Tendon Moment Arm Research Articles

Open Dorsal Closing-Wedge Calcaneal Osteotomy for Haglund Exostosis-Related Heel Pain.

Dorsal closing-wedge calcaneal osteotomy (DCWCO) is a treatment option for persistent Haglund exostosis-related heel pain after failed conservative management. In modifying the orientation of the calcaneal tendinous insertion site and reducing mechanical stress, the consequences of DCWCO-associated biomechanical changes on everyday foot function remain unknown. This retrospective cohort study analyzed routinely collected clinical data as well as data from our foot and ankle registry. One hundred twenty patients (66 males, 54 females, 17-77 years) who underwent DCWCO from January 2016 to December 2019 were included. Adverse events were collected from the patient files. Foot Function Index (FFI) scores were collected before (baseline) and at 6, 12, and 24 months postsurgery. Radiographic parameters including the Achilles tendon moment arm and X/Y ratio were evaluated from standard preoperative and 6-week postoperative radiographs. Correlations between FFI and biomechanical changes were calculated for men and women separately with the Pearson correlation coefficient and Bonferroni correction. One intra- and 18 postoperative adverse events were documented. Mean baseline FFI pain decreased from 47.9 ± 17.2 to 12.0 ± 17.5 points at 24 months with an average decrease of -21.8 ± 21.3 points occurring within the first 6 months postsurgery. A similar trend was also seen with the FFI disability score (49.6 ± 20.3 to 12.8 ± 17.6 points). The mean decrease in Achilles tendon moment arm was -8.1 ± 3.8 mm and mean X/Y ratio increased from 2.6 ± 0.3 to 3.8 ± 1.0. There were no significant correlations between the FFI score and radiographic changes. DCWCO effectively alleviates exostosis-related heel pain and associated disabilities. Improvements can still be expected up to 2 years after surgery. Radiographic changes of the foot and ankle are significant but do not correlate with patient-reported outcome measures.

Referencing the Center of Rotation of the Talus to Restore Tuber Length in Anatomic Reduction of Calcaneus Fractures

Introduction: The deforming forces of calcaneus fractures shorten, push into varus, and disrupt its articular surface. The height of the calcaneus depends on restoration of Bohler’s Angle (BA) and Tuber Length (TL). Contraction of the gastrocsoleus plantarflexes the ankle around the center of rotation of the talus (COR). The moment arm of the Achilles tendon is the calcaneal tuber. The purpose of this study is to define the COR, assess the TL after reconstruction of the calcaneal tuber and assess its influence on calcaneal height and work of the Achilles tendon. Methods: An IRB-approved retrospective study included 345 calcaneal fracture operative cases at a level 1 trauma center over 10 years. Of them, 39 cases had lateral x-rays of both operated and uninjured feet. X-rays were sized to each other on the Detroit Bonesetter App, which was used to find BA and COR. The moment arm of the Achilles tendon was defined as the distance from the tendon insertion to the COR of the talus. It was also the measurement used to describe TL. Results: The average postoperative TL was 5.72 ± 0.47 cm, and the average contralateral TL was 5.99 ± 0.42 cm (p=0.01). This resulted in a calculated average of 4.48% ± 5.28% increased gastrocsoleus work in all patients compared to the contralateral extremity. ORIF had shorter TL compared to CRPF (p=0.02). Eight of the 39 patients had shortened TL despite adequately restored BA. Conclusions: While BA restoration has served as the operative marker of success for intra-articular calcaneus fractures, it does not consider the change in mechanical work of the Achilles tendon, which may be a better indicator of the functional length of the calcaneus. This study demonstrates that there is increased work on the Achilles with shortened TL even when the reduction has adequately restored BA. Finding COR and referencing it to measure TL compared to the contralateral foot should be considered as an additional goal to restoration of BA, anatomic reduction, and varus deformity correction when treating calcaneal fractures.

Examination of knee extensor and valgus moment arms of the patellar tendon in older individuals with and without knee osteoarthritis

BackgroundJoint moment arm is a major element that determines joint torque. This study aimed to investigate factors associated with knee extensor and valgus moment arms of the patellar tendon in older individuals with and without knee osteoarthritis. MethodsThirty-six participants with knee osteoarthritis (mean age, 78.1 ± 6.0 years) and 43 healthy controls (mean age, 73.0 ± 6.3 years) were analyzed. Magnetic resonance images (MRI) from the knee joint and thigh were acquired using a 3.0 T MRI scanner. The three-dimensional moment arm was defined as the distance between the contact point of the tibiofemoral joint and the patellar tendon line. The three-dimensional moment arm was decomposed into sagittal and coronal components, which were calculated as knee extensor and valgus moment arms, respectively. Quadriceps muscle volume, epicondylar width, bisect offset, Insall–Salvati ratio, and Kellgren–Lawrence grade were assessed. Multiple regression analyses were performed in the healthy control and knee osteoarthritis groups, with knee extensor and valgus moment arms as dependent variables. FindingsKnee extensor moment arm was significantly associated with epicondylar width and the Insall–Salvati ratio in the healthy control group and with Kellgren–Lawrence grade, epicondylar width, and quadriceps muscle volume in the knee osteoarthritis group. Valgus knee moment arm was significantly associated with bisect offset in both the groups. InterpretationKnee size, osteoarthritis severity, and quadriceps muscle volume affect the knee extensor moment arm in knee osteoarthritis, whereas lateral patellar displacement affects the valgus knee moment arms in older individuals with and without knee osteoarthritis.

Correlations between Achilles tendon moment arm and plantarflexor muscle architecture variables.

The production of triceps surae plantarflexion moment is complex in that the Achilles tendon moment arm affects the Achilles tendon force by determining the muscle length change and shortening velocity during ankle rotation. In addition, there is evidence for associations between the sizes of muscles and their moment arm at the joints they span. These relationships between muscle architecture and tendon moment arm ultimately affect the muscle's force generating capacity and are thus important for understanding the roles played by muscles in producing locomotion. The purpose of this study was to investigate in vivo the relationship between architecture of two plantarflexors and the Achilles tendon moment arm in a healthy adult population. Ultrasound-based measurements were made of the architecture (fascicle length, muscle volume, physiological cross-sectional area, and anatomical cross-sectional area) of the lateral and medial gastrocnemius and the Achilles tendon moment arm was assessed using a technique that combined ultrasound imaging and motion analysis. Positive correlations were observed between the length (r = 0.499, p = 0.049) and size variables (muscle volume r = 0.621, p = 0.010; ACSA r = 0.536, p = 0.032) of the lateral gastrocnemius and the Achilles tendon moment arm, but correlations were only observed for size variables (muscle volume r = 0.638, p = 0.008; PCSA r = 0.525, p = 0.037; ACSA r = 0.544, p = 0.029), and not the length, of the medial gastrocnemius. These findings suggest lateral gastrocnemius adapts to moment arms to maintain force production throughout the range of motion across individuals, while the medial gastrocnemius does not and is thus better suited for static force generation.

A longer Achilles tendon moment arm length is not associated with superior hopping performance.

Variability in musculoskeletal and lower leg structure has the potential to influence hopping height. Achilles tendon moment arm length and plantarflexor muscle strength can influence ankle joint torque development and, consequently, hopping performance. While most studies have examined the connection of the Achilles tendon moment arm with hopping performance including the resting length, in this study we attempted to explore how the changes in Achilles tendon moment arm are related to hopping performance. Therefore, the purpose of this study was to test for correlations between foot and lower leg muscle structure parameters (i.e., muscle mass, volume, cross-sectional area and Achilles tendon moment arm length) and hopping height performance in relation to changes in Achilles tendon moment arm length. Eighteen participants (10 males 8 female) performed repetitive bilateral hopping on a force platform while sagittal plane kinematics of the lower leg were recorded. Additionally, maximal isometric plantarflexion was measured. To obtain structural parameters of the lower leg, the right lower leg of each participant was scanned with magnetic resonance imaging. The cross-sectional areas of the Achilles tendon, soleus, lateral and medial gastrocnemius were measured, while muscle volumes, muscle mass, and Achilles tendon moment arm length were calculated. Contrary to our initial assumption, longer Achilles tendon moment arm did not result in superior hopping performance. Interestingly, neither maximal isometric plantarflexion force nor muscle size correlated with repetitive bilateral hopping performance. We can assume that the mechanical characteristics of the tendon and the effective utilization of the stored strain energy in the tendon may play a more important role in repetitive hopping than the structural parameters of the lower leg.

The force-length relation of the young adult human tibialis anterior.

Knowledge of the muscle's lengths at which maximum active isometric force is attained is important for predicting forces during movement. However, there is limited information about the in vivo force-length properties of a human muscle that plays crucial roles during locomotion; the tibialis anterior (TA). We therefore aimed to estimate TA's force-length relation from dorsiflexor torque-angle curves constructed from eight women and eight men. Participants performed maximal voluntary fixed-end contractions with their right ankle dorsiflexors from 0° to 30° plantar flexion. Muscle fascicle lengths were estimated from B-mode ultrasound images, and net ankle joint torques were measured using dynamometry. Fascicle forces were estimated by dividing maximal active torques by literature-derived, angle-specific tendon moment arm lengths while assuming a fixed 50% force contribution of TA to the total dorsiflexor force and accounting for fascicle angles. Maximal active torques were higher at 15° than 20° and 30° plantar flexion (2.4-6.4 Nm, p≤0.012), whereas maximal active TA fascicle forces were higher at 15° than 0°, 20° and 30° plantar flexion (25-61 N, p≤0.042), but not different between 15° and 10° plantar flexion (15 N, p=0.277). TA fascicle shortening magnitudes during fixed-end contractions were larger at 15° than 30° plantar flexion (3.9 mm, p=0.012), but less at 15° than 0° plantar flexion (-2.4 mm, p=0.001), with no significant differences (≤0.7 mm, p=0.871) between TA's superficial and deep muscle compartments. Series elastic element stiffness was lowest and highest at lengths 5% shorter and 5% longer than optimum fascicle length, respectively (-30 and 15 N/mm, p≤0.003). TA produced its maximum active force at 10-15° plantar flexion, and its normalized force-length relation had ascending and descending limbs that agreed with a simple scaled sarcomere model when active fascicle lengths from within TA's superficial or deep muscle compartment were considered. These findings can be used to inform the properties of the contractile and series elastic elements of Hill-type muscle models.

How do differences in Achilles' tendon moment arm lengths affect muscle-tendon dynamics and energy cost during running?

The relationship between the Achilles tendon moment arm length (ATMA) and the energy cost of running (Erun) has been disputed. Some studies suggest a short ATMA reduces Erun while others claim a long ATMA reduces Erun. For a given ankle joint moment, a short ATMA permits a higher tendon strain energy storage, whereas a long ATMA reduces muscle fascicle force and muscle energy cost but shortening velocity is increased, elevating the metabolic cost. These are all conflicting mechanisms to reduce Erun, since AT energy storage comes at a metabolic cost. Neither of these proposed mechanisms have been examined together. We measured ATMA using the tendon travel method in 17 males and 3 females (24 ± 3 years, 75 ± 11 kg, 177 ± 7 cm). They ran on a motorized treadmill for 10 min at 2.5 m · s-1 while Erun was measured. AT strain energy storage, muscle lengths, velocities and muscle energy cost were calculated during time-normalized stance from force and ultrasound data. A short (SHORT n = 11, ATMA = 29.5 ± 2.0 mm) and long (LONG, n = 9, ATMA = 36.6 ± 2.5 mm) ATMA group was considered based on a bimodal distribution of measured ATMA. Mean Erun was 4.9 ± 0.4 J · kg-1 · m-1. The relationship between ATMA and Erun was not significant (r 2 = 0.13, p = 0.12). Maximum AT force during stance was significantly lower in LONG (5,819 ± 1,202 N) compared to SHORT (6,990 ± 920 N, p = 0.028). Neither AT stretch nor AT strain energy storage was different between groups (mean difference: 0.3 ± 1 J · step-1, p = 0.84). Fascicle force was significantly higher in SHORT (508 ± 93 N) compared to LONG (468 ± 84 N. p = 0.02). Fascicle lengths and velocities were similar between groups (p > 0.72). Muscle energy cost was significantly lower in LONG (0.028 ± 0.08 J · kg · step-1) compared to SHORT (0.045 ± 0.14 J · kg · step-1 p = 0.004). There was a significant negative relationship between ATMA and total muscle energy cost relative to body mass across the stance phase (r = -0.699, p < 0.001). Together these results suggest that a LONG ATMA serves to potentially reduce Erun by reducing the muscle energy cost of the plantarflexors during stance. The relative importance of AT energy storage and return in reducing Erun should be re-considered.

Increased lower limb length ratio in patients with patellar instability

PurposePatellar height is a risk factor for patellar instability, correlated with the tibia length/femur length (T/F) ratio. This study aimed to explore the changes in the T/F ratio in patients with patella instability and the potential correlation with the morphology of the patellofemoral joint and extensor moment arm.MethodA retrospective analysis was performed to assess the ratio of lower limb length morphological characteristics of the patellofemoral by full weight-bearing long-leg standing radiographs, magnetic resonance imaging, and computed tomography in 75 patients with patellar instability and 75 participants from a randomly selected control group from January 2020 to September 2021. A total of eight parts were measured, including mechanical tibia length/femur length (mT/F) ratio, anatomical tibia length/femur length (aT/F) ratio, hip–knee–ankle angle, femoral neck-shaft angle, femoral valgus cut angle, patellar height, Dejour classification, sulcus angle, trochlear angle, medial trochlear inclination, lateral trochlear inclination, patella tilt angle and patellar tendon moment arm to evaluate the difference of morphology between patient group and control groups.ResultsThe mT/F (0.840 ± 0.031 vs. 0.812 ± 0.026, p < 0.001) and aT/F (0.841 ± 0.033 vs. 0.808 ± 0.028, p < 0.001) ratios in the patient group were significantly greater than that in the control group. There was a significant correlation between patellar height and increased mT/F and aT/F ratios (p < 0.05).ConclusionPatients with patellar instability had a larger lower limb length ratio, and the change in lower limb length ratio was correlated with patellar height.Level of evidence IV.

Association of vastus lateralis diffusion properties with in vivo quadriceps contractile function in premenopausal women.

Diffusion tensor imaging (DTI) parameters correlate with muscle fiber composition, but it is unclear how these relate to in vivo contractile function. To determine the relationship between DTI parameters of the vastus lateralis (VL) and in vivo knee extensor contractile. Thirteen healthy, premenopausal women underwent magnetic resonance imaging of the mid-thigh to determine patellar tendon moment arm length and quadriceps cross-sectional area. Fractional anisotropy (FA), mean diffusivity (MD), axial diffusivity (AD), and radial diffusivity (RD) of the VL were determined using diffusion tensor imaging (DTI). Participants underwent an interpolated twitch (ITT) experiment before and after a fatiguing concentric-eccentric isokinetic knee extension (60°·s-1 ). During the ITT, supramaximal electrical stimuli were delivered to elicit twitch responses from the knee extensors before, during, and after a maximal voluntary isometric contraction (MVIC). Knee extensor-specific tension during twitch and MVIC were calculated from isometric torque data. Pearson's correlations were used to determine the relationship between muscle contractile properties and DTI parameters. MD and RD were moderately correlated with peak twitch force and rate of force development. FA and AD were moderately inversely related to percent change in MVIC following exercise. MD and RD are associated with in vivo quadriceps twitch properties but not voluntary strength, which may reflect the mechanical properties of constituent fiber types. FA and AD appear to relate to MVIC strength following fatiguing exercise.

Persons with patellar tendinopathy exhibit anatomical features that alter knee extensor mechanics: A comparison of persons with and without symptoms

It has been postulated that anatomical features of the patellofemoral joint may alter knee extensor mechanics in a way that may contribute to excessive patellar tendon loading. The purpose of this study was to compare the knee extensor mechanics in persons with and without patellar tendinopathy. Twenty-eight individuals participated (14 with patellar tendinopathy and 14 pain-free controls). Sagittal magnetic resonance images of the knee were acquired at the knee flexion angle that corresponded to the knee flexion angle at the time of peak knee extensor moment during a single-leg landing task. Measurements of patellar tendon/quadriceps tendon force ratio, quadriceps moment arm, patellar tendon moment arm, and patellar height (Insall-Salvati ratio) were obtained. Independent t-tests were used to compare the variables of interest between groups. When compared to the control group, the patellar tendinopathy group exhibited significantly a greater patellar tendon/quadriceps tendon force ratio (Mean ± SD, 1.0 ± 0.1 vs 0.8 ± 0.1, p < 0.05), a larger quadriceps moment arm (Mean ± SD, 23.9 ± 2.0 mm vs 22.1 ± 2.9 mm, p < 0.05), a smaller patellar tendon moment arm (Mean ± SD, 24.2 ± 1.7 mm vs 26.3 ± 2.4 mm, p < 0.05) and a greater Insall-Salvati ratio (Mean ± SD, 1.2 ± 0.1 vs 1.1 ± 0.1, p < 0.05). These results suggest that persons with patellar tendinopathy may experience greater forces in the patellar tendon for a given level of quadriceps force.

Anterior-cruciate-ligament reconstruction does not alter the knee-extensor moment arm during gait

BackgroundThe ability of the quadriceps muscles to extend the knee depends on the moment arm of the knee-extensor mechanism, which is described by the moment arm of the patellar tendon at the knee. The knee-extensor moment may be altered by a change in quadriceps force, a change in the patellar tendon moment arm (PTMA), or both. A change in quadriceps muscle strength after anterior-cruciate-ligament-reconstruction (ACLR) surgery is well documented, however, there is limited knowledge about how this procedure affects the PTMA. Research questionDoes ACLR surgery alter the moment arm of the knee-extensor mechanism during gait? MethodsWe measured the PTMA in both the ACLR knee and the uninjured contralateral knee in 10 young active individuals after unilateral ACLR surgery. Mobile biplane X-ray imaging was used to measure the three-dimensional positions of the femur, tibia and patella during level walking and downhill walking over ground. The PTMA was found from the location of the instantaneous axis of rotation at the knee and the line-of-action of the patellar tendon. ResultsThere was a small but statistically significant difference in the mean PTMA calculated over one cycle of level walking between the ACLR knee and the contralateral knee, with the mean PTMA in the ACLR knee being 1.5 mm larger (p < 0.01). In downhill walking, statistically significant differences were found in the range 15°– 25° of knee flexion, where the PTMA was 4.7 mm larger in the ACLR knee compared to the contralateral knee (p < 0.01). SignificanceSignificant differences were evident in the mean PTMA between the ACLR knee and the contralateral knee in both activities, however, the magnitudes of these differences were relatively small (range: 3–10%), indicating that ACLR surgery successfully restores the moment arm of the knee-extensor mechanism during dynamic activity.

Effects of Weight-Bearing on Tibiofemoral, Patellofemoral, and Patellar Tendon Kinematics in Older Adults.

Quantification of natural knee kinematics is essential for the assessment of joint function in the diagnosis of pathologies. Combined measurements of tibiofemoral and patellofemoral joint kinematics are necessary because knee pathologies, such as progression of osteoarthritis and patellar instability, are a frequent concern in both articulations. Combined measurement of tibiofemoral and patellofemoral kinematics also enables calculation of important quantities, specifically patellar tendon angle, which partly determines the loading vector at the tibiofemoral joint and patellar tendon moment arm. The goals of this research were to measure the differences in tibiofemoral and patellofemoral kinematics, patellar tendon angle (PTA), and patellar tendon moment arm (PTMA) that occur during non-weight-bearing and weight-bearing activities in older adults. Methods: High-speed stereo radiography was used to measure the kinematics of the tibiofemoral and patellofemoral joints in subjects as they performed seated, non-weight-bearing knee extension and two weight-bearing activities: lunge and chair rise. PTA and PTMA were extracted from the subject’s patellofemoral and tibiofemoral kinematics. Kinematics and the root mean square difference (RMSD) between non-weight-bearing and weight-bearing activities were compared across subjects and activities. Results: Internal rotation increased with weight-bearing (mean RMSD from knee extension was 4.2 ± 2.4° for lunge and 3.6 ± 1.8° for chair rise), and anterior translation was also greater (mean RMSD from knee extension was 2.2 ± 1.2 mm for lunge and 2.3 ± 1.4 mm for chair rise). Patellar tilt and medial–lateral translation changed from non-weight-bearing to weight-bearing. Changes of the patellar tendon from non-weight-bearing to weight-bearing were significant only for PTMA. Conclusions: While weight-bearing elicited changes in knee kinematics, in most degrees of freedoms, these differences were exceeded by intersubject differences. These results provide comparative kinematics for the evaluation of knee pathology and treatment in older adults.

Children who idiopathically toe-walk have greater plantarflexor effective mechanical advantage compared to typically developing children

PurposeThe effective mechanical advantage (EMA) of the plantarflexor muscles is important for gait function and is likely different from typical in equinus gait. However, this has never been quantified for children who idiopathically toe-walk (ITW), despite being routinely altered through clinical intervention.MethodsThis study quantified the Achilles tendon and ground reaction force (GRF) moment arms, and the plantarflexor EMA of 5 children who ITW and 14 typically developing (TD) children, whilst walking on an instrumented treadmill.ResultsThere was no difference in the Achilles tendon moment arm length throughout stance between groups (p > 0.05). Children who ITW had a significantly greater GRF moment arm length in early stance (20–24% p = 0.001), but a significantly shorter GRF moment arm length during propulsion (68–74% of stance; p = 0.013) than TD children. Therefore, children who ITW had a greater plantarflexor EMA than TD children when active plantarflexion moments were being generated (60–70% of stance; p = 0.007). Consequently, it was estimated that children who ITW required 30% less plantarflexor muscle force for propulsion.ConclusionClinical decision making should fully consider that interventions which aim to restore a typical heel-toe gait pattern risk compromising this advantageous leverage and thus, may increase the strength requirements for gait.

Factors correlated with running economy among elite middle‐ and long‐distance runners

Running economy (RE) at a given submaximal running velocity is defined as oxygen consumption per minute per kg body mass. We investigated RE in a group of 12 male elite runners of national class. In addition to RE at 14 and 18 km h−1 we measured the maximal oxygen consumption (VO2max) and anthropometric measures including the moment arm of the Achilles tendon (L Ach), shank and foot volumes, and muscular fascicle lengths. A 3‐D biomechanical movement analysis of treadmill running was also conducted. RE was on average 47.8 and 62.3 ml O2 min−1 kg−1 at 14 and 18 km h−1. Maximal difference between the individual athletes was 21% at 18 km h−1. Mechanical work rate was significantly correlated with VO2 measured in L min−1 at both running velocities. However, RE and relative work rate were not significantly correlated. L Ach was significantly correlated with RE at 18 km h−1 implying that a short moment arm is advantageous regarding RE. Neither foot volume nor shank volume were significantly correlated to RE. Relative muscle fascicle length of m. soleus was significantly correlated with RE at 18 km h−1. Whole body stiffness and leg stiffness were significantly correlated with L Ach indicating that a short moment arm coincided with high stiffness. It is concluded that a short L Ach is correlated with RE. Probably, a short L Ach allows for storage of a larger amount of elastic energy in the tendon and influences the force–velocity relation toward a lower contraction velocity.

Association between patellar tendon moment arm and running performance in endurance runners.

A shorter joint moment arm (MA) may help maintain the necessary muscle force when muscle contractions are repeated. This beneficial effect may contribute to reducing the energy cost during running. In this study, we examined the correlation between patellar tendon MA and running performance in endurance runners. The patellar tendon MA and quadriceps femoris muscle volume (MV) in 42 male endurance runners and 14 body size‐matched male untrained participants were measured using a 1.5‐T magnetic resonance system. The patellar tendon MA was significantly shorter in endurance runners than in untrained participants (p = 0.034, d = 0.65). In endurance runners, shorter patellar tendon MA correlated significantly with better personal best 5000‐m race rime (r = 0.322, p = 0.034). A trend toward such a significant correlation was obtained between quadriceps femoris MV and personal best 5000‐m race time (r = 0.303, p = 0.051). Although the correlation between patellar tendon MA and personal best 5000‐m race time did not remain significant after adjusting for the quadriceps femoris MV (partial r = 0.247, p = 0.120), a stepwise multiple regression analysis (conducted with body height, body mass, patellar tendon MA, and quadriceps femoris MV) selected the patellar tendon MA (β = 0.322) as only a predictive variable for the personal best 5000‐m race time (adjusted R 2 = 0.081, p = 0.038). These findings suggest that the shorter patellar tendon MA, partially accorded with the smaller quadriceps femoris size, may be a favorable morphological variable for better running performance in endurance runners.

Variation in the patellar tendon moment arm identified with an improved measurement framework.

The mechanical advantage of the knee extensor mechanism depends heavily on the patellar tendon moment arm (PTMA). Understanding which factors contribute to its variation may help improve functional outcomes following arthroplasty. This study optimized PTMA measurement, allowing us to quantify the contribution of different variables. The PTMA was calculated about the instantaneous helical axis of tibiofemoral rotation from optical tracked kinematics. A fabricated knee model facilitated calculation optimization, comparing four data smoothing techniques (raw, Butterworth filtering, generalized cross-validated cubic spline-interpolation and combined filtering/interpolation). The PTMA was then measured for 24 fresh-frozen cadaveric knees, under physiologically based loading and extension rates. Combined filtering/interpolation enabled sub-mm PTMA calculation accuracy throughout the range of motion (root-mean-squared error 0.2 mm, max error 0.4 mm), whereas large errors were measured for raw, filtered-only and interpolated-only techniques at terminal flexion/extension. Before scaling, the mean PTMA was 46 mm; PTMA magnitude was consistently larger in males (mean differences: 5 to 10 mm, p < .05) and was strongly related to knee size: larger knees have a larger PTMA. However, while scaling eliminated sex differences in PTMA magnitude, the peak PTMA occurred closer to terminal extension in females (female 15°, male 29°, p = .01). Knee size accounted for two-thirds of the variation in PTMA magnitude, but not the flexion angle where peak PTMA occurred. This substantial variation in angle of peak PTMA has implications for the design of musculoskeletal models and morphotype-specific arthroplasty. The developed calculation framework is applicable both in vivo and vitro for accurate PTMA measurement.

Normative Achilles and patellar tendon shear wave speeds and loading patterns during walking in typically developing children.

Motion analysis is commonly used to evaluate joint kinetics in children with cerebral palsy who exhibit gait disorders. However, one cannot readily infer muscle-tendon forces from joint kinetics. This study investigates the use of shear wave tensiometry to characterize Achilles and patellar tendon forces during gait. How do Achilles and patellar tendon wave speed and loading modulate with walking speed in typically developing children? Twelve typically developing children (9-16 years old) walked on an instrumented treadmill with shear wave tensiometers over their Achilles (n = 11) and patellar (n = 9) tendons. Wave speeds were recorded at five leg length-normalized walking speeds (very slow to very fast). Achilles and patellar tendon moment arms were measured with synchronized ultrasound and motion capture. The tendon wave speed-load relationship was calibrated at the typical walking speed and used to estimate tendon loading at other walking speeds. Characteristic Achilles and patellar tendon wave speed trajectories exhibited two peaks over a gait cycle. Peak Achilles tendon force closely aligned with peak ankle plantarflexor moment during pushoff, though force exhibited less modulation with walking speed. A second peak in late swing Achilles loading, which was not evident from the ankle moment, increased significantly with walking speed (p < 0.001). The two peaks in patellar tendon loading occurred at 12 ± 1% and 68 ± 6% of the gait cycle, matching the timing of peak knee extension moment in early stance and early swing. Both patellar tendon load peaks increased significantly with walking speed (p < 0.05). This is the first study to use shear wave tensiometry to characterize Achilles and patellar tendon loading during gait in children. These data could serve as a normative comparison when using tensiometry to identify abnormal tendon loading patterns in individuals who exhibit equinus and/or crouch gait.

The Human Muscle Size and Strength Relationship: Effects of Architecture, Muscle Force, and Measurement Location.

This study aimed to determine the best muscle size index of muscle strength by establishing if incorporating muscle architecture measurements improved the human muscle size-strength relationship. The influence of calculating muscle force and the location of anatomical cross-sectional area (ACSA) measurements on this relationship were also examined. Fifty-two recreationally active men completed unilateral isometric knee extension strength assessments and magnetic resonance imaging scans of the dominant thigh and knee to determine quadriceps femoris size variables (ACSA along the length of the femur, maximum ACSA (ACSAMAX), and volume (VOL)) and patellar tendon moment arm. Ultrasound images (two sites per constituent muscle) were analyzed to quantify muscle architecture (fascicle length, pennation angle) and, when combined with VOL (from magnetic resonance imaging), facilitated calculation of quadriceps femoris effective PCSA (EFFPCSA) as potentially the best muscle size determinant of strength. Muscle force was calculated by dividing maximum voluntary torque by the moment arm and addition of antagonist torque (derived from hamstring EMG). The associations of EFFPCSA (r = 0.685), ACSAMAX (r = 0.697), or VOL (r = 0.773) with strength did not differ, although qualitatively VOL explained 59.8% of the variance in strength, ~11%-13% greater than EFFPCSA or ACSAMAX. All muscle size variables had weaker associations with muscle force than maximum voluntary torque. The association of strength-ACSA at 65% of femur length (r = 0.719) was greater than for ACSA measured between 10%-55% and 75%-90% (r = -0.042-0.633) of femur length. In conclusion, using contemporary methods to assess muscle architecture and calculate EFFPCSA did not enhance the muscle strength-size association. For understanding/monitoring muscle size, the major determinant of strength, these findings support the assessment of muscle volume, which is independent of architecture measurements and was most highly correlated with strength.

Shorter heels are linked with greater elastic energy storage in the Achilles tendon

Previous research suggests that the moment arm of the m. triceps surae tendon (i.e., Achilles tendon), is positively correlated with the energetic cost of running. This relationship is derived from a model which predicts that shorter ankle moment arms place larger loads on the Achilles tendon, which should result in a greater amount of elastic energy storage and return. However, previous research has not empirically tested this assumed relationship. We test this hypothesis using an inverse dynamics approach in human subjects (n = 24) at speeds ranging from walking to sprinting. The spring function of the Achilles tendon was evaluated using specific net work, a metric of mechanical energy production versus absorption at a limb joint. We also combined kinematic and morphological data to directly estimate tendon stress and elastic energy storage. We find that moment arm length significantly determines the spring-like behavior of the Achilles tendon, as well as estimates of mass-specific tendon stress and elastic energy storage at running and sprinting speeds. Our results provide support for the relationship between short Achilles tendon moment arms and increased elastic energy storage, providing an empirical mechanical rationale for previous studies demonstrating a relationship between calcaneal length and running economy. We also demonstrate that speed and kinematics moderate tendon performance, suggesting a complex relationship between lower limb geometry and foot strike pattern.

Measurement of instantaneous Achilles tendon moment arm and force during the stance phase of running

Accurate estimates of the Achilles tendon (AT) moment arm (ATMA) are necessary for investigating triceps surae muscle-tendon unit loading and function. There are limited reported values of ATMA during running. By combining ultrasound and motion capture, ATMA was estimated during the stance phase of running. Group mean ATMA was estimated at 49.2 ± 3.8 mm and 37.5 ± 5.3 mm, relative to the centre of rotation (malleoli markers midpoint) and the ankle finite helical axis respectively. Differences in the corresponding estimated AT forces reached up to 3100 N approximately. Such discrepancies can lead to misinterpretation of the whole muscle-tendon unit function.