Hip abductor muscle volumes are smaller in individuals affected by patellofemoral joint osteoarthritis.

OBJECTIVE: The aims of this study were twofold: firstly, to compare hip abductor muscle volumes in individuals with patellofemoral joint (PFJ) osteoarthritis (PFJ OA) against those of healthy controls; and secondly, to determine whether hip muscle volumes and hip kinematics during walking are related in individuals with PFJ OA and healthy controls. METHODS: Fifty-one individuals with PFJ OA and thirteen asymptomatic, age-matched healthy controls ≥40 years were recruited. Volumes of the gluteus medius, gluteus minimus and tensor fasciae latae were obtained from magnetic resonance (MR) images. Video motion capture was used to measure three-dimensional hip joint kinematics during overground walking. RESULTS: Significantly smaller gluteus medius (P = 0.017), gluteus minimus (P = 0.001) and tensor fasciae latae (P = 0.027) muscle volumes were observed in PFJ OA participants compared to controls. Weak correlations were observed between smaller gluteus minimus volume and larger hip flexion angle at contralateral heel strike (CHS) (r = -0.279, P = 0.038) as well as between smaller gluteus minimus volume and increased hip adduction angle at CHS (r = -0.286, P = 0.046). CONCLUSION: Reduced hip abductor muscle volume is a feature of PFJ OA and is associated with increased hip flexion and adduction angles during the late stance phase of walking for PFJ OA participants and healthy controls.

Differences in in vivo muscle fascicle and tendinous tissue behavior between the ankle plantarflexors during running.

The primary human ankle plantarflexors, soleus (SO), medial gastrocnemius (MG), and lateral gastrocnemius (LG) are typically regarded as synergists and play a critical role in running. However, due to differences in muscle-tendon architecture and joint articulation, the muscle fascicles and tendinous tissue of the plantarflexors may exhibit differences in their behavior and interactions during running. We combined in vivo dynamic ultrasound measurements with inverse dynamics analyses to identify and explain differences in muscle fascicle, muscle-tendon unit, and tendinous tissue behavior of the primary ankle plantarflexors across a range of steady-state running speeds. Consistent with their role as a force generator, the muscle fascicles of the uniarticular SO shortened less rapidly than the fascicles of the MG during early stance. Furthermore, the MG and LG exhibited delays in tendon recoil during the stance phase, reflecting their ability to transfer power and work between the knee and ankle via tendon stretch and storage of elastic strain energy. Our findings add to the growing body of evidence surrounding the distinct mechanistic functions of uni- and biarticular muscles during dynamic movements.

Exercise, education, manual-therapy and taping compared to education for patellofemoral osteoarthritis: a blinded, randomised clinical trial.

OBJECTIVE: Patellofemoral joint osteoarthritis (PFJ OA) contributes considerably to knee OA symptoms. This study aimed to determine the efficacy of a PFJ-targeted exercise, education manual-therapy and taping program compared to OA education alone, in participants with PFJ OA. METHODS: A randomised, participant-blinded and assessor-blinded clinical trial was conducted in primary-care physiotherapy. 92 people aged ≥40 years with symptomatic and radiographic PFJ OA participated. Physiotherapists delivered the PFJ-targeted exercise, education, manual-therapy and taping program, or the OA-education (control condition) in eight sessions over 12 weeks. Primary outcomes at 3-month (primary) and 9-month follow-up: (1) patient-perceived global rating of change (2) pain visual analogue scale (VAS) (100 mm); and (3) activities of daily living (ADL) subscale of the Knee injury and Osteoarthritis Outcome Score (KOOS). RESULTS: 81 people (88%) completed the 3-month follow-up and data analysed on an intention-to-treat basis. Between-group baseline similarity for participant characteristics was observed. The exercise, education, manual-therapy and taping program resulted in more people reporting much improvement (20/44) than the OA-education group (5/48) (number needed to treat 3 (95% confidence interval (CI) 2 to 5)) and greater pain reduction (mean difference: -15.2 mm, 95% CI -27.0 to -3.4). No significant effects on ADL were observed (5.8; 95% CI -0.6 to 12.1). At 9 months there were no significant effects for self-report of improvement, pain (-10.5 mm, 95% CI -22.7 to 1.8) or ADL (3.0, 95% CI -3.7 to 9.7). CONCLUSION: Exercise, education, manual-therapy and taping can be recommended to improve short-term patient rating of change and pain severity. However over 9-months, both options were equivalent. TRIAL REGISTRATION: Australian New Zealand Clinical Trials Registry (ACTRN12608000288325): https://www.anzctr.org.au/Trial/Registration/TrialReview.aspx?id=82878.

A non-invasive, 3D, dynamic MRI method for measuring muscle moment arms in vivo: demonstration in the human ankle joint and Achilles tendon.

Muscle moment arms are used widely in biomechanical analyses. Often they are measured in 2D or at a series of static joint positions. In the present study we demonstrate a simple MRI method for measuring muscle moment arms dynamically in 3D from a single range-of-motion cycle. We demonstrate this method in the Achilles tendon for comparison with other methods, and validate the method using a custom apparatus. The method involves registration of high-resolution joint geometry from MRI scans of the stationary joint with low-resolution geometries from ultrafast MRI scans of the slowly moving joint. Tibio-talar helical axes and 3D Achilles tendon moment arms were calculated throughout passive rotation for 10 adult subjects, and compared with recently published data. A simple validation was conducted by comparing MRI measurements with direct physical measurements made on a phantom. The moment arms measured using our method and those of others were similar and there was good agreement between physical measurements (mean 41.0mm) and MRI measurements (mean 39.5mm) made on the phantom. This new method can accurately measure muscle moment arms from a single range-of-motion cycle without the need to control rotation rate or gate the scanning. Supplementary data includes custom software to assist implementation.

The effects of a varus unloader brace for lateral tibiofemoral osteoarthritis and valgus malalignment after anterior cruciate ligament reconstruction: a single case study.

We investigated the immediate effects of a varus knee brace on knee symptoms and knee-joint biomechanics in an individual with predominant lateral tibiofemoral joint osteoarthritis (TFJOA) and valgus malalignment after anterior cruciate ligament (ACL) reconstruction. A varus unloader brace was prescribed to a 48-year-old male with predominant lateral radiographic and symptomatic TFJOA and valgus malalignment eight-years following ACL reconstruction. During a step-down task, the participant rated knee pain, task-difficulty, knee-stability and knee-confidence on four separate visual analogue scales. Quantitative gait analysis was conducted during self-selected walking trials under three test conditions in a randomized order: (i) no brace; (ii) brace without frontal plane adjustment (no varus re-alignment); and (ii) brace with frontal plane adjustment (varus re-alignment). Post-processing of gait data involved calculation of knee kinematics and net joint moments for the reconstructed limb. The participant reported improved pain (3%), task difficulty (41%), stability (46%) and confidence (49%) when performing the step-down task with the brace. The varus brace resulted in immediate reductions in knee abduction angle (24%) and internal rotation angle (56%), and increased knee adduction moment (18%). These findings provide preliminary evidence for potentially beneficial effects of bracing on knee-symptoms and biomechanics in individuals with lateral TFJOA after reconstruction.

Altered hip muscle forces during gait in people with patellofemoral osteoarthritis.

OBJECTIVES: The study aimed to (1) assess whether higher vasti (VASTI), gluteus medius (GMED), gluteus maximus (GMAX) and gluteus minimus (GMIN) forces are associated with participant characteristics (lower age, male gender) and clinical characteristics (lower radiographic disease severity, lower symptom severity and higher walking speed); and (2) determine whether hip and knee muscle forces are lower in people with patellofemoral joint (PFJ) osteoarthritis (OA) compared to those without PFJ OA. DESIGN: Sixty participants with PFJ OA and 18 (asymptomatic, no radiographic OA) controls ≥40 years were recruited from the community or via referrals. A three-dimensional musculoskeletal model was used in conjunction with optimisation theory to calculate lower-limb muscle forces during walking. Associations of peak muscle forces with participant and clinical characteristics were conducted using Pearson's r or independent t-tests and between-group comparisons of mean peak muscle forces performed with walking speed as a covariate. RESULTS: Peak muscle forces were not significantly associated with participant, symptomatic or radiographic-specific characteristics. Faster walking speed was associated with higher VASTI muscle force in the PFJ OA (r = 0.495; P < 0.001) and control groups (r = 0.727; P = 0.001) and higher GMAX muscle force (r = 0.593; P = 0.009) in the control group only. Individuals with PFJ OA (N = 60) walked with lower GMED and GMIN muscle forces than controls (N = 18): GMED, mean difference 0.15 [95% confidence interval (CI): 0.01 to 0.29] body weight (BW); GMIN, 0.03 [0.01 to 0.06] BW. No between-group differences were observed in VASTI or GMAX muscle force: VASTI, 0.10 [-0.11 to 0.31] BW; GMAX, 0.01 [-0.11 to 0.09] BW. CONCLUSION: Individuals with PFJ OA ambulate with lower peak hip abductor muscle forces than their healthy counterparts.

Quadriceps volumes are reduced in people with patellofemoral joint osteoarthritis.

OBJECTIVES: This study aimed to (1) compare the volumes of vastus medialis (VM), vastus lateralis (VL), vastus intermedius and rectus femoris and the ratio of VM/VL volumes between asymptomatic controls and patellofemoral joint osteoarthritis (PFJ OA) participants; and (2) assess the relationships between cross-sectional area (CSA) and volumes of the VM and VL in individuals with and without PFJ OA. METHODS: Twenty-two participants with PFJ OA and 11 controls aged ≥ 40 years were recruited from the community and practitioner referrals. Muscle volumes of individual quadriceps components were measured from thigh magnetic resonance (MR) images. The CSA of the VM and lateralis were measured at 10 equally distributed levels (femoral condyles to lesser femoral trochanter). RESULTS: PFJ OA individuals had smaller normalized VM (mean difference 0.90 cm(3) · kg(-1), α = 0.011), VL (1.50 cm(3) · kg(-1), α = 0.012) and rectus femoris (0.71 cm(3) · kg(-1), α = 0.009) volumes than controls. No differences in the VM/VL ratio were observed. The CSA at the third level (controls) and fourth level (PFJ OA) above the femoral condyles best predicted VM volume, whereas the VL volume was best predicted by the CSA at the seventh level (controls) and sixth level (PFJ OA) above the femoral condyles. CONCLUSION: Reduced quadriceps muscle volume was a feature of PFJ OA. Muscle volume could be predicted from CSA measurements at specific levels in PFJ OA patients and controls.

Future trends in the use of X-ray fluoroscopy for the measurement and modelling of joint motion.

Knowledge of three-dimensional skeletal kinematics during functional activities such as walking, is required for accurate modelling of joint motion and loading, and is important in identifying the effects of injury and disease. For example, accurate measurement of joint kinematics is essential in understanding the pathogenesis of osteoarthritis and its symptoms and for developing strategies to alleviate joint pain. Bi-plane X-ray fluoroscopy has the capacity to accurately and non-invasively measure human joint motion in vivo. Joint kinematics obtained using bi-plane X-ray fluoroscopy will aid in the development of more complex musculoskeletal models, which may be used to assess joint function and disease and plan surgical interventions and post-operative rehabilitation strategies. At present, however, commercial C-arm systems constrain the motion of the subject within the imaging field of view, thus precluding recording of motions such as overground gait. These fluoroscopy systems also operate at low frame rates and therefore cannot accurately capture high-speed joint motion during tasks such as running and throwing. In the future, bi-plane fluoroscopy systems may include computer-controlled tracking for the measurement of joint kinematics over entire cycles of overground gait without constraining motion of the subject. High-speed cameras will facilitate measurement of high-impulse joint motions, and computationally efficient pose-estimation software may provide a fast and fully automated process for quantification of natural joint motion.

Integrating modelling, motion capture and x-ray fluoroscopy to investigate patellofemoral function during dynamic activity.

Accurate measurement of knee-joint kinematics is critical for understanding the biomechanical function of the knee in vivo. Measurements of the relative movements of the bones at the knee are often used in inverse dynamics analyses to estimate the net muscle torques exerted about the joint, and as inputs to finite-element models to accurately assess joint contact. The fine joint translations that contribute to patterns of joint stress are impossible to measure accurately using traditional video-based motion capture techniques. Sub-millimetre changes in joint translation can mean the difference between contact and no contact of the cartilage tissue, leading to incorrect predictions of joint loading. This paper describes the use of low-dose X-ray fluoroscopy, an in vivo dynamic imaging modality that is finding increasing application in human joint motion measurement. Specifically, we describe a framework that integrates traditional motion capture, X-ray fluoroscopy and anatomically-based finite-element modelling for the purpose of assessing joint function during dynamic activity. We illustrate our methodology by applying it to study patellofemoral joint function, wherein the relative movements of the patella are predicted and the corresponding joint-contact stresses are calculated for a step-up task.

Integrating modelling and experiments to assess dynamic musculoskeletal function in humans.

Magnetic resonance imaging, bi-plane X-ray fluoroscopy and biomechanical modelling are enabling technologies for the non-invasive evaluation of muscle, ligament and joint function during dynamic activity. This paper reviews these various technologies in the context of their application to the study of human movement. We describe how three-dimensional, subject-specific computer models of the muscles, ligaments, cartilage and bones can be developed from high-resolution magnetic resonance images; how X-ray fluoroscopy can be used to measure the relative movements of the bones at a joint in three dimensions with submillimetre accuracy; how complex 3-D dynamic simulations of movement can be performed using new computational methods based on non-linear control theory; and how musculoskeletal forces derived from such simulations can be used as inputs to elaborate finite-element models of a joint to calculate contact stress distributions on a subject-specific basis. A hierarchical modelling approach is highlighted that links rigid-body models of limb segments with detailed finite-element models of the joints. A framework is proposed that integrates subject-specific musculoskeletal computer models with highly accurate in vivo experimental data.

Determination of mechanical loading components of the equine metacarpus from measurements of strain during walking.

REASONS FOR PERFORMING STUDY: The mechanical environment of the distal limb is thought to be involved in the pathogenesis of many injuries, but has not yet been thoroughly described. OBJECTIVES: To determine the forces and moments experienced by the metacarpus in vivo during walking and also to assess the effect of some simplifying assumptions used in analysis. METHODS: Strains from 8 gauges adhered to the left metacarpus of one horse were recorded in vivo during walking. Two different models - one based upon the mechanical theory of beams and shafts and, the other, based upon a finite element analysis (FEA) - were used to determine the external loads applied at the ends of the bone. RESULTS: Five orthogonal force and moment components were resolved by the analysis. In addition, 2 orthogonal bending moments were calculated near mid-shaft. Axial force was found to be the major loading component and displayed a bi-modal pattern during the stance phase of the stride. The shaft model of the bone showed good agreement with the FEA model, despite making many simplifying assumptions. CONCLUSIONS: A 3-dimensional loading scenario was observed in the metacarpus, with axial force being the major component. POTENTIAL RELEVANCE: These results provide an opportunity to validate mathematical (computer) models of the limb. The data may also assist in the formulation of hypotheses regarding the pathogenesis of injuries to the distal limb.

Dynamic optimization of human walking.

A three-dimensional, neuromusculoskeletal model of the body was combined with dynamic optimization theory to simulate normal walking on level ground. The body was modeled as a 23 degree-of-freedom mechanical linkage, actuated by 54 muscles. The dynamic optimization problem was to calculate the muscle excitation histories, muscle forces, and limb motions subject to minimum metabolic energy expenditure per unit distance traveled. Muscle metabolic energy was calculated by slimming five terms: the basal or resting heat, activation heat, maintenance heat, shortening heat, and the mechanical work done by all the muscles in the model. The gait cycle was assumed to be symmetric; that is, the muscle excitations for the right and left legs and the initial and terminal states in the model were assumed to be equal. Importantly, a tracking problem was not solved. Rather only a set of terminal constraints was placed on the states of the model to enforce repeatability of the gait cycle. Quantitative comparisons of the model predictions with patterns of body-segmental displacements, ground-reaction forces, and muscle activations obtained from experiment show that the simulation reproduces the salient features of normal gait. The simulation results suggest that minimum metabolic energy per unit distance traveled is a valid measure of walking performance.

Computer modeling and simulation of human movement.

Recent interest in using modeling and simulation to study movement is driven by the belief that this approach can provide insight into how the nervous system and muscles interact to produce coordinated motion of the body parts. With the computational resources available today, large-scale models of the body can be used to produce realistic simulations of movement that are an order of magnitude more complex than those produced just 10 years ago. This chapter reviews how the structure of the neuromusculoskeletal system is commonly represented in a multijoint model of movement, how modeling may be combined with optimization theory to simulate the dynamics of a motor task, and how model output can be analyzed to describe and explain muscle function. Some results obtained from simulations of jumping, pedaling, and walking are also reviewed to illustrate the approach.

Musculoskeletal model of the upper limb based on the visible human male dataset.

A mathematical model of the human upper limb was developed based on high-resolution medical images of the muscles and bones obtained from the Visible Human Male (VHM) project. Three-dimensional surfaces of the muscles and bones were reconstructed from Computed Tomography (CT) images and Color Cryosection images obtained from the VHM cadaver. Thirteen degrees of freedom were used to describe the orientations of seven bones in the model: clavicle, scapula, humerus, radius, ulna, carpal bones, and hand. All of the major articulations from the shoulder girdle down to the wrist were included in the model. The model was actuated by 42 muscle bundles, which represented the actions of 26 muscle groups in the upper limb. The paths of the muscles were modeled using a new approach called the Obstacle-set Method [33]. The calculated paths of the muscles were verified by comparing the muscle moment arms computed in the model with the results of anatomical studies reported in the literature. In-vivo measurements of maximum isometric muscle torques developed at the shoulder, elbow, and wrist were also used to estimate the architectural properties of each musculotendon actuator in the model. The entire musculoskeletal model can be reconstructed using the data given in this paper, along with information presented in a companion paper which defines the kinematic structure of the model [26].

Static and dynamic optimization solutions for gait are practically equivalent.

The proposition that dynamic optimization provides better estimates of muscle forces during gait than static optimization is examined by comparing a dynamic solution with two static solutions. A 23-degree-of-freedom musculoskeletal model actuated by 54 Hill-type musculotendon units was used to simulate one cycle of normal gait. The dynamic problem was to find the muscle excitations which minimized metabolic energy per unit distance traveled, and which produced a repeatable gait cycle. In the dynamic problem, activation dynamics was described by a first-order differential equation. The joint moments predicted by the dynamic solution were used as input to the static problems. In each static problem, the problem was to find the muscle activations which minimized the sum of muscle activations squared, and which generated the joint moments input from the dynamic solution. In the first static problem, muscles were treated as ideal force generators; in the second, they were constrained by their force-length-velocity properties; and in both, activation dynamics was neglected. In terms of predicted muscle forces and joint contact forces, the dynamic and static solutions were remarkably similar. Also, activation dynamics and the force-length-velocity properties of muscle had little influence on the static solutions. Thus, for normal gait, if one can accurately solve the inverse dynamics problem and if one seeks only to estimate muscle forces, the use of dynamic optimization rather than static optimization is currently not justified. Scenarios in which the use of dynamic optimization is justified are suggested.

Dynamic simulation of human movement using large-scale models of the body.

A three-dimensional model of the body was used to simulate two different motor tasks: vertical jumping and normal walking on level ground. The pattern of muscle excitations, body motions, and ground-reaction forces for each task were calculated using dynamic optimization theory. For jumping, the performance criterion was to maximize the height reached by the center of mass of the body; for walking, the measure of performance was metabolic energy consumed per meter walked. Quantitative comparisons of the simulation results with experimental data obtained from people indicate that the model reproduces the salient features of maximum-height jumping and normal walking on the level. Analyses of the model solutions will allow detailed explanations to be given about the actions of specific muscles during each of these tasks.

Determinants of cruciate-ligament loading during rehabilitation exercise.

OBJECTIVES: To predict and explain the pattern of cruciate-ligament loading during squatting exercises; to determine the effect of hamstrings co-contraction on anterior cruciate ligament (ACL) load during squatting; and to determine the effect of the weightbearing force on ACL load during squatting. DESIGN: Mathematical modeling of the human musculoskeletal system. BACKGROUND: Squatting is a commonly prescribed exercise for strengthening the muscles of the thigh following ACL reconstruction. Although the forces induced in the ACL are purported to be low, no experimental data are available to corroborate this claim. The reason is that measurements of knee-ligament forces are difficult to obtain in vivo. METHODS: The human body was modeled as a four-segment, six-degrees of freedom, planar linkage. The hip, ankle and toes were each modeled as a hinge joint. The relative displacements of the femur, tibia and patella were calculated using a three-degrees of freedom, sagittal-plane model of the knee. Eleven elastic were used to describe the geometric and mechanical properties of the knee ligaments. The model was actuated by 22 musculotendinous units. Optimization theory was used to calculate the forces developed in the muscles and the forces transmitted to the knee ligaments during squatting. RESULTS: The model ACL was loaded from full extension to 10 degrees of knee flexion during squatting; the model PCL was loaded at knee-flexion angles greater than 10 degrees. The pattern of cruciate-ligament loading is determined by the shapes of the articulating surfaces of the bones and by the changing orientation of the hamstrings muscles at the knee. Hamstrings co-contraction is the major determinant of ACL loading during squatting exercises; the weightbearing force has a relatively small effect on the force induced in the ACL. CONCLUSION: The calculations support the contention that squatting is a relatively safe exercise for strengthening the muscles of the thigh following reconstruction of the ACL. RELEVANCE: Knowledge of the forces borne by the knee ligaments is important for designing exercise regimens subsequent to ligament injury and repair. The quadriceps and hamstrings muscles may be strengthened without loading a newly reconstructed ACL by performing squats with the knee flexed to 10 degrees and greater.

Dependence of cruciate-ligament loading on muscle forces and external load.

A sagittal-plane model of the knee is used to predict and explain the relationships between the forces developed by the muscles, the external loads applied to the leg, and the forces induced in the cruciate ligaments during isometric exercises. The geometry of the model bones is adapted from cadaver data. Eleven elastic elements describe the geometric and mechanical properties of the cruciate ligaments, the collateral ligaments, and the posterior capsule. The model is actuated by 11 musculotendinous units, each unit represented as a three-element muscle in series with tendon. For isolated contractions of the quadriceps, ACL force increases as quadriceps force increases for all flexion angles between 0 and 80 degrees; the ACL is unloaded at flexion angles greater than 80 degrees. When quadriceps force is held constant, ACL force decreases monotonically as knee-flexion angle increases. The relationship between ACL force, quadriceps force, and knee-flexion angle is explained by the geometry of the knee-extensor mechanism and by the changing orientation of the ACL in the sagittal plane. For isolated contractions of the hamstrings, PCL force increases as hamstrings force increases for all flexion angles greater than 10 degrees; the PCL is unloaded at flexion angles less than 10 degrees. When hamstrings force is held constant, PCL force increases monotonically with increasing knee flexion. The relationship between PCL force, hamstrings force, and knee-flexion angle is explained by the geometry of the hamstrings and by the changing orientation of the PCL in the sagittal plane. At nearly all knee-flexion angles, hamstrings co-contraction is an effective means of reducing ACL force. Hamstrings co-contraction cannot protect the ACL near full extension of the knee because these muscles meet the tibia at small angles near full extension, and so cannot apply a sufficiently large posterior shear force to the leg. Moving the restraining force closer to the knee-flexion axis decreases ACL force; varying the orientation of the restraining force has only a small effect on cruciate-ligament loading.

A musculoskeletal model of the knee for evaluating ligament forces during isometric contractions.

A model of the knee in the sagittal plane was developed to study the forces in the ligaments induced by isometric contractions of the extensor and flexor muscles. The geometry of the distal femur was obtained from cadaver data. The tibial plateau and patellar facet were modeled as flat surfaces. Eleven elastic elements were used to describe the mechanical behavior of the anterior and posterior cruciate ligaments (ACL and PCL), the medial and lateral collateral ligaments (MCL and LCL), and the posterior capsule. The model knee was actuated by 11 musculotendinous units, each muscle represented by a Hill-type contractile element, a series-elastic element, and a parallel-elastic element. Tendon was assumed to be elastic. The response of the model to anterior-posterior drawer suggests that the geometrical and mechanical properties of the model ligaments approximate the behavior of real ligaments in the intact knee. Calculations for a simulated quadriceps leg raise indicate further that the two-dimensional model reproduces the response of the three-dimensional knee under similar conditions of loading and constraint. During maximum isometric contractions of the quadriceps, the model ACL is loaded from full extension to 80 degrees C of flexion; the model PCL is loaded at 70 degrees of flexion and greater. For maximum isometric extension, ACL forces in the range 0-20 degrees of flexion depend most heavily upon the force-length properties of the quadriceps. At flexion angles greater than 20 degrees, cruciate ligament forces are determined by the geometry of the articulating surfaces of the bones. During isolated contractions of the hamstrings and gastrocnemius muscles, the model ACL is loaded from full extension to 10 degrees of flexion; the model PCL is loaded at all flexion angles greater than 10 degrees. Isolated contractions of the flexor muscles cannot unload the ACL near full extension, as the behavior of the ACL in this region is governed by the shapes of the bones. At 10 degrees of flexion or greater, the overall pattern of PCL force is explained by the force length properties of the hamstrings and by the geometrical arrangement of the flexor muscles about the knee.