The effects of Achilles tendon compliance on triceps surae mechanics and energetics in walking

Achilles tendon (AT) compliance can affect the generation and transmission of triceps surae muscle forces, and thus has important biomechanical consequences for walking performance. However, the uniarticular soleus (SOL) and the biarticular (GAS) function differently during walking, with in vivo evidence suggesting that their associated fascicles and tendinous structures exhibit unique kinematics during walking. Given the strong association between muscle fiber length, velocity and force production, we conjectured that SOL and GAS mechanics and energetic behavior would respond differently to altered AT compliance. To test this, we characterized GAS and SOL muscle and tendon mechanics and energetics due to systematic changes in tendon compliance using musculoskeletal simulations of walking. Increased tendon compliance enlarged GAS and SOL tendon excursions, shortened fiber operation lengths and affected muscle excitation patterns. For both muscles, an optimal tendon compliance (tendon strains of approximately 5% with maximum isometric force) existed that minimized metabolic energy consumption. However, GAS muscle-tendon mechanics and energetics were significantly more sensitive to changes in tendon compliance than were those for SOL. In addition, GAS was not able to return stored tendon energy during push-off as effectively as SOL, particularly for larger values of tendon compliance. These fundamental differences between GAS and SOL sensitivity to altered tendon compliance seem to arise from the biarticular nature of GAS. These insights are potentially important for understanding the functional consequences of altered Achilles tendon compliance due to aging, injury, or disease.     

Nonuniform strain of human soleus aponeurosis-tendon complex during submaximal voluntary contractions in vivo.

The distribution of strain along the soleus aponeurosis tendon was examined during voluntary contractions in vivo. Eight subjects performed cyclic isometric contractions (20 and 40% of maximal voluntary contraction). Displacement and strain in the apparent Achilles tendon and in the aponeurosis were calculated from cine phase-contrast magnetic resonance images acquired with a field of view of 32 cm. The apparent Achilles tendon lengthened 2.8 and 4.7% in 20 and 40% maximal voluntary contraction, respectively. The midregion of the aponeurosis, below the gastrocnemius insertion, lengthened 1.2 and 2.2%, but the distal aponeurosis shortened 2.1 and 2.5%, respectively. There was considerable variation in the three-dimensional anatomy of the aponeurosis and muscle-tendon junction. We suggest that the nonuniformity in aponeurosis strain within an individual was due to the presence of active and passive motor units along the length of the muscle, causing variable force along the measurement site. Force transmission along intrasoleus connective tissue may also be a significant source of nonuniform strain in the aponeurosis.     

Functional deficits may be explained by plantarflexor remodeling following Achilles tendon rupture repair: Preliminary findings

Achilles tendon ruptures are common injuries that often lead to long-term functional deficits. Despite the prevalence of these injuries, the mechanism responsible for limited function has not yet been established. Therefore, the purpose of this study was to present preliminary findings that support a hypothesis that skeletal muscle remodeling is the driving factor of poor outcomes in some patients. Biomechanical and ultrasonography assessments were performed on a patient that presented with poor functional outcomes 2.5 years after a surgically-repaired acute Achilles tendon rupture. Single-leg heel raise height was decreased by 75% in the affected limb (3.0 cm compared to 11.9 cm) while walking mechanics showed no deficits. Ultrasonography revealed that the affected medial gastrocnemius muscle was less thick and had shorter, more pennate fascicles compared to the unaffected limb. A simple computational model of a maximal-effort plantarflexion contraction was employed to test the implications of changes in muscle architecture on single-leg heel raise function. Subject-specific measurements of fascicle length and pennation were input into the model, which supported these architectural parameters as being drivers of heel raise function. These preliminary findings support the hypothesis that an Achilles tendon rupture elicits changes in skeletal muscle architecture, which reduces the amount of work and power the joint can generate. This multidisciplinary framework of biomechanical, imaging, and computational modeling provides a unique platform for studying the complex interactions between structure and function in patients recovering from Achilles tendon injuries.     

Dynamic creep and pre-conditioning of the Achilles tendon in-vivo

Warm-up exercises are often advocated prior to strenuous exercise, but the warm-up duration and effect on muscle–tendon behavior are not well defined. The gastrocnemius–Achilles tendon complexes of 18 subjects were studied to quantify the dynamic creep response of the Achilles tendon in-vivo and the warm-up dose required for the Achilles tendon to achieve steady-state behavior. A custom testing chamber was used to determine each subject's maximum voluntary contraction (MVC) during an isometric ankle plantar flexion effort. The subject's right knee and ankle were immobilized for one hour. Subjects then performed over seven minutes of cyclic isometric ankle plantar flexion efforts equal to 25–35% of their MVC at a frequency of 0.75 Hz. Ankle plantar flexion effort and images from dual ultrasound probes located over the gastrocnemius muscle–Achilles tendon and the calcaneus–Achilles tendon junction were acquired for eight seconds at the start of each sequential minute of the activity. Ultrasound images were analyzed to quantify the average relative Achilles tendon strain at 25% MVC force (ε_25%MVC) for each minute. The ε_25%MVC increased from 0.3% at the start of activity to 3.3% after seven minutes, giving a total dynamic creep of ~3.0%. The ε_25%MVC increased by more than 0.56% per minute for the first five minutes and increased by less than 0.13% per minute thereafter. Therefore, following a period of inactivity, a low intensity warm-up lasting at least six minutes or producing 270 loading cycles is required for an Achilles tendon to reach a relatively steady-state behavior.     

Elastic properties of human Achilles tendon are correlated to muscle strength.

The purpose of this study was to investigate whether the mechanical properties of the Achilles tendon were correlated to muscle strength in the triceps surae in humans. Twenty-four men and twelve women exerted maximal voluntary isometric plantar flexion (MVIP) torque. The elongation (DeltaX) and strain of the Achilles tendon (epsilon), the proximal part of which is the composite of the gastrocnemius tendon and the soleus aponeurosis, at MVIP were determined from the displacement of the distal myotendinous junction of the medial gastrocnemius using ultrasonography. The Achilles tendon force at MVIP (F) was calculated from the MVIP torque and the Achilles tendon moment arm. There were no significant differences in either the F-DeltaX or F-epsilon relationships between men and women. DeltaX and epsilon were 9.8 +/- 2.6 mm and 5.3 +/- 1.6%, respectively, and were positively correlated to F (r = 0.39, P < 0.05; r = 0.39, P < 0.05), which meant that subjects with greater muscle strength could store more elastic energy in the tendon. The regression y-intercepts for the F-DeltaX (P < 0.01) and F-epsilon (P < 0.05) relationship were significantly positive. These results might indicate that the Achilles tendon was stiffer in subjects with greater muscle strength, which may play a role in reducing the probability of tendon strain injuries. It was suggested that the Achilles tendon of subjects with greater muscle strength did not impair the potential for storing elastic energy in tendons and may be able to deliver the greater force supplied from a stronger muscle more efficiently. Furthermore, the difference in the Achilles tendon mechanical properties between men and women seemed to be correlated to the difference in muscle strength rather than gender.     

Fiberoptic measurement of tendon forces is influenced by skin movement artifact

Fiberoptic cables have previously been used for tendon force measurements in vivo. To measure forces in the Achilles tendon, a cable is passed mediolaterally through the skin and tendon, transverse to the loading axis. As the tendon is loaded, its fibers compress the cable and modulate the intensity of transmitted light, which can be related to tendon force by an in situ calibration. The relative movement between skin and tendon at the cable entry and exit sites may cause error by bending the cable and thus altering transducer output. Cadaver simulations of walking were conducted to compare fiberoptic measurements of Achilles tendon forces to known loads applied to the tendon by actuators attached in series. Force measurement errors, which were high when the skin was intact (RMS errors 24-81% peak forces), decreased considerably after skin removal (RMS errors 10-33% peak forces). The fiberoptic transducer is a useful tool for measurement of tendon forces in situ under natural loading conditions when skin can be removed, but caution should be exercised during in vivo use of this technique or under circumstances where skin is in contact with the fiberoptic cable at the insertion and exit sites.     

Quadriceps tendon allografts as an alternative to Achilles tendon allografts: a biomechanical comparison

Quadriceps tendon with a patellar bone block may be a viable alternative to Achilles tendon for anterior cruciate ligament reconstruction (ACL-R) if it is, at a minimum, a biomechanically equivalent graft. The objective of this study was to directly compare the biomechanical properties of quadriceps tendon and Achilles tendon allografts. Quadriceps and Achilles tendon pairs from nine research-consented donors were tested. All specimens were processed to reduce bioburden and terminally sterilized by gamma irradiation. Specimens were subjected to a three phase uniaxial tension test performed in a custom environmental chamber to maintain the specimens at a physiologic temperature (37 ± 2 °C) and misted with a 0.9 % NaCl solution. There were no statistical differences in seven of eight structural and mechanical between the two tendon types. Quadriceps tendons exhibited a significantly higher displacement at maximum load and significantly lower stiffness than Achilles tendons. The results of this study indicated a biomechanical equivalence of aseptically processed, terminally sterilized quadriceps tendon grafts with bone block to Achilles tendon grafts with bone block. The significantly higher displacement at maximum load, and lower stiffness observed for quadriceps tendons may be related to the failure mode. Achilles tendons had a higher bone avulsion rate than quadriceps tendons (86 % compared to 12 %, respectively). This was likely due to observed differences in bone block density between the two tendon types. This research supports the use of quadriceps tendon allografts in lieu of Achilles tendon allografts for ACL-R.     

Aging leads to inferior Achilles tendon mechanics and altered ankle function in rodents

Spontaneous rupture of the Achilles tendon is increasingly common in the middle aged population. However, the cause for the particularly high incidence of injury in this age group is not well understood. Therefore, the objective of this study was to identify age-specific differences in the Achilles tendon-muscle complex using an animal model. Functional measures were performed in vivo and tissues were harvested following euthanasia for mechanical, structural, and histological analysis from young, middle aged, and old rats. Numerous alterations in tendon properties were detected across age groups, including inferior material properties (maximum stress, modulus) with increasing age. Differences in function were also observed, as older animals exhibited increased ankle joint passive stiffness and decreased propulsion force during locomotion. Macroscale differences in tendon organization were not observed, although cell density and nuclear shape did vary between age groups. Muscle fiber size and type distribution were not notably affected by age, indicating that other factors may be more responsible for age-specific Achilles tendon rupture rates. This study improves our understanding of the role of aging in Achilles tendon biomechanics and ankle function, and helps provide a potential explanation for the disparate incidence of Achilles tendon ruptures in varying age groups.     

Conditioning of the Achilles tendon via ankle exercise improves correlations between sonographic measures of tendon thickness and body anthropometry

Although conditioning is routinely used in mechanical tests of tendon in vitro, previous in vivo research evaluating the influence of body anthropometry on Achilles tendon thickness has not considered its potential effects on tendon structure. This study evaluated the relationship between Achilles tendon thickness and body anthropometry in healthy adults both before and after resistive ankle plantarflexion exercise. A convenience sample of 30 healthy male adults underwent sonographic examination of the Achilles tendon in addition to standard anthropometric measures of stature and body weight. A 10-5 MHz linear array transducer was used to acquire longitudinal sonograms of the Achilles tendon, 20 mm proximal to the tendon insertion. Participants then completed a series (90-100 repetitions) of conditioning exercises against an effective resistance between 100% and 150% body weight. Longitudinal sonograms were repeated immediately on completion of the exercise intervention, and anteroposterior Achilles tendon thickness was determined. Achilles tendon thickness was significantly reduced immediately following conditioning exercise (t = 9.71, P < 0.001), resulting in an average transverse strain of -18.8%. In contrast to preexercise measures, Achilles tendon thickness was significantly correlated with body weight (r = 0.72, P < 0.001) and to a lesser extent height (r = 0.45, P = 0.01) and body mass index (r = 0.63, P < 0.001) after exercise. Conditioning of the Achilles tendon via resistive ankle exercises induces alterations in tendon structure that substantially improve correlations between Achilles tendon thickness and body anthropometry. It is recommended that conditioning exercises, which standardize the load history of tendon, are employed before measurements of sonographic tendon thickness in vivo.     

Low-intensity tensile loading increases intratendinous glucose uptake in the Achilles tendon.

The metabolic activity of tendinous tissues has traditionally been considered to be of limited magnitude. However, recent studies have suggested that glucose uptake increases in the force-transmitting tissues as a response to contractile loading, which in turn indicates an elevated tissue metabolism. The purpose of the present study was to investigate whether such a mechanism could be observed for the human Achilles tendon following tensile loading. Six subjects participated in the study. Unilateral Achilles tendon loading was applied by 25-min intermittent voluntary plantar flexor contractions. A radioactive tracer ([18F]-2-fluoro-2-deoxy-D-glucose) was administered during muscle action, and glucose uptake was measured by use of PET. Regions of interest were defined on the PET images corresponding to the cross section of Achilles tendon at two longitudinally separated sites (insertion and free tendon). Glucose uptake index was determined within respective regions of interest for the active and resting leg. Tendon force during voluntary contractions was approximately 13% of maximal voluntary contraction force. Tendon loading induced an elevated glucose uptake index compared with that of the contralateral resting tendon in the region of tendon insertion (0.13 +/- 0.05 vs. 0.09 +/- 0.02; P < 0.05) and at the free tendon (0.12 +/- 0.01 vs. 0.08 +/- 0.02; P < 0.05). The present data suggest that tissue metabolism is elevated in the human Achilles tendon in response to low-intensity loading.     

Medial gastrocnemius muscle fascicle active torque-length and Achilles tendon properties in young adults with spastic cerebral palsy

Individuals with spastic cerebral palsy (CP) typically experience muscle weakness. The mechanisms responsible for muscle weakness in spastic CP are complex and may be influenced by the intrinsic mechanical properties of the muscle and tendon. The purpose of this study was to investigate the medial gastrocnemius (MG) muscle fascicle active torque-length and Achilles tendon properties in young adults with spastic CP. Nine relatively high functioning young adults with spastic CP (GMFCS I, 17±2 years) and 10 typically developing individuals (18±2 years) participated in the study. Active MG torque-length and Achilles tendon properties were assessed under controlled conditions on a dynamometer. EMG was recorded from leg muscles and ultrasound was used to measure MG fascicle length and Achilles tendon length during maximal isometric contractions at five ankle angles throughout the available range of motion and during passive rotations imposed by the dynamometer. Compared to the typically developing group, the spastic CP group had 33% lower active ankle plantarflexion torque across the available range of ankle joint motion, partially explained by 37% smaller MG muscle and 4% greater antagonistic co-contraction. The Achilles tendon slack length was also 10% longer in the spastic CP group. This study confirms young adults with mild spastic CP have altered muscle–tendon mechanical properties. The adaptation of a longer Achilles tendon may facilitate a greater storage and recovery of elastic energy and partially compensate for decreased force and work production by the small muscles of the triceps surae during activities such as locomotion.     

Effect of joint rotation correction when measuring elongation of the gastrocnemius medialis tendon and aponeurosis

It is well known that during maximal plantar flexion contractions the ankle joint rotation overestimates the actual elongation of the tendon and aponeurosis. The aim of this study was to examine the influence of the curve length changes of the Achilles tendon on the joint rotation corrected elongation and strain of the gastrocnemius medialis (GM) tendon and aponeurosis. Nine subjects (age: 29.4 ± 5.7 years, body mass: 78.8 ± 6.8 kg, body height: 178 ± 4 cm) participated in the study. The subjects performed maximal voluntary isometric plantarflexion contractions in the prone position on a Biodex-dynamometer. Ultrasonography (Aloka SSD 4000) was used to visualize the muscle belly of the GM muscle-tendon unit. To calculate the curve length changes of the Achilles tendon its surface contour was reconstructed using a series of small reflective skin markers having a diameter of 2.5 mm. The elongation of the GM tendon and aponeurosis was calculated (a) as the difference of the measured and the passive (due to joint rotation) displacement of the tendon and aponeurosis and (b) as the difference of the measured displacement and the length changes of the reconstructed Achilles tendon surface contour. The absolute difference between the elongation obtained by both methods were 1.2 ± 0.4 mm. These differences were due to the higher changes in length obtained by the reconstruction of the tendon curved surface contour as compared to the changes observed in the passive displacement of the digitised point at the aponeurosis. Without correcting for angle joint rotation, the measured elongation clearly overestimates the actual elongation of the GM tendon and aponeurosis. After the passive displacement correction the calculated elongation still overestimates the actual elongation of the GM tendon and aponeurosis. However, this overestimation has a negligible effect on the examined in vivo strain (0.3%) of the tendon and aponeurosis.     

Slack length of gastrocnemius medialis and Achilles tendon occurs at different ankle angles

Although muscle–tendon slack length is a crucial parameter used in muscle models, this is one of the most difficult measures to estimate in vivo. The aim of this study was to determine the onset of the rise in tension (i.e., slack length) during passive stretching in both Achilles tendon and gastrocnemius medialis. Muscle and tendon shear elastic modulus was measured by elastography (supersonic shear imaging) during passive plantarflexion (0° and 90° of knee angle, 0° representing knee fully extended, in a random order) in 9 participants. The within-session repeatability of the determined slack length was good at 90° of knee flexion (SEM=3.3° and 2.2° for Achilles tendon and gastrocnemius medialis, respectively) and very good at 0° of knee flexion (SEM=1.9° and 1.9° for Achilles tendon and gastrocnemius medialis, respectively). The slack length of gastrocnemius medialis was obtained at a significantly lower plantarflexed angle than for Achilles tendon at both 0° (P<0.0001; mean difference=19.4±3.8°) and 90° of knee flexion (P<0.0001; mean difference=25.5±7.6°). In conclusion, this study showed that the joint angle at which the tendon falls slack can be experimentally determined using supersonic shear imaging. The slack length of gastrocnemius medialis and Achilles tendon occurred at different joint angles. Although reporting this result is crucial to a better understanding of muscle–tendon interactions, further experimental investigations are required to explain this result.     

Measurement of muscle and tendon stiffness in man

Human first dorsal interosseous muscle was stimulated tetanically using several levels of percutaneous electrical current which produced forces in the muscle-tendon complex of between 30% and 100% of maximum. During the tetanus the muscle was subjected to a small fast stretch. The ratio of the force response to the displacement of the muscle-tendon complex gave a measure of the stiffness of the total complex. An adaptation of the method of Morgan (1977) allowed the stiffness to be separated into two components the stiffness of the muscle fibres and the stiffness of the tendon. The results showed that at full activation the stiffness of the muscle fibres and the tendon are approximately the same. The normalised stiffness values obtained in the experiments compared well with animal data.     

Ultrasound estimates of Achilles tendon exhibit unexpected shortening during ankle plantarflexion

The purpose of this study was to investigate Achilles tendon (AT) length changes during a series of tasks that involved combinations of higher/lower force, and larger/smaller length changes of the medial gastrocnemius muscle-tendon unit (MTU). We sought to determine if common ultrasound-based estimates of AT length change were consistent with expectations for a passive elastic tendon acting in series with a muscle. We tested 8 healthy individuals during restricted joint calf contractions (high force, low displacement), ankle dorsi-/plantar-flexion (DF/PF) with the foot in the air (low force, high displacement), and heel raises (high force, high displacement). We experimentally estimated AT length change using two ultrasound methods, one based on muscle-tendon junction (MTJ) tracking and one based on muscle fascicle (MF) tracking. Estimates of AT length change were consistent with model expectations during restricted calf contractions, when the MTU underwent minimal length change. However, estimates of AT length changes were inconsistent with model expectations during the ankle DF/PF and heel raise tasks. Specifically, the AT was estimated to shorten substantially, often 10–20 mm, when the ankle plantarflexed beyond neutral position, despite loading conditions in which a passive, stiff spring would be expected to either lengthen (under increasing force) or maintain its length (under low force). These unexpected findings suggest the need for improvements in how we conceptually model and/or experimentally estimate MTU dynamics in vivo during motion analysis studies, particularly when the ankle plantarflexes beyond neutral.     

The contraction-induced increase in Achilles tendon moment arm: A three-dimensional study

The present study aimed to re-examine the influence of the isometric plantarflexors contraction on the Achilles tendon moment arm (ATMA) and the factors influencing the ATMA in three-dimensions. A series of coronal magnetic resonance images of the right ankle were recorded at foot positions of 10° of dorsiflexion, neutral position, and 10° of plantarflexion for the rest condition and the plantarflexors contraction condition at 30% maximal voluntary effort. The shortest distance between the talocrural joint axis and the line of action of the Achilles tendon force projected to the orthogonal plane of the talocrural joint axis was determined as the ATMA. The ATMA determined in the contraction condition was significantly greater by 8 mm than that determined in the rest condition. The talocrural joint axis was displaced anteriorly by 3 mm and distally by 2 mm due to the muscle contraction. As the same time, the line of action of the Achilles tendon force was displaced posteriorly by 5 mm and medially by 2 mm. These linear displacements of the talocrural joint axis and the line of action of the Achilles tendon force accounted for the difference in the ATMAs between the two conditions by 35.9 and 62.4%, respectively. These angular displacements accounted for the total of 0.4% increase in the ATMA. These results confirm the previous findings reported in two-dimensional studies and found that the linear displacement of the line of action of the Achilles tendon force is the primary source of the contraction-induced increase in the ATMA.     

Optimal muscle fascicle length and tendon stiffness for maximising gastrocnemius efficiency during human walking and running

Muscles generate force to resist gravitational and inertial forces and/or to undertake work, e.g. on the centre of mass. A trade-off in muscle architecture exists in muscles that do both; the fibres should be as short as possible to minimise activation cost but long enough to maintain an appropriate shortening velocity. Energetic cost is also influenced by tendon compliance which modulates the timecourse of muscle mechanical work. Here we use a Hill-type muscle model of the human medial gastrocnemius to determine the muscle fascicle length and Achilles tendon compliance that maximise efficiency during the stance phase of walking (1.2 m/s) and running (3.2 and 3.9 m/s). A broad range of muscle fascicle lengths (ranging from 45 to 70 mm) and tendon stiffness values (150-500 N/mm) can achieve close to optimal efficiency at each speed of locomotion; however, efficient walking requires shorter muscle fascicles and a more compliant tendon than running. The values that maximise efficiency are within the range measured in normal populations. A non-linear toe-region region of the tendon force-length properties may further influence the optimal values, requiring a stiffer tendon with slightly longer muscle fascicles; however, it does not alter the main results. We conclude that muscle fibre length and tendon compliance combinations may be tuned to maximise efficiency under a given gait condition. Efficiency is maximised when the required volume of muscle is minimised, which may also help reduce limb inertia and basal metabolic costs.     

Effect of muscle contraction levels on the force-length relationship of the human Achilles tendon during lengthening of the triceps surae muscle-tendon unit

Findings from animal experiments are sometimes contradictory to the idea that the tendon structure is a simple elastic spring in series with muscle fibers, and suggest influence of muscle contraction on the tendon mechanical properties. The purpose of the present study was to investigate the influence of muscle contraction levels on the force-length relationship of the human Achilles tendon during lengthening of the triceps surae muscle-tendon unit. For seven subjects, ankle dorsiflexion was performed without (passive condition) and with contraction of plantar flexor muscles (eccentric conditions, at 3 contraction levels) on an isokinetic dynamometer. Deformation of the Achilles tendon during each trial was measured using ultrasonography. The Achilles tendon force corresponding to the tendon elongation of 10mm in the passive condition was significantly smaller than those in the eccentric conditions (p<0.05 or p<0.01). Within the eccentric conditions, the Achilles tendon force corresponding to the tendon elongation of 10mm was significantly greater in the maximal contraction level than those in submaximal eccentric conditions (p<0.05 or p<0.01). In addition, the tendon stiffness was greater in higher contraction levels (p<0.05 or p<0.01). Present results suggest that the human tendon structure is not a simple elastic spring in series with muscle fibers.     

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.