Forces acting on the patella during maximal voluntary contraction of the quadriceps femoris muscle at different knee flexion/extension angles

From knee extension moments measured with a dynamometer, the quadriceps muscle force, the patellar ligament force and the reaction force in the patellofemoral joint at various knee angles (0-90 degrees) were estimated. The information needed to calculate the combined effect of both patellofemoral and tibiofemoral joint on the mechanical advantage of the muscle was obtained from lateral-view radiographs of autopsy knees. The results show that the smallest quadriceps force (2,000 N) is exerted at maximal extension, and the largest force (8,000 N) at about 75 degrees of flexion. The patellar ligament force reaches a maximum (5,000 N) at 60 degrees. The reaction force in the patellofemoral joint is the smallest (1,000 N) at extension and is of the same values as the muscle force in a range from 75 to 90 degrees. Especially at large flexion angles, the value of the estimated forces is considerably larger (by 100%) than reported in the literature. This difference is attributed to the influence of the patellofemoral joint on the mechanical advantage of the muscle, which has not been taken into account in other studies.     

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.     

Role of gastrocnemius activation in knee joint biomechanics: gastrocnemius acts as an ACL antagonist

Gastrocnemius is a premier muscle crossing the knee, but its role in knee biomechanics and on the anterior cruciate ligament (ACL) remains less clear when compared to hamstrings and quadriceps. The effect of changes in gastrocnemius force at late stance when it peaks on the knee joint response and ACL force was initially investigated using a lower extremity musculoskeletal model driven by gait kinematics—kinetics. The tibiofemoral joint under isolated isometric contraction of gastrocnemius was subsequently analyzed at different force levels and flexion angles (0°–90°). Changes in gastrocnemius force at late stance markedly influenced hamstrings forces. Gastrocnemius acted as ACL antagonist by substantially increasing its force. Simulations under isolated contraction of gastrocnemius confirmed this role at all flexion angles, in particular, at extreme knee flexion angles (0° and 90°). Constraint on varus/valgus rotations substantially decreased this effect. Although hamstrings and gastrocnemius are both knee joint flexors, they play opposite roles in respectively protecting or loading ACL. Although the quadriceps is also recognized as antagonist of ACL, at larger joint flexion and in contrast to quadriceps, activity in gastrocnemius substantially increased ACL forces (anteromedial bundle). The fact that gastrocnemius is an antagonist of ACL should help in effective prevention and management of ACL injuries.     

Effect of knee musculature on anterior cruciate ligament strain in vivo

Squatting is a commonly prescribed exercise following reconstruction of the anterior cruciate ligament (ACL). The objective of this paper was to measure the in vivo strain patterns of the normal ACL and the load at the knee for the simple squat and for squatting with a “sport cord”. A sport cord is a large elastic rubber tube used for added resistance. Strain patterns were deduced using displacement data from a Hall Effect Strain Transducer (HEST), while joint loads were determined by a mathematical model with inputs from a force plate and electrogoniometers. ACL strain for the free squat in one subject had a maximum of 2% at a knee angle of 10° and was slack for knee angles >17°. In squatting with a sport cord, peak strain was 1% at 10° and was slack at knee angles >14°. Since these peak strains are low, squatting appears to be a safe exercise for conservative rehabilitation of ACL reconstruction patients. In addition, the sport cord is a recommended augmentation to the activity. We believe that the decrease in strain with the sport cord results from added joint stiffness due to greater compressive forces at the tibiofemoral joint. This greater compressive force results from the approximately 10% increase in quadriceps activity. From shear force data predicted by the mathematical model, the maximum anterior drawer force for free squatting (50 N) was considerably less than for sport cord squatting (430 N). Therefore, the value of shear force at the tibiofemoral joint only partially determines the load placed on the ACL.     

Forward-dynamics simulation of anterior cruciate ligament forces developed during isokinetic dynamometry

A mathematical (computer) model was developed and used to study the mechanics of the human knee during extension exercises employing an isokinetic dynamometer. All parts of the body were fixed to ground, except for the right shank and foot, which were free to move in the parasagittal plane. A linkage attached the dynamometer to the shank; tibiofemoral articulation consisted of single-point contact, allowing both sliding and rolling to occur. Physiologically based representations of ligaments and muscles imparted forces to the shank. A forward dynamics simulation was performed to calculate the forces developed in the knee for isokinetic speeds ranging from 0 (isometric exercise) to 300 degrees /s. Simulations were conducted for a constant-speed phase during isokinetic knee extension exercise. It was assumed for the duration of each simulated exercise that the quadriceps were fully activated and the other muscles were fully deactivated. The force in the anterior cruciate ligament was found to be governed by the force-velocity properties of the quadriceps; the model predicts that 300 deg/sec isokinetic exercise can reduce the force transmitted to the ACL by almost a factor of two compared with that present during isometric knee extension.     

3-D anatomically based dynamic modeling of the human knee to include tibio-femoral and patello-femoral joints

An anatomical dynamic model consisting of three body segments, femur, tibia and patella, has been developed in order to determine the three-dimensional dynamic response of the human knee. Deformable contact was allowed at all articular surfaces, which were mathematically represented using Coons' bicubic surface patches. Nonlinear elastic springs were used to model all ligamentous structures. Two joint coordinate systems were employed to describe the six-degrees-of-freedom tibio-femoral (TF) and patello-femoral (PF) joint motions using twelve kinematic parameters. Two versions of the model were developed to account for wrapping and nonwrapping of the quadriceps tendon around the femur. Model equations consist of twelve nonlinear second-order ordinary differential equations coupled with nonlinear algebraic constraint equations resulting in a Differential-Algebraic Equations (DAE) system that was solved using the Differential/Algebraic System Solver (DASSL) developed at Lawrence Livermore National Laboratory. Model calculations were performed to simulate the knee extension exercise by applying non-linear forcing functions to the quadriceps tendon. Under the conditions tested, both "screw home mechanism" and patellar flexion lagging were predicted. Throughout the entire range of motion, the medial component of the TF contact force was found to be larger than the lateral one while the lateral component of the PF contact force was found to be larger than the medial one. The anterior and posterior fibers of both anterior and posterior cruciate ligaments, ACL and PCL, respectively, had opposite force patterns: the posterior fibers were most taut at full extension while the anterior fibers were most taut near 90 degrees of flexion. The ACL was found to carry a larger total force than the PCL at full extension, while the PCL carried a larger total force than the ACL in the range of 75 degrees to 90 degrees of flexion.     

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.     

Forward-dynamics Simulation of Anterior Cruciate Ligament Forces Developed During Isokinetic Dynamometry

A mathematical (computer) model was developed and used to study the mechanics of the human knee during extension exercises employing an isokinetic dynamometer. All parts of the body were fixed to ground, except for the right shank and foot, which were free to move in the parasagittal plane. A linkage attached the dynamometer to the shank; tibiofemoral articulation consisted of single-point contact, allowing both sliding and rolling to occur. Physiologically based representations of ligaments and muscles imparted forces to the shank. A forward dynamics simulation was performed to calculate the forces developed in the knee for isokinetic speeds ranging from 0 (isometric exercise) to 300°/s. Simulations were conducted for a constant-speed phase during isokinetic knee extension exercise. It was assumed for the duration of each simulated exercise that the quadriceps were fully activated and the other muscles were fully deactivated. The force in the anterior cruciate ligament was found to be governed by the force-velocity properties of the quadriceps; the model predicts that 300 deg/sec isokinetic exercise can reduce the force transmitted to the ACL by almost a factor of two compared with that present during isometric knee extension.     

Estimation of in vivo ACL force changes in response to increased weightbearing

Accurate knowledge of in vivo anterior cruciate ligament (ACL) forces is instrumental for understanding normal ACL function and improving surgical ACL reconstruction techniques. The objective of this study was to estimate the change in ACL forces under in vivo loading conditions using a noninvasive technique. A combination of magnetic resonance and dual fluoroscopic imaging system was used to determine ACL in vivo elongation during controlled weightbearing at discrete flexion angles, and a robotic testing system was utilized to determine the ACL force-elongation data in vitro. The in vivo ACL elongation data were mapped to the in vitro ACL force-elongation curve to estimate the change in in vivo ACL forces in response to full body weightbearing using a weighted mean statistical method. The data demonstrated that by assuming that there was no tension in the ACL under zero weightbearing, the changes in in vivo ACL force caused by full body weightbearing were 131.4 ± 16.8 N at 15 deg, 106.7 ± 11.2 N at 30 deg, and 34.6 ± 4.5 N at 45 deg of flexion. However, when the assumed tension in the ACL under zero weightbearing was over 20 N, the change in the estimated ACL force in response to the full body weightbearing approached an asymptotic value. With an assumed ACL tension of 40 N under zero weightbearing, the full body weight caused an ACL force increase in 202.7 ± 27.6 N at 15 deg, 184.9 ± 22.5 N at 30 deg, and 98.6 ± 11.7 N at 45 deg of flexion. The in vivo ACL forces were dependent on the flexion angle with higher force changes at low flexion angles. Under full body weightbearing, the ACL may experience less than 250 N. These data may provide a valuable insight into the biomechanical behavior of the ACL under in vivo loading conditions.     

Biomechanics of changes in ACL and PCL material properties or prestrains in flexion under muscle force-implications in ligament reconstruction

The effects of changes in cruciate ligament material and prestrain on knee joint biomechanics following ligament reconstruction surgery by a tendon are not adequately known. A 3D nonlinear finite element model of the entire knee joint was used to investigate the joint response at different flexion angles under a quadriceps force while varying ACL and PCL initial strains or material properties. The ACL and PCL forces as well as tibiofemoral contact forces/areas substantially increased with greater ACL or PCL initial strains or stiffness. The patellofemoral contact force slightly increased whereas the tibial extensor moment slightly decreased with tenser or stiffer ACL. Reverse trends were predicted with slacker ACL. Results confirm the hypotheses that changes in the prestrain of one cruciate ligament substantially influence the force in the other cruciate ligament and the entire joint and that the use of the patellar tendon (PT) as a replacement for cruciate ligaments markedly alters the joint biomechanics with trends similar to those predicted when increasing prestrains. Forces in both ACL and PCL ligaments increased as one of them became tenser or stiffer and diminished as it became slacker. These results have important consequences in joint biomechanics following ligament injuries or replacement and tend to recommend the use of grafts with smaller prestrains (i.e. slacker than intact) when using the PT as the replacement material with stiffness greater than that of replaced ligament itself.     

Biomechanics of changes in ACL and PCL material properties or prestrains in flexion under muscle force-implications in ligament reconstruction

The effects of changes in cruciate ligament material and prestrain on knee joint biomechanics following ligament reconstruction surgery by a tendon are not adequately known. A 3D nonlinear finite element model of the entire knee joint was used to investigate the joint response at different flexion angles under a quadriceps force while varying ACL and PCL initial strains or material properties. The ACL and PCL forces as well as tibiofemoral contact forces/areas substantially increased with greater ACL or PCL initial strains or stiffness. The patellofemoral contact force slightly increased whereas the tibial extensor moment slightly decreased with tenser or stiffer ACL. Reverse trends were predicted with slacker ACL. Results confirm the hypotheses that changes in the prestrain of one cruciate ligament substantially influence the force in the other cruciate ligament and the entire joint and that the use of the patellar tendon (PT) as a replacement for cruciate ligaments markedly alters the joint biomechanics with trends similar to those predicted when increasing prestrains. Forces in both ACL and PCL ligaments increased as one of them became tenser or stiffer and diminished as it became slacker. These results have important consequences in joint biomechanics following ligament injuries or replacement and tend to recommend the use of grafts with smaller prestrains (i.e. slacker than intact) when using the PT as the replacement material with stiffness greater than that of replaced ligament itself.     

Range of motion specificity resulting from closed and open kinetic chain resistance training after anterior cruciate ligament reconstruction

The purpose of this study was to examine whether joint angle specificity occurs in open and closed kinetic chain resistance training of the knee extensors after anterior cruciate ligament reconstruction (ACLR). Isokinetic knee extensor strength was measured at 60 and 210 degrees.s(-1) in 32 patients, 2 and 6 weeks after surgery. Between test sessions, patients participated in a 4-week program of injured leg resistance training of the knee extensors in either open kinetic chain (OKC) knee extension or leg press exercises. Isokinetic testing knee range of motion (ROM) was divided into 5 equal portions from flexion to extension, and the mean torque was calculated over those divisions: 0-20%, 20-40%, 40-60%, 60-80%, and 80-100% ROM. Analysis of variance indicated that there were no significant differences between patients in the knee extension or leg press exercise groups.     

Angle- and gender-specific quadriceps femoris muscle recruitment and knee extensor torque

The objectives were to examine knee angle-, and gender-specific knee extensor torque output and quadriceps femoris (QF) muscle recruitment during maximal effort, voluntary contractions. Fourteen young adult men and 15 young adult women performed three isometric maximal voluntary contractions (MVC), in a random order, with the knee at 0 degrees (terminal extension), 10 degrees, 30 degrees, 50 degrees, 70 degrees, and 90 degrees flexion. Knee extensor peak torque (PT), and average torque (AT) were expressed in absolute (N m), relative (N m kg(-1)) and allometric-modeled (N m kg(-n)) units. Vastus medialis (VM), vastus lateralis (VL), and rectus femoris (RF) muscle EMG signals were full-wave rectified and integrated over the middle 3 s of each contraction, averaged over the three trials at each knee angle, and normalized to the activity recorded at 0 degrees. Muscle recruitment efficiency was calculated as the ratio of the normalized EMG of each muscle to the allometric-modeled average torque (normalized to the values at 0 degrees flexion), and expressed as a percent. Men generated significantly greater knee extensor PT and AT than women in absolute, relative and allometric-modeled units. Absolute and relative PT and AT were significantly highest at 70 degrees, while allometric-modeled values were observed to increase significantly across knee joint angles 10-90 degrees. VM EMG was significantly greater than the VL and RF muscles across all angles, and followed a similar pattern to absolute knee extensor torque. Recruitment efficiency improved across knee joint angles 10-90 degrees and was highest for the VL muscle. VM recruitment efficiency improved more than the VL and RF muscles across 70-90 degrees flexion. The findings demonstrate angle-, and gender-specific responses of knee extensor torque to maximal-effort contractions, while superficial QF muscle recruitment was most efficient at 90 degrees, and less dependent on gender.     

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.     

A planar model of the knee joint to characterize the knee extensor mechanism

A simple planar static model of the knee joint was developed to calculate effective moment arms for the quadriceps muscle. A pathway for the instantaneous center of rotation was chosen that gives realistic orientations of the femur relative to the tibia. Using the model, nonlinear force and moment equilibrium equations were solved at one degree increments for knee flexion angles from 0 (full extension) to 90 degrees, yielding patellar orientation, patellofemoral contact force and patellar ligament force and direction with respect to both the tibial insertion point and the tibiofemoral contact point. The computer-derived results from this two-dimensional model agree with results from more complex models developed previously from experimentally obtained data. Due to our model's simplicity, however, the operation of the patellar mechanism as a lever as well as a spacer is clearly illustrated. Specifically, the thickness of the patella was found to increase the effective moment arm significantly only at flexions below 35 degrees even though the actual moment arm exhibited an increase throughout the flexion range. Lengthening either the patella or the patellar ligament altered the force transmitted from the quadriceps to the patellar ligament, significantly increasing the effective moment arm at flexions greater than 25 degrees. We conclude that the levering action of the patella is an essential mechanism of knee joint operation at moderate to high flexion angles.     

Are hamstrings activated to counteract shear forces during isometric knee extension efforts in healthy subjects?

The hamstring muscles have the potential to counteract anterior shear forces at the knee joint by co-contracting during knee extension efforts. Such a muscle recruitment pattern might protect the anterior cruciate ligament (ACL) by reducing its strain. In this study we investigated to what extent co-activation of the knee flexors during extension efforts is compatible with the hypothesis that this co-activation serves to counteract anterior tibial shear forces during isometric knee extension efforts in healthy subjects. To this aim, it is investigated whether co-activation varies with the required knee extension moment, with the knee joint angle, and with the position of the external flexing force relative to the knee joint. With unaltered moment and muscle activation, distal positioning of the flexing force on the tibia causes higher resultant (muscular plus external) forward shear forces at the knee as compared to proximal positioning. In ten subjects, knee flexor and extensor EMG was measured during a quasi-isometric positioning task for a range (5-50 degrees) of knee flexion angles. It was found that the co-activation of the knee flexors increased with the extension moment, but this increase was less than proportional (p<0.001). The extension moment increased 2.7 to 3.4 times, whereas the activation of Biceps Femoris and Semitendinosus increased only a factor 1.3 to 2.0 (joint angle dependent). Furthermore, a strong increase in co-activation was seen near full extension of the knee joint. The position of the external extension load on the tibia did not affect the level of co-contraction. It is argued that these results do not suggest a recruitment pattern that is directed at reduction of anterior shear forces in the knee joint during sub-maximal isometric knee extension efforts in healthy subjects.     

Knee joint biomechanics in closed-kinetic-chain exercises

Effective management of knee joint disorders demands appropriate rehabilitation programs to restore function while strengthening muscles. Excessive stresses in cartilage/menisci and forces in ligaments should be avoided to not exacerbate joint condition after an injury or reconstruction. Using a validated 3D nonlinear finite element model, detailed biomechanics of the entire joint in closed-kinetic-chain squat exercises are investigated at different flexion angles, weights in hands, femur-tibia orientations and coactivity in hamstrings. Predictions are in agreement with results of earlier studies. Estimation of small forces in cruciate ligaments advocates the use of squat exercises at all joint angles and external loads. In contrast, large contact stresses, especially at the patellofemoral joint, that approach cartilage failure threshold in compression suggest avoiding squatting at greater flexion angles, joint moments and weights in hands. Current results are helpful in comprehensive evaluation and design of effective exercise therapies and trainings with minimal risk to various components.     

Electromyographic comparison of standard and modified closed-chain isometric knee extension exercises

The purpose of this study was to compare electromyographic (EMG) activity during open kinetic chain (OKC) and a modified closed kinetic chain (MCKC) knee extension exercises. Both OKC and closed kinetic chain (CKC) exercises provide benefits when devising conditioning programs; however, there are no exercises that combine the benefits of both exercises. Subjects performed maximum isometric knee extensions for both traditional OKC and MCKC knee extension exercises. Surface electrodes were placed on 8 lower-extremity muscles. One second of integrated EMG activity followed 95% maximal knee extension force. The following muscles demonstrated greater EMG activity during the MCKC vs. the OKC knee extension exercises: vastus medialis, medial hamstring, lateral hamstrings, and gluteus maximus. There was no difference between force output between the 2 conditions. This study demonstrates that modifications to traditional OKC exercises demonstrate some characteristics of CKC exercises, and therefore provide another avenue of rehabilitation or strengthening.     

Lateral force–displacement behaviour of the human patella and its variation with knee flexion — a biomechanical study in vitro

This study measured the patellar lateral force–displacement behaviour at a range of knee flexion angles in normal human cadaver specimens. The knee extensor muscles were loaded in proportion to their physiological cross-sectional areas, the tensions being applied in physiological directions along the separate quadriceps muscles. Knee extension was blocked at a range of knee flexion angles from 0 to 90°, and patellar lateral displacement versus force characteristics were measured. This experiment was repeated with three total muscle forces, 20, 175 and 350 N, which were held constant at all flexion angles. It was shown that similar stability variation was obtained with the different total muscle loads, and also the forces required to produce a range of patellar displacements (1, 5, 9 mm) were examined. A 5 mm lateral patellar displacement required a constant displacing force (i.e. the patella had constant lateral stability) up to 60° knee flexion, and then a significant increase at 90°. The results were related to surgicaland anatomical observations.     

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.