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.     

Subject-specific knee joint geometry improves predictions of medial tibiofemoral contact forces

Estimating tibiofemoral joint contact forces is important for understanding the initiation and progression of knee osteoarthritis. However, tibiofemoral contact force predictions are influenced by many factors including muscle forces and anatomical representations of the knee joint. This study aimed to investigate the influence of subject-specific geometry and knee joint kinematics on the prediction of tibiofemoral contact forces using a calibrated EMG-driven neuromusculoskeletal model of the knee. One participant fitted with an instrumented total knee replacement walked at a self-selected speed while medial and lateral tibiofemoral contact forces, ground reaction forces, whole-body kinematics, and lower-limb muscle activity were simultaneously measured. The combination of generic and subject-specific knee joint geometry and kinematics resulted in four different OpenSim models used to estimate muscle–tendon lengths and moment arms. The subject-specific geometric model was created from CT scans and the subject-specific knee joint kinematics representing the translation of the tibia relative to the femur was obtained from fluoroscopy. The EMG-driven model was calibrated using one walking trial, but with three different cost functions that tracked the knee flexion/extension moments with and without constraint over the estimated joint contact forces. The calibrated models then predicted the medial and lateral tibiofemoral contact forces for five other different walking trials. The use of subject-specific models with minimization of the peak tibiofemoral contact forces improved the accuracy of medial contact forces by 47% and lateral contact forces by 7%, respectively compared with the use of generic musculoskeletal model.     

Comparison of lower limb kinetics,kinematics and muscle activation during drop jumping under shod and barefoot conditions

This study was to investigate the acute effects of wearing shoes on lower limb kinetics, kinematics and muscle activation during a drop jump. Eighteen healthy men performed a drop jump under barefoot and shod conditions. Vertical ground reaction force (GRF) was measured on a force plate during the contact phase of a drop jump, and GRF valuables were calculated for each condition. The angles of the knee and ankle joints, and the foot strike angle (the angle between the plantar surface of the foot and the ground during ground contact) as well as the electromyography of 7 muscles were measured. The shod condition showed a significant larger first peak GRF, longer time to first peak GRF from the initial ground contact and lower initial loading rate than the barefoot condition. The shod condition showed a significant larger ankle joint angle at initial ground contact, smaller knee joint angle between the second peak GRF and take-off as well as smaller foot strike angle at both initial ground contact and take-off than the barefoot condition. There were significant correlations between relative differences in ankle joint at the initial ground contact and relative differences in the initial loading rate. The muscle activity of all muscles during foot ground contact did not differ between two conditions; however, in the shod condition, muscle activation of 150 ms before foot ground contact was significantly higher in the rectus femoris, whereas it was lower in the biceps femoris and tibialis anterior muscles than the barefoot condition. These results indicate that wearing shoes alternates the GRF variables at initial ground contact, joint kinematics at the ground contact and muscle activation before foot ground contact during a drop jump, suggesting that the effects of wearing shoes on drop jump training differ from being barefoot.     

Measured and estimated ground reaction forces for multi-segment foot models

Accurate measurement of ground reaction forces under discrete areas of the foot is important in the development of more advanced foot models, which can improve our understanding of foot and ankle function. To overcome current equipment limitations, a few investigators have proposed combining a pressure mat with a single force platform and using a proportionality assumption to estimate subarea shear forces and free moments. In this study, two adjacent force platforms were used to evaluate the accuracy of the proportionality assumption on a three segment foot model during normal gait. Seventeen right feet were tested using a targeted walking approach, isolating two separate joints: transverse tarsal and metatarsophalangeal. Root mean square (RMS) errors in shear forces up to 6% body weight (BW) were found using the proportionality assumption, with the highest errors (peak absolute errors up to 12% BW) occurring between the forefoot and toes in terminal stance. The hallux exerted a small braking force in opposition to the propulsive force of the forefoot, which was unaccounted for by the proportionality assumption. While the assumption may be suitable for specific applications (e.g. gait analysis models), it is important to understand that some information on foot function can be lost. The results help highlight possible limitations of the assumption. Measured ensemble average subarea shear forces during normal gait are also presented for the first time.     

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.     

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.     

Abdominal muscle activation changes if the purpose is to control pelvis motion or thorax motion

The aim of this study was to compare trunk muscular recruitment and lumbar spine kinematics when motion was constrained to either the thorax or the pelvis. Nine healthy women performed four upright standing planar movements (rotations, anterior–posterior translations, medial–lateral translations, and horizontal circles) while constraining pelvis motion and moving the thorax or moving the pelvis while minimizing thorax motion, and four isometric trunk exercises (conventional curl-up, reverse curl-up, cross curl-up, and reverse cross curl-up). Surface EMG (upper and lower rectus abdominis, lateral and medial aspects of external oblique, internal oblique, and latissimus dorsi) and 3D lumbar displacements were recorded. Pelvis movements produced higher EMG amplitudes of the oblique abdominals than thorax motions in most trials, and larger lumbar displacements in the medial–lateral translations and horizontal circles. Conversely, thorax movements produced larger rotational lumbar displacement than pelvis motions during rotations and higher EMG amplitudes for latissimus dorsi during rotations and anterior–posterior translations and for lower rectus abdominis during the crossed curl-ups. Thus, different neuromuscular compartments appear when the objective changes from pelvis to thorax motion. This would suggest that both movement patterns should be considered when planning spine stabilization programs, to optimize exercises for the movement and muscle activations desired.     

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.     

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.     

Biomechanical characteristics of adults walking in shallow water and on land.

Although water environment has been employed for different physical activities, there is little available information regarding the biomechanical characteristics of walking in shallow water. In the present study, we investigated the kinematics, ground reaction forces (GRF), and electromyographic (EMG) activation patterns of eight selected muscles of adults walking in shallow water and on land. Ten healthy adults were videotaped while walking at self-selected comfortable speeds on land and in water (at the Xiphoid process level). In both conditions there was a force plate embedded in the middle of each walkway to register the GRF components. Reflective markers were placed over main anatomical landmarks and they were digitalized later to obtain stride characteristics and joint angle information. In general, walking in water was different to walking on land in many aspects and these differences were attributed to the drag force, the apparent body weight reduction, and the lower comfortable speed during walking in shallow water. The joint range of motions (ROM) were not different, the segment ROM, magnitudes of GRF components, impact force, and impulse were different between the two conditions. The present results will contribute to a better understanding of this activity in the context of training and rehabilitation.     

Developing simulations to reproduce in vivo fluoroscopy kinematics in total knee replacement patients

For clinically predictive testing and design-phase evaluation of prospective total knee replacement (TKR) implants, devices should ideally be evaluated under physiological loading conditions which incorporate population-level variability. A challenge exists for experimental and computational researchers in determining appropriate loading conditions for wear and kinematic knee simulators which reflect in vivo joint loading conditions. There is a great deal of kinematic data available from fluoroscopy studies. The purpose of this work was to develop computational methods to derive anterior–posterior (A–P) and internal–external (I–E) tibiofemoral (TF) joint loading conditions from in vivo kinematic data. Two computational models were developed, a simple TF model, and a more complex lower limb model. These models were driven through external loads applied to the tibia and femur in the TF model, and applied to the hip, ankle and muscles in the lower limb model. A custom feedback controller was integrated with the finite element environment and used to determine the external loads required to reproduce target kinematics at the TF joint. The computational platform was evaluated using in vivo kinematic data from four fluoroscopy patients, and reproduced in vivo A–P and I–E motions and compressive force with a root-mean-square (RMS) accuracy of less than 1 mm, 0.1°, and 40 N in the TF model and in vivo A–P and I–E motions, TF flexion, and compressive loads with a RMS accuracy of less than 1 mm, 0.1°, 1.4°, and 48 N in the lower limb model. The external loading conditions derived from these models can ultimately be used to establish population variability in loading conditions, for eventual use in computational as well as experimental activity simulations.     

Estimating total knee replacement joint load ratios from kinematics

Accurate prediction of loads acting at the joint in total knee replacement (TKR) patients is key to developing experimental or computational simulations which evaluate implant designs under physiological loading conditions. In vivo joint loads have been measured for a small number of telemetric TKR patients, but in order to assess device performance across the entire patient population, a larger patient cohort is necessary. This study investigates the accuracy of predicting joint loads from joint kinematics. Specifically, the objective of the study was to assess the accuracy of internal–external (I–E) and anterior–posterior (A–P) joint load predictions from I–E and A–P motions under a given compressive load, and to evaluate the repeatability of joint load ratios (I–E torque to compressive force (I–E:C), and A–P force to compressive force (A–P:C)) for a range of compressive loading profiles. A tibiofemoral finite element model was developed and used to simulate deep knee bend, chair-rise and step-up activities for five patients. Root-mean-square (RMS) differences in I–E:C and A–P:C load ratios between telemetric measurements and model predictions were less than 1.10e–3 Nm/N and 0.035 N/N for all activities. I–E:C and A–P:C load ratios were consistently reproduced regardless of the compressive force profile applied (RMS differences less than 0.53e–3 Nm/N and 0.010 N/N, respectively). When error in kinematic measurement was introduced to the model, joint load predictions were forgiving to kinematic measurement error when conformity between femoral and tibial components was low. The prevalence of kinematic data, in conjunction with the analysis presented here, facilitates determining the scope of A–P and I–E joint loading ratios experienced by the TKR population.     

Resonance-based oscillations could describe human gait mechanics under various loading conditions

The oscillatory behavior of the center of mass (CoM) and the corresponding ground reaction force (GRF) of human gait for various gait speeds can be accurately described in terms of resonance using a spring–mass bipedal model. Resonance is a mechanical phenomenon that reflects the maximum responsiveness and energetic efficiency of a system. To use resonance to describe human gait, we need to investigate whether resonant mechanics is a common property under multiple walking conditions. Body mass and leg stiffness are determinants of resonance; thus, in this study, we investigated the following questions: (1) whether the estimated leg stiffness increased with inertia, (2) whether a resonance-based CoM oscillation could be sustained during a change in the stiffness, and (3) whether these relationships were consistently observed for different walking speeds. Seven healthy young subjects participated in over-ground walking trials at three different gait speeds with and without a 25-kg backpack. We measured the GRFs and the joint kinematics using three force platforms and a motion capture system. The leg stiffness was incorporated using a stiffness parameter in a compliant bipedal model that best fitted the empirical GRF data. The results showed that the leg stiffness increased with the load such that the resonance-based oscillatory behavior of the CoM was maintained for a given gait speed. The results imply that the resonance-based oscillation of the CoM is a consistent gait property and that resonant mechanics may be useful for modeling human gait.     

A bipedal compliant walking model generates periodic gait cycles with realistic swing dynamics

A simple spring mechanics model can capture the dynamics of the center of mass (CoM) during human walking, which is coordinated by multiple joints. This simple spring model, however, only describes the CoM during the stance phase, and the mechanics involved in the bipedality of the human gait are limited. In this study, a bipedal spring walking model was proposed to demonstrate the dynamics of bipedal walking, including swing dynamics followed by the step-to-step transition. The model consists of two springs with different stiffnesses and rest lengths representing the stance leg and swing leg. One end of each spring has a foot mass, and the other end is attached to the body mass. To induce a forward swing that matches the gait phase, a torsional hip joint spring was introduced at each leg. To reflect the active knee flexion for foot clearance, the rest length of the swing leg was set shorter than that of the stance leg, generating a discrete elastic restoring force. The number of model parameters was reduced by introducing dependencies among stiffness parameters. The proposed model generates periodic gaits with dynamics-driven step-to-step transitions and realistic swing dynamics. While preserving the mimicry of the CoM and ground reaction force (GRF) data at various gait speeds, the proposed model emulated the kinematics of the swing leg. This result implies that the dynamics of human walking generated by the actuations of multiple body segments is describable by a simple spring mechanics.     

Quantifying plyometric intensity via rate of force development, knee joint, and ground reaction forces

Because the intensity of plyometric exercises usually is based simply upon anecdotal recommendations rather than empirical evidence, this study sought to quantify a variety of these exercises based on forces placed upon the knee. Six National Collegiate Athletic Association Division I athletes who routinely trained with plyometric exercises performed depth jumps from 46 and 61 cm, a pike jump, tuck jump, single-leg jump, countermovement jump, squat jump, and a squat jump holding dumbbells equal to 30% of 1 repetition maximum (RM). Ground reaction forces obtained via an AMTI force plate and video analysis of markers placed on the left hip, knee, lateral malleolus, and fifth metatarsal were used to estimate rate of eccentric force development (E-RFD), peak ground reaction forces (GRF), ground reaction forces relative to body weight (GRF/BW), knee joint reaction forces (K-JRF), and knee joint reaction forces relative to body weight (K-JRF/BW) for each plyometric exercise. One-way repeated measures analysis of variance indicated that E-RFD, K-JRF, and K-JRF/BW were different across the conditions (p < 0.05), but peak GRF and GRF/BW were not (p > 0.05). Results indicate that there are quantitative differences between plyometric exercises in the rate of force development during landing and the forces placed on the knee, though peak GRF forces associated with landing may not differ.     

Skeletal kinematics of the midtarsal joint during walking: Midtarsal joint locking revisited

The kinematics of the human foot complex have been investigated to understand the weight bearing mechanism of the foot. This study aims to investigate midtarsal joint locking during walking by noninvasively measuring the movements of foot bones using a high-speed bi-planar fluoroscopic system. Eighteen healthy subjects volunteered for the study; the subjects underwent computed tomography imaging and bi-planar radiographs of the foot in order to measure the three-dimensional (3D) midtarsal joint kinematics using a 2D-to-3D registration method and anatomical coordinate system in each bone. The relative movements on bone surfaces were also calculated in the talonavicular and calcaneocuboid joints and quantified as surface relative velocity vectors on articular surfaces to understand the kinematic interactions in the midtarsal joint. The midtarsal joint performed a coupled motion in the early stance to pronate the foot to extreme pose in the range of motion during walking and maintained this pose during the mid-stance. In the terminal stance, the talonavicular joint performed plantar-flexion, inversion, and internal rotation while the calcaneocuboid joint performed mainly inversion. The midtarsal joint moved towards an extreme supinated pose, rather than a minimum motion in the terminal stance. The study provides a new perspective to understand the kinematics and kinetics of the movement of foot bones and so-called midtarsal joint locking, during walking. The midtarsal joint continuously moved towards extreme poses together with the activation of muscle forces, which would support the foot for more effective force transfer during push-off in the terminal stance.     

The knee adduction moment measured with an instrumented force shoe in patients with knee osteoarthritis

The external knee adduction moment (KAdM) during gait is an important parameter in patients with knee osteoarthritis (OA). KAdM measurement is currently restricted to instruments only available in gait laboratories. However, ambulatory movement analysis technology, including instrumented force shoes (IFS) and inertial and magnetic measurement systems (IMMS), can measure kinetics and kinematics of human gait free of laboratory restrictions. The objective of this study was a quantitative validation of the accuracy of the KAdM in patients with knee OA, when estimated with an ambulatory-based method (AmbBM) versus a laboratory-based method (LabBM). AmbBM is employing the IFS and a linked-segment model, while LabBM is based on a force plate and optoelectronic marker system. Effects of ground reaction force (GRF), centre of pressure (CoP), and knee joint position measurement are evaluated separately. Twenty patients with knee OA were measured. The GRFs showed differences up to 0.22 N/kg, the CoPs showed differences up to 4 mm, and the medio-lateral and vertical knee position showed differences to 9 mm, between AmbBM and LabBM. The GRF caused an under-estimation in KAdM in early stance. However, this effect was counteracted by differences in CoP and joint position, resulting in a net 5% over-estimation. In midstance and late stance the accuracy of the KAdM was mainly limited by use of the linked-segment model for joint position estimation, resulting in an under-estimation (midstance 6% and late stance 22%). Further improvements are needed in the estimation of joint position from segment orientation.     

Ankle and midfoot kinetics during normal gait: a multi-segment approach

Multi-segment foot models are increasingly being used to evaluate intra and inter-segment foot kinematics such as the motion between the hindfoot/tibia (ankle) and the forefoot/hindfoot (midfoot) during walking. However, kinetic analysis have been mainly restricted to one-segment foot models and could be improved by considering a multi-segment approach. Therefore, the aims of this study were to (1) implement a kinetic analysis of the ankle and theoretical midfoot joints using the existing Oxford Foot Model (OFM) through a standard inverse dynamics approach using only marker, force plate and anthropometric data and (2) to compare OFM ankle joint kinetics to those output by the one-segment foot plugin-gait model (PIG). 10 healthy adolescents fitted with both the OFM and PIG markers performed barefoot comfortable speed walking trials over an instrumented walkway. The maximum ankle power generation was significantly reduced by approximately 40% through OFM calculations compared to PIG estimates (p<0.001). This result was not caused by a decrease in OFM computed joint moments, but by a reduction in the angular velocity between the tibia/hindfoot (OFM) compared to the tibia/foot (PIG) (p<0.001). Additionally, analysis revealed considerable midfoot loading. One-segment foot models overestimate ankle power, and may also overestimate the contribution of the triceps surae. A multi-segment approach may help quantify the important contribution of the midfoot ligaments and musculature to power generation. We therefore recommend the use of multi-segment foot models to estimate ankle and midfoot kinetics, especially when surgical decision-making is based on the results of three-dimensional gait analysis.     

Dynamic 3D scanning as a markerless method to calculate multi-segment foot kinematics during stance phase: Methodology and first application

Multi-segmental foot kinematics have been analyzed by means of optical marker-sets or by means of inertial sensors, but never by markerless dynamic 3D scanning (D3DScanning). The use of D3DScans implies a radically different approach for the construction of the multi-segment foot model: the foot anatomy is identified via the surface shape instead of distinct landmark points. We propose a 4-segment foot model consisting of the shank (Sha), calcaneus (Cal), metatarsus (Met) and hallux (Hal). These segments are manually selected on a static scan. To track the segments in the dynamic scan, the segments of the static scan are matched on each frame of the dynamic scan using the iterative closest point (ICP) fitting algorithm. Joint rotations are calculated between Sha–Cal, Cal–Met, and Met–Hal. Due to the lower quality scans at heel strike and toe off, the first and last 10% of the stance phase is excluded. The application of the method to 5 healthy subjects, 6 trials each, shows a good repeatability (intra-subject standard deviations between 1° and 2.5°) for Sha–Cal and Cal–Met joints, and inferior results for the Met–Hal joint (>3°). The repeatability seems to be subject-dependent. For the validation, a qualitative comparison with joint kinematics from a corresponding established marker-based multi-segment foot model is made. This shows very consistent patterns of rotation. The ease of subject preparation and also the effective and easy to interpret visual output, make the present technique very attractive for functional analysis of the foot, enhancing usability in clinical practice.     

Estimation of unmeasured ground reaction force data based on the oscillatory characteristics of the center of mass during human walking

To enhance the wearability of portable motion-monitoring devices, the size and number of sensors are minimized, but at the expense of quality and quantity of data collected. For example, owing to the size and weight of low-frequency force transducers, most currently available wearable gait measurement systems provide only limited, if any, elements of ground reaction force (GRF) data. To obtain the most GRF information possible with a minimal use of sensors, we propose a GRF estimation method based on biomechanical knowledge of human walking. This includes the dynamics of the center of mass (CoM) during steady human gait resembling the oscillatory behaviors of a mass-spring system. Available measurement data were incorporated into a spring-loaded inverted pendulum with translating pivot. The spring stiffness and simulation parameters were tuned to match, as accurately as possible, the available data and oscillatory characteristics of walking. Our results showed that the model simulation estimated reasonably well the unmeasured GRF. Using the vertical GRF and CoP profile for gait speeds ranging from 0.93 to 1.89 m/s, the anterior-posterior (A-P) GRF was estimated and resulted in an average correlation coefficient of R = 0.982 ± 0.009. Even when the ground contact timing and gait speed information were alone available, our method estimated GRFs resulting in R = 0.969 ± 0.022 for the A-P and R = 0.891 ± 0.101 for the vertical GRFs. This research demonstrates that the biomechanical knowledge of human walking, such as inherited oscillatory characteristics of the CoM, can be used to gain unmeasured information regarding human gait dynamics.