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

The development of lower limb musculoskeletal models with clinical relevance is dependent upon the fidelity of the mathematical description of the lower limb. Part 2: patient-specific geometry

Musculoskeletal models have the potential to evolve into sensitive clinical tools that provide relevant therapeutic guidance. A key impediment to this is the lack of understanding as to the function of such models. In order to improve this it is useful to recognise that musculoskeletal modelling is the mathematical description of musculoskeletal movement – a process that involves the construction and solution of equations of motion. These equations are derived from standard mechanical considerations and the mathematical representation of anatomy. The fidelity of musculoskeletal models is highly dependent on the assumption that such representations also describe the function of the musculoskeletal geometry. In addition, it is important to understand the sensitivity of such representations to patient-specific variations in anatomy. The exploration of these twin considerations will be fundamental to the creation of musculoskeletal modelling tools with clinical relevance and a systematic enquiry of these key parameters is recommended.

The minimum required muscle force for a sit-to-stand task

The purpose of this study was to reveal the minimum required muscle force for a sit-to-stand task. Combining experimental procedures and computational processing, movements of various sit-to-stand patterns were obtained. Muscle forces and activations during a movement were calculated with an inverse dynamics method and a static numerical optimization method. The required muscle force for each movement was calculated with peak muscle activation, muscle physiological cross sectional area and specific tension. The robustness of the results was quantitatively evaluated with sensitivity analyses. From the results, a distinct threshold was found for the total required muscle force of the hip and knee extensors. Specifically, two findings were revealed: (1) the total force of hip and knee extensors is appropriate as the index of minimum required muscle force for a sit-to-stand task and (2) the minimum required total force is within the range of 35.3-49.2 N/kg. A muscle is not mechanically independent from other muscles, since each muscle has some synergetic or antagonistic muscles. This means that the mechanical threshold of one muscle varies with the force exertion abilities of other muscles and cannot be evaluated independently. At the same time, some kinds of mechanical threshold necessarily exist in the sit-to-stand task, since a muscle force is an only force to drive the body and people cannot stand up from a chair without muscles. These indicate that the existence of the distinct threshold in the result of the total required muscle force is reasonable.

Inter-individual variability in the adaptation of human muscle specific tension to progressive resistance training

Considerable variation exists between people in the muscle response to resistance training, but there are numerous ways muscle might adapt to overload that might explain this variable response. Therefore, the aim of this study was to quantify the range of responses concerning the training-induced change in maximum voluntary contraction (MVC) knee joint torque, quadriceps femoris (QF) maximum muscle force (F), physiological cross-sectional area (PCSA) and specific tension (F/PCSA). It was hypothesized that the variable change in QF specific tension between individuals would be less than that of MVC. Fifty-three untrained young men performed progressive leg-extension training three times a week for 9 weeks. F was determined from MVC torque, voluntary muscle activation level, antagonist muscle co-activation and patellar tendon moment arm. QF specific tension was established by dividing F by QF PCSA, which was calculated from the ratio of QF muscle volume to muscle fascicle length. MVC torque increased by 26 ± 11% (P < 0.0001; range -1 to 52%), while F increased by 22 ± 11% (P < 0.0001; range -1 to 44%). PCSA increased by 6 ± 4% (P < 0.001; range -3 to 18%) and specific tension increased by 17 ± 11% (P < 0.0001; range -5 to 39%). In conclusion, training-induced changes in F and PCSA varied substantially between individuals, giving rise to greater inter-individual variability in the specific tension response compared to that of MVC. Furthermore, it appears that the change in specific tension is responsible for the variable change in MVC.

Resistance training increases in vivo quadriceps femoris muscle specific tension in young men

AIM

The present study investigated whether in vivo human quadriceps femoris (QF) muscle specific tension changed following strength training by systematically determining QF maximal force and physiological cross-sectional area (PCSA).

METHODS

Seventeen untrained men (20 +/- 2 years) performed high-intensity leg-extension training three times a week for 9 weeks. Maximum tendon force (F(t)) was calculated from maximum voluntary contraction (MVC) torque, corrected for agonist and antagonist muscle activation, and moment arm length (d(PT)) before and after training. QF PCSA was calculated as the sum of the four component muscle volumes, each divided by its fascicle length. Dividing F(t) by the sum of the component muscle PCSAs, each multiplied by the cosine of the respective fascicle pennation angle, provided QF specific tension.

RESULTS

MVC torque and QF activation increased by 31% (P < 0.01) and 3% (P < 0.05), respectively, but there was no change in antagonist co-activation or d(PT). Subsequently, F(t) increased by 27% (P < 0.01). QF volume increased by 6% but fascicle length did not change in any of the component muscles, leading to a 6% increase in QF PCSA (P < 0.05). Fascicle pennation angle increased by 5% (P < 0.01) but only in the vastus lateralis muscle. Consequently, QF specific tension increased by 20% (P < 0.01).

CONCLUSION

An increase in human muscle specific tension appears to be a real consequence of resistance training rather than being an artefact of measuring errors but the underlying cause of this phenomenon remains to be determined.

Moment arms of the knee extensor mechanism in children and adults

In the present study we investigated whether there are differences in the patellar tendon moment arm (PTMA)-knee angle relationship between pre-pubertal children and adults, and whether the PTMA length scales to relevant anthropometric measurements in the two groups. Anthropometric characteristics and the PTMA length-joint angle relationships were determined in 20 adults and 20 pre-pubertal children of both genders. The anthropometric characteristics measured were height, body mass, knee circumference, medio-lateral knee breadth, anterior-posterior knee depth, leg length, femur length and tibia length. The PTMA was quantified from magnetic resonance images using the geometric centre of the femoral condyle method, at every 5 degrees between 55 degrees and 90 degrees of knee flexion (0 degrees is full extension). Adults had a significantly greater PTMA length at all joint angles (4.2 +/- 0.4 vs. 3.6 +/- 0.3 cm at 90 degrees ; P < 0.01), with the PTMA length decreasing from knee extension to knee flexion similarly in both adults and children. There were no significant and strong correlations between the PTMA and anthropometric measures in adults for any joint angle. In contrast, the PTMA correlated and scaled with anthropometric characteristics for the children (P < 0.05, r = 0.49-0.9) at all joint angles. The PTMA length in children was most accurately predicted at 85 degrees of flexion from the equation PTMA = -0.25 + 0.083 x tibia length + 0.02 x leg length (R(2) = 0.83). These findings indicate that the knee extensor mechanism in pre-pubertal children should not be considered to be a 'scaled-down' version of that in adults.

Training-induced changes in structural and mechanical properties of the patellar tendon are related to muscle hypertrophy but not to strength gains

To obtain a better understanding of the adaptations of human tendon to chronic overloading, we examined the relationships between these adaptations and the changes in muscle structure and function. Fifteen healthy male subjects (20+/-2 yr) underwent 9 wk of knee extension resistance training. Patellar tendon stiffness and modulus were assessed with ultrasonography, and cross-sectional area (CSA) was determined along the entire length of the tendon by using magnetic resonance imaging. In the quadriceps muscles, architecture and volume measurements were combined to obtain physiological CSA (PCSA), and maximal isometric force was recorded. Following training, muscle force and PCSA increased by 31% (P<0.0001) and 7% (P<0.01), respectively. Tendon CSA increased regionally at 20-30%, 60%, and 90-100% of tendon length (5-6%; P<0.05), and tendon stiffness and modulus increased by 24% (P<0.001) and 20% (P<0.01), respectively. Although none of the tendon adaptations were related to strength gains, we observed a positive correlation between the increase in quadriceps PCSA and the increases in tendon stiffness (r=0.68; P<0.01) and modulus (r=0.75; P<0.01). Unexpectedly, the increase in muscle PCSA was inversely related to the distal and the mean increases in tendon CSA (in both cases, r=-0.64; P<0.05). These data suggest that, following short-term resistance training, changes in tendon mechanical and material properties are more closely related to the overall loading history and that tendon hypertrophy is driven by other mechanisms than those eliciting tendon stiffening.

A comparison of different two-dimensional approaches for the determination of the patellar tendon moment arm length

The purpose of this study was to estimate and compare the moment arm length of the patellar tendon (d) during passive knee extension using three different reference landmarks; instant centre of rotation (ICR), tibiofemoral contact point (TFCP) and geometrical centre of the posterior femoral condyles (GCFC). Measurements were taken on the right leg on seven healthy males during passive knee rotation performed by the motor of a Cybex Norm isokinetic dynamometer. Moment arms lengths were obtained by analysing lateral X-ray images recorded using a GE FlexiView 8800 C-arm videofluoroscopy system. The d-knee joint angle relations with respect to GCFC and ICR were similar, with decreasing values from full knee extension (~5.8 cm for d (GCFC) and ~5.9 cm for d (ICR)) to 90 degrees of knee flexion (~4.8 cm for both d (GCFC) and d (ICR)). However, the d (TFCP)-knee joint angle relation had an ascending-descending shape, with the highest d (TFCP) value (~5 cm) at 60 degrees of knee flexion. There was no significant difference between the GCFC and ICR methods at any knee joint angle. In contrast, there were significant differences (P < 0.01) between d (ICR) and d (TFCP) at 0 degrees , 15 degrees , 30 degrees and 45 degrees of knee flexion and between d (GCFC) and d (TFCP) at 0 degrees , 15 degrees and 30 degrees of knee flexion (P < 0.01). This study shows that when using different knee joint rotation centre definitions, there are significant differences in the estimates of the patellar tendon moment arm length, especially in more extended knee joint positions. These differences can have serious implications for joint modelling and loading applications.

Computational biomechanics of knee joint in open kinetic chain extension exercises

Open kinetic chain (OKC) extension exercises are commonly performed to strengthen quadriceps muscles and restore joint function in performance enhancement programs, in exercise therapies and following joint reconstruction. Using a validated 3D nonlinear finite element model, the detailed biomechanics of the entire joint in OKC extension exercises are investigated at 0, 30, 60 and 90 degrees joint angles. Two loading cases are simulated; one with only the weight of the leg and the foot while the second considers also a moderate resistant force of 30 N acting at the ankle perpendicular to the tibia. The presence of the 30 N markedly influences the results both in terms of the magnitude and the trend. The resistant load substantially increases the required quadriceps, patellar tendon, cruciate ligaments and joint contact forces, especially at near 90 degrees angles with the exception of ACL force that is increased at 0 degrees angle. At post-ACL reconstruction period or in the joint with ACL injury, the exercise should preferably be avoided at near full extension positions under large resistant forces.

Time course of muscular, neural and tendinous adaptations to 23 day unilateral lower-limb suspension in young men

Muscles and tendons are highly adaptive to changes in chronic loading, though little is known about the adaptative time course. We tested the hypothesis that, in response to unilateral lower limb suspension (ULLS), the magnitude of tendon mechanical adaptations would match or exceed those of skeletal muscle. Seventeen men (1.79 +/- 0.05 m, 76.6 +/- 10.3 kg, 22.3 +/- 3.8 years) underwent ULLS for 23 days (n = 9) or acted as controls (n = 8). Knee extensor (KE) torque, voluntary activation (VA), cross-sectional area (CSA) (by magnetic resonance imaging), vastus lateralis fascicle length (L(f)) and pennation angle (), patellar tendon stiffness and Young's modulus (by ultrasonography) were measured before, during and at the end of ULLS. After 14 and 23 days (i) KE torque decreased by 14.8 +/- 5.5% (P < 0.001) and 21.0 +/- 7.1% (P < 0.001), respectively; (ii) VA did not change; (iii) KE CSA decreased by 5.2 +/- 0.7% (P < 0.001) and 10.0 +/- 2.0% (P < 0.001), respectively; L(f) decreased by 5.9% (n.s.) and 7.7% (P < 0.05), respectively, and by 3.2% (P < 0.05) and 7.6% (P < 0.01); (iv) tendon stiffness decreased by 9.8 +/- 8.2% (P < 0.05) and 29.3 +/- 11.5% (P < 0.005), respectively, and Young's modulus by 9.2 +/- 8.2% (P < 0.05) and 30.1 +/- 11.9% (P < 0.01), respectively, with no changes in the controls. Hence, ULLS induces rapid losses of KE muscle size, architecture and function, but not in neural drive. Significant deterioration in tendon mechanical properties also occurs within 2 weeks, exacerbating in the third week of ULLS. Rehabilitation to limit muscle and tendon deterioration should probably start within 2 weeks of unloading.

Patellar tendon load in different types of eccentric squats

BACKGROUND

Differences in mechanical loading of the patellar tendon have been suggested as a reason for varying effects in rehabilitation of patellar tendinopathy using different eccentric squat exercises and devices. The aim was to characterize the magnitude and pattern of mechanical load at the knee and on the patellar tendon during four types of eccentric squat.

METHODS

Subjects performed squats with a submaximal free weight and with maximal effort in a device for eccentric overloading (Bromsman), on a decline board and horizontal surface. Kinematics was recorded with a motion-capture system, reaction forces with force plates, and electromyography from three leg muscles with surface electrodes. Inverse dynamics was used to calculate knee joint kinetics.

FINDINGS

Eccentric work, mean and peak patellar tendon force, and angle at peak force were greater (25-30%) for squats on decline board compared to horizontal surface with free weight, but not in Bromsman. Higher knee load forces (60-80%), but not work, were observed with Bromsman than free weight. Angular excursions at the knee and ankle were larger with decline board, particularly with free weight, and smaller in Bromsman than with free weight. Mean electromyography was greater on a decline board for gastrocnemius (13%) and vastus medialis (6%) with free weight, but in Bromsman only for gastrocnemius (7%).

INTERPRETATION

The results demonstrated clear differences in the biomechanical loading on the knee during different squat exercises. Quantification of such differences provides information that could be used to explain differences in rehabilitation effects as well as in designing more optimal rehabilitation exercises for patellar tendinopathy.

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

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

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

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