Subject-specific knee joint geometry improves predictions of medial tibiofemoral contact forces

Estimating tibiofemoral joint contact forces is important for understanding the initiation and progression of knee osteoarthritis. However, tibiofemoral contact force predictions are influenced by many factors including muscle forces and anatomical representations of the knee joint. This study aimed to investigate the influence of subject-specific geometry and knee joint kinematics on the prediction of tibiofemoral contact forces using a calibrated EMG-driven neuromusculoskeletal model of the knee. One participant fitted with an instrumented total knee replacement walked at a self-selected speed while medial and lateral tibiofemoral contact forces, ground reaction forces, whole-body kinematics, and lower-limb muscle activity were simultaneously measured. The combination of generic and subject-specific knee joint geometry and kinematics resulted in four different OpenSim models used to estimate muscle–tendon lengths and moment arms. The subject-specific geometric model was created from CT scans and the subject-specific knee joint kinematics representing the translation of the tibia relative to the femur was obtained from fluoroscopy. The EMG-driven model was calibrated using one walking trial, but with three different cost functions that tracked the knee flexion/extension moments with and without constraint over the estimated joint contact forces. The calibrated models then predicted the medial and lateral tibiofemoral contact forces for five other different walking trials. The use of subject-specific models with minimization of the peak tibiofemoral contact forces improved the accuracy of medial contact forces by 47% and lateral contact forces by 7%, respectively compared with the use of generic musculoskeletal model.     

A three-dimensional anatomical model of the human patello-femoral joint,for the determination of patello-femoral motions and contact characteristics

The object of this study is to develop a three-dimensional mathematical model of the patello-femoral joint, which is modelled as two rigid bodies representing a moving patella and a fixed femur. Two-point contact was assumed between the femur and patella at the medial and lateral sides and in the analysis, the femoral and patellar articular surfaces were mathematically represented using Coons' bicubic surface patches. Model equations include six equilibrium equations and eleven constraints: six contact conditions, four geometric compatibility conditions, and the condition of a rigid patellar ligament; the model required the solution of a system of 17 nonlinear equations in 17 unknowns, its response describing the six-degress-of-freedom patellar motions and the forces acting on the patella. Patellar motions are described by six motion parameters representing the translations and rotations of the patella with respect to the femur. The forces acting on the patella include the medial and lateral component of patello-femoral contact and the patellar ligament force, all of which were represented as ratios to the quadriceps tendon force. The model response also includes the locations of the medial and lateral contact points on the femur and the patella. A graphical display of its response was produced in order to visualize better the motion of the components of the extensor mechanism.Model calculations show good agreement with experimental results available from the literature. The patella was found to move distally and posteriorly on the femoral condyles as the knee was flexed from full extension. Results indicate that the relative orientation of the patellar ligament with respect to the patella remains unchanged during this motion. The model also predicts a patellar flexion which always lagged knee flexion.Our calculations show that as the angle of knee flexion increased, the lateral contact point moved distally on the femur without moving significantly either medially or laterally. The medial contact point also moved distally on the femur but moved medially from full extension to about 40° of knee flexion, then laterally as the knee flexion angle increased. The lateral contact point on the patella did not change significantly in the medial and lateral direction as the knee was flexed; however, this point moved proximally toward the basis of the patella with knee flexion. The medial contact point also moved proximally on the patella with knee flexion, and in a similar manner the medial contact point on the patella moved distally with flexion from full extension to about 40° of flexion. However, as the angle of flexion increased, the medial contact point did not move significantly in the medial-lateral direction.Model calculations also show that during the simulated knee extension exercise, the ratio of the force in the patellar ligament to the force in the quadriceps tendon remains almost unchanged for the first 30° of knee flexion, then decreases as the angle of knee flexion increases. Furthermore, model results show that the lateral component of the patello-femoral contact force is always greater than the medial component, both components increasing with knee flexion.     

Knee joint motion and ligament forces before and after ACL reconstruction

The goal of this in vitro study was to investigate the initial postoperative mechanical state of the knee with various types of anterior cruciate ligament (ACL) reconstructions. An experimental knee testing system was developed for the in vitro measurement of ligament forces and three-dimensional joint motion as external loads were applied to fresh knee specimens. Two groups of knee specimens were tested. In test series #1, two intraarticular reconstructions were performed in each of five specimens using semifree and free patellar tendon grafts with bone blocks. In test series #2, a more carefully controlled intraarticular reconstruction was performed in five specimens using a semifree composite graft consisting of the semitendinosus and gracilis tendons augmented with the Ligament Augmentation Device. Ligament force and joint motion data were collected as anteriorly directed tibial loads were applied to the normal joint, the joint with a cut ACL and the reconstructed joint. These knee joint states were compared on the basis of ACL or graft forces, joint motion and load sharing by the collateral ligaments. The dominate result of the study was that the forces and motions defining the mechanical state of the knee after the ACL reconstructions in both test series were highly variable and abnormal when compared to the normal knee state. The higher level of surgical control series #2 did not decrease this variability. There was a poor correlation between motion of the reconstructed knee relative to normal, and the ACL graft force. There was little consistent difference in force and motion results between the surgical procedures tested.     

A parametric approach to numerical modeling of TKR contact forces

In vivo knee contact forces are difficult to determine using numerical methods because there are more unknown forces than equilibrium equations available. We developed parametric methods for computing contact forces across the knee joint during the stance phase of level walking. Three-dimensional contact forces were calculated at two points of contact between the tibia and the femur, one on the lateral aspect of the tibial plateau, and one on the medial side. Muscle activations were parametrically varied over their physiologic range resulting in a solution space of contact forces. The obtained solution space was reasonably small and the resulting force pattern compared well to a previous model from the literature for kinematics and external kinetics from the same patient. Peak forces of the parametric model and the previous model were similar for the first half of the stance phase, but differed for the second half. The previous model did not take into account the transverse external moment about the knee and could not calculate muscle activation levels. Ultimately, the parametric model will result in more accurate contact force inputs for total knee simulators, as current inputs are not generally based on kinematics and kinetics inputs from TKR patients.     

A procedure for estimating the relevant forces in the human knee using a four-bar mechanism

Knee injuries, especially those that affect the cruciate and lateral ligaments, are one of the most serious and frequent pathologies that affect the lower human extremity. Hence, the aim of this study is to develop a dynamic model for the lower extremity capable of estimating forces, forces in the cruciate and collateral ligaments and those normal to the articular cartilage, generated in the knee. The proposed model considers a four-bar mechanism in the knee, a spherical joint in the pelvis and a revolute one in the ankle. The four-bar mechanism is obtained by a synthesis process. The dynamic model includes the inertial properties of the femur, tibia, patella and the foot, the ground reaction force and the most important muscles in the knee. Muscle forces are estimated using an optimisation technique. Results from the application of the model on a real human task are presented.     

Pattern of anterior cruciate ligament force in normal walking

The goal of this study was to calculate and explain the pattern of anterior cruciate ligament (ACL) loading during normal level walking. Knee-ligament forces were obtained by a two-step procedure. First, a three-dimensional (3D) model of the whole body was used together with dynamic optimization theory to calculate body-segmental motions, ground reaction forces, and leg-muscle forces for one cycle of gait. Joint angles, ground reaction forces, and muscle forces obtained from the gait simulation were then input into a musculoskeletal model of the lower limb that incorporated a 3D model of the knee. The relative positions of the femur, tibia, and patella and the forces induced in the knee ligaments were found by solving a static equilibrium problem at each instant during the simulated gait cycle. The model simulation predicted that the ACL bears load throughout stance. Peak force in the ACL (303 N) occurred at the beginning of single-leg stance (i.e., contralateral toe off). The pattern of ACL force was explained by the shear forces acting at the knee. The balance of muscle forces, ground reaction forces, and joint contact forces applied to the leg determined the magnitude and direction of the total shear force acting at the knee. The ACL was loaded whenever the total shear force pointed anteriorly. In early stance, the anterior shear force from the patellar tendon dominated the total shear force applied to the leg, and so maximum force was transmitted to the ACL at this time. ACL force was small in late stance because the anterior shear forces supplied by the patellar tendon, gastrocnemius, and tibiofemoral contact were nearly balanced by the posterior component of the ground reaction.     

Cruciate coupling and screw-home mechanism in passive knee joint during extension--flexion

The screw-home mechanism and coupling between forces in cruciate ligaments during passive knee joint flexion were investigated for various boundary conditions, flexion axis alignments and posterior cruciate ligaments (PCL)/anterior cruciate ligament (ACL) conditions. A developed non-linear 3D finite element model was used to perform detailed elasto-static response analyses of the human tibiofemoral joint as a function of flexion angle varying from 10 degrees hyper-extension to 90 degrees flexion. The tibia rotated internally as the femur flexed and externally as the femur extended. The re-alignment of the flexion axis by +/-5 degrees rotation about the axial (distal-proximal) axis, transection of the ACL and changes in cruciate ligament initial strains substantially influenced the 'screw-home' motion. On the other hand, restraint on this coupled rotation diminished ACL forces in flexion. A remarkable coupling was predicted between ACL and PCL forces in flexion; forces in both cruciate ligaments increased as the initial strain or pretension in one of them increased whereas they both diminished as one of them was cut or became slack. This has important consequences in joint functional biomechanics following a ligament injury or replacement surgery and, hence, in the proper management of joint disorders.     

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.     

Two-dimensional dynamic modelling of human knee joint

A mathematical dynamic model of the two-dimensional representation of the knee joint is presented. The profiles of the joint surfaces are determined from X-ray films and they are represented by polynomials. The joint ligaments are modelled as nonlinear elastic springs of realistic stiffness properties. Nonlinear equations of motion coupled with nonlinear constraint conditions are solved numerically. Time derivatives are approximated by Newmark difference formulae and the resulting nonlinear algebraic equations are solved employing the Newton-Raphson iteration scheme. Several dynamic loads are applied to the center of mass of the tibia and the ensuing motion is investigated. Numerical results on ligament forces, contact point locations between femur and tibia, and the orientation of tibia relative to femur are presented. The results are shown to be consistent with the anatomy of the knee joint.     

Knee contact force in subjects with symmetrical OA grades: Differences between OA severities

In using musculoskeletal models, researchers can calculate muscle forces, and subsequently joint contact forces, providing insight into joint loading and the progression of such diseases as osteoarthritis (OA). The purpose of this study was to estimate the knee contact force (KCF) in patients with varying degrees of OA severity using muscle forces and joint reaction forces derived from OpenSim. Walking data was obtained from healthy individuals (n=14) and those with moderate (n=10) and severe knee OA (n=2). For each subject, we generated 3D, muscle-actuated, forward dynamic simulations of the walking trials. Muscle forces that reproduced each subject’s gait were calculated. KCFs were then calculated using the vector sum of the muscle forces and joint reaction forces along the longitudinal axis of the femur. Moderate OA subjects exhibited a similar KCF pattern to healthy subjects, with lower second peaks (p=0.021). Although subjects with severe OA had similar initial peak KCF to healthy and moderate OA subjects (more than 4 times BW), the pattern of the KCF was very different between groups. After an initial peak, subjects with severe OA continually unloaded the joint, whereas healthy and moderate OA subjects reloaded the knee during late stance. In subjects with symmetric OA grades, there appears to be differences in loading between OA severities. Similar initial peaks of KCF imply that reduction of peak KCF may not be a compensatory strategy for OA patients; however, reducing duration of high magnitude loads may be employed.     

Construction of 3D human distal femoral surface models using a 3D statistical deformable model

Construction of 3D geometric surface models of human knee joint is always a challenge in biomedical engineering. This study introduced an improved statistical shape model (SSM) method that only uses 2D images of a joint to predict the 3D joint surface model. The SSM was constructed using 40 distal femur models of human knees. In this paper, a series validation and parametric analysis suggested that more than 25 distal femur models are needed to construct the SSM; each distal femur should be described using at least 3000 nodes in space; and two 2D fluoroscopic images taken in 45° directions should be used for the 3D surface shape prediction. Using this SSM method, ten independent distal femurs from 10 independent living subjects were predicted using their 2D plane fluoroscopic images. The predicted models were compared to their native 3D distal femur models constructed using their 3D MR images. The results demonstrated that using two fluoroscopic images of the knee, the overall difference between the predicted distal femur surface and the MR image-based surface was 0.16±1.16 mm. These data indicated that the SSM method could be a powerful method for construction of 3D surface geometries of the distal femur.     

Elastic properties of an intact and ACL-ruptured knee joint: measurement, mathematical modelling, and haptic rendering

An analytical, dynamic model of the human knee joint has been developed to simulate the unloaded knee joint behaviour in 6 degrees of freedom. It is based on extensive robot-based measurements of the elastic properties of a human cadaver knee joint. The measured data are compared with data from the literature to ensure that a proper database for modelling is used. The analytical modelling of the passive elastic joint properties is done with Local Linear Model Trees. The deduced knee joint model incorporates passive elastic properties of the internal knee joint structures, passive elastic muscle forces, damping forces, gravitational forces, and external forces. There are two sets of parameters, one simulating the movement of the intact knee joint, and a second simulating the knee joint with ruptured anterior cruciate ligament. The dynamic model can be easily processed in real-time. It is implemented in the haptic display of the Munich Knee Joint Simulator (MKS), which enables a person to move a plastic leg driven by a robot manipulator and feel the simulated knee joint force. Orthopaedic physicians judged the performance of the dynamic knee joint model by executing physical knee joint tests at the MKS.     

Adaptation of bone and tendon to prolonged hindlimb suspension in rats

The rat hindlimb suspension model was used to ascertain the importance of ground reaction forces in maintaining bone and tendon homeostasis. Young female Sprague-Dawley rats were randomly assigned to either a suspended or a nonsuspended group. After 28 days, femur bones and patellar tendons were obtained for morphological and biochemical analyses. Prolonged suspension induced a significant change in the geometric configuration of the femur middiaphysis by increasing the minimum diameter (12%) without any significant alterations in cortical area, density, mineral, and collagen concentrations. Femur wet weight, length, DNA, and uronic acid concentrations of suspended animals were not significantly different from bones of nonsuspended rats. However, the collagen and proteoglycan concentrations in patellar tendons of suspended rats were 28% lower than the concentrations of matrix proteins in tissues obtained from nonsuspended animals. These data suggest that elimination of ground reaction forces induces alterations in tendon composition and femur diaphyseal shape by changing regional rates in bone remodeling and localized tendon strain. Therefore it appears that ground reaction forces are an important factor in the maintenance of cortical bone and patellar tendon homeostasis during weight-bearing conditions.     

On the kinematic modeling and the parameter estimation of the human knee joint.

This paper presents some results on the modeling and the parameter estimation of the human knee joint. Based on the geometric characteristics of the femur condyle and the tibia plateau, a part of femoro-tibial joint model includes an involute-on-plane submodel. Data recorded by camera type device are used to analyze the kinematic characteristics of the knee joint and to estimate the corresponding submodel parameters. Experimental results are presented and the model is further validated.     

Accuracy of femur reconstruction from sparse geometric data using a statistical shape model

Sparse geometric information from limited field-of-view medical images is often used to reconstruct the femur in biomechanical models of the hip and knee. However, the full femur geometry is needed to establish boundary conditions such as muscle attachment sites and joint axes which define the orientation of joint loads. Statistical shape models have been used to estimate the geometry of the full femur from varying amounts of sparse geometric information. However, the effect that different amounts of sparse data have on reconstruction accuracy has not been systematically assessed. In this study, we compared shape model and linear scaling reconstruction of the full femur surface from varying proportions of proximal and distal partial femur geometry in combination with morphometric and landmark data. We quantified reconstruction error in terms of surface-to-surface error as well as deviations in the reconstructed femur’s anatomical coordinate system which is important for biomechanical models. Using a partial proximal femur surface, mean shape model-based reconstruction surface error was 1.8 mm with 0.15° or less anatomic axis error, compared to 19.1 mm and 2.7–5.6° for linear scaling. Similar results were found when using a partial distal surface. However, varying amounts of proximal or distal partial surface data had a negligible effect on reconstruction accuracy. Our results show that given an appropriate set of sparse geometric data, a shape model can reconstruct full femur geometry with far greater accuracy than simple scaling.     

Control exerted by ligaments

The function of the ligaments as local controllers, independent of the central nervous system, in maintaining the integrity of the joint is demonstrated by modelling the human knee in the sagittal plane, and studying its anterior-posterior motion. In addition to the ligaments, the model includes the characteristic geometry of the joint surface and some muscle groups. The connecting reaction forces at the point of contact between the tibia and the femur are considered to be constraint forces due to three different surface motions--gliding, rolling and combined gliding and rolling. It is demonstrated that the ligamentous structure maintains these holonomic and nonholonomic constraints that describe the joint motion, and that stability of the knee joint is provided mainly by ligaments. Muscular structures further stabilize and contribute to joint movement. Computer simulation of rolling movement of the knee is presented to illustrate the importance of the ligaments for joint integrity and stability.     

Analytic analysis of the force sharing among synergistic muscles in one- and two-degree-of-freedom models

Mathematical optimization of specific cost functions has been used in theoretical models to calculate individual muscle forces. Measurements of individual muscle forces and force sharing among individual muscles show an intensity-dependent, non-linear behavior. It has been demonstrated that the force sharing between the cat Gastrocnemius, Plantaris and Soleus shows distinct loops that change orientation systematically depending on the intensity of the movement. The purpose of this study was to prove whether or not static, non-linear optimization could inherently predict force sharing loops between agonistic muscles. Using joint moment data from a step cycle of cat locomotion, the forces in three cat ankle plantar flexors (Gastrocnemius, Plantaris and Soleus) were calculated using two popular optimization algorithms and two musculo-skeletal models. The two musculo-skeletal models included a one-degree-of-freedom model that considered the ankle joint exclusively and a two-degree-of-freedom model that included the ankle and the knee joint. The main conclusion of this study was that solutions of the one-degree-of-freedom model do not guarantee force-sharing loops, but the two-degree-of-freedom model predicts force-sharing loops independent of the specific values of the input parameters for the muscles and the musculo-skeletal geometry. The predicted force-sharing loops were found to be a direct result of the loops formed by the knee and ankle moments in a moment-moment graph.     

A dynamic model of the knee and lower limb for simulating rising movements

A two-dimensional dynamical model of the human body was developed and used to simulate muscle and knee-ligament loading during a fast rising movement. The hip, ankle, and toes were each modeled as a simple hinge joint. Relative movements of the femur, tibia, and patella in the sagittal plane were described using a more detailed representation of the knee. The geometry of the model bones was adapted from cadaver data. Eleven elastic elements described the geometric and mechanical properties of the knee ligaments and joint capsule. The patella was assumed to be massless. Smooth hypersurfaces were constructed and used to calculate the position and orientation of the patella during a forward integration of the model. Each hypersurface was formed by applying the principle of static equilibrium to approximate patellofemoral mechanics during the simulation. The model was actuated by 22 musculotendinous units, each unit represented as a three-element muscle in series with tendon. A first-order process was assumed to model muscle excitation-contraction dynamics. Dynamic optimization theory was used to calculate the pattern of muscle excitations that produces a coordinated rising movement from an initial squatting position in minimum time. The calculations support the contention that squatting is a relatively safe exercise for rehabilitation following ACL reconstruction. ACL forces remain less than 20 N for the duration of the task.