A model of stress and strain in the interosseous ligament of the forearm based on fiber network theory

Fiber network theory was developed to describe cloth, a thin material with strength in the fiber directions. The interosseous ligament (IOL) of the forearm is a broad, thin ligament with highly aligned fibers. The objectives of this study were to develop a model of the stress and strain distributions in the IOL, based on fiber network theory, to compare the strains from the model with the experimentally measured strains, and to evaluate the force distribution across the ligament fibers from the model. The geometries of the radius, ulna, and IOL were reconstructed from CT scans. Position and orientation of IOL insertion sites and force in the IOL were measured during a forearm compression experiment in pronation, neutral rotation, and supination. An optical image-based technique was used to directly measure strain in two regions of the IOL in neutral rotation. For the network model, the IOL was represented as a parametric ruled three-dimensional surface, with rulings along local fiber directions. Fiber strains were calculated from the deformation field, and fiber stresses were calculated from the strains using average IOL tensile properties from a previous study. The in situ strain in the IOL was assumed uniform and was calculated so that the net force predicted by the network model in neutral rotation matched the experimental result. The net force in the IOL was comparable to experimental results in supination and pronation. The model predicted higher stress and strain in fibers near the elbow in neutral rotation, and higher stresses in fibers near the wrist in supination. Strains in neutral forearm rotation followed the same trends as those measured experimentally. In this study, a model of stress and strain in the IOL utilizing fiber network theory was successfully implemented. The model illustrates variations in the stress and strain distribution in the IOL. This model can be used to show surgeons how different fibers are taut in different forearm rotation positions-this information is important for understanding the biomechanical role of the IOL and for planning an IOL reconstruction.     

The mechanism of forearm rotation in Varanus exanthematicus

In the sprawling gait of Varanus exanthematicus, the bicondylar distal humerus requires both the radius and ulna to rotate in the same direction. The joints between the radius and radiale and between the ulna and ulnare and pisiform accomodate these specific rotations. A ligament system between radius, ulna, radiale, and ulnare causes the radius and ulna to approximate one another during external rotation of the forearm. This approximation is conveyed distally resulting in a narrowing of the hand during external rotation of radius and ulna or during pronation of the free hand. The significance of these and related linkages is discussed.     

Estimation of ACL forces by reproducing knee kinematics between sets of knees: A novel non-invasive methodology

In situ force in the anterior cruciate ligament (ACL) has been quantified both in vitro in response to relatively simple loads by means of robotic technology, as well as in vivo in response to more complex loads by means of force transducers and computational models. However, a methodology has been suggested to indirectly estimate the in situ forces in the ACL in a non-invasive, non-contact manner by reproducing six-degree of freedom (six-DOF) in vivo kinematics on cadaveric knees using a robotic/UFS testing system. Therefore, the objective of this study was to determine the feasibility of this approach. Kinematics from eight porcine knees (source knees) were collected at 30 degrees , 60 degrees , and 90 degrees of flexion in response to: (1) an anterior load of 100 N and (2) a valgus load of 5 N m. The average of each kinematic data set was reproduced on a separate set of eight knees (target knees). The in situ forces in the ACL were determined for both sets of knees and compared. Significant differences (rho<0.05) were found between the source knees and the target knees for all flexion angles in response to an anterior load. However, in response to valgus loads, there was no significant difference between the source knees and the target knees at 30 degrees and 90 degrees of flexion. It was noted that there was a correlation between anterior knee laxity (the distance along the displacement axis from the origin to the beginning of the linear region of the load-displacement curve) and internal-external rotation. These data suggest that in order to obtain reproducible results one needs to first match knees to knees with comparable anterior knee laxity. Thus, an estimate of the in situ forces in the ACL during in vivo activities might be obtainable using this novel methodology.     

Simulating distal radius fracture strength using biomechanical tests: a modeling study examining the influence of boundary conditions

Distal radius fracture strength has been quantified using in vitro biomechanical testing. These tests are frequently performed using one of two methods: (1) load is applied directly to the embedded isolated radius or (2) load is applied through the hand with the wrist joint intact. Fracture loads established using the isolated radius method are consistently 1.5 to 3 times greater than those for the intact wrist method. To address this discrepancy, a validated finite element modeling procedure was used to predict distal radius fracture strength for 22 female forearms under boundary conditions simulating the isolated radius and intact wrist method. Predicted fracture strength was highly correlated between methods (r = 0.94; p < 0.001); however, intact wrist simulations were characterized by significantly reduced cortical shell load carriage and increased stress and strain concentrations. These changes resulted in fracture strength values less than half those predicted for the isolated radius simulations (2274 ± 824 N for isolated radius, 1124 ± 375 N for intact wrist; p < 0.001). The isolated radius method underestimated the mechanical importance of the trabecular compartment compared to the more physiologically relevant intact wrist scenario. These differences should be borne in mind when interpreting the physiologic importance of mechanical testing and simulation results.     

The importance of quadriceps and hamstring muscle loading on knee kinematics and in-situ forces in the ACL

This study investigated the effect of hamstring co-contraction with quadriceps on the kinematics of the human knee joint and the in-situ forces in the anterior cruciate ligament (ACL) during a simulated isometric extension motion of the knee. Cadaveric human knee specimens (n = 10) were tested using the robotic universal force moment sensor (UFS) system and measurements of knee kinematics and in-situ forces in the ACL were based on reference positions on the path of passive flexion/extension motion of the knee. With an isolated 200 N quadriceps load, the knee underwent anterior and lateral tibial translation as well as internal tibial rotation with respect to the femur. Both translation and rotation increased when the knee was flexed from full extension to 30 of flexion; with further flexion, these motion decreased. The addition of 80 N antagonistic hamstrings load significantly reduced both anterior and lateral tibial translation as well as internal tibial rotation at knee flexion angles tested except at full extension. At 30 of flexion, the anterior tibial translation, lateral tibial translation, and internal tibial rotation were significantly reduced by 18, 46, and 30%, respectively (p<0.05). The in-situ forces in the ACL under the quadriceps load were found to increase from 27.8+/-9.3 N at full extension to a maximum of 44.9+/-13.8 N at 15 of flexion and then decrease to 10 N beyond 60 of flexion. The in-situ force at 15 was significantly higher than that at other flexion angles (p<0.05). The addition of the hamstring load of 80 N significantly reduced the in-situ forces in the ACL at 15, 30 and 60 of flexion by 30, 43, and 44%, respectively (p<0.05). These data demonstrate that maximum knee motion may not necessarily correspond to the highest in-situ forces in the ACL. The data also suggest that hamstring co-contraction with quadriceps is effective in reducing excessive forces in the ACL particularly between 15 and 60 of knee flexion.     

中医推拿法手部受力的生物力学建模及分析

目的建立中医法的简化生物力学模型,对法过程中手部主要部位的受力进行定量分析。方法应用摄像机和推拿手法测定仪实测推拿专家法推拿的运动学和力信号,建立含手部及桡骨、尺骨的简化的生物力学模型和方程,求解手部桡骨和尺骨远端点处的受力。结果 法外推时,手部桡骨和尺骨远端点处X方向（动方向）受力方向不变,出现两个峰值,近外推结束时受力最大;回收时两处受力大小和方向出现波动。手部桡骨和尺骨远端点处,Y方向和Z方向受力趋势相同,在逐步上升后出现了一个平缓变化的阶段,之后急骤下降。结论建立的简化生物力学模型可对中医法推拿手部受力进行较好的定量分析。     

Fall arrest strategy affects peak hand impact force in a forward fall

We measured the peak hand impact force involved in bimanually arresting a forward fall to the ground from a 1-m shoulder height in five healthy young males. The effects of three different subject instruction sets: "arrest the fall naturally"; "keep the head as far from the ground as possible"; and "minimize the peak hand forces" were studied by measuring body segment kinematics, ground reaction forces, and upper-extremity myoelectric activity. The hypotheses were tested that the (a) arrest strategy did not influence peak impact force, (b) arm configuration, impact velocity and upper-extremity electromyography (EMG) levels correlate to the peak impact force (c) and impacting the ground with one hand leading the other does not increase the impact force over that obtained with simultaneous hand use. The results show that these subjects were able to volitionally decrease the peak impact force at the wrist by an average of 27% compared with a "natural landing" (p=0.014) and 40% compared with a "stiff-arm landing" (p<0.0005). The magnitude of the peak unilateral wrist force varied from 0.65 to 1.7 body weight for these moderate falls onto a padded surface. Peak force correlated with the elbow angle at impact, wrist velocity at impact and with pre-EMG triceps activity. The force was not significantly higher for non-simultaneous hand impacts. We conclude that fall arrest strategy can substantially alter the peak impact forces applied to the distal forearm during a fall arrest. Therefore, the fall arrest strategy likely influences wrist injury risk independent of bone strength.     

Prediction of handgrip forces using surface EMG of forearm muscles.

Evaluation of handgrip forces constitutes an essential component of ergonomic evaluation (e.g. of hand tools), but is difficult to perform at the workplace. The present study describes a series of experiments on 8 healthy male subjects to determine the validity of linear regression models using the surface electromyography (EMG) of up to 6 forearm muscles to predict handgrip forces. For isometric gripping tasks, normalized EMG to grip force calibrations using a series of dynamic force bursts up to 300 N resulted in a valid prediction of grip forces based on the EMG of 6 forearm muscles. Absolute differences between observed and predicted grip force were small (between 27 and 41 N) which shows that the proposed method might be used for the ergonomic evaluation of the use of hand tools. The EMG - handgrip force model appeared to be minimally affected by grip width, i.e. a model for 67 mm grip width was able to validly predict grip forces for 59 and 75 mm grip widths. Furthermore, it was shown that of the 6 forearm muscles studied at least 3 have to be assessed to arrive at a sufficient level of validity, while it seems to be irrelevant which 3 of those 6 forearm muscles are assessed.     

The effects of wrist motion and hand orientation on muscle forces: A physiologic wrist simulator study

Although the orientations of the hand and forearm vary for different wrist rehabilitation protocols, their effect on muscle forces has not been quantified. Physiologic simulators enable a biomechanical evaluation of the joint by recreating functional motions in cadaveric specimens. Control strategies used to actuate joints in physiologic simulators usually employ position or force feedback alone to achieve optimum load distribution across the muscles. After successful tests on a phantom limb, unique combinations of position and force feedback – hybrid control and cascade control – were used to simulate multiple cyclic wrist motions of flexion-extension, radioulnar deviation, dart thrower’s motion, and circumduction using six muscles in ten cadaveric specimens. Low kinematic errors and coefficients of variation of muscle forces were observed for planar and complex wrist motions using both novel control strategies. The effect of gravity was most pronounced when the hand was in the horizontal orientation, resulting in higher extensor forces (p < 0.017) and higher out-of-plane kinematic errors (p < 0.007), as compared to the vertically upward or downward orientations. Muscle forces were also affected by the direction of rotation during circumduction. The peak force of flexor carpi radialis was higher in clockwise circumduction (p = 0.017), while that of flexor carpi ulnaris was higher in anticlockwise circumduction (p = 0.013). Thus, the physiologic wrist simulator accurately replicated cyclic planar and complex motions in cadaveric specimens. Moreover, the dependence of muscle forces on the hand orientation and the direction of circumduction could be vital in the specification of such parameters during wrist rehabilitation.     

Control scheme of two d.o.f. CPM device to suppress the extension of ligament of the elbow

Continuous passive motion (CPM) is an orthopedic treatment or a physiotherapy and has been applied after surgery. After surgery for the injured ulna collateral ligament (UCL) which is a major clinical case in the elbow joint, the reaction force at the hand of the patient increases and may be excessively large due to an increase of the joint stiffness. For this, it will be effective to reduce the excessive reaction force by controlling pro-/supination of forearm. The UCL in the elbow joint is extended due to pro-/supination of forearm, but the excessive extension may aggravate the injury of the UCL. Thus, it is required to suppress both the excessive extension of the UCL and the reaction force. In this paper, a control scheme of CPM device that can suppress both the excessive extension of the UCL and the reaction force is proposed, and its effectiveness is confirmed from the experimental results.     

Development and validation of a 3-D model to predict knee joint loading during dynamic movement

The purpose of this study was to develop a subject-specific 3-D model of the lower extremity to predict neuromuscular control effects on 3-D knee joint loading during movements that can potentially cause injury to the anterior cruciate ligament (ACL) in the knee. The simulation consisted of a forward dynamic 3-D musculoskeletal model of the lower extremity, scaled to represent a specific subject. Inputs of the model were the initial position and velocity of the skeletal elements, and the muscle stimulation patterns. Outputs of the model were movement and ground reaction forces, as well as resultant 3-D forces and moments acting across the knee joint. An optimization method was established to find muscle stimulation patterns that best reproduced the subject's movement and ground reaction forces during a sidestepping task. The optimized model produced movements and forces that were generally within one standard deviation of the measured subject data. Resultant knee joint loading variables extracted from the optimized model were comparable to those reported in the literature. The ability of the model to successfully predict the subject's response to altered initial conditions was quantified and found acceptable for use of the model to investigate the effect of altered neuromuscular control on knee joint loading during sidestepping. Monte Carlo simulations (N = 100,000) using randomly perturbed initial kinematic conditions, based on the subject's variability, resulted in peak anterior force, valgus torque and internal torque values of 378 N, 94 Nm and 71 Nm, respectively, large enough to cause ACL rupture. We conclude that the procedures described in this paper were successful in creating valid simulations of normal movement, and in simulating injuries that are caused by perturbed neuromuscular control.     

Effect of upper and lower extremity control strategies on predicted injury risk during simulated forward falls: a study in healthy young adults

Fall-related wrist fractures are common at any age. We used a seven-link, sagittally symmetric, biomechanical model to test the hypothesis that systematically alterations in the configuration of the body during a forward fall from standing height can significantly influence the impact force on the wrists. Movement of each joint was accomplished by a pair of agonist and antagonist joint muscle torque actuators with assigned torque-angle, torque-velocity, and neuromuscular latency properties. Proportional-derivative joint controllers were used to achieve desired target body segment configurations in the pre- andor postground contact phases of the fall. Outcome measures included wrist impact forces and whole-body kinetic energy at impact in the best, and worst, case impact injury risk scenarios. The results showed that peak wrist impact force ranged from less than 1 kN to more than 2.5 kN, reflecting a fourfold difference in whole-body kinetic energy at impact (from less than 40 J to more than 160 J) over the range of precontact hip and knee joint angles used at impact. A reduction in the whole-body kinetic energy at impact was primarily associated with increasing negative work associated with hip flexion. Altering upper extremity configuration prior to impact significantly reduced the peak wrist impact force by up to 58% (from 919 N to 2212 N). Increased peak wrist impact forces associated greater shoulder flexion and less elbow flexion. Increasing postcontact arm retraction can reduce the peak wrist impact force by 28% (from 1491 N to 1078 N), but postcontact hip and knee rotations had a relatively small effect on the peak wrist impact force (8% reduction; from 1411 N to 1303 N). In summary, the choice of the joint control strategy during a forward fall can significantly affect the risk of wrist injury. The most effective strategy was to increase the negative work during hip flexion in order to dissipate kinetic energy thereby reducing the loss in potential energy prior to first impact. Extended hip or elbow configurations should be avoided in order to reduce forearm impact forces.     

A single-spring model predicts the majority of variance in impact force during a fall onto the outstretched hand

The objective of this study was to validate a single-spring model in predicting measured impact forces during an outstretched arm falling scenario. Using an integrated force plate, impact forces were assessed from 10 young adults (5 males; 5 females), falling from planted knees onto outstretched arms, from a random order of drop heights: 3, 5, 7, 10, 15, 20, and 25 cm. A single-spring model incorporating body mass, drop height plus the estimated linear stiffness of the upper extremity (hand, wrist and arm) was used to predict impact force on the hand. We used an analysis of variance linearity test to test the validity of using a linear stiffness coefficient in the model. We used linear regression to assess variance (R²) in experimental impact force predicted by the single-spring model. We derived optimum linear stiffness coefficients for male, female and sex-combined. Our results indicated that the association between experimental and predicted impact forces was linear (P < 0.05). Explain variance in experimental impact force was R² = 0.82 for sex-combined, R² = 0.88 for males and R² = 0.84 for females. Optimum stiffness coefficients were 7436 N/m for sex-combined, 8989 N/m for males and 4527 N/m for females. In conclusion, a linear spring coefficient used in the single-spring model proved valid for predicting impact forces from fall heights up to 25 cm. Results also suggest the use of sex-specific spring coefficients when estimating impact force using the single-spring model. This model may improve impact force to bone strength ratios (factor-of-risk) and prediction of forearm and wrist fracture.     

Forces in anterior cruciate ligament during simulated weight-bearing flexion with anterior and internal rotational tibial load

This study determined in-vitro anterior cruciate ligament (ACL) force patterns and investigated the effect of external tibial loads on the ACL force patterns during simulated weight-bearing knee flexions. Nine human cadaveric knee specimens were mounted on a dynamic knee simulator, and weight-bearing knee flexions with a 100N of ground reaction force were simulated; while a robotic/universal force sensor (UFS) system was used to provide external tibial loads during the movement. Three external tibial loading conditions were simulated, including no external tibial load (termed BW only), a 50N anterior tibial force (ATF), and a 5Nm internal rotation tibial torque (ITT). The tibial and femoral kinematics was measured with an ultrasonic motion capture system. These movement paths were then accurately reproduced on a robotic testing system, and the in-situ force in the ACL was determined via the principle of superposition. The results showed that the ATF significantly increased the in-situ ACL force by up to 60% during 0-55 degrees of flexion, while the ITT did not. The magnitude of ACL forces decreased with increasing flexion angle for all loading conditions. The tibial anterior translation was not affected by the application of ATF, whereas the tibial internal rotation was significantly increased by the application of ITT. These data indicate that, in a weight-bearing knee flexion, ACL provides substantial resistance to the externally applied ATF but not to the ITT.     

Prediction of fluid forces acting on a hand model in unsteady flow conditions

The aim of this study was to develop a method to predict fluid forces acting on the human hand in unsteady flow swimming conditions. A mechanical system consisting of a pulley and chain mechanism and load cell was constructed to rotate a hand model in fluid flows. To measure the angular displacement of the hand model a potentiometer was attached to the axis of the rotation. The hand model was then fixed at various angles about the longitudinal axis of the hand model and rotated at different flow velocities in a swimming flume for 258 different trials to approximate a swimmer's stroke in unsteady flow conditions. Pressures were taken from 12 transducers embedded in the hand model at a sampling frequency of 200Hz. The resultant fluid force acting on the hand model was then determined on the basis of the kinetic and kinematic data taken from the mechanical system at the frequency of 200Hz. A stepwise regression analysis was applied to acquire higher order polynomial equations that predict the fluid force acting on the accelerating hand model from the 12 pressure values. The root mean square (RMS) difference between the resultant fluid force measured and that predicted from the single best-fit polynomial equation across all trials was 5N. The method developed in the present study accurately predicted the fluid forces acting on the hand model.     

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.     

A digital database of wrist bone anatomy and carpal kinematics

The skeletal wrist consists of eight small, intricately shaped carpal bones. The motion of these bones is complex, occurs in three dimensions, and remains incompletely defined. Our previous efforts have been focused on determining the in vivo three-dimensional (3-D) kinematics of the normal and abnormal carpus. In so doing we have developed an extensive database of carpal bone anatomy and kinematics from a large number of healthy subjects. The purpose of this paper is to describe that database and to make it available to other researchers. CT volume images of both wrists from 30 healthy volunteers (15 males and 15 females) were acquired in multiple wrist positions throughout the normal range of wrist motion. The outer cortical surfaces of the carpal bones, radius and ulna, and proximal metacarpals were segmented and the 3-D motion of each bone was calculated for each wrist position. The database was constructed to include high-resolution surface models, measures of bone volume and shape, and the 3-D kinematics of each segmented bone. The database does not include soft tissues of the wrist. While there are numerous digital anatomical databases, this one is unique in that it includes a large number of subjects and it contains in vivo kinematic data as well as the bony anatomy.     

Three-dimensional model to predict muscle forces and their relation to motor variances in reaching arm movements

A three-dimensional (3-D) arm movement model is presented to simulate kinematic properties and muscle forces in reaching arm movements. Healthy subjects performed reaching movements repetitively either with or without a load in the hand. Joint coordinates were measured. Muscle moment arms, 3-D angular acceleration, and moment of inertias of arm segments were calculated to determine 3-D joint torques. Variances of hand position, arm configuration, and muscle activities were calculated. Ratios of movement variances observed in the two conditions (load versus without load) showed no differences for hand position and arm configuration variances. Virtual muscle force variances for all muscles except deltoid posterior and EMG variances for four muscles increased significantly by moving with the load. The greatly increased variances in muscle activity did not imply equally high increments in kinematic variances. We conclude that enhanced muscle cooperation through synergies helps to stabilize movement at the kinematic level when a load is added.     

The effect of static muscle forces on the fracture strength of the intact distal radius in vitro in response to simulated forward fall impacts

The distal radius fracture (DRF) is a particularly dominant injury of the wrist, commonly resulting from a forward fall on an outstretched hand. In an attempt to reduce the prevalence, costs, and potential long-term pain/deformities associated with this injury, in vivo and in vitro investigations have sought to classify the kinematics and kinetics of DRFs. In vivo forward fall work has identified a preparatory muscle contraction that occurs in the upper extremity prior to peak impact force. The present investigation constitutes the first attempt to systematically determine the effect of static muscle forces on the fracture threshold of the distal radius in vitro. Paired human cadaveric forearm specimens were divided into two groups, one that had no muscle forces applied (i.e., right arms) and the other that had muscle forces applied to ECU, ECRL, FCU and FCR (i.e., left arms), with magnitudes based on peak muscle forces and in vivo lower bound forward fall activation patterns. The specimens were secured in a custom-built pneumatic impact loading device and subjected to incremental impacts at pre-fracture (25 J) and fracture (150  J) levels. Similar fracture forces (6565 (866) N and 8665 (5133) N), impulses (47 (6) Ns and 57 (30) Ns), and energies (152 (38) J and 144 (45) J) were observed for both groups of specimens (p>0.05). Accordingly, it is suggested that, at the magnitudes presently simulated, muscle forces have little effect on the way the distal radius responds to forward fall initiated impact loading.     

The influence of patellofemoral joint contact geometry on the modeling of three dimensional patellofemoral joint forces

The purpose of this study was to determine the influence of patellofemoral joint contact geometry on the modeling of three-dimensional patellofemoral joint forces. To achieve this goal, patellofemoral joint reaction forces (PFJRFs) that were measured from an in-vitro cadaveric set-up were compared to PFJRFs estimated from a computer model that did not consider patellofemoral joint contact geometry. Ten cadaver knees were used in this study. Each was mounted on a custom jig that was fixed to an Instron frame. Quadriceps muscle loads were accomplished using a pulley system and weights. The force in the patellar ligament was obtained using a buckle transducer. To quantify the magnitude and direction of the PFJRF, a six-axis load cell was incorporated into the femoral fixation system so that a rigid body assumption could be made. PFJRF data were obtained at 0 degrees , 20 degrees , 40 degrees and 60 degrees of knee flexion. Following in vitro testing, SIMM modeling software was used to develop computational models based on the three-dimensional coordinates (Microscribe digitizer) of individual muscle and patellar ligament force vectors obtained from the cadaver knees. The overall magnitude of the PFJRF estimated from the computer generated models closely matched the direct measurements from the in vitro set-up (Pearson's correlation coefficient, R(2)=0.91, p<0.001). Although the computational model accurately estimated the posteriorly directed forces acting on the joint, some discrepancies were noted in the forces acting in the superior and lateral directions. These differences however, were relatively small when expressed as a total of the overall PFJRF magnitude.