Lower-extremity musculoskeletal geometry affects the calculation of patellofemoral forces in vertical jumping and weightlifting

General Muscle Torque Generator Model for a Two Degree-of-Freedom Shoulder Joint

Muscle torque generators (MTGs) have been developed as an alternative to muscle-force models, reducing the muscle-force model complexity to a single torque at the joint. Current MTGs can only be applied to single Degree-of-freedom (DoF) joints, leading to complications in modeling joints with multiple-DoFs such as the shoulder. This study aimed to develop an MTG model that accounts for the coupling between 2-DoF at the shoulder joint: shoulder plane of elevation (horizontal abduction/adduction) and shoulder elevation (flexion/extension). Three different 2-DoF MTG equations were developed to model the coupling between these two movements. Net joint torques at the shoulder were determined for 20 participants (10 females and 10 males) in isometric, isokinetic, and passive tests. Curve and surface polynomial fitting were used to find the best general fit for the experimental data in terms of the different degrees of coupling. The models were validated against experimental isokinetic torque data. It was determined that implicit coupling that used interpolation between single-DoF MTGs resulted in the lowest root-mean-square percent error of 8.5%. The work demonstrated that general MTG models can predict torque results that are dependent on multiple-DoFs of the shoulder.

Bilateral Asymmetry in Knee and Hip Musculoskeletal Loading During Stair Ascending/Descending in Individuals with Unilateral Mild-to-Moderate Medial Knee Osteoarthritis

Most cases of unilateral knee osteoarthritis (OA) progress to bilateral OA within 10 years. Biomechanical asymmetries have been implicated in contralateral OA development; however, gait analysis alone does not consistently detect asymmetries in OA patient gait. Stair ambulation is a more demanding activity that may be more suited to reveal between-leg asymmetries in OA patients. The objective of this study was to investigate the between-leg biomechanical differences in patients with unilateral mild-to-moderate knee OA. Sixteen unilateral mild-to-moderate medial knee OA patients and 16 healthy individuals underwent kinematic and kinetic analysis of stair ascent and descent. Stair ascent produced higher loading and muscle forces in the unaffected limb compared to the OA limb, and stair descent produced lower loading on the OA limb compared to healthy subjects. These biomechanical differences were apparent in the ankle, knee, and hip joints. The implications of these findings are that OA patients rely more heavily on their unaffected sides than the affected side in stair ascent, a strategy that may be detrimental to the unaffected joint health. The reduction in affected limb loading in stair descent is thought to be related to minimizing pain.

A Musculoskeletal Model Customized for Sagittal and Frontal Knee Kinematics with Improved Knee Joint Stability

Current lower limb musculoskeletal (MSK) models focus on sagittal plane kinematics. However, abnormal gait is typically associated with sagittal plane motions crossing into other planes, limiting the use of current MSK models. The purpose of this study was twofold, first, to extend the capability of a full-body MSK model from the literature to include frontal knee plane kinematics during healthy gait, and second, to propose and implement a realistic muscle discretization technique. Two MSK model constructs were derived - the first construct (Knee2_SM) allowed two degrees of freedom (sagittal and coronal) at the knee and the second construct (Knee2_MM) implemented multi-line elements for all the lower limb muscles in conjunction with two knee degrees of freedom. Motion analysis data of normal gait cycle from 10 healthy adults were used to compare joint kinematics, muscle moment arms, muscle forces, and muscle activations, between new constructs and the original model. Knee varus-valgus trajectories were estimated with the mean peak values ranging from 9.49° valgus to 1.57° varus. Knee2_MM predicted significant difference (p < 0.05) in moment arms and forces in those muscles responsible for medial-lateral stability of the knee. The simulated muscle activations generated by Knee2_MM model matched more closely to the experimental EMG when qualitatively compared. This study enhances the capability of sagittal plane full-body MSK model to incorporate knee varus-valgus motion while keeping the joint stability intact and improving muscle prediction.

Knee Forces During Landing in Men and Women

Sex differences in biomechanics may provide one explanation for the greater incidence of knee injuries in women, but few studies have compared internal forces. In this study, a musculoskeletal model was used to compare male and female, bilateral and unilateral landings based on motion capture and force plate data. Participants were classified as landing medially or laterally loaded based upon the mediolateral load share at the knee (bilateral: p < 0.001, η²=0.452; unilateral: p < 0.001, η² = 0.444). Knee kinematics and ground reaction forces were not different between the two groups (p > 0.05, η² = 0.001 - 0.059), but there were differences in muscular recruitment. Landing strategy did not appear to be dependent on sex. However, for both medially and laterally loaded bilateral landings men had greater gluteal (p = 0.017, η² = 0.085) and hamstrings forces (p < 0.001, η² = 0.183), whereas women had greater quadriceps forces (p = 0.004, η² = 0.116). This study demonstrates an association between muscular recruitment and medially loaded landings. Landing strategy seems to be a function of skill not sex; however, within a particular landing strategy there may be sex differences in muscular activation that contribute to the difference in injury rates.

Extra excitation of biceps femoris during neuromuscular electrical stimulation reduces knee medial loading

Medial knee joint osteoarthritis (OA) is a debilitating and prevalent condition. Surgical treatment consists of redistributing the forces from the medial to the lateral compartment through osteotomy, or replacing the joint surfaces. As the mediolateral load distribution is related to the action of the musculature around the knee, the aim of this study was to devise a technique to redistribute these forces non-surgically through changes in muscle excitation. Eight healthy subjects participated in the experiment, and neuromuscular electrical stimulation was used to change the muscle forces around the knee. A musculoskeletal model was used to quantify the loading on the medial compartment of the knee, and a novel algorithm devised and implemented to simulate neuromuscular electrical stimulation. The forces and moments at the knee, ground reaction forces, walking velocity and step length were quantified before and after stimulation. Stimulation of the biceps femoris resulted in a significant decrease in the second peak of the medial knee joint loading by up to 0.17 body weight (p = 0.016). Kinematic parameters were not significantly affected. Neuromuscular electrical stimulation can decrease the peak loads on the medial compartment of the knee, and thus offers a promising therapy for medial knee joint OA.

Advancing System Performance with Redundancy: From Biological to Artificial Designs

Redundancy is a fundamental characteristic of many biological processes such as those in the genetic, visual, muscular, and nervous systems, yet its driven mechanism has not been fully comprehended. Until recently, the only understanding of redundancy is as a mean to attain fault tolerance, which is reflected in the design of many man-made systems. On the contrary, our previous work on redundant sensing (RS) has demonstrated an example where redundancy can be engineered solely for enhancing accuracy and precision. The design was inspired by the binocular structure of human vision, which we believe may share a similar operation. In this letter, we present a unified theory describing how such utilization of redundancy is feasible through two complementary mechanisms: representational redundancy (RPR) and entangled redundancy (ETR). We also point out two additional examples where our new understanding of redundancy can be applied to justify a system's superior performance. One is the human musculoskeletal system (HMS), a biological instance, and the other is the deep residual neural network (ResNet), an artificial counterpart. We envision that our theory would provide a framework for the future development of bio-inspired redundant artificial systems, as well as assist studies of the fundamental mechanisms governing various biological processes.

An important role of the biarticular hamstrings is to exert internal/external rotation moments on the tibia during vertical jumping

Most research considering biarticular muscle function has tended to focus on the sagittal plane. Instead, the purpose of this study was to evaluate the internal/external rotation moment arms of the biarticular muscles of the knee, and then to explore their function. The FreeBody musculoskeletal model of the lower limb was used to calculate the moment arms and moments that each of the muscles of the knee exerted on the proximal tibia of 12 athletic males during vertical jumping. Biceps femoris and tensor fascia latae were external rotators of the tibia, whereas semimembranosus, semitendinosus, sartorius, gracilis, popliteus and the patellar tendon were internal rotators. The magnitudes of the internal/external rotation and flexion moments exerted on the tibia by the biarticular hamstrings were similar, suggesting that the creation of internal/external rotation is a key aspect of their role. One potential reason is to stabilise the tibia during femoral extension (and it is argued that it may be helpful to characterise the creation of active joint stability as the stabilisation of one segment during the rotation of an adjacent segment). A second explanation may be to mechanically couple hip abduction when the hip is flexed with internal rotation of the tibia.

Effects of an 8-week strength training intervention on tibiofemoral joint loading during landing: a cohort study

Objectives

To use a musculoskeletal model of the lower limb to evaluate the effect of a strength training intervention on the muscle and joint contact forces experienced by untrained women during landing.

Methods

Sixteen untrained women between 18 and 28 years participated in this cohort study, split equally between intervention and control groups. The intervention group trained for 8 weeks targeting improvements in posterior leg strength. The mechanics of bilateral and unilateral drop landings from a 30 cm platform were recorded preintervention and postintervention, as was the isometric strength of the lower limb during a hip extension test. The internal muscle and joint contact forces were calculated using FreeBody, a musculoskeletal model.

Results

The strength of the intervention group increased by an average of 35% (P<0.05; pre: 133±36 n, post: 180±39 n), whereas the control group showed no change (pre: 152±36 n, post: 157±46 n). There were only small changes from pre-test to post-test in the kinematics and ground reaction forces during landing that were not statistically significant. Both groups exhibited a post-test increase in gluteal muscle force during landing and a lateral to medial shift in tibiofemoral joint loading in both landings. However, the magnitude of the increase in gluteal force and lateral to medial shift was significantly greater in the intervention group.

Conclusion

Strength training can promote a lateral to medial shift in tibiofemoral force (mediated by an increase in gluteal force) that is consistent with a reduction in valgus loading. This in turn could help prevent injuries that are due to abnormal knee loading such as anterior cruciate ligament ruptures, patellar dislocation and patellofemoral pain.

Reliability and Minimal Detectable Change Values for Predictions of Knee Forces during Gait and Stair Ascent Derived from the FreeBody Musculoskeletal Model of the Lower Limb

FreeBody is a musculoskeletal model of the lower limb used to calculate predictions of muscle and joint contact forces. The validation of FreeBody has been described in a number of publications; however, its reliability has yet to be established. The purpose of this study was, therefore, to establish the test-retest reliability of FreeBody in a population of healthy adults in order to add support to previous and future research using FreeBody that demonstrates differences between cohorts after an intervention. We hypothesized that test-retest estimations of knee contact forces from FreeBody would demonstrate a high intra-class correlation. Kinematic and kinetic data from nine older participants (4 men: mean age = 63 ± 11 years; 5 women: mean age = 49 ± 4 years) performing level walking and stair ascent was collected on consecutive days and then analyzed using FreeBody. There was a good level of intra-session agreement between the waveforms for the individual trials of each activity during testing session 1 (R = 0.79-0.97). Similarly, overall there was a good inter-session agreement within subjects (R = 0.69-0.97) although some subjects showed better agreement than others. There was a high level of agreement between the group mean waveforms of the two sessions for all variables (R = 0.882-0.997). The intra-class correlation coefficients (ICC) were very high for peak tibiofemoral joint contact forces (TFJ) and hamstring forces during gait, for peak patellofemoral joint contact forces and quadriceps forces during stair ascent and for peak lateral TFJ and the proportion of TFJ accounted for by the medial compartment during both tasks (ICC = 0.86-0.96). Minimal detectable change (MDC) of the peak knee forces during gait ranged between 0.43 and 1.53 × body weight (18-170% of the mean peak values). The smallest MDCs were found for medial TFJ share (4.1 and 5.8% for walking and stair ascent, respectively, or 4.8 and 6.7% of the mean peak values). In conclusion, the results of this study support the use of FreeBody to investigate the effect of interventions on muscle and joint contact forces at the cohort level, but care should be taken if using FreeBody at the subject level.

Effect of a gluteal activation warm-up on explosive exercise performance

Objectives

To evaluate the effect of a gluteal activation warm-up on the performance of an explosive exercise (the high hang pull (HHP)).

Methods

Seventeen professional rugby union players performed one set of three HHPs (with 80% of their one repetition maximum load) following both a control and activation warm-up. Peak electrical activity of the gluteus maximus and medius was quantified using electromyography (EMG). In addition, the kinematics and kinetics of nine players was also recorded using force plate and motion capture technology. These data were analysed using a previously described musculoskeletal model of the right lower limb in order to provide estimates of the muscular force expressed during the movement.

Results

The mean peak EMG activity of the gluteus maximus was significantly lower following the activation warm-up as compared with the control (p<0.05, effect size d=0.30). There were no significant differences in the mean peak estimated forces in gluteus maximus and medius, the quadriceps or hamstrings (p=0.053), although there was a trend towards increased force in gluteus maximus and hamstrings following the activation warm-up. There were no differences between the ground reaction forces following the two warm-ups.

Conclusion

This study suggests that a gluteal activation warm-up may facilitate recruitment of the gluteal musculature by potentiating the glutes in such a way that a smaller neural drive evokes the same or greater force production during movement. This could in turn potentially improve movement quality.

Prediction of In Vivo Knee Joint Loads Using a Global Probabilistic Analysis

Musculoskeletal models are powerful tools that allow biomechanical investigations and predictions of muscle forces not accessible with experiments. A core challenge modelers must confront is validation. Measurements of muscle activity and joint loading are used for qualitative and indirect validation of muscle force predictions. Subject-specific models have reached high levels of complexity and can predict contact loads with surprising accuracy. However, every deterministic musculoskeletal model contains an intrinsic uncertainty due to the high number of parameters not identifiable in vivo. The objective of this work is to test the impact of intrinsic uncertainty in a scaled-generic model on estimates of muscle and joint loads. Uncertainties in marker placement, limb coronal alignment, body segment parameters, Hill-type muscle parameters, and muscle geometry were modeled with a global probabilistic approach (multiple uncertainties included in a single analysis). 5-95% confidence bounds and input/output sensitivities of predicted knee compressive loads and varus/valgus contact moments were estimated for a gait activity of three subjects with telemetric knee implants from the "Grand Challenge Competition." Compressive load predicted for the three subjects showed confidence bounds of 333 ± 248 N, 408 ± 333 N, and 379 ± 244 N when all the sources of uncertainty were included. The measured loads lay inside the predicted 5-95% confidence bounds for 77%, 83%, and 76% of the stance phase. Muscle maximum isometric force, muscle geometry, and marker placement uncertainty most impacted the joint load results. This study demonstrated that identification of these parameters is crucial when subject-specific models are developed.

Influence of the Level of Muscular Redundancy on the Validity of a Musculoskeletal Model

While recent literature has clearly demonstrated that an extensive personalization of the musculoskeletal models was necessary to reach high accuracy, several components of the generic models may be further investigated before defining subject-specific parameters. Among others, the choice in muscular geometry and thus the level of muscular redundancy in the model may have a noticeable influence on the predicted musculotendon and joint contact forces. In this context, the aim of this study was to investigate if the level of muscular redundancy can contribute or not to reduce inaccuracies in tibiofemoral contact forces predictions. For that, the dataset disseminated through the Sixth Grand Challenge Competition to Predict In Vivo Knee Loads was applied to a versatile 3D lower limb musculoskeletal model in which two muscular geometries (i.e., two different levels of muscular redundancy) were implemented. This dataset provides tibiofemoral implant measurements for both medial and lateral compartments and thus allows evaluation of the validity of the model predictions. The results suggest that an increase of the level of muscular redundancy corresponds to a better accuracy of total tibiofemoral contact force whatever the gait pattern investigated. However, the medial and lateral contact forces ratio and accuracy were not necessarily improved when increasing the level of muscular redundancy and may thus be attributed to other parameters such as the location of contact points. To conclude, the muscular geometry, among other components of the generic model, has a noticeable impact on joint contact forces predictions and may thus be correctly chosen even before trying to personalize the model.

Non-linear scaling of a musculoskeletal model of the lower limb using statistical shape models

Accurate muscle geometry for musculoskeletal models is important to enable accurate subject-specific simulations. Commonly, linear scaling is used to obtain individualised muscle geometry. More advanced methods include non-linear scaling using segmented bone surfaces and manual or semi-automatic digitisation of muscle paths from medical images. In this study, a new scaling method combining non-linear scaling with reconstructions of bone surfaces using statistical shape modelling is presented. Statistical Shape Models (SSMs) of femur and tibia/fibula were used to reconstruct bone surfaces of nine subjects. Reference models were created by morphing manually digitised muscle paths to mean shapes of the SSMs using non-linear transformations and inter-subject variability was calculated. Subject-specific models of muscle attachment and via points were created from three reference models. The accuracy was evaluated by calculating the differences between the scaled and manually digitised models. The points defining the muscle paths showed large inter-subject variability at the thigh and shank – up to 26 mm; this was found to limit the accuracy of all studied scaling methods. Errors for the subject-specific muscle point reconstructions of the thigh could be decreased by 9% to 20% by using the non-linear scaling compared to a typical linear scaling method. We conclude that the proposed non-linear scaling method is more accurate than linear scaling methods. Thus, when combined with the ability to reconstruct bone surfaces from incomplete or scattered geometry data using statistical shape models our proposed method is an alternative to linear scaling methods.

The development of a segment-based musculoskeletal model of the lower limb: introducing FreeBody

Traditional approaches to the biomechanical analysis of movement are joint-based; that is the mechanics of the body are described in terms of the forces and moments acting at the joints, and that muscular forces are considered to create moments about the joints. We have recently shown that segment-based approaches, where the mechanics of the body are described by considering the effect of the muscle, ligament and joint contact forces on the segments themselves, can also prove insightful. We have also previously described a simultaneous, optimization-based, musculoskeletal model of the lower limb. However, this prior model incorporates both joint- and segment-based assumptions. The purpose of this study was therefore to develop an entirely segment-based model of the lower limb and to compare its performance to our previous work. The segment-based model was used to estimate the muscle forces found during vertical jumping, which were in turn compared with the muscular activations that have been found in vertical jumping, by using a Geers' metric to quantify the magnitude and phase errors. The segment-based model was shown to have a similar ability to estimate muscle forces as a model based upon our previous work. In the future, we will evaluate the ability of the segment-based model to be used to provide results with clinical relevance, and compare its performance to joint-based approaches. The segment-based model described in this article is publicly available as a GUI-based Matlab® application and in the original source code (at www.msksoftware.org.uk).

Is my model good enough? Best practices for verification and validation of musculoskeletal models and simulations of movement

Computational modeling and simulation of neuromusculoskeletal (NMS) systems enables researchers and clinicians to study the complex dynamics underlying human and animal movement. NMS models use equations derived from physical laws and biology to help solve challenging real-world problems, from designing prosthetics that maximize running speed to developing exoskeletal devices that enable walking after a stroke. NMS modeling and simulation has proliferated in the biomechanics research community over the past 25 years, but the lack of verification and validation standards remains a major barrier to wider adoption and impact. The goal of this paper is to establish practical guidelines for verification and validation of NMS models and simulations that researchers, clinicians, reviewers, and others can adopt to evaluate the accuracy and credibility of modeling studies. In particular, we review a general process for verification and validation applied to NMS models and simulations, including careful formulation of a research question and methods, traditional verification and validation steps, and documentation and sharing of results for use and testing by other researchers. Modeling the NMS system and simulating its motion involves methods to represent neural control, musculoskeletal geometry, muscle-tendon dynamics, contact forces, and multibody dynamics. For each of these components, we review modeling choices and software verification guidelines; discuss variability, errors, uncertainty, and sensitivity relationships; and provide recommendations for verification and validation by comparing experimental data and testing robustness. We present a series of case studies to illustrate key principles. In closing, we discuss challenges the community must overcome to ensure that modeling and simulation are successfully used to solve the broad spectrum of problems that limit human mobility.

Knee moments of anterior cruciate ligament reconstructed and control participants during normal and inclined walking

OBJECTIVES

Prior injury to the knee, particularly anterior cruciate ligament (ACL) injury, is known to predispose one to premature osteoarthritis (OA). The study sought to explore if there was a biomechanical rationale for this process by investigating changes in external knee moments between people with a history of ACL injury and uninjured participants during walking: (1) on different surface inclines and (2) at different speeds. In addition we assessed functional differences between the groups.

PARTICIPANTS

12 participants who had undergone ACL reconstruction (ACLR) and 12 volunteers with no history of knee trauma or injury were recruited into this study. Peak knee flexion and adduction moments were assessed during flat (normal and slow speed), uphill and downhill walking using an inclined walkway with an embedded Kistler Force plate, and a ten-camera Vicon motion capture system. Knee injury and Osteoarthritis Outcome Score (KOOS) was used to assess function. Multivariate analysis of variance (MANOVA) was used to examine statistical differences in gait and KOOS outcomes.

RESULTS

No significant difference was observed in the peak knee adduction moment between ACLR and control participants, however, in further analysis, MANOVA revealed that ACLR participants with an additional meniscal tear or collateral ligament damage (7 participants) had a significantly higher adduction moment (0.33±0.12 Nm/kg m) when compared with those with isolated ACLR (5 participants, 0.1±0.057 Nm/kg m) during gait at their normal speed (p<0.05). A similar (non-significant) trend was seen during slow, uphill and downhill gait.

CONCLUSIONS

Participants with an isolated ACLR had a reduced adductor moment rather an increased moment, thus questioning prior theories on OA development. In contrast, those participants who had sustained associated trauma to other key knee structures were observed to have an increased adduction moment. Additional injury concurrent with an ACL rupture may lead to a higher predisposition to osteoarthritis than isolated ACL deficiency alone.

Measuring body weight distribution during sit-to-stand in patients with early knee osteoarthritis

People with severe degenerative conditions, such as osteoarthritis (OA), have been shown to have altered movement patterns during sit-to-stand. However it remains unclear whether such alterations exist in people with early OA, in the absence of pain. This study aimed to determine if a novel seat could be used to discriminate people with early OA compared with controls. The sit-to-stand task was performed by 20 people with early medial knee OA and 20 age and gender-matched control subjects, using an instrumented seat. OA subjects showed altered weight distribution in the transition phase from sit to stand, in that they placed more load through their unaffected side. Task duration was significantly longer for OA subjects, and ground reaction force integrals were significantly greater for both legs of OA subjects. OA subjects had significantly higher knee flexion and adduction moments in their unaffected compared with affected side. This study has demonstrated that a novel instrumented seat can be used to discriminate people with early medial knee OA during the sit-to-stand activity. These results may be relevant for early interventions to delay or prevent changes in muscle function of the affected limb as well as contralateral knee or hip osteoarthritis in these patients.

Musculoskeletal shoulder models: A technical review and proposals for research foci

Musculoskeletal shoulder models allow non-invasive prediction of parameters that cannot be measured, particularly the loading applied to morphological structures and neurological control. This insight improves treatment and avoidance of pathology and performance evaluation and optimisation. A lack of appropriate validation and knowledge of model parameters’ accuracy may cause reduced clinical success for these models. Instrumented implants have recently been used to validate musculoskeletal models, adding important information to the literature. This development along with increasing prevalence of shoulder models necessitates a fresh review of available models and their utility. The practical uses of models are described. Accuracy of model inputs, modelling techniques and model sensitivity is the main technical review undertaken. Collection and comparison of these parameters are vital to understanding disagreement between model outputs. Trends in shoulder modelling are highlighted: validation through instrumented prostheses, increasing openness and strictly constrained, optimised, measured kinematics. Future directions are recommended: validation through focus on model sub-sections, increased subject specificity with imaging techniques determining muscle and body segment parameters and through different scaling and kinematics optimisation approaches.

Intersegmental moment analysis characterizes the partial correspondence of jumping and jerking

The aim of this study was to quantify internal joint moments of the lower limb during vertical jumping and the weightlifting jerk to improve awareness of the control strategies and correspondence between these activities, and to facilitate understanding of the likely transfer of training effects. Athletic men completed maximal unloaded vertical jumps (n = 12) and explosive push jerks at 40 kg (n = 9). Kinematic data were collected using optical motion tracking and kinetic data via a force plate, both at 200 Hz. Joint moments were calculated using a previously described biomechanical model of the right lower limb. Peak moment results highlighted that sagittal plane control strategies differed between jumping and jerking (p < 0.05) with jerking being a knee dominant task in terms of peak moments as opposed to a more balanced knee and hip strategy in jumping and landing. Jumping and jerking exhibited proximal to distal joint involvement and landing was typically reversed. High variability was seen in nonsagittal moments at the hip and knee. Significant correlations were seen between jump height and hip and knee moments in jumping (p < 0.05). Although hip and knee moments were correlated between jumping and jerking (p < 0.05), joint moments in the jerk were not significantly correlated to jump height (p > 0.05) possibly indicating a limit to the direct transferability of jerk performance to jumping. Ankle joint moments were poorly related to jump performance (p > 0.05). Peak knee and hip moment generating capacity are important to vertical jump performance. The jerk appears to offer an effective strategy to overload joint moment generation in the knee relative to jumping. However, an absence of hip involvement would appear to make it a general, rather than specific, training modality in relation to jumping.

Hip and knee joint loading during vertical jumping and push jerking

BACKGROUND

The internal joint contact forces experienced at the lower limb have been frequently studied in activities of daily living and rehabilitation activities. In contrast, the forces experienced during more dynamic activities are not well understood, and those studies that do exist suggest very high degrees of joint loading.

METHODS

In this study a biomechanical model of the right lower limb was used to calculate the internal joint forces experienced by the lower limb during vertical jumping, landing and push jerking (an explosive exercise derived from the sport of Olympic weightlifting), with a particular emphasis on the forces experienced by the knee.

FINDINGS

The knee experienced mean peak loadings of 2.4-4.6×body weight at the patellofemoral joint, 6.9-9.0×body weight at the tibiofemoral joint, 0.3-1.4×body weight anterior tibial shear and 1.0-3.1×body weight posterior tibial shear. The hip experienced a mean peak loading of 5.5-8.4×body weight and the ankle 8.9-10.0×body weight.

INTERPRETATION

The magnitudes of the total (resultant) joint contact forces at the patellofemoral joint, tibiofemoral joint and hip are greater than those reported in activities of daily living and less dynamic rehabilitation exercises. The information in this study is of importance for medical professionals, coaches and biomedical researchers in improving the understanding of acute and chronic injuries, understanding the performance of prosthetic implants and materials, evaluating the appropriateness of jumping and weightlifting for patient populations and informing the training programmes of healthy populations.

The sensitivity of a lower limb model to axial rotation offsets and muscle bounds at the knee

Soft tissue artifacts during motion capture can lead to errors in kinematics and incorrect estimation of joint angles and segment motion. The aim of this study was to evaluate the effect of shank segment axial rotation and knee rotator muscle bounds on predicted muscle and joint forces in a musculoskeletal model of the lower limb. A maximal height jump for ten subjects was analysed using the original motion data and then modified for different levels of internal and external rotation, and with the upper force bound doubled for five muscles. Both externally rotating the shank and doubling the muscle bounds increased the ability of the model to find a solution in regions of high loading. Muscle force levels in popliteus and tensor fascia latae showed statistically significant differences, but less so in plantaris, sartorius or gracilis. The shear and patellofemoral joint forces were found to be significantly affected by axial rotation during specific phases of the motion and were dependent on the amount of rotation. Fewer differences were observed when doubling the muscle bounds, except for the patellofemoral force and plantaris and sartorius muscle force, which were significantly increased in many of the jump phases. These results give an insight into the behaviour of the model and give an indication of the importance of accurate kinematics and subject-specific geometry.

The development of lower limb musculoskeletal models with clinical relevance is dependent upon the fidelity of the mathematical description of the lower limb. Part I: Equations of motion

Contemporary musculoskeletal modelling research is based upon the assumption that such models will evolve into clinical tools that can be used to guide therapeutic interventions. However, there are a number of questions that must be addressed before this becomes a reality. At its heart, musculoskeletal modelling is a process of formulating and then solving the equations of motion that describe the movement of body segments. Both of these steps are challenging. This article argues that traditional approaches to musculoskeletal modelling have been heavily influenced by the need to simplify this process (and in particular the solution process), and that this has to some degree resulted in approaches that are contrary to the principles of classical mechanics. It is suggested that future work is required to understand how these simplifications affect the outputs of musculoskeletal modelling studies. Equally, to increase their clinical relevance, the models of the future should adhere more closely to the classical mechanics on which they are based.

Influence of joint models on lower-limb musculo-tendon forces and three-dimensional joint reaction forces during gait

Several three-dimensional (3D) lower-limb musculo-skeletal models have been developed for gait analysis and different hip, knee and ankle joint models have been considered in the literature. Conversely to the influence of the musculo-tendon geometry, the influence of the joint models - i.e. number of degrees of freedom and passive joint moments - on the estimated musculo-tendon forces and 3D joint reaction forces has not been extensively examined.

In this paper musculo-tendon forces and 3D joint reaction forces have been estimated for one subject and one gait cycle with nine variations of a musculoskeletal model and outputs have been compared to measured electromyographic signals and knee joint contact forces. The model outputs are generally in line with the measured signals. However, the 3D joint reaction forces were higher than published values and the contact forces measured for the subject. The results of this study show that, with more degrees of freedom in the model, the musculo-tendon forces and the 3D joint reaction forces tend to increase but with some redistribution between the muscles. In addition, when taking into account passive joint moments, the 3D joint reaction forces tend to decrease during the stance phase and increase during the swing phase.

Although further investigations are needed, a five-degree-of-freedom lower-limb musculo-skeletal model with some angle-dependent joint coupling and stiffness seems to provide satisfactory musculo-tendon forces and 3D joint reaction forces.

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.

Muscle discretization affects the loading transferred to bones in lower-limb musculoskeletal models

Modelling the mechanical effect of muscles is important in several research and clinical contexts. However, few studies have investigated the effect of different muscle discretizations from a mechanical standpoint. The present study evaluated the errors of a reduced discretization of the lower-limb muscles in reproducing the muscle loading transferred to bones. Skeletal geometries and a muscle data collection were derived from clinical images and dissection studies of two cadaver specimens. The guidelines of a general method previously proposed for a different anatomical district were followed. The data collection was used to calculate the mechanical effect of muscles, i.e. the generalized force vectors, and the errors between a large and a reduced discretization, in a reference skeletal pose and in the extreme poses of the range of motion of joints. The results showed that the errors committed using a reduced representation of muscles could be significant and higher than those reported for a different anatomical region. In particular, the calculated errors were found to be dependent on the individual anatomy and on the skeletal pose. Since different biomechanical applications may require different discretization levels, care is suggested in identifying the number of muscle lines of action to be used in musculoskeletal models.

Knee and hip joint forces – sensitivity to the degrees of freedom classification at the knee

Previous research has demonstrated that the number of degrees of freedom (DOF) modelled at a given joint affects the antagonistic muscle activity predicted by inverse dynamics optimization techniques. This higher level of muscle activity in turn results in greater joint contact forces. For instance, modelling the knee as a 3 DOF joint has been shown to result in higher hip and knee joint forces commensurate with a higher level of muscular activity than when the knee is modelled with 1 DOF. In this study, a previously described musculoskeletal model of the lower limb was used to evaluate the sensitivity of the knee and hip joint contact forces to the DOF at the knee during vertical jumping in both a 1 and a 3 DOF knee model. The 3 DOF knee was found to predict higher tibiofemoral and hip joint contact forces and lower patellofemoral joint contact forces. The magnitude of the difference in hip contact force was at least as significant as that found in previous research exploring the effect of subject-specific hip geometry on hip contact force. This study therefore demonstrates a key sensitivity of knee and hip joint contact force calculations to the DOF at the knee. Finally, it is argued that the results of this study highlight an important physiological question with practical implications for the loading of the structures of the knee; that is, the relative interaction of muscular, ligamentous, and articular structures in creating moment equilibrium at the knee.

Influence of inverse dynamics methods on the calculation of inter-segmental moments in vertical jumping and weightlifting

BACKGROUND

A vast number of biomechanical studies have employed inverse dynamics methods to calculate inter-segmental moments during movement. Although all inverse dynamics methods are rooted in classical mechanics and thus theoretically the same, there exist a number of distinct computational methods. Recent research has demonstrated a key influence of the dynamics computation of the inverse dynamics method on the calculated moments, despite the theoretical equivalence of the methods. The purpose of this study was therefore to explore the influence of the choice of inverse dynamics on the calculation of inter-segmental moments.

METHODS

An inverse dynamics analysis was performed to analyse vertical jumping and weightlifting movements using two distinct methods. The first method was the traditional inverse dynamics approach, in this study characterized as the 3 step method, where inter-segmental moments were calculated in the local coordinate system of each segment, thus requiring multiple coordinate system transformations. The second method (the 1 step method) was the recently proposed approach based on wrench notation that allows all calculations to be performed in the global coordinate system. In order to best compare the effect of the inverse dynamics computation a number of the key assumptions and methods were harmonized, in particular unit quaternions were used to parameterize rotation in both methods in order to standardize the kinematics.

RESULTS

Mean peak inter-segmental moments calculated by the two methods were found to agree to 2 decimal places in all cases and were not significantly different (p > 0.05). Equally the normalized dispersions of the two methods were small.

CONCLUSIONS

In contrast to previously documented research the difference between the two methods was found to be negligible. This study demonstrates that the 1 and 3 step method are computationally equivalent and can thus be used interchangeably in musculoskeletal modelling technology. It is important that future work clarifies the influence of the other inverse dynamics methods on the calculation of inter-segmental moments. Equally future work is needed to explore the sensitivity of kinematics computations to the choice of rotation parameterization.

An optimization approach to inverse dynamics provides insight as to the function of the biarticular muscles during vertical jumping

Traditional inverse dynamics approaches to calculating the inter-segmental moments are limited in their ability to accurately reflect the function of the biarticular muscles. In particular they are based on the assumption that the net inter-segmental moment is zero and that total joint moments are independent of muscular activity. Traditional approaches to calculating muscular forces from the inter-segmental moments are based on a consideration of joint moments which do not encapsulate the potential moment asymmetry between segments. In addition, traditional approaches may artificially constrain the activity of the biarticular muscles. In this study, an optimization approach to the simultaneous inverse determination of inter-segmental moments and muscle forces (the 1-step method) based on a consideration of segmental rotations was employed to study vertical jumping and contrasted with the more traditional 2-step approach of determining inter-segmental moments from an inverse dynamics analysis then muscle forces using optimization techniques. The 1-step method resulted in significantly greater activation of both the monoarticular and biarticular musculature which was then translated into significantly greater joint contact forces, muscle powers, and inter-segmental moments. The results of this study suggest that traditional conceptions of inter-segmental moments do not completely encapsulate the function of the biarticular muscles and that joint function can be better understood by recognizing the asymmetry in inter-segmental moments.