Prediction of ground reaction forces in level and incline/decline walking from a multistage analysis of plantar pressure data

Knowing the ground reaction forces (GRFs) during walking has various biomechanical applications in injury prevention, gait analysis, as well as prosthetic and footwear design. The current study presents a method for predicting the GRFs in level and incline/decline walking that may be used in various outdoor biomechanics studies geared towards the above applications. The method was developed to predict the complete set of GRFs at walking inclinations of 0°, ±5°, ±10°, ±15°, and ±20°. Plantar pressure insoles were used to obtain inclination-specific, linear regression models based on three periods of gait stance phase, and the model-determined GRFs were compared with those measured from a forceplate. The three periods were determined based on the observed shifting of load-bearing insole sensors from heel to forefoot during walking, i.e., heel-strike, midstance, and toe-off. Six subjects wearing minimalist shoes fitted with plantar pressure insoles containing 99 pressure sensors performed ten walking trials at each of the aforementioned inclinations on an adjustable ramp with an embedded forceplate. Data from contact of the instrumented shoes with the forceplate were used to create linear regressions to transform insole pressure data into a complete set of GRFs. The root mean square error (RMSE) over peak recorded values were on average 10%, 3%, 21% for level walking and 11%, 4%, 23% for ramp walking in the respective anteroposterior, vertical, and mediolateral directions. The multistage linear regression model developed in the current study may be an acceptable option for estimating GRFs during walking in various environments without the restraint of a forceplate.     

Ground reaction forces during treadmill running in microgravity

Astronauts perform treadmill exercise during long-duration space missions to counter the harmful effects of microgravity exposure upon bone, muscle, and cardiopulmonary health. When exercising in microgravity, astronauts wear a harness and bungee system that provides forces that maintain attachment to the treadmill. Typical applied forces are less than body weight. The decreased gravity-replacement force could result in differences in ground-reaction force at a given running speed when compared to those achieved in normal gravity, which could influence the adaptive response to the performed exercise.     

An individual and dynamic Body Segment Inertial Parameter validation method using ground reaction forces

Over the last decades a variety of research has been conducted with the goal to improve the Body Segment Inertial Parameters (BSIP) estimations but to our knowledge a real validation has never been completely successful, because no ground truth is available. The aim of this paper is to propose a validation method for a BSIP identification method (IM) and to confirm the results by comparing them with recalculated contact forces using inverse dynamics to those obtained by a force plate. Furthermore, the results are compared with the recently proposed estimation method by Dumas et al. (2007). Additionally, the results are cross validated with a high velocity overarm throwing movement. Throughout conditions higher correlations, smaller metrics and smaller RMSE can be found for the proposed BSIP estimation (IM) which shows its advantage compared to recently proposed methods as of Dumas et al. (2007). The purpose of the paper is to validate an already proposed method and to show that this method can be of significant advantage compared to conventional methods.     

Ground reaction force estimation using an insole-type pressure mat and joint kinematics during walking

Kinetic analysis of walking requires joint kinematics and ground reaction force (GRF) measurement, which are typically obtained from a force plate. GRF is difficult to measure in certain cases such as slope walking, stair climbing, and track running. Nevertheless, estimating GRF continues to be of great interest for simulating human walking. The purpose of the study was to develop reaction force models placed on the sole of the foot to estimate full GRF when only joint kinematics are provided (Type-I), and to estimate ground contact shear forces when both joint kinematics and foot pressure are provided (Type-II and Type-II-val). The GRF estimation models were attached to a commercial full body skeletal model using the AnyBody Modeling System, which has an inverse dynamics-based optimization solver. The anterior–posterior shear force and medial–lateral shear force could be estimated with approximate accuracies of 6% BW and 2% BW in all three methods, respectively. Vertical force could be estimated in the Type-I model with an accuracy of 13.75% BW. The accuracy of the force estimation was the highest during the mid-single-stance period with an average RMS for errors of 3.10% BW, 1.48% BW, and 7.48% BW for anterior–posterior force, medial–lateral force, and vertical force, respectively. The proposed GRF estimation models could predict full and partial GRF with high accuracy. The design of the contact elements of the proposed model should make it applicable to various activities where installation of a force measurement system is difficult, including track running and treadmill walking.     

The use of a single inertial sensor to estimate 3-dimensional ground reaction force during accelerative running tasks

The purpose of this investigation was to determine the feasibility of using a single inertial measurement unit (IMU) placed on the sacrum to estimate 3-dimensional ground reaction force (F) during linear acceleration and change of direction tasks. Force plate measurements of F and estimates from the proposed IMU method were collected while subjects (n = 15) performed a standing sprint start (SS) and a 45° change of direction task (COD). Error in the IMU estimate of step-averaged component and resultant F was quantified by comparison to estimates from the force plate using Bland-Altman 95% limits of agreement (LOA), root mean square error (RMSE), Pearson’s product-moment correlation coefficient (r), and the effect size (ES) of the differences between the two systems. RMSE of the IMU estimate of step-average F ranged from 37.70 N to 77.05 N with ES between 0.04 and 0.47 for SS while for COD, RMSE was between 54.19 N to 182.92 N with ES between 0.08 and 1.69. Correlation coefficients between the IMU and force plate measurements were significant (p ≤ 0.05) for all values (r = 0.53 to 0.95) except the medio-lateral component of step-average F. The average angular error in the IMU estimate of the orientation of step-average F was ≤10° for all tasks. The results of this study suggest the proposed IMU method may be used to estimate sagittal plane components and magnitude of step-average F during a linear standing sprint start as well as the vertical component and magnitude of step-average F during a 45° change of direction task.     

Influence of IMU position and orientation placement errors on ground reaction force estimation

Wearable inertial measurement units (IMU) have been proposed to estimate GRF outside of specialized laboratories, however the precise influence of sensor placement error on accuracy is unknown. We investigated the influence of IMU position and orientation placement errors on GRF estimation accuracy. Methods: Kinematic data from twelve healthy subjects based on marker trajectories were used to simulate 1848 combinations of sensor position placement errors (range ± 100 mm) and orientation placement errors (range ± 25°) across eight body segments (trunk, pelvis, left/right thighs, left/right shanks, and left/right feet) during normal walking trials for baseline cases when a single sensor was misplaced and for the extreme cases when all sensors were simultaneously misplaced. Three machine learning algorithms were used to estimate GRF for each placement error condition and compared with the no placement error condition to evaluate performance. Results: Position placement errors for a single misplaced IMU reduced vertical GRF (VGRF), medio-lateral GRF (MLGRF), and anterior-posterior GRF (APGRF) estimation accuracy by up to 1.1%, 2.0%, and 0.9%, respectively and for all eight simultaneously misplaced IMUs by up to 4.9%, 6.0%, and 4.3%, respectively. Orientation placement errors for a single misplaced IMU reduced VGRF, MLGRF, and APGRF estimation accuracy by up to 4.8%, 7.3%, and 1.5%, respectively and for all eight simultaneously misplaced IMUs by up to 20.8%, 23.4%, and 12.3%, respectively. Conclusion: IMU sensor misplacement, particularly orientation placement errors, can significantly reduce GRF estimation accuracy and thus measures should be taken to account for placement errors in implementations of GRF estimation via wearable IMUs.     

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.     

A probabilistic method to estimate gait kinetics in the absence of ground reaction force measurements

Human joint torques during gait are usually computed using inverse dynamics. This method requires a skeletal model, kinematics and measured ground reaction forces and moments (GRFM). Measuring GRFM is however only possible in a controlled environment. This paper introduces a probabilistic method based on probabilistic principal component analysis to estimate the joint torques for healthy gait without measured GRFM. A gait dataset of 23 subjects was obtained containing kinematics, measured GRFM and joint torques from inverse dynamics in order to obtain a probabilistic model. This model was then used to estimate the joint torques of other subjects without measured GRFM. Only kinematics, a skeletal model and timing of gait events are needed. Estimation only takes 0.28 ms per time instant. Using cross-validation, the resulting root mean square estimation errors for the lower-limb joint torques are found to be approximately 0.1 Nm/kg, which is 6–18% of the range of the ground truth joint torques. Estimated joint torque and GRFM errors are up to two times smaller than model-based state-of-the-art methods. Model-free artificial neural networks can achieve lower errors than our method, but are less repeatable, do not contain uncertainty information on the estimates and are difficult to use in situations which are not in the learning set. In contrast, our method performs well in a new situation where the walking speed is higher than in the learning dataset. The method can for example be used to estimate the kinetics during overground walking without force plates, during treadmill walking without (separate) force plates and during ambulatory measurements.     

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.     

Ground reaction forces and lower-limb joint kinetics of turning gait in typically developing children

Turning is a common locomotor task essential to daily activity; however, very little is known about the forces and moments responsible for the kinematic adaptations occurring relative to straight-line gait in typically developing children. Thus, the aims of this study were to analyse ground reaction forces (GRFs), ground reaction free vertical torque (T_Z), and the lower-limb joint kinetics of 90° outside (step) and inside (spin) limb turns. Step, spin, and straight walking trials from fifty-four typically developing children were analysed. All children were fit with the Plug-in Gait and Oxford Foot Model marker sets while walking over force plates embedded in the walkway. Net internal joint moments and power were computed via a standard inverse dynamics approach. All dependent variables were statistically analysed over the entire curves using the mean difference 95% bootstrap confidence band approach. GRFs were directed medially for step turns and laterally for spin turns during the turning phase. Directions were reversed and magnitudes decreased during the approach phase. Step turns showed reduced ankle power generation, while spin turns showed large T_Z. Both strategies required large knee and hip coronal and transverse plane moments during swing. These kinetic differences highlight adaptations required to maintain stability and reorient the body towards the new walking direction during turning. From a clinical perspective, turning gait may better reveal weaknesses and motor control deficits than straight walking in pathological populations, such as children with cerebral palsy, and could potentially be implemented in standard gait analysis sessions.     

Estimation of vertical ground reaction force during running using neural network model and uniaxial accelerometer

Wearable technology has been viewed as one of the plausible alternatives to capture human motion in an unconstrained environment, especially during running. However, existing methods require kinematic and kinetic measurements of human body segments and can be complicated. This paper investigates the use of neural network model (NN) and accelerometer to estimate vertical ground reaction force (VGRF). An experimental study was conducted to collect sufficient samples for training, validation and testing. The estimated results were compared with VGRF measured using an instrumented treadmill. The estimates yielded an average root mean square error of less than 0.017 of the body weight (BW) and a cross-correlation coefficient greater than 0.99. The results also demonstrated that NN could estimate impact force and active force with average errors ranging between 0.10 and 0.18 of BW at different running speeds. Using NN and uniaxial accelerometer can (1) simplify the estimation of VGRF, (2) reduce the computational requirement and (3) reduce the necessity of multiple wearable sensors to obtain relevant parameters.     

New technique for studying reaction forces during primate behaviors on vertical substrates

Recording reaction forces from primates during behaviors on vertical substrates, such as leaping, climbing, or biting trees, typically requires the design and construction of customized recording devices or mounting commercially available force platforms in a vertical position. The technical difficulties imposed by either option have hindered in vivo research on the kinetics of primate behaviors on vertical substrates. We describe a simple, inexpensive apparatus for recording forces from primate behaviors on vertical substrates. The apparatus includes an instrumented beam fastened directly to a horizontal force platform and a surrounding vertical substrate that does not contact the instrumented beam or platform. The contact piece at the end of the instrumented beam is positioned flush with the noninstrumented vertical substrate, and reaction forces elicited on this instrumented section are directed to the force platform. Because most of the vertical substrate is not instrumented, we can isolate and record forces from a single limb or jaw during a behavior. Biewener and Full ([1992] Biomechanics Structures and Positions: A Practical Approach; New York: Oxford University press, p. 45-73) gave seven criteria to consider when designing a customized force-recording device. Where appropriate, we tested if our apparatus met their criteria. The apparatus accurately records forces in three orthogonal directions, has low cross-talk, maintains a high frequency response, exhibits a linear response up to at least 200 Newtons, and displays a uniform response to a given force across the instrumented contact piece. Our design does not easily facilitate the identification of the point of force application. Therefore, joint moments cannot be easily calculated. This limitation, however, does not affect the apparatus's ability to accurately record the magnitude and direction of a force (as shown by other tests). We developed this apparatus to measure jaw forces during tree gouging in common marmosets (Callithrix jacchus), but the general design can be readily modified to study a variety of primate behaviors on vertical substrates.     

Ability of the planar spring-mass model to predict mechanical parameters in running humans

The planar spring-mass model is a simple mathematical model of bouncing gaits, such as running, trotting and hopping. Although this model has been widely used in the study of locomotion, its accuracy in predicting locomotor mechanics has not been systematically quantified. We determined the percent error of the model in predicting 10 locomotor parameters in running humans by comparing the model predictions to experimental data from humans running in normal gravity and simulated reduced gravity. We tested the hypotheses that the model would overestimate horizontal impulse and the change in mechanical energy of the centre of mass (COM) during stance. The model provided good predictions of stance time, vertical impulse, contact length, duty factor, relative stride length and relative peak force. All predictions of these parameters were within 20% of measured values and at least 90% of predictions of each parameter were within 10% of measured values (median absolute errors: <7%). This suggests that the model incorporates all features of running humans that have a significant influence upon these six parameters. As simulated gravity level decreased, the magnitude of the errors in predicting each of these parameters either decreased or stayed constant, indicating that this is a good model of running in simulated reduced gravity. As hypothesised, horizontal impulse and change in mechanical energy of the COM during stance were overestimated (median absolute errors: 43.6% and 26.2%, respectively). Aerial time and peak vertical COM displacement during stance were also systematically overestimated (median absolute errors: 17.7% and 22.9%, respectively). Care should be taken to ensure that the model is used only to investigate parameters which it can predict accurately. It would be useful to extend this analysis to other species and gaits.     

Evaluating dynamic error of a treadmill and the effect on measured kinetic gait parameters: Implications and possible solutions

The dynamic properties of instrumented treadmills influence the force measurement of the embedded force platform. We investigated these properties using a frequency response function, which evaluates the ratio between the measured and applied forces in the frequency domain. For comparison, the procedure was also performed on the gold-standard ground-embedded force platform. A predictive model of the systematic error of both types of force platform was then developed and tested against different input signals that represent three types of running patterns. Results show that the treadmill structure distorts the measured force signal. We then modified this structure with a simple stiffening frame in an attempt to reduce measurement error. Consequently, the overall absolute error was reduced (−22%), and the error in force-derived metrics was also sufficiently reduced: −68% for average loading rate error and −80% for impact peak error. Our procedure shows how to measure, predict, and reduce systematic dynamic error associated with treadmill-installed force platforms. We suggest this procedure should be implemented to appraise data quality, and frequency response function values should be included in research reports.     

Multi-segment foot kinematics and ground reaction forces during gait of individuals with plantar fasciitis

Background

Clinically, plantar fasciitis (PF) is believed to be a result and/or prolonged by overpronation and excessive loading, but there is little biomechanical data to support this assertion. The purpose of this study was to determine the differences between healthy individuals and those with PF in (1) rearfoot motion, (2) medial forefoot motion, (3) first metatarsal phalangeal joint (FMPJ) motion, and (4) ground reaction forces (GRF).

Methods

We recruited healthy (n=22) and chronic PF individuals (n=22, symptomatic over three months) of similar age, height, weight, and foot shape (p>0.05). Retro-reflective skin markers were fixed according to a multi-segment foot and shank model. Ground reaction forces and three dimensional kinematics of the shank, rearfoot, medial forefoot, and hallux segment were captured as individuals walked at 1.35 ms⁻¹.

Results

Despite similarities in foot anthropometrics, when compared to healthy individuals, individuals with PF exhibited significantly (p<0.05) (1) greater total rearfoot eversion, (2) greater forefoot plantar flexion at initial contact, (3) greater total sagittal plane forefoot motion, (4) greater maximum FMPJ dorsiflexion, and (5) decreased vertical GRF during propulsion.

Conclusion

These data suggest that compared to healthy individuals, individuals with PF exhibit significant differences in foot kinematics and kinetics. Consistent with the theoretical injury mechanisms of PF, we found these individuals to have greater total rearfoot eversion and peak FMPJ dorsiflexion, which may put undue loads on the plantar fascia. Meanwhile, increased medial forefoot plantar flexion at initial contact and decreased propulsive GRF are suggestive of compensatory responses, perhaps to manage pain.     

The scaling of ground reaction forces and duty factor in monitor lizards: implications for locomotion in sprawling tetrapods

Geometric scaling predicts a major challenge for legged, terrestrial locomotion. Locomotor support requirements scale identically with body mass (α M¹), while force-generation capacity should scale α M^2/3 as it depends on muscle cross-sectional area. Mammals compensate with more upright limb postures at larger sizes, but it remains unknown how sprawling tetrapods deal with this challenge. Varanid lizards are an ideal group to address this question because they cover an enormous body size range while maintaining a similar bent-limb posture and body proportions. This study reports the scaling of ground reaction forces and duty factor for varanid lizards ranging from 7 g to 37 kg. Impulses (force×time) (α M^0.99−1.34) and peak forces (α M^0.73−1.00) scaled higher than expected. Duty factor scaled α M^0.04 and was higher for the hindlimb than the forelimb. The proportion of vertical impulse to total impulse increased with body size, and impulses decreased while peak forces increased with speed.     

Allometric scaling laws for water uptake by plant roots

This paper develops scaling laws for plant roots of any arbitrary volume and branching configuration that maximize water uptake. Water uptake can occur along any part of the root network, and thus there is no branch-to-branch fluid conservation. Maximizing water uptake, therefore, involves balancing two flows that are inversely related: axial and radial conductivity. The scaling laws are tested against the root data of 1759 plants from 77 herbaceous species, and compared with those from the WBE model. I further discuss whether the scaling laws are invariant to soil water distribution. A summary of some of the results follows. (1) The optimal radius for a single root (no branches) scales with volume as . (2) The basic allometric scaling for root radius branches (r_i+1=β*r_i) is of the form , where f(N)=A(N)/(n_b*(1+A(N))), n_b is the number of branches, and A(N) and ε(N) are functions of the number of root diameter classes (not constants as in the WBE model). (3) For large N, β converges to the β from the WBE model. For small N, the β's for the two models diverge, but are highly correlated. (4) The fractal assumption of volume filling of the WBE model are also met in the root model even though they are not explicitly incorporated into it. (5) The WBE model for rigid tubes is an asymptotic solution for large root systems (large N and biomass). (6) The optimal scaling solutions for the root network appears to be independent of soil water distribution or water demand. The data set used for testing is included in the electronic supplementary archive of the journal.     

Amputee locomotion: Frequency content of prosthetic vs. intact limb vertical ground reaction forces during running and the effects of filter cut-off frequency

Compared to intact limbs, running-specific prostheses have high resonance non-biologic materials and lack active tissues to damp high frequencies. These differences may lead to ground reaction forces (GRFs) with high frequency content. If so, ubiquitously applying low-pass filters to prosthetic and intact limb GRFs may attenuate veridical high frequency content and mask important and ecologically valid data from prostheses. To explore differences in frequency content between prosthetic and intact limbs we divided signal power from transtibial unilateral amputees and controls running at 2.5, 3.0, and 3.5 m/s into Low (<10 Hz), High (10–25 Hz), and Non-biologic (>25 Hz) frequency bandwidths. Faster speeds tended to reduce the proportion of signal power in the Low bandwidth while increasing it in the High and Non-biologic bandwidths. Further, prostheses had lower proportions of signal power at the High frequency bandwidth but greater proportions at the Non-biologic bandwidth. To evaluate whether these differences in frequency content interact with filter cut-offs and alter results, we filtered GRFs with cut-offs from 1 to 100 Hz and calculated vertical impact peak (VIP). Changing cut-off had inconsistent effects on VIP across speeds and limbs: Faster speeds had significantly larger changes in VIP per change in cut-off while, compared to controls, prosthetic limbs had significantly smaller changes in VIP per change in cut-off. These findings reveal differences in GRF frequency content between prosthetic and intact limbs and suggest that a cut-off frequency that is appropriate for one limb or speed may be inappropriate for another.