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 subject-specific finite element musculoskeletal framework for mechanics analysis of a total knee replacement

Concurrent use of finite element (FE) and musculoskeletal (MS) modeling techniques is capable of considering the interactions between prosthetic mechanics and subject dynamics after a total knee replacement (TKR) surgery is performed. However, it still has not been performed in terms of favorable prediction accuracy and systematic experimental validation. In this study, we presented a methodology to develop a subject-specific FE-MS model of a human right lower extremity including the interactions among the subject-specific MS model, the knee joint model with ligament bundles, and the deformable FE prosthesis model. In order to evaluate its accuracy, the FE-MS model was compared with a traditional hinge-constraint MS model and experimentally verified over a gait cycle. Both models achieved good temporal agreement between the predicted muscle force and the electromyography results, though the magnitude on models is different. A higher predicted accuracy, quantified by the root-mean-square error (RMSE) and the squared Pearson correlation coefficient (r²), was found in the FE-MS model (RMSE = 177.2 N, r² = 0.90) when compared with the MS model (RMSE = 224.1 N, r² = 0.81) on the total tibiofemoral contact force. The contact mechanics, including the contact area, pressure, and stress were synchronously simulated, and the maximum contact pressure, 22.06 MPa, occurred on the medial side of the tibial insert without exceeding the yield strength of the ultra-high-molecular-weight polyethylene, 24.79 MPa. The approach outlines an accurate knee joint biomechanics analysis and provides an effective method of applying individualized prosthesis design and verification in TKR.     

Knee medial and lateral contact forces in a musculoskeletal model with subject-specific contact point trajectories

Contact point (CP) trajectory is a crucial parameter in estimating medial/lateral tibio-femoral contact forces from the musculoskeletal (MSK) models. The objective of the present study was to develop a method to incorporate the subject-specific CP trajectories into the MSK model. Ten healthy subjects performed 45 s treadmill gait trials. The subject-specific CP trajectories were constructed on the tibia and femur as a function of extension-flexion using low-dose bi-plane X-ray images during a quasi-static squat. At each extension-flexion position, the tibia and femur CPs were superimposed in the three directions on the medial side, and in the anterior-posterior and proximal-distal directions on the lateral side to form the five kinematic constraints of the knee joint. The Lagrange multipliers associated to these constraints directly yielded the medial/lateral contact forces. The results from the personalized CP trajectory model were compared against the linear CP trajectory and sphere-on-plane CP trajectory models which were adapted from the commonly used MSK models. Changing the CP trajectory had a remarkable impact on the knee kinematics and changed the medial and lateral contact forces by 1.03 BW and 0.65 BW respectively, in certain subjects. The direction and magnitude of the medial/lateral contact force were highly variable among the subjects and the medial-lateral shift of the CPs alone could not determine the increase/decrease pattern of the contact forces. The suggested kinematic constraints are adaptable to the CP trajectories derived from a variety of joint models and those experimentally measured from the 3D imaging techniques.     

Development and validation of a computational model of the knee joint for the evaluation of surgical treatments for osteoarthritis

A three-dimensional (3D) knee joint computational model was developed and validated to predict knee joint contact forces and pressures for different degrees of malalignment. A 3D computational knee model was created from high-resolution radiological images to emulate passive sagittal rotation (full-extension to 65°-flexion) and weight acceptance. A cadaveric knee mounted on a six-degree-of-freedom robot was subjected to matching boundary and loading conditions. A ligament-tuning process minimised kinematic differences between the robotically loaded cadaver specimen and the finite element (FE) model. The model was validated by measured intra-articular force and pressure measurements. Percent full scale error between FE-predicted and in vitro-measured values in the medial and lateral compartments were 6.67% and 5.94%, respectively, for normalised peak pressure values, and 7.56% and 4.48%, respectively, for normalised force values. The knee model can accurately predict normalised intra-articular pressure and forces for different loading conditions and could be further developed for subject-specific surgical planning.     

Simultaneous prediction of muscle and contact forces in the knee during gait

Musculoskeletal models are currently the primary means for estimating in vivo muscle and contact forces in the knee during gait. These models typically couple a dynamic skeletal model with individual muscle models but rarely include articular contact models due to their high computational cost. This study evaluates a novel method for predicting muscle and contact forces simultaneously in the knee during gait. The method utilizes a 12 degree-of-freedom knee model (femur, tibia, and patella) combining muscle, articular contact, and dynamic skeletal models. Eight static optimization problems were formulated using two cost functions (one based on muscle activations and one based on contact forces) and four constraints sets (each composed of different combinations of inverse dynamic loads). The estimated muscle and contact forces were evaluated using in vivo tibial contact force data collected from a patient with a force-measuring knee implant. When the eight optimization problems were solved with added constraints to match the in vivo contact force measurements, root-mean-square errors in predicted contact forces were less than 10 N. Furthermore, muscle and patellar contact forces predicted by the two cost functions became more similar as more inverse dynamic loads were used as constraints. When the contact force constraints were removed, estimated medial contact forces were similar and lateral contact forces lower in magnitude compared to measured contact forces, with estimated muscle forces being sensitive and estimated patellar contact forces relatively insensitive to the choice of cost function and constraint set. These results suggest that optimization problem formulation coupled with knee model complexity can significantly affect predicted muscle and contact forces in the knee during gait. Further research using a complete lower limb model is needed to assess the importance of this finding to the muscle and contact force estimation process.     

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.     

Ultrasound-based subject-specific parameters improve fascicle behaviour estimation in Hill-type muscle model

The estimation of muscle fascicle behaviour is decisive in a Hill-type model as they are related to muscle force by the force–length–velocity relationship and the tendon force–strain relationship. This study was aimed at investigating the influence of subject-specific tendon force–strain relationship and initial fascicle geometry (IFG) on the estimation of muscle forces and fascicle behaviour during isometric contractions. Ultrasonography was used to estimate the in vivo muscle fascicle behaviour and compare the muscle fascicle length and pennation angle estimated from the Hill-type model. The calibration–prediction process of the electromyography-driven model was performed using generic or subject-specific tendon definition with or without IFG as constraint. The combination of subject-specific tendon definition and IFG led to muscle fascicle behaviour closer to ultrasound data and significant lower forces of the ankle dorsiflexor and plantarflexor muscles compared to the other conditions. Thus, subject-specific ultrasound measurements improve the accuracy of Hill-type models on muscle fascicle behaviour.     

Sensitivity of medial and lateral knee contact force predictions to frontal plane alignment and contact locations

Musculoskeletal models are increasingly used to estimate medial and lateral knee contact forces, which are difficult to measure in vivo. The sensitivity of contact force predictions to modeling parameters is important to the interpretation and implication of results generated by the model. The purpose of this study was to quantify the sensitivity of knee contact force predictions to simultaneous errors in frontal plane knee alignment and contact locations under different dynamic conditions. We scaled a generic musculoskeletal model for N = 23 subjects’ stature and radiographic knee alignment, then perturbed frontal plane alignment and mediolateral contact locations within experimentally-possible ranges of 10° to −10° and 10 to −10 mm, respectively. The sensitivity of first peak, second peak, and mean medial and lateral knee contact forces to knee adduction angle and contact locations was modeled using linear regression. Medial loads increased, and lateral loads decreased, by between 3% and 6% bodyweight for each degree of varus perturbation. Shifting the medial contact point medially increased medial loads and decreased lateral loads by between 1% and 4% bodyweight per millimeter. This study demonstrates that realistic measurement errors of 5 mm (contact distance) or 5° (frontal plane alignment) could result in a combined 50% BW error in subject specific contact force estimates. We also show that model sensitivity varies between subjects as a result of differences in gait dynamics. These results demonstrate that predicted knee joint contact forces should be considered as a range of possible values determined by model uncertainty.     

Change in knee contact force with simulated change in body weight

The relationship between obesity, weight gain and progression of knee osteoarthritis is well supported, suggesting that excessive joint loading may be a mechanism responsible for cartilage deterioration. Examining the influence of weight gain on joint compressive forces is difficult, as both muscles and ground reaction forces can have a significant impact on the forces experienced during gait. While previous studies have examined the relationship between body weight and knee forces, these studies have used models that were not validated using experimental data. Therefore, the objective of this study was to evaluate the relationship between changes in body weight and changes in knee joint contact forces for an individual's gait pattern using musculoskeletal modeling that is validated against known internal compressive forces. Optimal weighting constants were determined for three subjects to generate valid predictions of knee contact forces (KCFs) using in vivo data collection with instrumented total knee arthroplasty. A total of five simulations per walking trial were generated for each subject, from 80% to 120% body weight in 10% increments, resulting in 50 total simulations. The change in peak KCF with respect to body weight was found to be constant and subject-specific, predominantly determined by the peak force during the baseline condition at 100% body weight. This relationship may be further altered by any change in kinematics or body mass distribution that may occur as a result of a change in body weight or exercise program.     

Protocol for constructing subject-specific biomechanical models of knee joint

A robust protocol for building subject-specific biomechanical models of the human knee joint is proposed which uses magnetic resonance imaging, motion analysis and force platform data in conjunction with detailed 3D finite element models. The proposed protocol can be used for determining stress and strain distributions and contact kinetics in different knee elements at different body postures during various physical activities. Several examples are provided to highlight the capabilities and potential applications of the proposed protocol. This includes preliminary results on the role of body weight on the stresses and strains induced in the knee articular cartilages and meniscus during single-leg stance and calculations of the induced stresses and ligament forces during the gait cycle.     

Quantified in vitro tibiofemoral contact during bodyweight back squats

Squats are a common lower extremity task used in strength and conditioning, balance training, and rehabilitation. It is important to understand how slight alterations in lower extremity kinematics during a squat affect the internal joint loading of the knee. This study directly quantified tibiofemoral contact throughout the in vitro simulation of a bodyweight back squat performed two ways: a heel squat (knees in line with toes) and a toe squat (knees anterior to the toes) at peak knee flexion. Three cadaveric right lower extremities were instrumented and positioned into the University of Texas Joint Load Simulator. Kinematics, kinetics, and predicted muscle forces from a 20-year-old athletic male performing the two back squats were used as inputs for the in vitro simulations. The quantified tibiofemoral contact area, peak pressure, net force, and center of pressure location were significantly different between squat types (p > 0.05). Net contact area on the tibial plateau at peak knee flexion was significantly larger in the heel versus toe squat (599 ± 80 mm² vs. 469 ± 125 mm²; p < 0.05). Peak lateral pressure was significantly higher in the heel versus toe squat (2.73 ± 0.54 MPa vs. 0.87 ± 0.56 MPa; p < 0.05). Results suggest the heel squat generates an even load distribution, which is less likely to affect joint degeneration. Future in vitro simulations should quantify the effects lower extremity kinematics, kinetics, and individual muscle forces have on tibiofemoral contact parameters during common athletic tasks.     

A multibody knee model with discrete cartilage prediction of tibio-femoral contact mechanics

Combining musculoskeletal simulations with anatomical joint models capable of predicting cartilage contact mechanics would provide a valuable tool for studying the relationships between muscle force and cartilage loading. As a step towards producing multibody musculoskeletal models that include representation of cartilage tissue mechanics, this research developed a subject-specific multibody knee model that represented the tibia plateau cartilage as discrete rigid bodies that interacted with the femur through deformable contacts. Parameters for the compliant contact law were derived using three methods: (1) simplified Hertzian contact theory, (2) simplified elastic foundation contact theory and (3) parameter optimisation from a finite element (FE) solution. The contact parameters and contact friction were evaluated during a simulated walk in a virtual dynamic knee simulator, and the resulting kinematics were compared with measured in vitro kinematics. The effects on predicted contact pressures and cartilage–bone interface shear forces during the simulated walk were also evaluated. The compliant contact stiffness parameters had a statistically significant effect on predicted contact pressures as well as all tibio-femoral motions except flexion–extension. The contact friction was not statistically significant to contact pressures, but was statistically significant to medial–lateral translation and all rotations except flexion–extension. The magnitude of kinematic differences between model formulations was relatively small, but contact pressure predictions were sensitive to model formulation. The developed multibody knee model was computationally efficient and had a computation time 283 times faster than a FE simulation using the same geometries and boundary conditions.     

Loading of the knee joint during activities of daily living measured in vivo in five subjects

Detailed knowledge about loading of the knee joint is essential for preclinical testing of implants, validation of musculoskeletal models and biomechanical understanding of the knee joint. The contact forces and moments acting on the tibial component were therefore measured in 5 subjects in vivo by an instrumented knee implant during various activities of daily living.Average peak resultant forces, in percent of body weight, were highest during stair descending (346% BW), followed by stair ascending (316% BW), level walking (261% BW), one legged stance (259% BW), knee bending (253% BW), standing up (246% BW), sitting down (225% BW) and two legged stance (107% BW). Peak shear forces were about 10–20 times smaller than the axial force. Resultant forces acted almost vertically on the tibial plateau even during high flexion. Highest moments acted in the frontal plane with a typical peak to peak range ?2.91% BWm (adduction moment) to 1.61% BWm (abduction moment) throughout all activities. Peak flexion/extension moments ranged between ?0.44% BWm (extension moment) and 3.16% BWm (flexion moment). Peak external/internal torques lay between ?1.1% BWm (internal torque) and 0.53% BWm (external torque).The knee joint is highly loaded during daily life. In general, resultant contact forces during dynamic activities were lower than the ones predicted by many mathematical models, but lay in a similar range as measured in vivo by others. Some of the observed load components were much higher than those currently applied when testing knee implants.     

Sensitivity of a subject-specific musculoskeletal model to the uncertainties on the joint axes location

Subject-specific musculoskeletal models have become key tools in the clinical decision-making process. However, the sensitivity of the calculated solution to the unavoidable errors committed while deriving the model parameters from the available information is not fully understood. The aim of this study was to calculate the sensitivity of all the kinematics and kinetics variables to the inter-examiner uncertainty in the identification of the lower limb joint models. The study was based on the computer tomography of the entire lower-limb from a single donor and the motion capture from a body-matched volunteer. The hip, the knee and the ankle joint models were defined following the International Society of Biomechanics recommendations. Using a software interface, five expert anatomists identified on the donor's images the necessary bony locations five times with a three-day time interval. A detailed subject-specific musculoskeletal model was taken from an earlier study, and re-formulated to define the joint axes by inputting the necessary bony locations. Gait simulations were run using OpenSim within a Monte Carlo stochastic scheme, where the locations of the bony landmarks were varied randomly according to the estimated distributions. Trends for the joint angles, moments, and the muscle and joint forces did not substantially change after parameter perturbations. The highest variations were as follows: (a) 11° calculated for the hip rotation angle, (b) 1% BW × H calculated for the knee moment and (c) 0.33 BW calculated for the ankle plantarflexor muscles and the ankle joint forces. In conclusion, the identification of the joint axes from clinical images is a robust procedure for human movement modelling and simulation.     

Image based weighted center of proximity versus directly measured knee contact location during simulated gait

To understand the mechanical consequences of knee injury requires a detailed analysis of the effect of that injury on joint contact mechanics during activities of daily living. Three-dimensional (3D) knee joint geometric models have been combined with knee joint kinematics to dynamically estimate the location of joint contact during physiological activities—using a weighted center of proximity (WCoP) method. However, the relationship between the estimated WCoP and the actual location of contact has not been defined. The objective of this study was to assess the relationship between knee joint contact location as estimated using the image-based WCoP method, and a directly measured weighted center of contact (WCoC) method during simulated walking. To achieve this goal, we created knee specific models of six human cadaveric knees from magnetic resonance imaging. All knees were then subjected to physiological loads on a knee simulator intended to mimic gait. Knee joint motion was captured using a motion capture system. Knee joint contact stresses were synchronously recorded using a thin electronic sensor throughout gait, and used to compute WCoC for the medial and lateral plateaus of each knee. WCoP was calculated by combining knee kinematics with the MRI-based knee specific model. Both metrics were compared throughout gait using linear regression. The anteroposterior (AP) location of WCoP was significantly correlated with that of WCoC on both tibial plateaus in all specimens (p<0.01, 95% confidence interval of Pearson?s coefficient r>0), but the correlation was not significant in the mediolateral (ML) direction for 4/6 knees (p>0.05). Our study demonstrates that while the location of joint contact obtained from 3D knee joint contact model, using the WCoP method, is significantly correlated with the location of actual contact stresses in the AP direction, that relationship is less certain in the ML direction.     

Agreement of measured and calculated muscle activity during highly dynamic movements modelled with a spherical knee joint

The inclusion of muscle forces into the analysis of joint contact forces has improved their accuracy. But it has not been validated if such force and activity calculations are valid during highly dynamic multidirectional movements. The purpose of this study was to validate calculated muscle activation of a lower extremity model with a spherical knee joint for running, sprinting and 90°-cutting. Kinematics, kinetics and lower limb muscle activation of ten participants were investigated in a 3D motion capture setup including EMG. A lower extremity rigid body model was used to calculate the activation of these muscles with an inverse dynamics approach and a cubic cost function. Correlation coefficients were calculated to compare measured and calculated activation. The results showed good correlation of the modelled and calculated data with a few exceptions. The highest average correlations were found during walking (r = 0.81) and the lowest during cutting (r = 0.57). Tibialis anterior had the lowest average correlation (r = 0.33) over all movements while gastrocnemius medius had the highest correlation (r = 0.9). The implementation of a spherical knee joint increased the agreement between measured and modelled activation compared to studies using a hinge joint knee. Although some stabilizing muscles showed low correlations during dynamic movements, the investigated model calculates muscle activity sufficiently.     

In vivo tests of an improved method for functional location of the subtalar joint axis

The subtalar joint is important in frontal plane movement and posture of the hindfoot. Abnormal subtalar joint moments caused by muscle forces and the ground reaction force acting on the foot are thought to play a role in various foot deformities. Calculating joint moments typically requires knowledge of the location of the joint axis; however, location of the subtalar axis from measured movement is difficult because the talus cannot be tracked using skin-mounted markers. The accuracy of a novel technique for locating the subtalar axis was assessed in vivo using magnetic resonance imaging. The method was also tested with skin-mounted markers and video motion analysis. The technique involves applying forces to the foot that cause pure subtalar joint motion (with negligible talocrural joint motion), and then using helical axis decomposition of the resulting tibiocalcaneal motion. The resulting subtalar axis estimates differed by 6° on average from the true best-fit subtalar axes in the MRI tests. Motion was found to have been applied primarily about the subtalar joint with an average of only 3° of talocrural joint motion. The proposed method provides a potential means for obtaining subject-specific subtalar axis estimates which can then be used in inverse dynamic analyses and subject-specific musculoskeletal models.     

Subject-specific hip geometry and hip joint centre location affects calculated contact forces at the hip during gait

Hip loading affects the development of hip osteoarthritis, bone remodelling and osseointegration of implants. In this study, we analyzed the effect of subject-specific modelling of hip geometry and hip joint centre (HJC) location on the quantification of hip joint moments, muscle moments and hip contact forces during gait, using musculoskeletal modelling, inverse dynamic analysis and static optimization. For 10 subjects, hip joint moments, muscle moments and hip loading in terms of magnitude and orientation were quantified using three different model types, each including a different amount of subject-specific detail: (1) a generic scaled musculoskeletal model, (2) a generic scaled musculoskeletal model with subject-specific hip geometry (femoral anteversion, neck-length and neck-shaft angle) and (3) a generic scaled musculoskeletal model with subject-specific hip geometry including HJC location. Subject-specific geometry and HJC location were derived from CT. Significant differences were found between the three model types in HJC location, hip flexion–extension moment and inclination angle of the total contact force in the frontal plane. No model agreement was found between the three model types for the calculation of contact forces in terms of magnitude and orientations, and muscle moments. Therefore, we suggest that personalized models with individualized hip joint geometry and HJC location should be used for the quantification of hip loading. For biomechanical analyses aiming to understand modified hip joint loading, and planning hip surgery in patients with osteoarthritis, the amount of subject-specific detail, related to bone geometry and joint centre location in the musculoskeletal models used, needs to be considered.     

A computationally efficient strategy to estimate muscle forces in a finite element musculoskeletal model of the lower limb

Concurrent multiscale simulation strategies are required in computational biomechanics to study the interdependence between body scales. However, detailed finite element models rarely include muscle recruitment due to the computational burden of both the finite element method and the optimization strategies widely used to estimate muscle forces. The aim of this study was twofold: first, to develop a computationally efficient muscle force prediction strategy based on proportional-integral-derivative (PID) controllers to track gait and chair rise experimental joint motion with a finite element musculoskeletal model of the lower limb, including a deformable knee representation with 12 degrees of freedom; and, second, to demonstrate that the inclusion of joint-level deformability affects muscle force estimation by using two different knee models and comparing muscle forces between the two solutions. The PID control strategy tracked experimental hip, knee, and ankle flexion/extension with root mean square errors below 1°, and estimated muscle, contact and ligament forces in good agreement with previous results and electromyography signals. Differences up to 11% and 20% in the vasti and biceps femoris forces, respectively, were observed between the two knee models, which might be attributed to a combination of differing joint contact geometry, ligament behavior, joint kinematics, and muscle moment arms. The tracking strategy developed in this study addressed the inevitable tradeoff between computational cost and model detail in musculoskeletal simulations and can be used with finite element musculoskeletal models to efficiently estimate the interdependence between muscle forces and tissue deformation.     

Patella tendon moment arm function considerations for human vastus lateralis force estimates

In vivo muscle forces are typically estimated using literature-based or subject-specific moment arms (MAs) because it is not possible to measure in vivo muscle forces non-invasively. However, even subject-specific muscle-tendon MAs vary across contraction levels and are impossible to determine at high contraction levels without techniques that use ionized radiation. Therefore, different generic MA functions are often used to estimate in vivo muscle forces, which may alter force predictions and the shape of the muscle’s force-length relationship. The aim of this study was to examine the influence of different literature-based patella tendon MA functions on the vastus lateralis (VL) force-angle relationship. Participants (n = 11) performed maximum voluntary isometric knee extension contractions at six knee flexion angles, ranging from 40° to 90°. To estimate in vivo VL muscle force, the peak knee extension torque at each joint angle was multiplied by the VL’s physiological cross-sectional area (PCSA) relative to the quadriceps’ PCSA (34%) and then divided by the angle-specific patella tendon MA for 19 different functions. Maximum VL force was significantly different across MA functions (p ≤ 0.039) and occurred at different knee flexion angles. The shape of the VL force-angle relationship also differed significantly (p < 0.01) across MA functions. According to the maximum force generated by VL based on its literature-derived PSCA, only the VL force-angle relationships estimated using geometric imaging-based MA functions are feasible across the knee angles studied here. We therefore recommend that an average of these MA functions is calculated to estimate quadriceps muscle forces if subject-specific MAs cannot be determined.