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.     

Energy exchange between subject and belt during treadmill walking

Treadmill walking aims to simulate overground walking, but intra-stride belt speed variations of treadmills result in some interaction between treadmill and subject, possibly obstructing this aim. Especially in self-paced treadmill walking, in which the belt speed constantly adjusts to the subject, these interactions might affect the gait pattern significantly. The aim of this study was to quantify the energy exchange between subject and treadmill, during the fixed speed (FS) and self-paced (SP) modes of treadmill walking. Eighteen subjects walked on a dual-belt instrumented treadmill at both modes. The energy exchange was calculated as the integration of the product of the belt speed deviation and the fore-aft ground reaction force over the stride cycle. The total positive energy exchange was 0.44 J/stride and the negative exchange was 0.11 J/stride, which was both less than 1.6% of the performed work on the center of mass. Energy was mainly exchanged from subject to treadmill during both the braking and propulsive phase of gait. The two treadmill modes showed a similar pattern of energy exchange, with a slightly increased energy exchange during the braking phase of SP walking. It is concluded that treadmill walking is only mildly disturbed by subject-belt interactions when using instrumented treadmills with adequate belt control.     

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.     

Can treadmill walking be used to assess propulsion generation?

Instrumented treadmills offer significant advantages for analysis of human locomotion, including recording consecutive steady-state gait cycles, precisely controlling walking speed, and avoiding force plate targeting. However, some studies of hemiparetic walking on a treadmill have suggested that the moving treadmill belt may fundamentally alter propulsion mechanics. Any differences in propulsion mechanics during treadmill walking would be problematic since recent studies assessing propulsion have provided fundamental insight into hemiparetic walking. The purpose of this study was to test the hypothesis that there would be no difference in the generation of anterior/posterior (A/P) propulsion by performing a carefully controlled comparison of the A/P ground reaction forces (GRFs) and impulses in healthy adults during treadmill and overground walking. Gait data were collected from eight subjects walking overground and on a treadmill with speed and cadence controlled. Peak negative and positive horizontal GRFs in early and late stance, respectively, were reduced by less than 5% of body weight (p<0.05) during treadmill walking compared to overground walking. The magnitude of the braking impulse was similarly lower (p<0.05) during treadmill walking, but no significant difference was found between propulsion impulses. While there were some subtle differences in A/P GRFs between overground and treadmill walking, these results suggest there is no fundamental difference in propulsion mechanics. We conclude that treadmill walking can be used to investigate propulsion generation in healthy and by implication clinical populations.     

Determining the centre of pressure during walking and running using an instrumented treadmill

In this paper, a new method of determining spatial and temporal gait parameters by using centre of pressure (CoP) data is presented. A treadmill is used which was developed to overcome limitations of regular methods for the analysis of spatio-temporal gait parameters and ground reaction forces during walking and running. The design of the treadmill is based on the use of force transducers underneath a separate left and right plate, which together form the treadmill walking surface. The results of test procedures and measurements show that accurate recordings of vertical ground reaction force can be obtained. These recordings enable a separate analysis of vertical ground reaction forces during double support phases in walking, and the analysis of changes in the centre of pressure (CoP) position during subsequent foot placements. From the CoP data, temporal gait parameters (e.g. duration of left/right support and swing phases) and spatial gait parameters (i.e. left/right step lengths and widths) can be derived.     

Validity and reliability of peak tibial accelerations as real-time measure of impact loading during over-ground rearfoot running at different speeds

Studies seeking to determine the effects of gait retraining through biofeedback on peak tibial acceleration (PTA) assume that this biometric trait is a valid measure of impact loading that is reliable both within and between sessions. However, reliability and validity data were lacking for axial and resultant PTAs along the speed range of over-ground endurance running. A wearable system was developed to continuously measure 3D tibial acceleration and to detect PTAs in real-time. Thirteen rearfoot runners ran at 2.55, 3.20 and 5.10 m·s⁻¹ over an instrumented runway in two sessions with re-attachment of the system. Intraclass correlation coefficients (ICCs) were used to determine within-session reliability. Repeatability was evaluated by paired T-tests and ICCs. Concerning validity, axial and resultant PTAs were correlated to the peak vertical impact loading rate (LR) of the ground reaction force. Additionally, speed should affect impact loading magnitude. Hence, magnitudes were compared across speeds by RM-ANOVA. Within a session, ICCs were over 0.90 and reasonable for clinical measurements. Between sessions, the magnitudes remained statistically similar with ICCs ranging from 0.50 to 0.59 for axial PTA and from 0.53 to 0.81 for resultant PTA. Peak accelerations of the lower leg segment correlated to LR with larger coefficients for axial PTA (r range: 0.64–0.84) than for the resultant PTA per speed condition. The magnitude of each impact measure increased with speed. These data suggest that PTAs registered per stand-alone system can be useful during level, over-ground, rearfoot running to evaluate impact loading in the time domain when force platforms are unavailable in studies with repeated measurements.     

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.     

Estimating the complete ground reaction forces with pressure insoles in walking

This study presented a method to estimate the complete ground reaction forces from pressure insoles in walking. Five male subjects performed 10 walking trials in a laboratory. The complete ground reaction forces were collected during a right foot stride by a force plate at 1000Hz. Simultaneous plantar pressure data were collected at 100Hz by a pressure insole system with 99 sensors covering the whole plantar area. Stepwise linear regressions were performed to individually reconstruct the complete ground reaction forces in three directions from the 99 individual pressure data until redundancy among the predictors occurred. An additional linear regression was performed to reconstruct the vertical ground reaction force by the sum of the value of the 99 pressure sensors. Five other subjects performed the same walking test for validation. Estimated ground reaction forces in three directions were calculated with the developed regression models, and were compared with the real data recorded from force plate. Accuracy was represented by the correlation coefficient and the root mean square error. Results showed very good correlation in anterior-posterior (0.928) and vertical (0.989) directions, and reasonable correlation in medial-lateral direction (0.719). The root mean square error was about 12%, 5% and 28% of the peak recorded value. Future studies should aim to generalize the methods or to establish specific methods to other subjects, patients, motions, footwear and floor conditions. The method gives an extra option to study an estimation of the complete ground reaction forces in any environment without the constraints from the number and location of force plates.     

Can a reduction approach predict reliable joint contact and musculo-tendon forces?

Musculoskeletal models generally solve the muscular redundancy by numerical optimisation. They have been extensively validated using instrumented implants. Conversely, a reduction approach considers only one flexor or extensor muscle group at the time to equilibrate the inter-segmental joint moment. It is not clear if such models can still predict reliable joint contact and musculo-tendon forces during gait.Tibiofemoral contact force and gastrocnemii, quadriceps, and hamstrings musculo-tendon forces were estimated using a reduction approach for five subjects walking with an instrumented prosthesis. The errors in the proximal-distal tibiofemoral contact force fell in the range (0.3–0.9 body weight) reported in the literature for musculoskeletal models using numerical optimisation. The musculo-tendon forces were in agreement with the EMG envelops and appeared comparable to the ones reported in the literature with generic musculoskeletal models.Although evident simplifications and limitations, it seems that the reduction approach can provided quite reliable results. It can be a useful pedagogical tool in biomechanics, e.g. to illustrate the theoretical differences between inter-segmental and contact forces, and can provide a first estimate of the joint loadings in subjects with limited musculoskeletal deformities and neurological disorders.     

Foot centre of pressure and ground reaction force during quadriceps resistance exercises; a comparison between force plates and a pressure insole system

The study compared the centre of pressure measurements (COP) and vertical ground reaction forces (vGRF) from a pressure insole system to that from force plates (FP) during two flywheel quadriceps resistance exercises: leg press and squat. The comparison was performed using a motion capture system and simultaneous measurements of COP and vGRF from FP and insoles. At lower insole-vGRF (<250 N/insole) COP accuracy deteriorated and those data were excluded from further analysis. The insoles systematically displaced the COP slightly posteriorly and medially compared to the FP measurements. Pearson’s coefficient of correlation (r) between insole- and FP-COP showed good agreement in both the anteroposterior (squat: r = 0.96, leg press: r = 0.97) and mediolateral direction (squat: r = 0.84, leg press: r = 0.90), whereas the root-mean-square errors (RMSE) were lower in the mediolateral (squat: 3.9 mm, leg press: 4.5 mm) than the anteroposterior (squat and leg press: 11.8 mm) direction. Vertical GRF was slightly overestimated by the insoles in leg press and RMSE were greater in leg press (8% of peak force) than in squat (6%). Overall, results were within the range of previous studies performed on gait. The strong agreement between insole and FP measurements indicates that insoles may replace FPs in field applications and biomechanical computations during resistance exercise, provided that the applied force is sufficient.     

Direct measurement of power during one single sprint on treadmill

We tested the validity of an instrumented treadmill dynamometer for measuring maximal propulsive power during sprint running, and sought to verify whether this could be done over one single sprint, as shown during sprint cycling. The treadmill dynamometer modified towards sprint use (constant motor torque) allows vertical and horizontal forces to be measured at the same location as velocity, i.e. at the foot, which is novel compared to existing methods in which power is computed as the product of belt velocity and horizontal force measured by transducers placed in the tethering system. Twelve males performed 6 s sprints against default, high and low loads set from the motor torque necessary to overcome the friction due to subjects’ weight on the belt (default load), and 20% higher and lower motor torque values. Horizontal ground reaction force, belt velocity, propulsive power and linear force–velocity relationships were compared between the default load condition and when taking all conditions together. Force and velocity traces and values were reproducible and consistent with the literature, and no significant difference was found between maximal power and force–velocity relationships obtained in the default load condition only vs. adding data from all conditions. The presented method allows one to measure maximal propulsive power and calculate linear force–velocity relationships from one single sprint data. The main novelties are that both force and velocity are measured at the same location, and that instantaneous values are averaged over one contact period, and not over a constant arbitrary time-window.     

Effect of surgery to implant motion and force sensors on vertical ground reaction forces in the ovine model

Activities of daily living (ADLs) generate complex, multidirectional forces in the anterior cruciate ligament (ACL). While calibration problems preclude direct measurement in patients, ACL forces can conceivably be measured in animals after technical challenges are overcome. For example, motion and force sensors can be implanted in the animal but investigators must determine the extent to which these sensors and surgery affect normal gait. Our objectives in this study were to determine (1) if surgically implanting knee motion sensors and an ACL force sensor significantly alter normal ovine gait and (2) how increasing gait speed and grade on a treadmill affect ovine gait before and after surgery. Ten skeletally mature, female sheep were used to test four hypotheses: (1) surgical implantation of sensors would significantly decrease average and peak vertical ground reaction forces (VGRFs) in the operated limb, (2) surgical implantation would significantly decrease single limb stance duration for the operated limb, (3) increasing treadmill speed would increase VGRFs pre- and post operatively, and (4) increasing treadmill grade would increase the hind limb VGRFs pre- and post operatively. An instrumented treadmill with two force plates was used to record fore and hind limb VGRFs during four combinations of two speeds (1.0 m/s and 1.3 m/s) and two grades (0 deg and 6 deg). Sensor implantation decreased average and peak VGRFs less than 10% and 20%, respectively, across all combinations of speed and grade. Sensor implantation significantly decreased the single limb stance duration in the operated hind limb during inclined walking at 1.3 m/s but had no effect on single limb stance duration in the operated limb during other activities. Increasing treadmill speed increased hind limb peak (but not average) VGRFs before surgery and peak VGRF only in the unoperated hind limb during level walking after surgery. Increasing treadmill grade (at 1 m/s) significantly increased hind limb average and peak VGRFs before surgery but increasing treadmill grade post op did not significantly affect any response measure. Since VGRF values exceeded 80% of presurgery levels, we conclude that animal gait post op is near normal. Thus, we can assume normal gait when conducting experiments following sensor implantation. Ultimately, we seek to measure ACL forces for ADLs to provide design criteria and evaluation benchmarks for traditional and tissue engineered ACL repairs and reconstructions.     

A weighted least squares method for inverse dynamic analysis

Internal forces in the human body can be estimated from measured movements and external forces using inverse dynamic analysis. Here we present a general method of analysis which makes optimal use of all available data, and allows the use of inverse dynamic analysis in cases where external force data is incomplete. The method was evaluated for the analysis of running on a partially instrumented treadmill. It was found that results correlate well with those of a conventional analysis where all external forces are known.     

Ground reaction forces during downhill and uphill running

We investigated the normal and parallel ground reaction forces during downhill and uphill running. Our rationale was that these force data would aid in the understanding of hill running injuries and energetics. Based on a simple spring-mass model, we hypothesized that the normal force peaks, both impact and active, would increase during downhill running and decrease during uphill running. We anticipated that the parallel braking force peaks would increase during downhill running and the parallel propulsive force peaks would increase during uphill running. But, we could not predict the magnitude of these changes. Five male and five female subjects ran at 3m/s on a force treadmill mounted on the level and on 3 degrees, 6 degrees, and 9 degrees wedges. During downhill running, normal impact force peaks and parallel braking force peaks were larger compared to the level. At -9 degrees, the normal impact force peaks increased by 54%, and the parallel braking force peaks increased by 73%. During uphill running, normal impact force peaks were smaller and parallel propulsive force peaks were larger compared to the level. At +9 degrees, normal impact force peaks were absent, and parallel propulsive peaks increased by 75%. Neither downhill nor uphill running affected normal active force peaks. Combined with previous biomechanics studies, our normal impact force data suggest that downhill running substantially increases the probability of overuse running injury. Our parallel force data provide insight into past energetic studies, which show that the metabolic cost increases during downhill running at steep angles.     

A treadmill ergometer for three-dimensional ground reaction forces measurement during walking.

This report describes new treadmill ergometer designed to measure the vertical and horizontal ground reaction forces produced by the left and right legs during walking. It was validated by static and dynamic tests. Non-linearity was from 0.2% (left vertical force) to 1.4% (right antero-posterior force). The resonance frequency was from 219 (right vertical direction) to 58 Hz (left medio-lateral direction). A calibration "leg", an air jack in series with a strain gauge, was developed and used to produce force signals comparable to those obtained during human locomotion. The mean differences between the force measured by the calibration leg and treadmill ergometer at 5 km h(-1) were 3.7 N (0.7%) for the left side and 6.5 N (1.2%) for the right. Measurements obtained during human walking showed that the treadmill ergometer has considerable potential for analysing human gait.     

Metabolic cost of generating horizontal forces during human running.

Previous studies have suggested that generating vertical force on the ground to support body weight (BWt) is the major determinant of the metabolic cost of running. Because horizontal forces exerted on the ground are often an order of magnitude smaller than vertical forces, some have reasoned that they have negligible cost. Using applied horizontal forces (AHF; negative is impeding, positive is aiding) equal to -6, -3, 0, +3, +6, +9, +12, and +15% of BWt, we estimated the cost of generating horizontal forces while subjects were running at 3.3 m/s. We measured rates of oxygen consumption (VO2) for eight subjects. We then used a force-measuring treadmill to measure ground reaction forces from another eight subjects. With an AHF of -6% BWt, VO2 increased 30% compared with normal running, presumably because of the extra work involved. With an AHF of +15% BWt, the subjects exerted approximately 70% less propulsive impulse and exhibited a 33% reduction in VO2. Our data suggest that generating horizontal propulsive forces constitutes more than one-third of the total metabolic cost of normal running.     

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.     

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.     

Fore-Aft Ground Force Adaptations to Induced Forelimb Lameness in Walking and Trotting Dogs

Animals alter their locomotor mechanics to adapt to a loss of limb function. To better understand their compensatory mechanisms, this study evaluated the changes in the fore-aft ground forces to forelimb lameness and tested the hypothesis that dogs unload the affected limb by producing a nose-up pitching moment via the exertion of a net-propulsive force when the lame limb is on the ground. Seven healthy Beagles walked and trotted at steady speed on an instrumented treadmill while horizontal force data were collected before and after a moderate lameness was induced. Peak, mean and summed braking and propulsive forces as well as the duration each force was exerted and the time to reach maximum force were evaluated for both the sound and the lame condition. Compared with the sound condition, a net-propulsive force was produced by the lame diagonal limbs due to a reduced braking force in the affected forelimb and an increased propulsive force in the contralateral hindlimb when the dogs walked and trotted. To regain pitch stability and ensure steady speed for a given locomotor cycle, the dogs produced a net-braking force when the sound diagonal limbs were on the ground by exerting greater braking forces in both limbs during walking and additionally reducing the propulsive force in the hindlimb during trotting. Consistent with the proposed mechanism, dogs maximize their double support phases when walking. Likely associated with the fore-aft force adaptations to lameness are changes in muscle recruitment that potentially result in short- and long-term effects on the limb and trunk muscles.