A mechanical model to determine the influence of masses and mass distribution on the impact force during running

Simple spring-damper-mass models have been widely used to simulate human locomotion. However, most previous models have not accounted for the effect of non-rigid masses (wobbling masses) on impact forces. A simple mechanical model of the human body developed in this study included the upper and lower bodies with each part represented by a rigid and a wobbling mass. Spring-damper units connected different masses to represent the stiffness and damping between the upper and lower bodies, and between the rigid and wobbling masses. The simulated impact forces were comparable to experimentally measured impact forces. Trends in changes of the impact forces due to changes in touch-down velocity reported in previous studies could be reproduced with the model. Simulated results showed that the impact force peaks increased with increasing rigid or wobbling masses of the lower body. The ratio of mass distribution between the rigid and wobbling mass in the lower body was also shown to affect the impact force peak, for example, the impact force peak increased with increasing rigid contribution. The variation in the masses of upper body was shown to have a minimum effect on the impact force peak, but a great effect on the active force peak (the second peak in the ground reaction force). Future studies on the dynamics and neuro-muscular control of human running are required to take into consideration the influence of individual variation in lower body masses and mass distribution.     

A model-based parametric study of impact force during running

This paper deals with the impact force during foot-ground impact activities such as the running. A previously developed model is used for this study. The model is a lumped-parameter one consisting of four masses connected to each other via linear springs and viscous dampers. A shoe-specific nonlinear function is used for representation of the ground reaction force. The authors have previously showed that the previous version of the model as well as its simulation is incorrect. This paper slightly modifies the previous model so as it is able to produce results in agreement with the experiments. Then, the modified model is simulated for two typical shoe types. A parametric study is also conducted. The parametric study concerns with the effects of masses, mass ratios, stiffness constants, and damping coefficients on the dynamics of the impact. It is shown that the impact forces increase as the rigid and wobbling masses increase. However, the increase in the impact forces is not the same for all the masses. It is found that the impact force increases as the touchdown velocities increase. Simulations imply that the variations of the damping coefficients result in larger variations of the impact force compared to the stiffness. The effect of the variation of gravity on the simulated impact force is also explored. It is concluded that both the first and the second peaks of the impact force are increased with gravity. An in-depth discussion is included to compare results of the current paper with results of other investigators.     

Experimental/analytical analysis of human locomotion using bondgraphs

A new vectorial bondgraph approach for modeling and simulation of human locomotion is introduced. The vectorial bondgraph is applied to an eight-segment gait model to derive the equations of motion for studying ground reaction forces (GRFs) and centers of pressure (COPs) in single and double support phases of ground and treadmill walking. A phase detection technique and accompanying transition equation is proposed with which the GRFs and COPs may be calculated for the transitions from double-to-single and single-to-double support phases. Good agreement is found between model predictions and experimental data obtained from force plate measurements. The bondgraph modeling approach is shown to be both informative and adaptable, in the sense that the model resembles the human body structure, and that modeled body segments can be easily added or removed.     

The influence of soft tissue movement on ground reaction forces, joint torques and joint reaction forces in drop landings

The aim of this study was to determine the effects that soft tissue motion has on ground reaction forces, joint torques and joint reaction forces in drop landings. To this end a four body-segment wobbling mass model was developed to reproduce the vertical ground reaction force curve for the first 100 ms of landing. Particular attention was paid to the passive impact phase, while selecting most model parameters a priori, thus permitting examination of the rigid body assumption on system kinetics. A two-dimensional wobbling mass model was developed in DADS (version 9.00, CADSI) to simulate landing from a drop of 43 cm. Subject-specific inertia parameters were calculated for both the rigid links and the wobbling masses. The magnitude and frequency response of the soft tissue of the subject to impulsive loading was measured and used as a criterion for assessing the wobbling mass motion. The model successfully reproduced the vertical ground reaction force for the first 100 ms of the landing with a peak vertical ground reaction force error of 1.2% and root mean square errors of 5% for the first 15 ms and 12% for the first 40 ms. The resultant joint forces and torques were lower for the wobbling mass model compared with a rigid body model, up to nearly 50% lower, indicating the important contribution of the wobbling masses on reducing system loading.     

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.     

Determination of subject-specific model parameters for visco-elastic elements

The determination of subject-specific model parameter values is necessary in order for a computer simulation model of human motion to be evaluated quantitatively. This study used an optimisation procedure along with a kinematically driven simulation model of the contact phase in running jumps to determine the elastic parameters of segmental wobbling masses and the foot-ground interface. Kinetic and kinematic data were obtained on running jumps for height and distance performed by an elite male high jumper. Stiffness and damping coefficients of the visco-elastic elements in the model were varied until the difference between simulation and performance was minimised. Percentage differences of 6% and 9% between the simulated and recorded performances were obtained in the jumps for height and distance, respectively. When the parameters obtained from the jump for height were used in a simulation of the jump for distance (and vice versa), there was poor agreement with the recorded jump. On the other hand, a common set of visco-elastic parameters were obtained using the data from both recorded jumps resulting in a mean difference of only 8% (made up of 7% and 10%) between simulation and performance that was almost as good as the individual matches. Simulations were not overly sensitive to perturbations of the common set of visco-elastic parameters. It is concluded that subject-specific elastic parameters should be calculated from more than a single jump in order to provide a robust set of values that can be used in different simulations.     

Parameter determination for a computer simulation model of a diver and a springboard

This study used kinematic data on springboard diving performances to estimate viscoelastic parameters of a planar model of a springboard and diver with wobbling masses in the trunk, thigh, and calf segments and spring dampers acting at the heel, ball, and toe of the foot segment. A subject-specific angle-driven eight-segment model was used with an optimization algorithm to determine viscoelastic parameter values by matching simulations to four diving performances. Using the parameters determined from the matching of a single dive in a simulation of another dive resulted in up to 31% difference between simulation and performance, indicating the danger of using too small a set of kinematic data. However, using four dives in a combined matching process to obtain a common set of parameters resulted in a mean difference of 8.6%. Because these four dives included very different rotational requirements, it is anticipated that the combined parameter set can be used with other dives from these two groups.     

Estimates of muscle function in human gait depend on how foot-ground contact is modelled

Computational analyses of leg-muscle function in human locomotion commonly assume that contact between the foot and the ground occurs at discrete points on the sole of the foot. Kinematic constraints acting at these contact points restrict the motion of the foot and, therefore, alter model calculations of muscle function. The aim of this study was to evaluate how predictions of muscle function obtained from musculoskeletal models are influenced by the model used to simulate ground contact. Both single- and multiple-point contact models were evaluated. Muscle function during walking and running was determined by quantifying the contributions of individual muscles to the vertical, fore-aft and mediolateral components of the ground reaction force (GRF). The results showed that two factors--the number of foot-ground contact points assumed in the model and the type of kinematic constraint enforced at each point--affect the model predictions of muscle coordination. Whereas single- and multiple-point contact models produced similar predictions of muscle function in the sagittal plane, inconsistent results were obtained in the mediolateral direction. Kinematic constraints applied in the sagittal plane altered the model predictions of muscle contributions to the vertical and fore-aft GRFs, while constraints applied in the frontal plane altered the calculations of muscle contributions to the mediolateral GRF. The results illustrate the sensitivity of calculations of muscle coordination to the model used to simulate foot-ground contact.     

Estimates of muscle function in human gait depend on how foot-ground contact is modelled

Computational analyses of leg-muscle function in human locomotion commonly assume that contact between the foot and the ground occurs at discrete points on the sole of the foot. Kinematic constraints acting at these contact points restrict the motion of the foot and, therefore, alter model calculations of muscle function. The aim of this study was to evaluate how predictions of muscle function obtained from musculoskeletal models are influenced by the model used to simulate ground contact. Both single- and multiple-point contact models were evaluated. Muscle function during walking and running was determined by quantifying the contributions of individual muscles to the vertical, fore-aft and mediolateral components of the ground reaction force (GRF). The results showed that two factors – the number of foot-ground contact points assumed in the model and the type of kinematic constraint enforced at each point – affect the model predictions of muscle coordination. Whereas single- and multiple-point contact models produced similar predictions of muscle function in the sagittal plane, inconsistent results were obtained in the mediolateral direction. Kinematic constraints applied in the sagittal plane altered the model predictions of muscle contributions to the vertical and fore-aft GRFs, while constraints applied in the frontal plane altered the calculations of muscle contributions to the mediolateral GRF. The results illustrate the sensitivity of calculations of muscle coordination to the model used to simulate foot-ground contact.     

Use of a backpack alters gait initiation of high school students

We assessed how backpack carriage influences the gait initiation (GI) process in high school students, who extensively use backpacks. GI involves different dynamics from gait itself, while the excessive use of backpacks can result in adverse effects. 117 high school students were evaluated in three experimental conditions: no backpack (NB), bilateral backpack (BB), and unilateral backpack (UB). Two force plates were used to acquire ground reaction forces (GRFs) and moments for each foot separately. Center of pressure (COP) scalar variables were extracted, and statistical parametric mapping analysis was performed over the entire COP/GRFs time series. GI anticipatory postural adjustments (APAs) were reduced and were faster in backpack conditions; medial–lateral COP excursion was smaller in this phase. The uneven distribution of the extra load in the UB condition led to a larger medial–lateral COP shift in the support-foot unloading phase, with a corresponding vertical GRF change that suggests a more pronounced unloading swing foot/loading support foot mechanism. The anterior–posterior GRFs were altered, but the COP was not. A possible explanation for these results may be the forward trunk lean and the center of mass proximity of the base of support boundary, which induced smaller and faster APA, increased swing foot/support foot weight transfer, and increased load transfer to the first step.     

Component inertia modeling of segmental wobbling and rigid masses

A modification to an existing mathematical model is described, which permits the determination of subject-specific inertia parameters for wobbling and rigid masses of female body segments. The model comprises segment-specific soft tissue, bone, and lung components. A total of 59 geometric solids (40 soft tissue, 17 bone, 2 lung) were used to represent the body components. Ninety-five anthropometric measurements were collected from 7 female participants and were used to develop and evaluate the model. The success of the model is evaluated using predicted mass and mass distribution. The overall absolute accuracy in predicted whole body mass was better than 3.0%, with a maximum error of 4.9%. The appropriateness of the cadaver-based density values used in the model is addressed and the accuracy of the component inertia model in relation to uniform density models is discussed. The model offers a novel approach for determining component inertia parameters, which have been used successfully in a wobbling mass model to produce realistic kinetic analyses of drop-landings.     

Prediction of ground reaction forces during gait based on kinematics and a neural network model

Kinetic information during human gait can be estimated with inverse dynamics, which is based on anthropometric, kinematic, and ground reaction data. While collecting ground reaction data with a force plate is useful, it is costly and requires regulated space. The goal of this study was to propose a new, accurate methodology for predicting ground reaction forces (GRFs) during level walking without the help of a force plate. To predict GRFs without a force plate, the traditional method of Newtonian mechanics was used for the single support phase. In addition, an artificial neural network (ANN) model was applied for the double support phase to solve statically indeterminate structure problems. The input variables of the ANN model, which were selected to have both dependency and independency, were limited to the trajectory, velocity, and acceleration of the whole segment's mass centre to minimise errors. The predicted GRFs were validated with actual GRFs through a ten-fold cross-validation method, and the correlation coefficients (R) for the ground forces were 0.918 in the medial–lateral axis, 0.985 in the anterior–posterior axis, and 0.991 in the vertical axis during gait. The ground moments were 0.987 in the sagittal plane, 0.841 in the frontal plane, and 0.868 in the transverse plane during gait. The high correlation coefficients(R) are due to the improvement of the prediction rate in the double support phase. This study also proved the possibility of calculating joint forces and moments based on the GRFs predicted with the proposed new hybrid method. Data generated with the proposed method may thus be used instead of raw GRF data in gait analysis and in calculating joint dynamic data using inverse dynamics.     

Stress analysis of the standing foot following surgical plantar fascia release

Plantar fascia release is a surgical alternative for patients who suffer chronic heel pain due to plantar fasciitis and are unaffected by conservative treatment. A computational (finite element) model for analysis of the structural behavior of the human foot during standing was utilized to investigate the biomechanical effects of releasing the plantar fascia. The model integrates a system of five planar structures in the directions of the foot rays. It was built according to accurate geometric data of MRI, and includes linear and non-linear elements that represent bony, cartilaginous, ligamentous and fatty tissues. The model was successfully validated by comparing its resultant ground reactions with foot-ground pressure measurements and its predicted displacements with those observed in radiological tests. Simulation of plantar fascia release (partial or total) was accomplished by gradually removing parts of the fascia in the model. The results showed that total fascia release causes extensive arch deformation during standing, which is greater than normal deformation by more than 2.5mm. Tension stresses carried by the long plantar ligaments increased significantly, and may exceed the normal average stress by more than 200%. Since the contribution of the plantar fascia to the foot's load-bearing ability is of major importance, its release must be very carefully considered, and the present model may be used to help surgeons decide upon the desired degree of release.     

ASSESSMENT OF EXTERNAL AND INTERNAL LOADS IN THE TRIPLE JUMP VIA INVERSE DYNAMICS SIMULATION

The triple jump is a demanding athletics event that, after an approach run, consists of three consecutive phases: the hop, the bound, and the jump. During the involved three take-off actions a jumper is exposed to increased risk of injury due to the high impact forces from the ground and powerful muscle/tendon efforts, which are further reflected in the internal loads of the lower limb joints. While external ground reactions can possibly be measured using force platforms, in vivo measurements of the internal loads are practically not feasible. The purpose of the paper is to present the development of an effective formulation for the inverse dynamics simulation of the triple jump, based on the jumper dynamical model and non-invasive kinematic recordings of the movement. The developed simulation model serves for the analysis of all the triple jump phases, irrespective of whether the jumper is in flight or in contact with the ground with one of his feet, and is focused on effective assessment of the external reactions on the supporting leg as well as the muscle forces and joint reaction forces in the leg. Some numerical results of inverse dynamics simulation of the triple jump are reported.     

Determination of joint moments with instrumented force shoes in a variety of tasks

Ground reaction forces (GRFs) are often used in inverse dynamics analyses to determine joint loading. These GRFs are usually measured using force plates (FPs). As an alternative, instrumented force shoes (FSs) can be used, which have the advantage over FPs that they do not constrain foot placement. This study tested the FS system in one normal weight subject (77 kg) performing 19 different lifting, pushing and pulling and walking tasks. Kinematics were measured with an optoelectronic system and the GRFs and the positions of the centre of pressure (CoP) were synchronously measured with FPs and FSs. Differences between the outcomes of the two measurement systems (i.e. CoP and GRFs) and the resulting ankle and L5/S1 joint moments were determined at the instant of the peak GRF (DaPF). For most lifting and pushing and pulling tasks, the difference between the FP and FS measurements remained small: GRF DaPF remained below 3% body weight, CoP DaPF remained below 10 mm, ankle moment DaPF remained below 7% of the peak total ankle moment that occurred during normal walking and L5/S1 moment DaPF remained below 7% of the peak total L5/S1 moment that occurred during normal symmetric lifting. More substantial differences were only found in the maximal pushing tasks. For the walking tasks, peak vertical GRFs were somewhat underestimated. However, differences in ankle and L5/S1 moments remained small, i.e. DaPF below 7% of the peak total moment that occurred during normal walking.     

Force measurements during running on different instrumented treadmills

One method to determine the forces produced during running is to conduct extensive kinematic and kinetic analysis. These analyses can be performed by having an individual perform repeated over-ground running trials or simply run continuously on an instrumented treadmill. The forces produced during over-ground running may not be the same as the forces during treadmill running and these differences could be attributed to a number of factors, including the design of the instrumented treadmill. The purpose of this paper was to determine whether there are differences in force measurements on different instrumented treadmill setups in comparison to over-ground running and to correct for any of these differences using a theoretical model. 11 participants ran on three different treadmills and performed over-ground running at 2.7, 3.6, and 4.5 m/s. Ground reaction forces were measured via force plates and an instrumented pressure insole. We found that the magnitude of the vertical ground reaction force differed between the three treadmills and over-ground running. The difference in ground reaction forces estimated by the pressure insole and the treadmill-force-plate system or instrumented treadmill can be explained by a three degree of freedom mechanical model of a person running on a treadmill and this model could potentially be used to correct for errors in force measurement from instrumented treadmills. The model included a force plate, a treadmill, and a wobbling mass with varying natural frequencies and damping characteristics, and constant masses. These findings provide researchers a method to correct forces from an instrumented treadmill set-up to determine a close approximation of the actual forces experienced by a participant during treadmill running.     

Lower-extremity ground reaction forces in collegiate baseball pitchers

The purpose of this study was to investigate ground reaction forces (GRF) in collegiate baseball pitchers and their relationship to pitching mechanics. Fourteen healthy collegiate baseball pitchers participated in this study. High-speed video and force plate data were collected for fastballs from each pitcher. The average ball speed was 35 ± 3 m/sec (78 ± 7 mph). Peak GRFs of 245 ± 20% body weight (BW) were generated in an anterior or braking direction to control descent. Horizontal GRFs tended to occur in a laterally directed fashion, reaching a peak of 45 ± 63% BW. The maximum vertical GRF averaged 202 ± 43% BW approximately 45 milliseconds after stride foot contact. A correlation between braking force and ball velocity was evident. Because of the downward inclination and rotation of the pitching motion, in addition to volume, shear forces may occur in the musculoskeletal tissues of the stride limb leading to many of the lower-extremity injuries seen in this athletic population.     

Three-dimensional data-tracking dynamic optimization simulations of human locomotion generated by direct collocation

The aim of this study was to perform full-body three-dimensional (3D) dynamic optimization simulations of human locomotion by driving a neuromusculoskeletal model toward in vivo measurements of body-segmental kinematics and ground reaction forces. Gait data were recorded from 5 healthy participants who walked at their preferred speeds and ran at 2 m/s. Participant-specific data-tracking dynamic optimization solutions were generated for one stride cycle using direct collocation in tandem with an OpenSim-MATLAB interface. The body was represented as a 12-segment, 21-degree-of-freedom skeleton actuated by 66 muscle-tendon units. Foot-ground interaction was simulated using six contact spheres under each foot. The dynamic optimization problem was to find the set of muscle excitations needed to reproduce 3D measurements of body-segmental motions and ground reaction forces while minimizing the time integral of muscle activations squared. Direct collocation took on average 2.7 ± 1.0 h and 2.2 ± 1.6 h of CPU time, respectively, to solve the optimization problems for walking and running. Model-computed kinematics and foot-ground forces were in good agreement with corresponding experimental data while the calculated muscle excitation patterns were consistent with measured EMG activity. The results demonstrate the feasibility of implementing direct collocation on a detailed neuromusculoskeletal model with foot-ground contact to accurately and efficiently generate 3D data-tracking dynamic optimization simulations of human locomotion. The proposed method offers a viable tool for creating feasible initial guesses needed to perform predictive simulations of movement using dynamic optimization theory. The source code for implementing the model and computational algorithm may be downloaded at http://simtk.org/home/datatracking.     

Models for boundary effects on molecular rotation in membranes

Rotational and wobbling diffusion coefficients for spherical and long-chain molecules in membranes are calculated using a simple hydrodynamic model. Estimates of the contributions to the diffusion coefficients arising from hydrodynamic interactions between molecules and membrane interfaces are obtained and found to be small. For molecules containing polar head groups, we show that the presence of a membrane interface can produce a significant reduction in the wobbling diffusion coefficient over what would be obtained in an isotropic fluid.