mathematical model of the knee was developed, in which the articular surfaces in the lateral and medial compartments and the isometric fascicles in the ACL, PCL and MCL were represented as five constraints in a one degree-of-freedom parallel spatial mechanism. Mechanism analysis techniques were used to predict the path of motion of the tibia relative to the femur. Using a set of anatomical parameters obtained from a cadaver specimen, the model predicts coupled internal rotation and ab/adduction with flexion. These predictions correspond well to measurements of the cadaver specimen’s motion. The model also predicts posterior translation of contact on the tibia with flexion. Although this is a well-known feature of passive knee flexion, the model predicts more translation than has been reported from experiments in the literature. Modelling of uncertainty in the anatomical parameters demonstrated that the discrepancy between theoretical predictions and experimental measurement can be attributed to parameter sensitivity of the model. This study shows that the ligaments and articular surfaces work together to guide passive knee motion. A principal implication of the work is that both articular surface geometry and ligament geometry must be preserved or replicated by surgical reconstruction and replacement procedures to ensure normal knee kinematics and by extension, mechanics.     

Study of the joint configuration of the knee using a morpho-functional analysis

Skin marker motion analyses are the most widespread techniques to study human movements. Nevertheless, trajectories obtained through such methods are biased because of soft tissue artifacts and lead, consequently, to false collisions and dislocations when bone motion is under investigation. It's an open challenge to enhance kinematics curves particularly for the knee joint involved in the mechanics of gait. The kinematics of flexion/extension of the knee is classically modeled by a rotation around a fixed axis. However, the trend of current biomechanical studies is to improve this modeling by introducing a morphological knowledge such as ligament constraints. In this paper, we propose to highlight the morpho-functionnal link on this joint thanks to two contributions. The first one consists in proposing a method capable of extracting a kinematics of flexion/extension of the knee from a unique CT scan. This method is based on the determination of a mobile axis capable of keeping the information of rolling/sliding. The second one consists in a qualitative and quantitative temporal analysis of the position of the bones during the movement. We compare the results of the two kinematics (static and mobile axis) using original figures of articular coherence and an associated index.     

A three-dimensional finite element analysis of the combined behavior of ligaments and menisci in the healthy human knee joint

We present here a three-dimensional FE model of the healthy human knee that included the main structures of the joint: bones, all the relevant ligaments and patellar tendon, menisci and articular cartilages. Bones were considered to be rigid, articular cartilage and menisci linearly elastic, isotropic and homogeneous and ligaments hyperelastic and transversely isotropic. Initial strains on the ligaments and patellar tendon were also considered. This model was validated using experimental and numerical results obtained by other authors. Our main goal was to analyze the combined role of menisci and ligaments in load transmission and stability of the human knee. The results obtained reproduce the complex, nonuniform stress and strain fields that occur in the biological soft tissues involved and the kinematics of the human knee joint under a physiological external load.     

1998 Basmajian Student Award Paper: Movement patterns after anterior cruciate ligament injury: a comparison of patients who compensate well for the injury and those who require operative stabilization

The purpose of this study was to describe kinematic and kinetic differences between a group of ACL deficient subjects who were grouped according to functional ability. Sixteen patients with complete ACL rupture were studied; eight subjects had instability with activities of daily living (non-copers) and eight subjects had returned to all pre-injury activity without limitation (copers). Three-dimensional joint kinematics and kinetics were collected from the knee and ankle during walking, jogging and going up and over a step. Results showed that both groups mitigated the force with which they contacted the floor but non-copers consistently demonstrated less knee flexion in the involved limb. The copers used joint kinematics similar to those of their uninvolved knees and similar to knee motions reported in uninjured subjects. The reduced knee motion in the involved knee of the non-copers did not correlate directly with quadriceps femoris muscle weakness.

The data suggest that the non-copers utilize a stabilization strategy which stiffens the knee joint which not only is unsuccessful but may lead to excessive joint contact forces which have the potential to damage articular structures. The copers use a strategy which permits normal knee kinematics and bodes well for joint integrity.     

Intrinsic innervation of the rat knee joint articular capsule and ligaments

In spite of the practical importance of having a detailed knowledge of knee joint innervation to understand the pathophysiologic aspects, little information is now available concerning the density and pattern of the nerve fibres which are distributed to it. The present study has been designed to investigate the density and distribution of nerve fibres and receptor corpuscles in the knee joint articular capsule, cruciate and collateral ligaments in the rat, using the acetylcholinesterase (AChE) histochemical in toto staining technique. The investigation was performed on male Wistar rats of 3 months of age, some of which had been treated with capsaicin to deplete their afferent 'C' fibres of their content of neuropeptides. AChE-positive nerve fibres and different types of receptor corpuscle endings were found within articular capsule and ligaments. The highest density of AChE-positive nerve fibres was noticeable in the fibular collateral ligament followed by the tibial collateral ligament, the posterior cruciate ligament, the anterior cruciate ligament and the articular capsule. In the articular capsule the number of type I endings was higher than in the ligaments. The opposite is true for the other type of receptor corpuscles found as well as for nerve endings. Capsaicin treatment significantly reduced the density of AChE-positive nerve fibres in knee joint ligaments but did not affect nerve fibres in the articular capsule. Moreover, it caused the disappearance of some kind of receptor corpuscles within the collateral and cruciate ligaments. The above data collectively suggest that the AChE in toto staining technique may represent a good method for investigating joint innervation and that a significant percentage of nerve fibres supplying knee joint ligaments is represented by C fibre afferents.     

A validated three-dimensional computational model of a human knee joint

This paper presents a three-dimensional finite element tibio-femoral joint model of a human knee that was validated using experimental data. The geometry of the joint model was obtained from magnetic resonance (MR) images of a cadaveric knee specimen. The same specimen was biomechanically tested using a robotic/universal force-moment sensor (UFS) system and knee kinematic data under anterior-posterior tibial loads (up to 100 N) were obtained. In the finite element model (FEM), cartilage was modeled as an elastic material, ligaments were represented as nonlinear elastic springs, and menisci were simulated by equivalent-resistance springs. Reference lengths (zero-load lengths) of the ligaments and stiffness of the meniscus springs were estimated using an optimization procedure that involved the minimization of the differences between the kinematics predicted by the model and those obtained experimentally. The joint kinematics and in-situ forces in the ligaments in response to axial tibial moments of up to 10 Nm were calculated using the model and were compared with published experimental data on knee specimens. It was also demonstrated that the equivalent-resistance springs representing the menisci are important for accurate calculation of knee kinematics. Thus, the methodology developed in this study can be a valuable tool for further analysis of knee joint function and could serve as a step toward the development of more advanced computational knee models.     

Fatigue effects on the coordinative pattern during cycling: Kinetics and kinematics evaluation

The aim of the present study was to analyze the net joint moment distribution, joint forces and kinematics during cycling to exhaustion. Right pedal forces and lower limb kinematics of ten cyclists were measured throughout a fatigue cycling test at 100% of PO_MAX. The absolute net joint moments, resultant force and kinematics were calculated for the hip, knee and ankle joint through inverse dynamics. The contribution of each joint to the total net joint moments was computed. Decreased pedaling cadence was observed followed by a decreased ankle moment contribution to the total joint moments in the end of the test. The total absolute joint moment, and the hip and knee moments has also increased with fatigue. Resultant force was increased, while kinematics has changed in the end of the test for hip, knee and ankle joints. Reduced ankle contribution to the total absolute joint moment combined with higher ankle force and changes in kinematics has indicated a different mechanical function for this joint. Kinetics and kinematics changes observed at hip and knee joint was expected due to their function as power sources. Kinematics changes would be explained as an attempt to overcome decreased contractile properties of muscles during fatigue.     

An improved OpenSim gait model with multiple degrees of freedom knee joint and knee ligaments

Musculoskeletal models are widely used to investigate joint kinematics and predict muscle force during gait. However, the knee is usually simplified as a one degree of freedom joint and knee ligaments are neglected. The aim of this study was to develop an OpenSim gait model with enhanced knee structures. The knee joint in this study included three rotations and three translations. The three knee rotations and mediolateral translation were independent, with proximodistal and anteroposterior translations occurring as a function of knee flexion/extension. Ten elastic elements described the geometrical and mechanical properties of the anterior and posterior cruciate ligaments (ACL and PCL), and the medial and lateral collateral ligaments (MCL and LCL). The three independent knee rotations were evaluated using OpenSim to observe ligament function. The results showed that the anterior and posterior bundles of ACL and PCL (aACL, pACL and aPCL, pPCL) intersected during knee flexion. The aACL and pACL mainly provided force during knee flexion and adduction, respectively. The aPCL was slack throughout the range of three knee rotations; however, the pPCL was utilised for knee abduction and internal rotation. The LCL was employed for knee adduction and rotation, but was slack beyond 20° of knee flexion. The MCL bundles were mainly used during knee adduction and external rotation. All these results suggest that the functions of knee ligaments in this model approximated the behaviour of the physical knee and the enhanced knee structures can improve the ability to investigate knee joint biomechanics during various gait activities.     

A mathematical model for the evaluation of the behaviour during flexion of condylar-type knee prostheses

A 3D knee model was developed in order to evaluate the mechanical behaviour during flexion of condylar-type knee prosthesis. Based on the total energy minimization principle, it takes into account the articular surfaces (the tibial surface being deformable), the body weight, and the patello femoral joint. It generates the kinematics of the joint, the motion of the centre of contact, the quadriceps forces, the pressure distribution on the tibial plateau, and ligament lengths and forces between 0 and 120 degrees of flexion. The results for ten digitized knees and the commercially available prostheses are presented. They are in general agreement with experimental results published in the literature. It is concluded that this computer program may be, within its limitations, a useful tool in the preliminary evaluation of new condylar-type knee prosthesis designs.     

A method of calculating physiologically relevant joint reaction forces during forward dynamic simulations of movement from an existing knee model

In the commonly used SIMM software, which includes a complete musculoskeletal model of the lower limbs, the reaction forces at the knee are computed. These reaction forces represent the bone-on-bone contact forces and the soft tissue forces (e.g. ligaments) other than muscles acting at the joint. In the knee model integrated into this software, a patellotibial joint rather than a patellofemoral joint is defined, and a force acting along the direction of the patellar ligament is not included. Although this knee model results in valid kinematics and muscle moment arms, the reaction forces at the knee calculated do not represent physiologic knee joint reaction forces. Hence our objectives were to develop a method of calculating physiologic knee joint reaction forces using the knee model incorporated into the SIMM software and to demonstrate the differences in the forces returned by SIMM and the physiologic forces in an example. Our method converts the anatomically fictional patellotibial joint into a patellofemoral joint and computes the force in an inextensible patellar ligament. In our example, the rectus femoris was fully excited isometrically, with the knee and hip flexed to 90 degrees . The resulting SIMM tibiofemoral joint reaction force was primarily shear, because the quadriceps force was applied to the tibia via the fictional patellotibial joint. In contrast the physiologic tibiofemoral joint reaction force was primarily compression, because the quadriceps force was applied through the patellar ligament. This result illustrates that the physiologic knee joint reaction forces are profoundly different than the forces returned by SIMM. However physiologic knee joint reaction forces can be computed with postprocessing of SIMM results.     

The collateral ligaments of the knee joint in the cat and man. Morphological and functional study of the internal arrangement of fibers

The present investigation of fiber arrangement in the collateral ligaments of the knee was carried out in cats and man in various positions of flexion and extension, without compression load. In all knee joint positions, the fibers of the collateral ligaments are twisted except for the fibers in the meniscal part of the medial collateral ligament which have a parallel arrangement. Furthermore, most of the fibers in the collateral ligaments are taut in all positions of the knee joint in both cat and man. By means of planar models representing different fiber arrangements, the kinematic behavior of the collateral ligaments was analyzed. It appears that a crossed (twisted) arrangement of the fibers is most effective in rotatory movements, whereas a parallel orientation is most effective in translation. Our data further indicate that, in measuring the changes in lengths of ligaments during joint motion, one cannot neglect the internal arrangement of fibers and the geometry of the articular surfaces and menisci.     

Measuring the sensitivity of total knee replacement kinematics and laxity to soft tissue imbalances

Ligament balancing during total knee replacement (TKR) is receiving increased attention due to its influence on resulting joint kinematics and laxity. We employed a novel in vitro technique to measure the kinematics and laxity of TKR implants during gait, and measured how these characteristics are influenced by implant shape and soft tissue balancing, simulated using virtual ligaments. Compared with virtual ligaments that were equally balanced in flexion and extension, the largest changes in stance-phase tibiofemoral AP and IE kinematics occurred when the virtual ligaments were simulated to be tighter in extension (tibia offset 1.0 ± 0.1 mm posterior and 3.6 ± 0.1° externally rotated). Virtual ligaments which were tight in flexion caused the largest swing-phase changes in AP kinematics (tibia offset 2.3 ± 0.2 mm), whereas ligaments which were tight in extension caused the largest swing-phase changes in IE kinematics (4.2 ± 0.1° externally rotated). When AP and IE loads were superimposed upon normal gait loads, incremental changes in AP and IE kinematics occurred (similar to laxity testing); and these incremental changes were smallest for joints with virtual ligaments that were tight in extension (in both the stance and swing phases). Two different implant designs (symmetric versus medially congruent) exhibited different kinematics and sensitivities to superimposed loads, but demonstrated similar responses to changes in ligament balancing. Our results demonstrate the potential for pre-clinical testing of implants using joint motion simulators with virtual soft tissues to better understand how ligament balancing affects implant motion.     

The influence of ligament modelling strategies on the predictive capability of finite element models of the human knee joint

In finite element (FE) models knee ligaments can represented either by a group of one-dimensional springs, or by three-dimensional continuum elements based on segmentations. Continuum models closer approximate the anatomy, and facilitate ligament wrapping, while spring models are computationally less expensive. The mechanical properties of ligaments can be based on literature, or adjusted specifically for the subject. In the current study we investigated the effect of ligament modelling strategy on the predictive capability of FE models of the human knee joint. The effect of literature-based versus specimen-specific optimized material parameters was evaluated. Experiments were performed on three human cadaver knees, which were modelled in FE models with ligaments represented either using springs, or using continuum representations. In spring representation collateral ligaments were each modelled with three and cruciate ligaments with two single-element bundles. Stiffness parameters and pre-strains were optimized based on laxity tests for both approaches. Validation experiments were conducted to evaluate the outcomes of the FE models.Models (both spring and continuum) with subject-specific properties improved the predicted kinematics and contact outcome parameters. Models incorporating literature-based parameters, and particularly the spring models (with the representations implemented in this study), led to relatively high errors in kinematics and contact pressures. Using a continuum modelling approach resulted in more accurate contact outcome variables than the spring representation with two (cruciate ligaments) and three (collateral ligaments) single-element-bundle representations. However, when the prediction of joint kinematics is of main interest, spring ligament models provide a faster option with acceptable outcome.     

A new one-DOF fully parallel mechanism for modelling passive motion at the human tibiotalar joint

Knowledge on how ligaments and articular surfaces guide passive motion at the human ankle joint complex is fundamental for the design of relevant surgical treatments. The paper presents a possible improvement of this knowledge by a new kinematic model of the tibiotalar articulation. Passive motion, i.e. in virtually unloaded conditions, was captured in vitro in four lower leg specimens by means of a surgical navigation system with cluster of active markers attached to the tibia and talus. The anatomical geometry of the passive structures, i.e. articular surfaces and attachment areas of the ligaments, were taken by digitisation with a pointer. An equivalent spatial mechanism for the passive motion simulation was defined by three sphere-to-sphere contact points and two rigid links. These contact points were identified at the lateral talo-fibular articulation and at the medial and lateral aspects of the articulation between tibial mortise and trochlea tali. The two rigid links were identified by the isometric fibres at the calcaneofibular and tibiocalcaneal ligaments. An optimisation algorithm was developed for the identification of the final geometrical parameters resulting from an iterative refining process, which targets best matching between model predictions and corresponding experimental measurements of the spatial motion. The specimen-specific equivalent spatial mechanisms replicated the original passive motion very well, with mean discrepancies in position smaller than 2.5 mm and in rotation smaller than 1°. The study demonstrates that the articular surfaces and the ligaments, acting together as a mechanism, control the passive kinematics of the ankle joint.     

A three-dimensional study of the kinematics of the human knee

This paper represents a three-dimensional study of the human knee-joint and studies kinematic effects of the cruciate ligaments. Two methods were used for our studies, one method was preferred. This method used a time lapse photograph and strobe light to give us a plot of reference points to carry out our analysis using the method of Rouleaux applied to three dimensions. Five cadaver joints were used, each of which was used for three series of experiments, including the joint with capsule intact, with one of the ligaments cut and with the remaining ligament cut. Both lateral and medial studies were conducted to provide data for a three-dimensional study.

It was found that the cruciate ligaments had little effect on the kinematics of the knee, and that the knee motion remained unchanged after cutting one or both of the cruciate ligaments. It was concluded that the motion of the knee was due to the geometry of the bones and perhaps the collateral ligaments, and that the joint could be replaced with a prosthesis having a three dimensional axis of rotation with a fixed center.