Static and dynamic optimization solutions for gait are practically equivalent

The proposition that dynamic optimization provides better estimates of muscle forces during gait than static optimization is examined by comparing a dynamic solution with two static solutions. A 23-degree-of-freedom musculoskeletal model actuated by 54 Hill-type musculotendon units was used to simulate one cycle of normal gait. The dynamic problem was to find the muscle excitations which minimized metabolic energy per unit distance traveled, and which produced a repeatable gait cycle. In the dynamic problem, activation dynamics was described by a first-order differential equation. The joint moments predicted by the dynamic solution were used as input to the static problems. In each static problem, the problem was to find the muscle activations which minimized the sum of muscle activations squared, and which generated the joint moments input from the dynamic solution. In the first static problem, muscles were treated as ideal force generators; in the second, they were constrained by their force-length-velocity properties; and in both, activation dynamics was neglected. In terms of predicted muscle forces and joint contact forces, the dynamic and static solutions were remarkably similar. Also, activation dynamics and the force-length-velocity properties of muscle had little influence on the static solutions. Thus, for normal gait, if one can accurately solve the inverse dynamics problem and if one seeks only to estimate muscle forces, the use of dynamic optimization rather than static optimization is currently not justified. Scenarios in which the use of dynamic optimization is justified are suggested.     

A contact model to simulate human–artifact interaction based on force optimization: implementation and application to the analysis of a training machine

Musculoskeletal multibody models are increasingly used to analyze and optimize physical interactions between humans and technical artifacts. Since interaction is conveyed by contact between the human body and the artifact, a computationally robust modeling approach for frictional contact forces is a crucial aspect. In this contribution, we propose a parametric contact model and formulate an associated force optimization problem to simultaneously estimate unknown muscle and contact forces in an inverse dynamic manner from a prescribed motion trajectory. Unlike existing work, we consider both the static and the kinetic regime of Coulomb’s friction law. The approach is applied to the analysis of a leg extension training machine with the objective to reduce the stress on the tibiofemoral joint. The uncertainty of the simulation results due to a tunable parameter of the contact model is of particular interest.     

Coordination of contact forces during multifinger static prehension

This study investigated the effects of modifying contact finger forces in one direction-normal or tangential-on the entire set of the contact forces, while statically holding an object. Subjects grasped a handle instrumented with finger force-moment sensors, maintained it at rest in the air, and then slowly: (1) increased the grasping force, (2) tried to spread fingers apart, and (3) tried to squeeze fingers together. Analysis was mostly performed at the virtual finger (VF) level (the VF is an imaginable finger that generates the same force and moment as the four fingers combined). For all three tasks there were statistically significant changes in the VF normal and tangential forces. For finger spreading/squeezing the tangential force neutral point was located between the index and middle fingers. We conclude that the internal forces are regulated as a whole, including adjustments in both normal and tangential force, instead of only a subset of forces (normal or tangential). The effects of such factors as EFFORT and TORQUE were additive; their interaction was not statistically significant, thus supporting the principle of superposition in human prehension.     

Effect of Microscale Contact State of Polyurethane Surface on Adhesion and Friction

The effect of microscale contact of rough surfaces on the adhesion and friction under negative normal forces was experimentally investigated. The adhesive force of single point contact - sapphire ball to flat polyurethane did not vary with the normal force. With rough surface contact, which was assumed to be a great number of point contacts, the adhesive force increased logarithmically with the normal force. Under negative normal force adhesive state, the tangential force （more than hundred mN） were much larger than the negative normal force （several mN） and increased with the linear decrease of negative normal force. The results reveal why the gecko＇s toe must slide slightly on the target surface when it makes contact on a surface and suggest how a biomimetic gecko foot might be designed.     

A 3D lower limb musculoskeletal model for simultaneous estimation of musculo-tendon,joint contact,ligament and bone forces during gait

Musculo-tendon forces and joint reaction forces are typically estimated using a two-step method, computing first the musculo-tendon forces by a static optimization procedure and then deducing the joint reaction forces from the force equilibrium. However, this method does not allow studying the interactions between musculo-tendon forces and joint reaction forces in establishing this equilibrium and the joint reaction forces are usually overestimated. This study introduces a new 3D lower limb musculoskeletal model based on a one-step static optimization procedure allowing simultaneous musculo-tendon, joint contact, ligament and bone forces estimation during gait. It is postulated that this approach, by giving access to the forces transmitted by these musculoskeletal structures at hip, tibiofemoral, patellofemoral and ankle joints, modeled using anatomically consistent kinematic models, should ease the validation of the model using joint contact forces measured with instrumented prostheses. A blinded validation based on four datasets was made under two different minimization conditions (i.e., C1 – only musculo-tendon forces are minimized, and C2 – musculo-tendon, joint contact, ligament and bone forces are minimized while focusing more specifically on tibiofemoral joint contacts). The results show that the model is able to estimate in most cases the correct timing of musculo-tendon forces during normal gait (i.e., the mean coefficient of active/inactive state concordance between estimated musculo-tendon force and measured EMG envelopes was C1: 65.87% and C2: 60.46%). The results also showed that the model is potentially able to well estimate joint contact, ligament and bone forces and more specifically medial (i.e., the mean RMSE between estimated joint contact force and in vivo measurement was C1: 1.14BW and C2: 0.39BW) and lateral (i.e., C1: 0.65BW and C2: 0.28BW) tibiofemoral contact forces during normal gait. However, the results remain highly influenced by the optimization weights that can bring to somewhat aphysiological musculo-tendon forces.     

Simultaneous prediction of muscle and contact forces in the knee during gait

Musculoskeletal models are currently the primary means for estimating in vivo muscle and contact forces in the knee during gait. These models typically couple a dynamic skeletal model with individual muscle models but rarely include articular contact models due to their high computational cost. This study evaluates a novel method for predicting muscle and contact forces simultaneously in the knee during gait. The method utilizes a 12 degree-of-freedom knee model (femur, tibia, and patella) combining muscle, articular contact, and dynamic skeletal models. Eight static optimization problems were formulated using two cost functions (one based on muscle activations and one based on contact forces) and four constraints sets (each composed of different combinations of inverse dynamic loads). The estimated muscle and contact forces were evaluated using in vivo tibial contact force data collected from a patient with a force-measuring knee implant. When the eight optimization problems were solved with added constraints to match the in vivo contact force measurements, root-mean-square errors in predicted contact forces were less than 10 N. Furthermore, muscle and patellar contact forces predicted by the two cost functions became more similar as more inverse dynamic loads were used as constraints. When the contact force constraints were removed, estimated medial contact forces were similar and lateral contact forces lower in magnitude compared to measured contact forces, with estimated muscle forces being sensitive and estimated patellar contact forces relatively insensitive to the choice of cost function and constraint set. These results suggest that optimization problem formulation coupled with knee model complexity can significantly affect predicted muscle and contact forces in the knee during gait. Further research using a complete lower limb model is needed to assess the importance of this finding to the muscle and contact force estimation process.     

In vivo glenohumeral contact forces--measurements in the first patient 7 months postoperatively

Knowledge of forces in the glenohumeral joint is essential for understanding normal and pathologic shoulder function. It forms the basis for performing fracture treatment or joint replacement surgery, for optimizing implant design and fixation and for improving and verifying analytical biomechanical models of the shoulder. An instrumented shoulder implant with telemetric data transmission was developed to measure six components of joint contact forces and moments. A patient with humeral head arthrosis achieved good joint function after its implantation. During the first 7 postoperative months, the contact force remained below 100% BW (percent body weight) for most activities of daily living. It ranged up to 130% BW for arm positions close to the limits of motion or when acting against external resistance. When the patient tried to turn a blocked steering wheel with maximum effort, the force rose to about 150% BW, the highest level observed thus far. Of great interest were the force directions relative to the humerus, especially those in the sagittal plane, which were not greatly influenced by the type of exercise, the arm position or the external resistance. The moments due to friction in the joint reached 5.2 Nm. The friction-induced shift of contact forces relative to the implant head centre ranged up to 6.3mm. These first worldwide in vivo measurements of glenohumeral contact forces are being continued in more patients and for longer postoperative times.     

Prediction of ground reaction forces and moments during various activities of daily living

Inverse dynamics based simulations on musculoskeletal models is a commonly used method for the analysis of human movement. Due to inaccuracies in the kinematic and force plate data, and a mismatch between the model and the subject, the equations of motion are violated when solving the inverse dynamics problem. As a result, dynamic inconsistency will exist and lead to residual forces and moments. In this study, we present and evaluate a computational method to perform inverse dynamics-based simulations without force plates, which both improves the dynamic consistency as well as removes the model?s dependency on measured external forces. Using the equations of motion and a scaled musculoskeletal model, the ground reaction forces and moments (GRF&Ms) are derived from three-dimensional full-body motion. The method entails a dynamic contact model and optimization techniques to solve the indeterminacy problem during a double contact phase and, in contrast to previously proposed techniques, does not require training or empirical data. The method was applied to nine healthy subjects performing several Activities of Daily Living (ADLs) and evaluated with simultaneously measured force plate data. Except for the transverse ground reaction moment, no significant differences (P>0.05) were found between the mean predicted and measured GRF&Ms for almost all ADLs. The mean residual forces and moments, however, were significantly reduced (P>0.05) in almost all ADLs using our method compared to conventional inverse dynamic simulations. Hence, the proposed method may be used instead of raw force plate data in human movement analysis using inverse dynamics.     

Joint moments and contact forces in the foot during walking

The net force and moment of a joint have been widely used to understand joint disease in the foot. Meanwhile, it does not reflect the physiological forces on muscles and contact surfaces. The objective of the study is to estimate active moments by muscles, passive moments by connective tissues and joint contact forces in the foot joints during walking. Joint kinematics and external forces of ten healthy subjects (all males, 24.7 ± 1.2 years) were acquired during walking. The data were entered into the five-segment musculoskeletal foot model to calculate muscle forces and joint contact forces of the foot joints using an inverse dynamics-based optimization. Joint reaction forces and active, passive and net moments of each joint were calculated from muscle and ligament forces. The maximum joint reaction forces were 8.72, 4.31, 2.65, and 3.41 body weight (BW) for the ankle, Chopart’s, Lisfranc and metatarsophalangeal joints, respectively. Active and passive moments along with net moments were also obtained. The maximum net moments were 8.6, 8.4, 5.4 and 0.8%BW∙HT, respectively. While the trend of net moment was very similar between the four joints, the magnitudes and directions of the active and passive moments varied between joints. The active and passive moments during walking could reveal the roles of muscles and ligaments in each of the foot joints, which was not obvious in the net moment. This method may help narrow down the source of joint problems if applied to clinical studies.     

A two-step EMG-and-optimization process to estimate muscle force during dynamic movement

The present study proposed a two-step EMG-and-optimization method for muscle force estimation in dynamic condition. Considering the strengths and the limitations of existing methods, the proposed approach exploited the advantages of min/max optimization with constraints on the contributions of the flexor and extensor muscle groups to the net joint moment estimated through an EMG-to-moment approach. Our methodology was tested at the knee joint during dynamic half squats, and was compared with traditional min/max optimization. In general, results showed significant differences in muscle force estimates from EMG-and-optimization method when compared with those from traditional min/max optimization. Muscle forces were higher – especially in the antagonist muscles – and more consistent with EMG patterns because of the ability of the proposed approach to properly account for agonist/antagonist cocontraction. In addition, muscle forces agree with mechanical constraints regarding the net, the agonist, and the antagonist moments, thus greatly improving the confidence in muscle force estimates. The proposed two-step EMG-and-optimization method for muscle force estimation is easy to implement with relatively low computational requirements and, thus, could offer interesting advantages for various applications in many fields, including rehabilitation, clinical, and sports biomechanics.     

Handwriting: Hand–pen contact force synergies in circle drawing tasks

This study investigated synergistic actions of hand–pen contact forces during circle drawing tasks in three-dimensional (3D) space. Twenty-four right-handed participants drew thirty concentric circles in the counterclockwise (CCW) and clockwise (CW) directions. Three-dimensional forces acting on an instrumented pen as well as 3D linear and angular positions of the pen were recorded. These contact forces were then transformed into the 3D radial, tangential, and normal force components specific to circle drawing. Uncontrolled manifold (UCM) analysis was employed to calculate the magnitude of the hand–pen contact force synergy. Three hypotheses were tested. First, hand–pen contact force synergies during circle drawing are dependent on the angular position of the pen tip. Second, hand–pen contact force synergies are dependent on force components in circle drawing. Third, hand–pen contact force synergies are greater in CCW direction than CW direction. The results showed that the strength of the hand–pen contact force synergy increased during the initial phase of circle drawing and decreased during the final phase. The synergy strength was greater for the radial and tangential components as compared to the normal component. Also, the circle drawing in CW direction was associated with greater hand–pen contact force synergy than the CCW direction. The results of this study suggest that the central nervous system (CNS) prioritizes hand–pen contact force synergies for the force components (i.e., radial and tangential) that are critical for circle drawing. The CNS modulates hand–pen contact force synergies for preparation and conclusion of circle drawing, respectively.     

A hub dynamometer for measurement of wheel forces in off-road bicycling

A dynamometric hubset that measures the two ground contact force components acting on a bicycle wheel in the plane of the bicycle during off-road riding while either coasting or braking was designed, constructed, and evaluated. To maintain compatibility with standard mountain bike construction, the hubs use commercially available shells with modified, strain gage-equipped axles. The axle strain gages are sensitive to forces acting in the radial and tangential directions, while minimizing sensitivity to transverse forces, steering moments, and variations in the lateral location of the center of pressure. Static calibration and a subsequent accuracy check that computed differences between applied and apparent loads developed during coasting revealed root mean squared errors of 1 percent full-scale or less (full-scale load = 4500 N). The natural frequency of the rear hub with the wheel attached exceeded 350 Hz. These performance capabilities make the dynamometer useful for its intended purpose during coasting. To demonstrate this usefulness, sample ground contact forces are presented for a subject who coasted downhill over rough terrain. The dynamometric hubset can also be used to determine ground contact forces during braking providing that the brake reaction force components are known. However, compliance of the fork can lead to high cross-sensitivity and corresponding large (> 5 percent FS) measurement errors at the front wheel.     

A technique to determine friction at the fingertips

This article proposes a technique to calculate the coefficient of friction for the fingertip- object interface. Twelve subjects (6 males and 6 females) participated in two experiments. During the first experiment (the imposed displacement method), a 3-D force sensor was moved horizontally while the subjects applied a specified normal force (4 N, 8 N, 12 N) on the surface of a sensor covered with different materials (sandpaper, cotton, rayon, polyester, and silk).The normal force and the tangential force (i.e., the force due to the sensor motion) were recorded. The coefficient of friction (mu(d)) was calculated as the ratio between the tangential force and the normal force. In the second experiment (the beginning slip method), a small instrumented object was gripped between the index finger and the thumb, held stationary in the air, and then allowed to drop. The weight (200 g, 500 g, and 1,000 g) and the surface (sandpaper, cotton, rayon, polyester, and silk) in contact with the digits varied across trials. The same sensor as in the first experiment was used to record the normal force (in a horizontal direction) and the tangential force (in the vertical direction). The slip force (i.e., the minimal normal force or grip force necessary to prevent slipping) was estimated as the force at the moment when the object just began to slip. The coefficient of friction was calculated as the ratio between the tangential force and the slip force. The results show that (1) the imposed displacement method is reliable; (2) except sandpaper, for all other materials the coefficient of friction did not depend on the normal force; (3) the skin-sandpaper coefficient of friction was the highest mu(d) =0.96+/-0.09 (for 4-N normal force) and the skin-rayon rayon coefficient of friction was the smallest mu(d) =0.36+/-0.10; (4) no significant difference between the coefficients of friction determined with the imposed displacement method and the beginning slip method was observed. We view the imposed displacement technique as having an advantage as compared with the beginning slip method, which is more cumbersome (e.g., dropped object should be protected from impacts) and prone to subjective errors owing to the uncertainty in determining the instance of the slip initiation (i.e., impeding sliding).     

Direct mechanical force measurements during the migration of Dictyostelium slugs using flexible substrata

We use the flexible substrate method to study how and where mechanical forces are exerted during the migration of Dictyostelium slugs. This old and contentious issue has been left poorly understood so far. We are able to identify clearly separate friction forces in the tip and in the tail of the slug, traction forces mostly localized in the inner slug/surface contact area in the prespore region and large perpendicular forces directed in the outward direction at the outline of contact area. Surprisingly, the magnitude of friction and traction forces is decreasing with slug velocity indicating that these quantities are probably related to the dynamics of cell/substrate adhesion complexes. Contrary to what is always assumed in models and simulations, friction is not of fluid type (viscous drag) but rather close to solid friction. We suggest that the slime sheath confining laterally the cell mass of the slug experiences a tension that in turn is pulling out the elastic substrate in the direction tangential to the slug profile where sheath is anchored. In addition, we show in the appendix that the iterative method we developed is well adapted to study forces over large and continuous fields when the experimental error is sufficiently low and when the plane of recorded bead deformations is close enough to the elastomer surface, requirements fulfilled in this experimental study of Dictyostelium slugs.     

Tangential finger forces use mechanical advantage during static grasping

When grasping and manipulating objects, the central controller utilizes the mechanical advantage of the normal forces of the fingers for torque production. Whether the same is valid for tangential forces is unknown. The main purpose of this study was to determine the patterns of finger tangential forces and the use of mechanical advantage as a control mechanism when dealing with objects of nonuniform finger positioning. A complementary goal was to explore the interaction of mechanical advantage (moment arm) and the role a finger has as a torque agonist/antagonist with respect to external torques (±0.4 N m). Five 6-df force/torque transducers measured finger forces while subjects held a prism handle (6 cm width × 9 cm height) with and without a single finger displaced 2 cm (handle width). The effect of increasing the tangential moment arm was significant (p < .01) for increasing tangential forces (in >70% of trials) and hence creating greater moments. Thus, the data provides evidence that the grasping system as a rule utilizes mechanical advantage for generating tangential forces. The increase in tangential force was independent of whether the finger was acting as a torque agonist or antagonist, revealing their effects to be additive.     

Joint contact loading in forefoot and rearfoot strike patterns during running

Research concerning forefoot strike pattern (FFS) versus rearfoot strike pattern (RFS) running has focused on the ground reaction force even though internal joint contact forces are a more direct measure of the loads responsible for injury. The main purpose of this study was to determine the internal loading of the joints for each strike pattern. A secondary purpose was to determine if converted FFS and RFS runners can adequately represent habitual runners with regards to the internal joint loading. Using inverse dynamics to calculate the net joint moments and reaction forces and optimization techniques to estimate muscle forces, we determined the axial compressive loading at the ankle, knee, and hip. Subjects consisted of 15 habitual FFS and 15 habitual RFS competitive runners. Each subject ran at a preferred running velocity with their habitual strike pattern and then converted to the opposite strike pattern. Plantar flexor muscle forces and net ankle joint moments were greater in the FFS running compared to the RFS running during the first half of the stance phase. The average contact forces during this period increased by 41.7% at the ankle and 14.4% at the knee joint during FFS running. Peak ankle joint contact force was 1.5 body weights greater during FFS running (p<0.05). There was no evidence to support a difference between habitual and converted running for joint contact forces. The increased loading at the ankle joint for FFS is an area of concern for individuals considering altering their foot strike pattern.     

Contributions of individual muscles to hip joint contact force in normal walking

The human hip joint withstands high contact forces during daily activity and is therefore susceptible to injury and structural deterioration over time. Knowledge of muscle-force contributions to hip joint loading may assist in the development of strategies to prevent and manage conditions such as osteoarthritis, femoro-acetabular impingement and fracture. The main aim of this study was to determine the contributions of individual muscles to hip contact force in normal walking. Muscle contributions to hip contact force were calculated based on a previously published dynamic optimization solution for normal walking, which provided the time histories of joint motion, ground reaction forces, and muscle forces during the stance and swing phases of gait. The force developed by each muscle plus its contribution to the ground reaction force were used to determine the muscle’s contribution to hip contact force. Muscles were the major contributors to hip contact force, with gravitational and centrifugal forces combined contributing less than 5% of the total contact force. Four muscles that span the hip – gluteus medius, gluteus maximus, iliopsoas, and hamstrings – contributed most significantly to the three components of the hip contact force and hip contact impulse (integral of hip contact force over time). Three muscles that do not span the hip – vasti, soleus, and gastrocnemius – also contributed substantially to hip joint loading. These results provide additional insight into lower-limb muscle function during walking and may also be relevant to studies of cartilage degeneration and bone remodelling at the hip.     

Effects of EMG processing on biomechanical models of muscle joint systems: sensitivity of trunk muscle moments, spinal forces, and stability

Biomechanical models are in use to estimate parameters such as contact forces and stability at various joints. In one class of these models, surface electromyography (EMG) is used to address the problem of mechanical indeterminacy such that individual muscle activation patterns are accounted for. Unfortunately, because of the stochastical properties of EMG signals, EMG based estimates of muscle force suffer from substantial estimation errors. Recent studies have shown that improvements in muscle force estimation can be achieved through adequate EMG processing, specifically whitening and high-pass (HP) filtering of the signals. The aim of this paper is to determine the effect of such processing on outcomes of a biomechanical model of the lumbosacral joint and surrounding musculature. Goodness of fit of estimated muscle moments to net moments and also estimated joint stability significantly increased with increasing cut-off frequencies in HP filtering, whereas no effect on joint contact forces was found. Whitening resulted in moment estimations comparable to those obtained from optimal HP filtering with cut-off frequencies over 250 Hz. Moreover, compared to HP filtering, whitening led to a further increase in estimated joint-stability. Based on theoretical models and on our experimental results, we hypothesize that the processing leads to an increase in pick-up area. This then would explain the improvements from a better balance between deep and superficial motor unit contributions to the signal.     

A comparison of Coulomb and pseudo-Coulomb friction implementations: Application to the table contact phase of gymnastics vaulting

In the table contact phase of gymnastics vaulting both dynamic and static friction act. The purpose of this study was to develop a method of simulating Coulomb friction that incorporated both dynamic and static phases and to compare the results with those obtained using a pseudo-Coulomb implementation of friction when applied to the table contact phase of gymnastics vaulting. Kinematic data were obtained from an elite level gymnast performing handspring straight somersault vaults using a Vicon optoelectronic motion capture system. An angle-driven computer model of vaulting that simulated the interaction between a seven segment gymnast and a single segment vaulting table during the table contact phase of the vault was developed. Both dynamic and static friction were incorporated within the model by switching between two implementations of the tangential frictional force. Two vaulting trials were used to determine the model parameters using a genetic algorithm to match simulations to recorded performances. A third independent trial was used to evaluate the model and close agreement was found between the simulation and the recorded performance with an overall difference of 13.5%. The two-state simulation model was found to be capable of replicating performance at take-off and also of replicating key contact phase features such as the normal and tangential motion of the hands. The results of the two-state model were compared to those using a pseudo-Coulomb friction implementation within the simulation model. The two-state model achieved similar overall results to those of the pseudo-Coulomb model but obtained solutions more rapidly.     

A computationally efficient strategy to estimate muscle forces in a finite element musculoskeletal model of the lower limb

Concurrent multiscale simulation strategies are required in computational biomechanics to study the interdependence between body scales. However, detailed finite element models rarely include muscle recruitment due to the computational burden of both the finite element method and the optimization strategies widely used to estimate muscle forces. The aim of this study was twofold: first, to develop a computationally efficient muscle force prediction strategy based on proportional-integral-derivative (PID) controllers to track gait and chair rise experimental joint motion with a finite element musculoskeletal model of the lower limb, including a deformable knee representation with 12 degrees of freedom; and, second, to demonstrate that the inclusion of joint-level deformability affects muscle force estimation by using two different knee models and comparing muscle forces between the two solutions. The PID control strategy tracked experimental hip, knee, and ankle flexion/extension with root mean square errors below 1°, and estimated muscle, contact and ligament forces in good agreement with previous results and electromyography signals. Differences up to 11% and 20% in the vasti and biceps femoris forces, respectively, were observed between the two knee models, which might be attributed to a combination of differing joint contact geometry, ligament behavior, joint kinematics, and muscle moment arms. The tracking strategy developed in this study addressed the inevitable tradeoff between computational cost and model detail in musculoskeletal simulations and can be used with finite element musculoskeletal models to efficiently estimate the interdependence between muscle forces and tissue deformation.