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

Biomechanical Study of a Tricompartmental Unloader Brace for Patellofemoral or Multicompartment Knee Osteoarthritis

Objective: Off-loader knee braces have traditionally focused on redistributing loads away from either the medial or lateral tibiofemoral (TF) compartments. In this article, we study the potential of a novel "tricompartment unloader" (TCU) knee brace intended to simultaneously unload both the patellofemoral (PF) and TF joints during knee flexion. Three different models of the TCU brace are evaluated for their potential to unload the knee joint. Methods: A sagittal plane model of the knee was used to compute PF and TF contact forces, patellar and quadriceps tendon forces, and forces in the anterior and posterior cruciate ligaments during a deep knee bend (DKB) test using motion analysis data from eight participants. Forces were computed for the observed (no brace) and simulated braced conditions. A sensitivity and validity analysis was conducted to determine the valid output range for the model, and Statistical Parameter Mapping was used to quantify the effectual region of the different TCU brace models. Results: PF and TF joint force calculations were valid between ~0 and 100 degrees of flexion. All three simulated brace models significantly (p < 0.001) reduced predicted knee joint loads (by 30-50%) across all structures, at knee flexion angles >~30 degrees during DKB. Conclusions: The TCU brace is predicted to reduce PF and TF knee joint contact loads during weight-bearing activity requiring knee flexion angles between 30 and 100 degrees; this effect may be clinically beneficial for pain reduction or rehabilitation from common knee injuries or joint disorders. Future work is needed to assess the range of possible clinical and prophylactic benefits of the TCU brace.

The effective quadriceps and patellar tendon moment arms relative to the tibiofemoral finite helical axis

The moment arm is a crucial parameter for understanding musculoskeletal dynamics as it defines how linear muscle force is transformed into a moment. Yet, for the quadriceps tendon this parameter cannot be directly calculated, as the patella creates a dynamic fulcrum. Thus, the effective quadriceps moment arm (EQma) was developed to define the quadriceps force to tibial moment relationship. In vivo data in regards to the EQma are lacking and the critical question of how patellofemoral kinematics may influence the EQma remains unresolved. Therefore, the purpose of this study was to quantify the in vivo EQma during a knee extension exercise in asymptomatic controls and to correlate the EQma with sagittal plane patellofemoral kinematics. While subjects (30F/10M, 26.5±5.6 years, 167.5±10.2 cm, 62.6±10.7 kg) cyclically flexed-extended their knees within the MR scanner, dynamic cine-phase contrast and cine MR images were acquired. From these data, patellofemoral kinematics, the ratio of the patellar tendon to quadriceps force, the patellar tendon moment arm, and the EQma were quantified. The EQma trended upwards (32.9-45.5 mm (females) and 31.5-47.1 mm (males)) as the knee angle decreased (50-10°). The quadriceps had a mechanical advantage (ratio of patellar to quadriceps tendon forces >1.0) for knee angles ≤20°. The EQma did not correlate with sagittal plane patellofemoral kinematics. As this is the first study to characterize the EQma in vivo during dynamic volitional activity, in a large group of asymptomatic controls, it can serve as a foundation for future knee joint models and to explore how pathological conditions affect the EQma.

Relative contributions of design, alignment, and loading variability in knee replacement mechanics

Substantial variation in total knee replacement (TKR) outcomes exists within the patient population. Some of this variability is due to differences in the design of the implanted components and variation in surgical alignment, while other variability is due to differences in the applied forces and torques due to anatomic and physiological differences within a patient population. We evaluated the relative contributions of implant design, surgical alignment, and patient-specific loading variability to overall tibiofemoral joint mechanics to provide insight into which measures can be influenced through design and surgical decisions, and which are inherently dependent on variation within the patient population and should be considered in the robustness of the implant design and surgical procedure. Design, surgical, and loading parameters were assessed using probabilistic finite element methods during simulated stance-phase gait and squat activities. Patient-specific loading was found to be the primary contributor to joint loading and kinematics during low flexion, particularly under conditions of high external loads (for instance, the gait cycle with high internal-external torque), while design and surgical factors, particularly femoral posterior radius and posterior slope of the tibial insert became increasingly important in TKR performance in deeper flexion.

Dynamic in vivo 3-dimensional moment arms of the individual quadriceps components

The purpose of this study was to provide the first in vivo 3-dimensional (3D) measures of knee extensor moment arms, measured during dynamic volitional activity. The hypothesis was that the vastus lateralis (VL) and vastus medialis (VM) have significant off-axis moment arms compared to the central quadriceps components. After obtaining informed consent, three 3D dynamic cine phase contrast (PC) MRI sets (x,y,z velocity and anatomic images) were acquired from 22 subjects during active knee flexion and extension. Using a sagittal-oblique and two coronal-oblique imaging planes, the origins and insertions of each quadriceps muscle were identified and tracked through each time frame by integrating the cine-PC velocity data. The moment arm (MA) and relative moment (RM, defined as the cross product of the tendon line-of-action and a line connecting the line-of-action with the patellar center of mass) were calculated for each quadriceps component. The tendencies of the VM and VL to produce patellar tilt were evenly balanced. Interestingly, the magnitude of RM-P(Spin) for the VM and VL is approximately four times greater than the magnitude of RM-P(Tilt) for the same muscles suggesting that patellar spin may play a more important role in patellofemoral kinematics than previously thought. Thus, a force imbalance that leads to excessive lateral tilt, such as VM weakness in patellofemoral pain syndrome, would produce excessive negative spin (positive spin: superior patellar pole rotates laterally) and to a much greater degree. This would explain the increased negative spin found in recent studies of patellar maltracking. Assessing the contribution of each quadriceps component in three dimensions provides a more complete understanding of muscle functionality.

[Musculoskeletal biomechanics of the knee joint. Principles of preoperative planning for osteotomy and joint replacement]

The long-term clinical outcome of surgical interventions at the knee is dependent upon the quality of the restoration of normal function, together with moderate musculoskeletal loading conditions. In order to achieve this, it is essential to consider biomechanical knowledge during the planning and execution of the procedures. Until now, such knowledge has only been available in books and journal manuscripts and is merely considered during preoperative planning. Its transfer into the specific intraoperative situation is, however, primarily dependent upon the surgeon's skills and understanding. Mathematical models hold the potential to provide the surgeon with detailed, patient-specific information on the in vivo forces, as well as their spatial and temporal distribution. Their application in clinical routine, however, requires a comprehensive validation. Based on a model validated against patient data, it has been shown that - mainly as a result of the action of the muscles - both the tibiofemoral as well as the patellofemoral joints experience substantial mechanical loads even during normal activities of daily living. The calculations further indicate that malalignment at the knee in the frontal plane of more than approximately 4 degrees results in considerably increased forces across the tibiofemoral joint. The actual change in force to a given degree of malalignment might, however, vary greatly between subjects. In order to additionally determine the distribution of the forces in more detail, a sufficiently accurate model of knee joint kinematics is required. In combination with MR-based in vivo imaging techniques, new mathematical models offer the possibility to capture the individual characteristics of knee kinematics and might additionally allow the effect of muscle activity on joint kinematics to be considered. By implementing these technologies in preoperative planning and navigation systems, up-to-date biomechanical knowledge can be made available at the surgeons' fingertips. We propose that optimizing the biomechanical conditions through using these approaches will allow the long-term function of the replaced joint to be significantly enhanced.

Probabilistic Modeling of Knee Muscle Moment Arms: Effects of Methods, Origin–Insertion, and Kinematic Variability

In musculoskeletal modeling, reliable estimates of muscle moment arms are an important step in accurately predicting muscle forces and joint moments. The degree of agreement between the two common methods of calculating moment arms-tendon excursion (TE) and geometric origin-insertion, is currently unknown for the muscles crossing the knee joint. Further, measured moment arm data are subject to variability in estimation of attachment sites as points from irregular surfaces on the bones, and due to differences in joint kinematics observed in vivo. Thus, the objectives of the present study were to compare moment arms of major muscles crossing the knee joint obtained from TE and geometric methods using a finite element-based lower extremity model, and to quantify the effects of potential muscle origin-insertion and tibiofemoral kinematic variability on the predicted moment arms using probabilistic methods. A semiconstrained, fixed bearing, posterior cruciate-retaining total knee arthroplasty was included due to available in vivo kinematic data. In this study, muscle origin and insertion locations and kinematic variables were represented as normal distributions with standard deviations of 5 mm for origin-insertion locations and up to 1.6 mm and 3.0 degrees for the kinematic parameters. Agreement between the deterministic moment arm calculations from the two methods was excellent for the flexors, while differences in trends and magnitudes were observed for the extensor muscles. Model-predicted deterministic moment arms from both methods agreed reasonably with the experimental values from available literature. The uncertainty in input parameters resulted in substantial variability in predicted moment arms, with the size of 1-99% confidence interval being up to 41.3 and 35.8 mm for the TE and geometric methods, respectively. The sizeable range of moment arm predictions and associated excursions has the potential to affect a muscle's operating range on the force-length curve, thus affecting joint moments. In this study, moment arm predictions were more dependent on muscle origin-insertion locations than the kinematic variables. The important parameters from the TE method were the origin and insertion locations in the sagittal plane, while the insertion location in the sagittal plane was the dominant parameter using the geometric method.

A new model to predict in vivo human knee kinematics under physiological-like muscle activation

Although a number of approaches have attempted to model knee kinematics, rarely have they been validated against in vivo data in a larger subject cohort. Here, we assess the feasibility of four-bar linkage mechanisms in addressing knee kinematics and propose a new approach that is capable of accounting for lengthening characteristics of the ligaments, including possible laxity, as well as the internal/external rotation of the joint. MR scans of the knee joints of 12 healthy volunteers were taken at flexion angles of 0 degrees , 30 degrees and 90 degrees under both passive and active muscle conditions. By reconstructing the surfaces at each position, the accuracy of the four-bar linkage mechanism was assessed for every possible combination of points within each cruciate ligament attachment area. The specific set of parameters that minimized the deviation between the predictions and the in vivo pose was derived, producing a mean error of 1.8 and 2.5 on the medial and 1.7 and 2.4mm on the lateral side at 30 degrees and 90 degrees flexion, respectively, for passive motion, significantly improving on the models that did not consider internal/external rotation. For active flexion, mean medial errors were 3.3 and 4.7 mm and lateral errors 3.4 and 4.8 mm. Using this best parameter set, a generic predictive model was created and assessed against the known in vivo positions, producing a maximum average error of 4.9 mm at 90 degrees flexion. The accuracy achieved shows that kinematics may be accurately reconstructed for subject specific musculoskeletal models to allow a better understanding of the load distribution within the knee.

In vivo changes in the human patellar tendon moment arm length with different modes and intensities of muscle contraction

The purpose of this study was to examine the effect of different muscle contraction modes and intensities on patellar tendon moment arm length (d(PT)). Five men performed isokinetic concentric, eccentric and passive knee extensions at an angular velocity of 60 deg/s and six men performed gradually increasing to maximum effort isometric muscle contractions at 90( composite function) and 20( composite function) of knee flexion. During the tests, lateral X-ray fluoroscopy imaging was used to scan the knee joint. The d(PT) differences between the passive state and the isokinetic concentric and extension were quantified at 15( composite function) intervals of knee joint flexion angle. Furthermore, the changes of the d(PT) as a function of the isometric muscle contraction intensities were determined during the isometric knee extension at 90( composite function) and 20( composite function) of knee joint flexion. Muscle contraction-induced changes in knee joint flexion angle during the isometric muscle contraction were also taken into account for the d(PT) measurements. During the two isometric knee extensions, d(PT) increased from rest to maximum voluntary muscle contraction (MVC) by 14-15%. However, when changes in knee joint flexion angle induced by the muscle contraction were taken into account, d(PT) during MVC increased by 6-26% compared with rest. Moreover, d(PT) increased during concentric and eccentric knee extension by 3-15%, depending on knee flexion angle, compared with passive knee extension. These findings have important implications for estimating musculoskeletal loads using modelling under static and dynamic conditions.

The biomechanical function of the patellar tendon during in-vivo weight-bearing flexion

Few studies have investigated the function of the patellar tendon in-vivo. This study quantified the three-dimensional (3D) kinematics of the patellar tendon during weight-bearing flexion. Eleven subjects were imaged using magnetic resonance (MR). Sagittal plane images were outlined to create a 3D model of the patella, tibia, and femur and included the attachment sites of the patellar tendon. Each attachment site was divided into central, medial, and lateral thirds. Next, the subjects were imaged using fluoroscopy from two orthogonal directions while performing a single-leg lunge. The models and fluoroscopic images were used to reproduce the motion of the patella, tibia, and femur. The apparent elongation, sagittal plane angle, and coronal plane angle of each third of the patellar tendon were measured from the relative motion of the attachment sites. All three portions of the patellar tendon deformed similarly with flexion. The length of the patellar tendon significantly from full extension to 30 degrees . From 30 degrees -110 degrees , no significant change in the length of the patellar tendon was observed. The patellar tendon was oriented anteriorly at flexion angles less than 60 degrees and posteriorly thereafter. From full extension to 60 degrees , the medial orientation of the patellar tendon decreased significantly with flexion. These data may have important implications for anterior cruciate ligament reconstruction using patellar tendon autografts and for the design of rehabilitation regimens for patients of patellar tendon repair.

Human patellar tendon moment arm length: measurement considerations and clinical implications for joint loading assessment

Detailed understanding of the knee joint loading requires the calculation of muscle and joint forces in different conditions. In these applications the patellar tendon moment arm length is essential for the accurate estimation of the tibiofemoral joint loading. In this article, different methods that have been used to determine the patellar tendon moment arm length under in vivo and in vitro conditions are reviewed. The limitations and advantages associated with each of the methods are evaluated together with their applications in the different loading conditions that the musculoskeletal system is subjected to. The three main measurement methods that this review considers are the geometric method, the tendon excursion method and the direct load method. A comparison of relevant quantitative results is presented to asses the impact of the errors of each method on the quantification of the patellar tendon moment arm and the implications for joint loading assessment in clinical applications.

Can the patellar tendon moment arm be predicted from anthropometric measurements?

The purpose of this study was to examine the relations between patellar tendon moment arm length and several relevant anthropometric characteristics of 22 healthy men. The patellar tendon moment arm length was measured using magnetic resonance imaging with two different methods: (1) measurement of patellar tendon moment arm length (d(PT)) with respect to the tibiofemoral contact point (d(PTCP)) and (2) measurement of d(PT) with respect to the intersection point of the anterior and posterior cruciate ligament (d(PTIP)). Pearson correlation coefficients and a stepwise linear regression analysis were used to examine the relationships between the d(PT) and anthropometric measurements taken. Furthermore, a Student's t-test was used to determine differences between the d(PTCP) and d(PTIP) values. Only knee circumference was a significant d(PTCP) predictor (P < 0.05) but with a very low R2 (0.139). None of the anthropometric parameters examined was found to be a significant d(PTIP) predictor. The correlation coefficients ranged from -0.04 to 0.42. The d(PTIP) values were significantly higher (by 0.84-1.89 cm) than the d(PTCP) values (P < 0.05). These results are in disagreement with previous in vitro findings that d(PT) variance may be explained by knee joint size differences. Hence, existing imaging-based methodologies remain necessary for accurate quantification of the patellar tendon moment arm.

Orientation of tendons in vivo with active and passive knee muscles

Tendon orientations in knee models are often taken from cadaver studies. The aim of this study was to investigate the effect of muscle activation on tendon orientation in vivo. Magnetic resonance imaging (MRI) images of the knee were made during relaxation and isometric knee extensions and flexions with 0 degrees , 15 degrees and 30 degrees of knee joint flexion. For six tendons, the orientation angles in sagittal and frontal plane were calculated. In the sagittal plane, muscle activation pulled the patellar tendon to a more vertical orientation and the semitendinosus and sartorius tendons to a more posterior orientation. In the frontal plane, the semitendinosus had a less lateral orientation, the biceps femoris a more medial orientation and the patellar tendon less medial orientation in loaded compared to unloaded conditions. The knee joint angle also influenced the tendon orientations. In the sagittal plane, the patellar tendon had a more anterior orientation near full extension and the biceps femoris had an anterior orientation with 0 degrees and 15 degrees flexions and neutral with 30 degrees flexions. Within 0 degrees to 30 degrees of flexion, the biceps femoris cannot produce a posterior shear force and the anterior angle of the patellar tendon is always larger than the hamstring tendons. Therefore, co-contraction of the hamstring and quadriceps is unlikely to reduce anterior shear forces in knee angles up to 30 degrees . Finally, inter-individual variation in tendon angles was large. This suggests that the amount of shear force produced and the potential to counteract shear forces by co-contraction is subject-specific.

Ligament fibre recruitment and forces for the anterior drawer test at the human ankle joint

Although the anterior drawer test at the ankle joint is commonly used in routine clinical practice, very little is known about the sharing of load between the individual passive structures and the joint response at different flexion angles.A mathematical model of the ankle joint was devised to calculate ligament fibre recruitment and load/displacement curves at different flexion angles. Ligaments were modelled as three-dimensional arrays of fibres, and their orientations at different flexion angles were taken from a previously validated four-bar-linkage model in the sagittal plane. A non-linear stress/strain relationship was assumed for ligament fibres and relevant mechanical parameters were taken from two reports in the literature. Talus and calcaneus were assumed to move as a single rigid body. Antero/distal motion of the talus relative to the tibia was analysed. The ankle joint was found to be stiffer at the two extremes of the flexion range, and the highest laxity was found around the neutral position, confirming previous experimental works. With a first dataset, a 20N anterior force produced 4.3, 5.5, and 4.4mm displacement respectively at 20 degrees plantarflexion, at neutral, and at 20 degrees dorsiflexion. At 10 degrees plantarflexion, for a 6mm displacement, 65% of the external force was supported by the anterior talofibular, 11% by the deep anterior tibiotalar and 5.5% by the tibionavicular ligament. Corresponding results from a second dataset were 1.4, 2.4 and 1.8mm at 40N force, and 80%, 0% and 2% for a 3mm displacement. A component of the contact force supported the remainder.

A model for lever-arm length calculation of the flexor and extensor muscles at the ankle

A sagittal-plane mathematical model of joint mobility, including the mechanical effect of the extensor retinacula, was used to predict the lever arm lengths of the main flexor and extensor muscles of the human ankle over the range of movement. In plantarflexion, the centre of rotation lies posteriorly and distally, maximising the lever arm of the tibialis anterior. The action of the gastrocnemius and soleus is maximised in dorsiflexion. Traditional calculation of ankle joint moment based on a fixed centre of rotation is acceptable only in exercises such as level walking with a limited range of motion about the neutral position. The present model with a moving centre is particularly advised in exercises which take the joint nearer to the extremes of sagittal motion.