A Dynamic Optimization Solution for Vertical Jumping in Three Dimensions

Predictive Neuromuscular Fatigue of the Lower Extremity Utilizing Computer Modeling

This paper studies the modeling of lower extremity muscle forces and their correlation to neuromuscular fatigue. Two analytical fatigue models were combined with a musculoskeletal model to estimate the effects of hamstrings fatigue on lower extremity muscle forces during a side step cut. One of the fatigue models (Tang) used subject-specific knee flexor muscle fatigue and recovery data while the second model (Xia) used previously established fatigue and recovery parameters. Both fatigue models were able to predict hamstrings fatigue within 20% of the experimental data, with the semimembranosus and semitendinosus muscles demonstrating the largest (11%) and smallest (1%) differences, respectively. In addition, various hamstrings fatigue levels (10-90%) on lower extremity muscle force production were assessed using one of the analytical fatigue models. As hamstrings fatigue levels increased, the quadriceps muscle forces decreased by 21% (p < 0.01), while gastrocnemius muscle forces increased by 36% (p < 0.01). The results of this study validate the use of two analytical fatigue models in determining the effects of neuromuscular fatigue during a side step cut, and therefore, this model can be used to assess fatigue effects on risk of lower extremity injury during athletic maneuvers. Understanding the effects of fatigue on muscle force production may provide insight on muscle group compensations that may lead to altered lower extremity motion patterns as seen in noncontact anterior cruciate ligament (ACL) injuries.

A unified approach for revealing multiple balance recovery strategies

In human balance recovery, different strategies have been proposed with generally overlooked knee motions but extensive focus on the ankle, hip, and step strategies. It is not well understood whether maintaining balance is regulated at the lower "muscular-articular" level of coordinating segment joints or at a higher level of controlling whole body dynamics. Whether balance control is to minimize joint degrees of freedom (DOF) or utilize all the available DOF also remains unclear. This study aimed to use a realistic musculoskeletal human model to identify multiple balance recovery strategies with a single optimization criterion. Movements were driven by neural excitations (which activated muscle force generation) and were assumed to be symmetric. Balance recoveries were simulated with forward-inclined straight body postures as the initial conditions. When the position of the toes was fixed, balance was regained with virtually straight knees and mixed ankle/hip strategies. Under a severely perturbed condition, use of the forward hop strategy after releasing the fixed-toes constraint indicated spontaneous recruitment or suppression of DOF, which mimicked functions of optimally computed CNS commands in humans. The results also indicated that increase/decrease in the number of DOF depends on the imposed perturbation intensity and movement constraints.

Effect of lower-limb joint models on subject-specific musculoskeletal models and simulations of daily motor activities

Understanding the validity of using musculoskeletal models is critical, making important to assess how model parameters affect predictions. In particular, assumptions on joint models can affect predictions from simulations of movement, and the identification of image-based joints is unavoidably affected by uncertainty that can decrease the benefits of increasing model complexity. We evaluated the effect of different lower-limb joint models on muscle and joint contact forces during four motor tasks, and assessed the sensitivity to the uncertainties in the identification of anatomical four-bar-linkage joints. Three MRI-based musculoskeletal models having different knee and ankle joint models were created and used for the purpose. Model predictions were compared against a baseline model including simpler and widely-adopted joints. In addition, a probabilistic analysis was performed by perturbing four-bar-linkage joint parameters according to their uncertainty. The differences between models depended on the motor task analyzed, and there could be marked differences at peak loading (up to 2.40 BW at the knee and 1.54 BW at the ankle), although they were rather small over the motor task cycles (up to 0.59 BW at the knee and 0.31 BW at the ankle). The model including more degrees of freedom showed more discrepancies in predicted muscle activations compared to measured muscle activity. Further, including image-based four-bar-linkages was robust to simulate walking, chair rise and stair ascent, but not stair descent (peak standard deviation of 2.66 BW), suggesting that joint model complexity should be set according to the imaging dataset available and the intended application, performing sensitivity analyses.

A superellipsoid-plane model for simulating foot-ground contact during human gait

Musculoskeletal models and forward dynamics simulations of human movement often include foot-ground interactions, with the foot-ground contact forces often determined using a constitutive model that depends on material properties and contact kinematics. When using soft constraints to model the foot-ground interactions, the kinematics of the minimum distance between the foot and planar ground needs to be computed. Due to their geometric simplicity, a considerable number of studies have used point-plane elements to represent these interacting bodies, but few studies have provided comparisons between point contact elements and other geometrically based analytical solutions. The objective of this work was to develop a more general-purpose superellipsoid-plane contact model that can be used to determine the three-dimensional foot-ground contact forces. As an example application, the model was used in a forward dynamics simulation of human walking. Simulation results and execution times were compared with a point-like viscoelastic contact model. Both models produced realistic ground reaction forces and kinematics with similar computational efficiency. However, solving the equations of motion with the surface contact model was found to be more efficient (~18% faster), and on average numerically ~37% less stiff. The superellipsoid-plane elements are also more versatile than point-like elements in that they allow for volumetric contact during three-dimensional motions (e.g. rotating, rolling, and sliding). In addition, the superellipsoid-plane element is geometrically accurate and easily integrated within multibody simulation code. These advantages make the use of superellipsoid-plane contact models in musculoskeletal simulations an appealing alternative to point-like elements.

Primary functions of the quadratus femoris and obturator externus muscles indicated from lengths and moment arms measured in mobilized cadavers

BACKGROUND

The small muscles of the pelvis and hip are often implicated in painful conditions. Although the quadratus femoris and obturator externus are usually described as external rotators of the hip, little is known about how they change their lengths and moment arms during human movement. Therefore, more precise measurements defining the positions and directions for their maximal strength and stretch are needed to better describe their functions and guide the clinical approach to pain.

METHODS

Repeated measurements of the muscle lengths and range of motion were obtained using wires simulating dissected muscles on human cadaver hips. The lengths were measured at every 15° of flexion with and without maximal range of ab/adduction, rotation, and combinations of the two motions. Measurements were obtained from normal hips (n=3), and movement-lengthening relations were later differentiated into movement-moment arm relations.

FINDINGS

The quadratus femoris showed maximum lengthening by flexion, adduction or abduction, and internal rotation, with the largest moment arms observed for extension in the deduced force-length efficient range of 60-90° flexion. The obturator externus showed maximum lengthening by extension, abduction, and internal rotation, with the largest moment arms observed for flexion and adduction in the deduced force-length efficient range around the hip's neutral position.

INTERPRETATION

Our findings indicate that maximal strength of the quadratus femoris muscle will be delivered in a flexed position towards extension, while maximal strength of the obturator externus muscle will be delivered in an extended position towards flexion and adduction.

Assessment of lower leg muscle force distribution during isometric ankle dorsi and plantar flexion in patients with diabetes: a preliminary study

AIM

The aim of this study was to evaluate the differences in ankle muscle strength using hand-held dynamometry and to assess difference in the isometric muscle force distribution between the people with diabetes and control participants.

METHODS

The maximal muscle strength of ankle plantarflexion, dorsiflexion, eversion, inversion, lesser toes flexors and extensors, hallux flexors, and extensors was assessed in 20 people with diabetes and 20 healthy participants using hand-held dynamometry. The maximal isometric ankle plantarflexion and dorsiflexion were imported to OpenSim software to calculate 12 individual muscle (8 plantarflexors and 4 dorsiflexors) forces acting on ankle joint.

RESULTS

A significant reduction in ankle strength for all measured actions and a significant decrease in muscle force for each of the 12 muscles during dorsi and plantar flexion were observed. Furthermore, the ratios of agonist to antagonist muscle force for 6 of the muscles were significantly different between the control group and the group with diabetes.

CONCLUSIONS

It is likely that the muscles for which the agonist/antagonist muscle force ratio was significantly different for the healthy people and the people with diabetes could be more affected by diabetes.

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.

A novel computational framework for deducing muscle synergies from experimental joint moments

Prior experimental studies have hypothesized the existence of a "muscle synergy" based control scheme for producing limb movements and locomotion in vertebrates. Such synergies have been suggested to consist of fixed muscle grouping schemes with the co-activation of all muscles in a synergy resulting in limb movement. Quantitative representations of these groupings (termed muscle weightings) and their control signals (termed synergy controls) have traditionally been derived by the factorization of experimentally measured EMG. This study presents a novel approach for deducing these weightings and controls from inverse dynamic joint moments that are computed from an alternative set of experimental measurements-movement kinematics and kinetics. This technique was applied to joint moments for healthy human walking at 0.7 and 1.7 m/s, and two sets of "simulated" synergies were computed based on two different criteria (1) synergies were required to minimize errors between experimental and simulated joint moments in a musculoskeletal model (pure-synergy solution) (2) along with minimizing joint moment errors, synergies also minimized muscle activation levels (optimal-synergy solution). On comparing the two solutions, it was observed that the introduction of optimality requirements (optimal-synergy) to a control strategy solely aimed at reproducing the joint moments (pure-synergy) did not necessitate major changes in the muscle grouping within synergies or the temporal profiles of synergy control signals. Synergies from both the simulated solutions exhibited many similarities to EMG derived synergies from a previously published study, thus implying that the analysis of the two different types of experimental data reveals similar, underlying synergy structures.

Can stability really predict an impending slip-related fall among older adults?

The primary purpose of this study was to systematically evaluate and compare the predictive power of falls for a battery of stability indices, obtained during normal walking among community-dwelling older adults. One hundred and eighty seven community-dwelling older adults participated in the study. After walking regularly for 20 strides on a walkway, participants were subjected to an unannounced slip during gait under the protection of a safety harness. Full body kinematics and kinetics were monitored during walking using a motion capture system synchronized with force plates. Stability variables, including feasible-stability-region measurement, margin of stability, the maximum Floquet multiplier, the Lyapunov exponents (short- and long-term), and the variability of gait parameters (including the step length, step width, and step time), were calculated for each subject. Sensitivity of predicting slip outcome (fall vs. recovery) was examined for each stability variable using logistic regression. Results showed that the feasible-stability-region measurement predicted fall incidence among these subjects with the highest sensitivity (68.4%). Except for the step width (with an sensitivity of 60.2%), no other stability variables could differentiate fallers from those who did not fall for the sample included in this study. The findings from the present study could provide guidance to identify individuals at increased risk of falling using the feasible-stability-region measurement or variability of the step width.

Lengths of the external hip rotators in mobilized cadavers indicate the quadriceps coxa as a primary abductor and extensor of the flexed hip

BACKGROUND

The primary function of the external rotators of the hip is inadequately described. The descriptions for peak strength and stretch take no account of how these muscles change their length during normal movement. The latter relationship is known to greatly influence contraction forces and reflect moment arms. The aim of the present study was to indicate positions and directions for peak strength and stretch of piriformis and obturator internus (including the gemelli), collectively defined as the quadriceps coxa, by measuring their changes in length due to normal movements.

METHODS

Repeated measurements of muscle lengths and range of motions were acquired from dissected muscles on human cadaver hips. We measured at every 15° of flexion with and without adding end ab/adduction, rotations, and combinations thereof. Measurements were taken in three normal hips (1 female aged 59 years, 2 males aged 68 and 70 years) using a custom-engineered frame, electronic calipers, goniometer, and a string muscle model. Movement-lengthening relations were differentiated into movement-moment arm relations.

FINDINGS

The piriformis and obturator internus were maximally lengthened (35 and 30mm) by 105° flexion and 10° adduction and relaxed by extension and abduction. With significant moment arms for extension and abduction in the movement-lengthening range deduced as force-efficient, our findings indicate peak strength by extension and abduction at 60° to 90° flexed positions.

INTERPRETATION

This cadaver study indicates that the quadriceps coxa is a primary abductor and extensor from flexed positions, a strength function which may be of major importance in rising and propulsive motions.

Reduced hamstring strength increases anterior cruciate ligament loading during anticipated sidestep cutting

BACKGROUND

Dynamic knee stability is considered a critical factor in reducing anterior cruciate ligament loads. While the relationships between hamstring force production and anterior cruciate ligament loading are well known in vitro, the influence of hamstring strength to anterior cruciate ligament loading during athletic maneuvers remains unknown. Therefore, the purpose of this study was to determine the influence of hamstring strength on anterior cruciate ligament loading during anticipated sidestep cut.

METHODS

Seventeen recreationally active females were recruited to perform sidestep cutting maneuvers pre/post an acute hamstring strength reduction protocol. Kinematics and kinetics were calculated during the cut and a musculoskeletal model was used to estimate muscle, joint, and anterior cruciate ligament loads. Dependent t-tests were conducted to investigate differences between the two cutting conditions.

FINDINGS

Anterior cruciate ligament loading increased by 36% due to reduced hamstring strength. This was mostly due to a 44% increase in sagittal plane loading and a 24% increase in frontal plane loading. Post strength reduction sidestep cuts were also performed with decreased anterior tibiofemoral shear force, an outcome that would theoretically reduce anterior cruciate ligament loading. However, the overall decrease in hamstring force production coupled with a more axial hamstring line of action yielded a net increase in anterior cruciate ligament loading.

INTERPRETATION

These results suggest that decreased hamstring strength significantly increases anterior cruciate ligament loading during anticipated sidestep cutting. Additionally, these results support the premise that preseason screening programs should monitor hamstring strength to identify female athletes with potential deficits and increased injury risk.

Analytical and multibody modeling for the power analysis of standing jumps

Two methods for the power analysis of standing jumps are proposed and compared in this article. The first method is based on a simple analytical formulation which requires as input the coordinates of the center of gravity in three specified instants of the jump. The second method is based on a multibody model that simulates the jumps processing the data obtained by a three-dimensional (3D) motion capture system and the dynamometric measurements obtained by the force platforms. The multibody model is developed with OpenSim, an open-source software which provides tools for the kinematic and dynamic analyses of 3D human body models. The study is focused on two of the typical tests used to evaluate the muscular activity of lower limbs, which are the counter movement jump and the standing long jump. The comparison between the results obtained by the two methods confirms that the proposed analytical formulation is correct and represents a simple tool suitable for a preliminary analysis of total mechanical work and the mean power exerted in standing jumps.

Arm swing in human walking: what is their drive?

Although previous research has studied arm swing during walking, to date, it remains unclear what the contribution of passive dynamics versus active muscle control to arm swing is. In this study, we measured arm swing kinematics with 3D-motion analysis. We used a musculoskeletal model in OpenSim and generated dynamic simulations of walking with and without upper limb muscle excitations. We then compared arm swing amplitude and relative phase during both simulations to verify the extent to which passive dynamics contribute to arm swing. The results confirm that passive dynamics are partly responsible for arm swing during walking. However, without muscle activity, passive swing amplitude and relative phase decrease significantly (both p<0.05), the latter inducing a more in-phase swing pattern of the arms. Therefore, we conclude that muscle activity is needed to increase arm swing amplitude and modify relative phase during human walking to obtain an out-phase movement relative to the legs.

Biomechanical analysis of squat jump and countermovement jump from varying starting positions

The purpose of this study was to investigate the effect of 2 strategies, defined by foot placement during the initiation of the take-off on performance in vertical jumps. The additional area of interest in this experiment was whether technique of the take-off phase might be an exploratory factor that has different electromyogram (EMG) muscle activity during squat jump (SJ) and countermovement jump (CMJ) performed starting from the standard position, with parallel foot placement, and from the experimental one, with straddle foot placement. Six well-experienced male 100-400 m sprinters, who were members of the Polish youth and senior national team (mean values: age 21.6 years, best performance: 100 m in 10.54 seconds and 400 m in 45.54 seconds), performed vertical SJ and vertical CMJ from 2 initial positions with different foot placement. To collect all selected kinematic and kinetic data, the video recording system BTS Vixta was used in conjunction with force platforms (Kistler model 9286B). The latest system for 3D motion analysis, BTS SMART, based on the passive IR reflective markers was also applied. Electromyograms of 6 lower limb muscles were collected using a Noraxon EMG device. The CMJ was on average 7 cm higher than the SJ (CMJ, 85 cm and SJ, 78 cm), which amounts to 8.97%. This was not because of the increase of center of gravity (COG) velocity at take-off because velocities of center of gravity (COG) projection were almost equal (SJ, 2.93 m·scompared with CMJ, 2.99 m·s). No significant differences of both magnitude and rate of development of the muscle torques and powers between jumps were found, but when we analyzed the problem with division into single legs (right and left) and with division into different jumps (SJ and CMJ), the differences were evident. The profiles of EMG activity of selected muscles showed some differences between SJ and CMJ. The vertical SJ and CMJ performance measurement may be of value to coaches and conditioning specialists who wish to develop or assess the power ability of lower extremities either unilaterally (single leg) or bilaterally (sum of both legs).

Contributions of individual muscles to the sagittal- and frontal-plane angular accelerations of the trunk in walking

This study was conducted to analyze the unimpaired control of the trunk during walking. Studying the unimpaired control of the trunk reveals characteristics of good control. These characteristics can be pursued in the rehabilitation of impaired control. Impaired control of the trunk during walking is associated with aging and many movement disorders. This is a concern as it is considered to increase fall risk. Muscles that contribute to the trunk control in normal walking may also contribute to it under perturbation circumstances, attempting to prevent an impending fall. Knowledge of such muscles can be used to rehabilitate impaired control of the trunk. Here, angular accelerations of the trunk induced by individual muscles, in the sagittal and frontal planes, were calculated using 3D muscle-driven simulations of seven young healthy subjects walking at free speed. Analysis of the simulations demonstrated that the abdominal and back muscles displayed large contributions throughout the gait cycle both in the sagittal and frontal planes. Proximal lower-limb muscles contributed more than distal muscles in the sagittal plane, while both proximal and distal muscles showed large contributions in the frontal plane. Along with the stance-limb muscles, the swing-limb muscles also exhibited considerable contribution. The gluteus medius was found to be an important individual frontal-plane control muscle; enhancing its function in pathologies could ameliorate gait by attenuating trunk sway. In addition, since gravity appreciably accelerated the trunk in the frontal plane, it may engender excessive trunk sway in pathologies.

Optimization of prosthetic foot stiffness to reduce metabolic cost and intact knee loading during below-knee amputee walking: a theoretical study

Unilateral below-knee amputees develop abnormal gait characteristics that include bilateral asymmetries and an elevated metabolic cost relative to non-amputees. In addition, long-term prosthesis use has been linked to an increased prevalence of joint pain and osteoarthritis in the intact leg knee. To improve amputee mobility, prosthetic feet that utilize elastic energy storage and return (ESAR) have been designed, which perform important biomechanical functions such as providing body support and forward propulsion. However, the prescription of appropriate design characteristics (e.g., stiffness) is not well-defined since its influence on foot function and important in vivo biomechanical quantities such as metabolic cost and joint loading remain unclear. The design of feet that improve these quantities could provide considerable advancements in amputee care. Therefore, the purpose of this study was to couple design optimization with dynamic simulations of amputee walking to identify the optimal foot stiffness that minimizes metabolic cost and intact knee joint loading. A musculoskeletal model and distributed stiffness ESAR prosthetic foot model were developed to generate muscle-actuated forward dynamics simulations of amputee walking. Dynamic optimization was used to solve for the optimal muscle excitation patterns and foot stiffness profile that produced simulations that tracked experimental amputee walking data while minimizing metabolic cost and intact leg internal knee contact forces. Muscle and foot function were evaluated by calculating their contributions to the important walking subtasks of body support, forward propulsion and leg swing. The analyses showed that altering a nominal prosthetic foot stiffness distribution by stiffening the toe and mid-foot while making the ankle and heel less stiff improved ESAR foot performance by offloading the intact knee during early to mid-stance of the intact leg and reducing metabolic cost. The optimal design also provided moderate braking and body support during the first half of residual leg stance, while increasing the prosthesis contributions to forward propulsion and body support during the second half of residual leg stance. Future work will be directed at experimentally validating these results, which have important implications for future designs of prosthetic feet that could significantly improve amputee care.

Is midsole thickness a key parameter for the running pattern?

Many studies have highlighted differences in foot strike pattern comparing habitually shod runners who ran barefoot and with running shoes. Barefoot running results in a flatter foot landing and in a decreased vertical ground reaction force compared to shod running. The aim of this study was to investigate one possible parameter influencing running pattern: the midsole thickness. Fifteen participants ran overground at 3.3 ms(-1) barefoot and with five shoes of different midsole thickness (0 mm, 2 mm, 4 mm, 8 mm, 16 mm) with no difference of height between rearfoot and forefoot. Impact magnitude was evaluated using transient peak of vertical ground reaction force, loading rate, tibial acceleration peak and rate. Hip, knee and ankle flexion angles were computed at touch-down and during stance phase (range of motion and maximum values). External net joint moments and stiffness for hip, knee and ankle joints were also observed as well as global leg stiffness. No significant effect of midsole thickness was observed on ground reaction force and tibial acceleration. However, the contact time increased with midsole thickness. Barefoot running compared to shod running induced ankle in plantar flexion at touch-down, higher ankle dorsiflexion and lower knee flexion during stance phase. These adjustments are suspected to explain the absence of difference on ground reaction force and tibial acceleration. This study showed that the presence of very thin footwear upper and sole was sufficient to significantly influence the running pattern.

A comparison of muscle energy models for simulating human walking in three dimensions

The popular Hill model for muscle activation and contractile dynamics has been extended with several different formulations for predicting the metabolic energy expenditure of human muscle actions. These extended models differ considerably in their approach to computing energy expenditure, particularly in their treatment of active lengthening and eccentric work, but their predictive abilities have never been compared. In this study, we compared the predictions of five different Hill-based muscle energy models in 3D forward dynamics simulations of normal human walking. In a data-tracking simulation that minimized muscle fatigue, the energy models predicted metabolic costs that varied over a three-fold range (2.45-7.15 J/m/kg), with the distinction arising from whether or not eccentric work was subtracted from the net heat rate in the calculation of the muscle metabolic rate. In predictive simulations that optimized neuromuscular control to minimize the metabolic cost, all five models predicted similar speeds, step lengths, and stance phase durations. However, some of the models predicted a hip circumduction strategy to minimize metabolic cost, while others did not, and the accuracy of the predicted knee and ankle angles and ground reaction forces also depended on the energy model used. The results highlights the need to clarify how eccentric work should be treated when calculating muscle energy expenditure, the difficulty in predicting realistic metabolic costs in simulated walking even with a detailed 3D musculoskeletal model, the potential for using such models to predict energetically-optimal gait modifications, and the room for improvement in existing muscle energy models and locomotion simulation frameworks.

Quantitative evaluation of the major determinants of human gait

Accurate knowledge of the isolated contributions of joint movements to the three-dimensional displacement of the center of mass (COM) is fundamental for understanding the kinematics of normal walking and for improving the treatment of gait disabilities. Saunders et al. (1953) identified six kinematic mechanisms to explain the efficient progression of the whole-body COM in the sagittal, transverse, and coronal planes. These mechanisms, referred to as the major determinants of gait, were pelvic rotation, pelvic list, stance knee flexion, foot and knee mechanisms, and hip adduction. The aim of the present study was to quantitatively assess the contribution of each major gait determinant to the anteroposterior, vertical, and mediolateral displacements of the COM over one gait cycle. The contribution of each gait determinant was found by applying the concept of an 'influence coefficient', wherein the partial derivative of the COM displacement with respect to a prescribed determinant was calculated. The analysis was based on three-dimensional measurements of joint angular displacements obtained from 23 healthy young adults walking at slow, normal and fast speeds. We found that hip flexion, stance knee flexion, and ankle-foot interaction (comprised of ankle plantarflexion, toe flexion and the displacement of the center of pressure) are the major determinants of the displacements of the COM in the sagittal plane, while hip adduction and pelvic list contribute most significantly to the mediolateral displacement of the COM in the coronal plane. Pelvic rotation and pelvic list contribute little to the vertical displacement of the COM at all walking speeds. Pelvic tilt, hip rotation, subtalar inversion, and back extension, abduction and rotation make negligible contributions to the displacements of the COM in all three anatomical planes.

UPWARD JUMP OF A BIPED

This paper explores the vertical upward jumping of a planar biped. There are two stance phases and one flight phase in the jump. One stance phase takes place before the flight phase, another one after the flight phase. The stance phase before the flight phase is decomposed into several parts: A crouching, a thrust at the knees, a rotation of both feet (massless) around their toes. The second stance phase (after the flight phase) starts with a touchdown of the toes. It consists of a feet rotation, a touchdown of the whole soles and finally of a straightening up movement of the biped. A mathematical model for this kind of jump is developed. Torques are applied at the hip, knee and ankle joints. The control algorithm is designed to ensure the jump of the biped. The synthesis of the jumping process is supported by simulation, which gives consistent results with human data from biomechanical literature. The stick diagram of the jump derived from simulation results seems natural for the human jumping.

Tendon elastic strain energy in the human ankle plantar-flexors and its role with increased running speed

The human ankle plantar-flexors, soleus (SOL) and gastrocnemius (GAS), utilize tendon elastic strain energy to reduce muscle fiber work and optimize contractile conditions during running. However, studies to date have considered only slow to moderate running speeds up to 5 m/s. Little is known about how the human ankle plantar-flexors utilize tendon elastic strain energy as running speed is advanced towards maximum sprinting. We used data obtained from gait experiments in conjunction with musculoskeletal modeling and optimization techniques to calculate muscle-tendon unit (MTU) work, tendon elastic strain energy and muscle fiber work for the ankle plantar-flexors as participants ran at five discrete steady-state speeds ranging from jogging (~2 m/s) to sprinting (≥8 m/s). As running speed progressed from jogging to sprinting, the contribution of tendon elastic strain energy to the positive work generated by the MTU increased from 53% to 74% for SOL and from 62% to 75% for GAS. This increase was facilitated by greater muscle activation and the relatively isometric behavior of the SOL and GAS muscle fibers. Both of these characteristics enhanced tendon stretch and recoil, which contributed to the bulk of the change in MTU length. Our results suggest that as steady-state running speed is advanced towards maximum sprinting, the human ankle plantar-flexors continue to prioritize the storage and recovery of tendon elastic strain energy over muscle fiber work.

Influence of lumbar spine extension on vertical jump height during maximal squat jumping

The purpose of this study was to determine the influence of lumbar spine extension and erector spinae muscle activation on vertical jump height during maximal squat jumping. Eight male athletes performed maximal squat jumps. Electromyograms of the erector spinae were recorded during these jumps. A simulation model of the musculoskeletal system was used to simulate maximal squat jumping with and without spine extension. The effect on vertical jump height of changing erector spinae strength was also tested through the simulated jumps. Concerning the participant jumps, the kinematics indicated a spine extension and erector spinae activation. Concerning the simulated jumps, vertical jump height was about 5.4 cm lower during squat jump without trunk extension compared to squat jump. These results were explained by greater total muscle work during squat jump, more especially by the erector spinae work (+119.5 J). The erector spinae may contribute to spine extension during maximal squat jumping. The simulated jumps confirmed this hypothesis showing that vertical jumping was decreased if this muscle was not taken into consideration in the model. Therefore it is concluded that the erector spinae should be considered as a trunk extensor, which enables to enhance total muscle work and consequently vertical jump height.

Effects of gait speed on stability of walking revealed by simulated response to tripping perturbation

The objective of this work was to study stability of walking over a range of gait speeds by means of muscle-driven simulations. Fast walking has previously been related to high likelihood of falling due to tripping. Various measures of stability have shown different relationships between walking speed and stability. These measures may not be associated with tripping, so it is unclear whether the increase in likelihood of falling is explicable by an increase in instability. Here, stability with respect to a constant tripping perturbation was quantified as the immediate passive response of torso to the perturbation. Subject-specific muscle-driven simulations of eight young healthy subjects walking at four speeds, created by combining a generic musculoskeletal model with gait data, were analyzed. In the simulations, short perturbations were performed several times throughout the swing-phase by applying a constant backward force to the swing-foot of the model. Maxima of changes in the torso (angular) velocity components during the swing-phase were studied. These changes in the velocity components correlated with the walking speed as follows: anterior-posterior r=0.37 (p<0.05), vertical r=0.41 (p<0.05), and medio-lateral r=-0.40 (p<0.05). Of the angular velocity components, only the vertical component correlated statistically significantly with speed, r=0.52 (p<0.01). The weak and varying speed effects suggest that fast walking is not necessarily more unstable than slow walking, in the sense of response to a constant perturbation.

Flexing computational muscle: modeling and simulation of musculotendon dynamics

Muscle-driven simulations of human and animal motion are widely used to complement physical experiments for studying movement dynamics. Musculotendon models are an essential component of muscle-driven simulations, yet neither the computational speed nor the biological accuracy of the simulated forces has been adequately evaluated. Here we compare the speed and accuracy of three musculotendon models: two with an elastic tendon (an equilibrium model and a damped equilibrium model) and one with a rigid tendon. Our simulation benchmarks demonstrate that the equilibrium and damped equilibrium models produce similar force profiles but have different computational speeds. At low activation, the damped equilibrium model is 29 times faster than the equilibrium model when using an explicit integrator and 3 times faster when using an implicit integrator; at high activation, the two models have similar simulation speeds. In the special case of simulating a muscle with a short tendon, the rigid-tendon model produces forces that match those generated by the elastic-tendon models, but simulates 2-54 times faster when an explicit integrator is used and 6-31 times faster when an implicit integrator is used. The equilibrium, damped equilibrium, and rigid-tendon models reproduce forces generated by maximally-activated biological muscle with mean absolute errors less than 8.9%, 8.9%, and 20.9% of the maximum isometric muscle force, respectively. When compared to forces generated by submaximally-activated biological muscle, the forces produced by the equilibrium, damped equilibrium, and rigid-tendon models have mean absolute errors less than 16.2%, 16.4%, and 18.5%, respectively. To encourage further development of musculotendon models, we provide implementations of each of these models in OpenSim version 3.1 and benchmark data online, enabling others to reproduce our results and test their models of musculotendon dynamics.

Anticipatory effects on anterior cruciate ligament loading during sidestep cutting

BACKGROUND

A key to understanding potential anterior cruciate ligament injury mechanisms is to determine joint loading characteristics associated with an injury-causing event. However, direct measurement of anterior cruciate ligament loading during athletic tasks is invasive. Thus, previous research has been unable to study the association between neuromuscular variables and anterior cruciate ligament loading. Therefore, the purpose of this study was to determine the influence of movement anticipation on anterior cruciate ligament loading using a musculoskeletal modeling approach.

METHODS

Twenty healthy recreationally active females were recruited to perform anticipated and unanticipated sidestep cutting. Three-dimensional kinematics and kinetics of the right leg were calculated. Muscle, joint and anterior cruciate ligament forces were then estimated using a musculoskeletal model. Dependent t-tests were conducted to investigate differences between the two cutting conditions.

FINDINGS

ACL loading significantly increased during unanticipated sidestep cutting (p<0.05). This increase was primarily due to a significant increase in the sagittal plane ACL loading, which contributed 62% of the total loading. Frontal plane ACL loading contributed 26% and transverse plane ACL loading contributed 12%.

INTERPRETATION

These results suggest that anterior cruciate ligament loading resulted from a multifaceted interaction of the sagittal plane shear forces (i.e., quadriceps, hamstrings, and tibiofemoral), as well as the frontal and transverse plane knee moments. Additionally, the results of this study confirm the hypothesis in the current literature that unanticipated movements such as sidestep cutting increase anterior cruciate ligament loading.

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.

Muscle contributions to vertical and fore-aft accelerations are altered in subjects with crouch gait

The goals of this study were to determine if the muscle contributions to vertical and fore-aft acceleration of the mass center differ between crouch gait and unimpaired gait and if these muscle contributions change with crouch severity. Examining muscle contributions to mass center acceleration provides insight into the roles of individual muscles during gait and can provide guidance for treatment planning. We calculated vertical and fore-aft accelerations using musculoskeletal simulations of typically developing children and children with cerebral palsy and crouch gait. Analysis of these simulations revealed that during unimpaired gait the quadriceps produce large upward and backward accelerations during early stance, whereas the ankle plantarflexors produce large upward and forward accelerations later in stance. In contrast, during crouch gait, the quadriceps and ankle plantarflexors produce large, opposing fore-aft accelerations throughout stance. The quadriceps force required to accelerate the mass center upward was significantly larger in crouch gait than in unimpaired gait and increased with crouch severity. The gluteus medius accelerated the mass center upward during midstance in unimpaired gait; however, during crouch gait the upward acceleration produced by the gluteus medius was significantly reduced. During unimpaired gait the quadriceps and ankle plantarflexors accelerate the mass center at different times, efficiently modulating fore-aft accelerations. However, during crouch gait, the quadriceps and ankle plantarflexors produce fore-aft accelerations at the same time and the opposing fore-aft accelerations generated by these muscles contribute to the inefficiency of crouch gait.

Force enhancement and force depression in a modified muscle model used for muscle activation prediction

This article introduces history-dependent effects in a skeletal muscle model applied to dynamic simulations of musculoskeletal system motion. Force depression and force enhancement induced by active muscle shortening and lengthening, respectively, represent muscle history effects. A muscle model depending on the preceding contractile events together with the current parameters was developed for OpenSim software, and applied in simulations of standing heel-raise and squat movements. Muscle activations were computed using joint kinematics and ground reaction forces recorded from the motion capture of seven individuals. In the muscle-actuated simulations, a modification was applied to the computed activation, and was compared to the measured electromyography data. For the studied movements, the history gives a small but visible effect to the muscular force trace, but some parameter values must be identified before the exact magnitude can be analysed. The muscle model modification improves the existing muscle models and gives a more accurate description of underlying forces and activations in musculoskeletal system movement simulations.

Hamstrings and quadriceps muscle contributions to energy generation and dissipation at the knee joint during stance, swing and flight phases of level running

BACKGROUND

Human movements involve the generation and dissipation of mechanical energy at the lower extremity joints. However, it is unclear how the individual knee muscles contribute to the energetics during running.

OBJECTIVE

This study aimed to determine how each hamstring and quadricep muscle generates and dissipates energy during stance, swing and flight phases of running.

METHODS

A three-dimensional lower extremity musculoskeletal model was used to estimate the energetics of the individual hamstrings (semimembranosus, semitendinosus, biceps femoris long and short-heads) and quadriceps (rectus femoris, vastus medialis, vastus intermedius and vastus lateralis) muscles for a male subject during level running on a treadmill at a speed of 3.96 m/s.

RESULTS

Our findings demonstrated that the knee flexors generated energy during stance phase and dissipated energy during swing phase, while the knee extensors dissipated energy during the flexion mode of both stance and swing phases, and generated energy during the extension mode. During flight phase, the knee flexors generated energy during the flight phase transiting from toe-off to swing, while the knee extensors generated energy during the flight phase transiting from swing to heel-strike.

CONCLUSION

Individual knee flexors and extensors in the hamstrings and quadriceps play important roles in knee joint energetics, which are necessary for proper execution and stabilization of the stance, swing and flight phases of running.

The application of musculoskeletal modeling to investigate gender bias in non-contact ACL injury rate during single-leg landings

The central tenet of this study was to develop, validate and apply various individualised 3D musculoskeletal models of the human body for application to single-leg landings over increasing vertical heights and horizontal distances. While contributing to an understanding of whether gender differences explain the higher rate of non-contact anterior cruciate ligament (ACL) injuries among females, this study also correlated various musculoskeletal variables significantly impacted by gender, height and/or distance and their interactions with two ACL injury-risk predictor variables; peak vertical ground reaction force (VGRF) and peak proximal tibia anterior shear force (PTASF). Kinematic, kinetic and electromyography data of three male and three female subjects were measured. Results revealed no significant gender differences in the musculoskeletal variables tested except peak VGRF (p = 0.039) and hip axial compressive force (p = 0.032). The quadriceps and the gastrocnemius muscle forces had significant correlations with peak PTASF (r = 0.85, p < 0.05 and r = - 0.88, p < 0.05, respectively). Furthermore, hamstring muscle force was significantly correlated with peak VGRF (r = - 0.90, p < 0.05). The ankle flexion angle was significantly correlated with peak PTASF (r = - 0.82, p < 0.05). Our findings indicate that compared to males, females did not exhibit significantly different muscle forces, or ankle, knee and hip flexion angles during single-leg landings that would explain the gender bias in non-contact ACL injury rate. Our results also suggest that higher quadriceps muscle force increases the risk, while higher hamstring and gastrocnemius muscle forces as well as ankle flexion angle reduce the risk of non-contact ACL injury.

QUANTIFYING THE EFFECT OF PLYOMETRIC HOPPING EXERCISES ON THE MUSCULOSKELETAL SYSTEM: CONTRIBUTIONS OF THE LOWER LIMB JOINT MOMENTS OF FORCE TO GROUND REACTION FORCES IN HOPPING EXERCISE

The purpose of this study was to estimate the ability of joint moments of force in transferring mechanical energy through all the leg segments during a cyclic hopping sequence, performed until exhaustion. The technique was applied to data from four healthy active students to characterize the relative contribution of the lower limb net joint moments of force to accelerate the ankle, knee, and hip joints. Our findings showed that the strategies used to maintain the same jumping height rely on the balance between the net joint moments to guarantee the acceleration of the joints. It seems that while the ankle and knee moments reduce their contribution to accelerate the ankle and the knee joints, the hip moments increase their participation and have an important influence in the re-arrangement of the musculoskeletal system to maintain the same mechanical output.

Muscle contributions to fore-aft and vertical body mass center accelerations over a range of running speeds

Running is a bouncing gait in which the body mass center slows and lowers during the first half of the stance phase; the mass center is then accelerated forward and upward into flight during the second half of the stance phase. Muscle-driven simulations can be analyzed to determine how muscle forces accelerate the body mass center. However, muscle-driven simulations of running at different speeds have not been previously developed, and it remains unclear how muscle forces modulate mass center accelerations at different running speeds. Thus, to examine how muscles generate accelerations of the body mass center, we created three-dimensional muscle-driven simulations of ten subjects running at 2.0, 3.0, 4.0, and 5.0m/s. An induced acceleration analysis determined the contribution of each muscle to mass center accelerations. Our simulations included arms, allowing us to investigate the contributions of arm motion to running dynamics. Analysis of the simulations revealed that soleus provides the greatest upward mass center acceleration at all running speeds; soleus generates a peak upward acceleration of 19.8m/s(2) (i.e., the equivalent of approximately 2.0 bodyweights of ground reaction force) at 5.0m/s. Soleus also provided the greatest contribution to forward mass center acceleration, which increased from 2.5m/s(2) at 2.0m/s to 4.0m/s(2) at 5.0m/s. At faster running speeds, greater velocity of the legs produced larger angular momentum about the vertical axis passing through the body mass center; angular momentum about this vertical axis from arm swing simultaneously increased to counterbalance the legs. We provide open-access to data and simulations from this study for further analysis in OpenSim at simtk.org/home/nmbl_running, enabling muscle actions during running to be studied in unprecedented detail.

Optimal isn't good enough

The notion that biological systems come to embody optimal solutions seems consistent with the competitive drive of evolution. It has been used to interpret many examples of sensorimotor behavior. It is attractive from the viewpoint of control engineers because it solves the redundancy problem by identifying the one optimal motor strategy out of many similarly acceptable possibilities. This perspective examines whether there is sufficient basis to apply the formal engineering tools of optimal control to a reductionist understanding of biological systems. For an experimental biologist, this translates into whether the theory of optimal control generates nontrivial and testable hypotheses that accurately predict novel phenomena, ideally at deeper levels of structure than the observable behavior. The methodology of optimal control is applicable when there is (i) a single, known cost function to be optimized, (ii) an invertible model of the plant, and (iii) simple noise interfering with optimal performance. None of these is likely to be true for biological organisms. Furthermore, their motivation is usually good-enough rather than globally optimal behavior. Even then, the performance of a biological organism is often much farther from optimal than the physical limits of its hardware because the brain is continuously testing the acceptable limits of performance as well as just performing the task. This perspective considers an alternative strategy called "good-enough" control, in which the organism uses trial-and-error learning to acquire a repertoire of sensorimotor behaviors that are known to be useful, but not necessarily optimal. This leads to a diversity of solutions that tends to confer robustness on the individual organism and its evolution. It is also more consistent with the capabilities of higher sensorimotor structures, such as cerebral cortex, which seems to be designed to classify and recall complex sets of information, thereby allowing the organism to learn from experience, rather than to compute new strategies online. Optimal control has been a useful metaphor for understanding some superficial aspects of motor psychophysics. Reductionists who want to understand the underlying neural mechanisms need to move on.

A musculoskeletal modeling approach for estimating anterior cruciate ligament strains and knee anterior-posterior shear forces in stop-jumps performed by young recreational female athletes

The central goal of this study was to contribute to the advancements being made in determining the underlying causes of anterior cruciate ligament (ACL) injuries. ACL injuries are frequently incurred by recreational and professional young female athletes during non-contact impact activities in sports like volleyball and basketball. This musculoskeletal-neuromuscular study investigated stop-jumps and factors related to ACL injury like knee valgus and internal-external moment loads, knee anterior-posterior (AP) shear forces, ACL strains and internal forces. Motion capture data was obtained from the landing phase of stop-jumps performed by eleven young recreational female athletes and electromyography (EMG) data collected from quadriceps, hamstring and gastrocnimius muscles which were then compared to numerically estimated activations. Numerical simulation tools used were Inverse Kinematics, Computed Muscle Control and Forward Dynamics and the knee modeled as a six degree of freedom joint. Results showed averaged peak strains of 12.2 ± 4.1% in the right and 11.9 ± 3.0% in the left ACL. Averaged peak knee AP shear forces were 482.3 ± 65.7 N for the right and 430.0 ± 52.4 N for the left knees, approximately equal to 0.7-0.8 times body weight across both knees. A lack of symmetry was observed between the knees for valgus angles (p < 0.04), valgus moments (p < 0.001) and muscle activations (p < 0.001), all of which can be detrimental to ACL stability during impact activities. Comparisons between recorded EMG data and estimated muscle activations show the relation between electrical signal and muscle depolarization. In summary, this study outlines a musculoskeletal simulation approach that provides numerical estimations for a number of variables associated with ACL injuries in female athletes performing stop-jumps.

How much muscle strength is required to walk in a crouch gait?

Muscle weakness is commonly cited as a cause of crouch gait in individuals with cerebral palsy; however, outcomes after strength training are variable and mechanisms by which muscle weakness may contribute to crouch gait are unclear. Understanding how much muscle strength is required to walk in a crouch gait compared to an unimpaired gait may provide insight into how muscle weakness contributes to crouch gait and assist in the design of strength training programs. The goal of this study was to examine how much muscle groups could be weakened before crouch gait becomes impossible. To investigate this question, we first created muscle-driven simulations of gait for three typically developing children and six children with cerebral palsy who walked with varying degrees of crouch severity. We then simulated muscle weakness by systematically reducing the maximum isometric force of each muscle group until the simulation could no longer reproduce each subject's gait. This analysis indicated that moderate crouch gait required significantly more knee extensor strength than unimpaired gait. In contrast, moderate crouch gait required significantly less hip abductor strength than unimpaired gait, and mild crouch gait required significantly less ankle plantarflexor strength than unimpaired gait. The reduced strength required from the hip abductors and ankle plantarflexors during crouch gait suggests that weakness of these muscle groups may contribute to crouch gait and that these muscle groups are potential targets for strength training.

Best-compromise between mechanical energy expenditure and foot clearance predicts leading limb motion during obstacle-crossing

This study aimed to identify the control strategy of obstacle-crossing of different heights with a multi-objective optimal control technique. Twelve young healthy adults walked and crossed obstacles of three different heights while their kinematic and ground reaction force data were measured simultaneously. Obstacle-crossing was formulated as an optimal control problem with two conflicting objectives: minimization of mechanical energy expenditure and maximization of foot-obstacle clearance. The results supported the hypothesis that experimentally measured ankle trajectories and joint angles of the swing limb and the joint moments of the stance limb could be predicted by the best compromise between these objectives, which was also independent of obstacle height. This control strategy was fundamentally different from that for unobstructed gait, and appeared to be pre-programmed into the nervous system. The results will serve as baseline data and the current technique be used for identifying changes in obstacle-crossing control strategies in people at higher risk of falling.

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.