Prediction Of Reaction Forces Research Articles

Robust and novel attention guided MultiResUnet model for 3D ground reaction force and moment prediction from foot kinematics

Ground reaction force and moment (GRF&M) measurements are vital for biomechanical analysis and significantly impact the clinical domain for early abnormality detection for different neurodegenerative diseases. Force platforms have become the de facto standard for measuring GRF&M signals in recent years. Although the signal quality achieved from these devices is unparalleled, they are expensive and require laboratory setup, making them unsuitable for many clinical applications. For these reasons, predicting GRF&M from cheaper and more feasible alternatives has become a topic of interest. Several works have been done on predicting GRF&M from kinematic data captured from the subject’s body with the help of motion capture cameras. The problem with these solutions is that they rely on markers placed on the whole body to capture the movements, which can be very infeasible in many practical scenarios. This paper proposes a novel deep learning-based approach to predict 3D GRF&M from only 5 markers placed on the shoe. The proposed network “Attention Guided MultiResUNet” can predict the force and moment signals accurately and reliably compared to the techniques relying on full-body markers. The proposed deep learning model is tested on two publicly available datasets containing data from 66 healthy subjects to validate the approach. The framework has achieved an average correlation coefficient of 0.96 for 3D ground reaction force prediction and 0.86 for 3D ground reaction momentum prediction in cross-dataset validation. The framework can provide a cheaper and more feasible alternative for predicting GRF&M in many practical applications.

Using Wearable Accelerometers to Develop a Vertical Ground Reaction Force Prediction Model during Running: A Sensitivity Study

The estimation of vertical ground reaction forces (VGRFs) during running is necessary to understand running mechanisms. For this purpose, the use of force platforms is fundamental. However, to extend the study of VGRFs to real conditions, wearable accelerometers are a promising alternative to force platforms, whose use is often limited to the laboratory environment. The objective of this study was to develop a VGRF model using wearable accelerometers and a stepwise regression algorithm. Several models were developed and validated using the VGRFs and acceleration signals collected during 100 stances performed by one participant. The validated models were tested on eight participants. In a sensitivity study, the strongest correlations were observed at cut-off frequencies of ≤25 Hz and in models developed with 30 to 90 stances. After the validation phase, the 10 best models had, on average, low relative differences (≤10%) in the estimation of discrete VGRF parameters, i.e., the passive peak (εpp=6.26%), active peak (εap=2.22%), and loading rate (εlr=2.17%). The results indicate that the development of personalized models is more suitable for achieving the best estimates. The proposed methodology opens many perspectives for monitoring VGRFs under real conditions using a limited number of wearable sensors.

Mechanical loading prediction through accelerometry data during walking and running

ABSTRACT Currently, there is no way to assess mechanical loading variables such as peak ground reaction forces (pGRF) and peak loading rate (pLR) in clinical settings. The purpose of this study was to develop accelerometry-based equations to predict both pGRF and pLR during walking and running. One hundred and thirty one subjects (79 females; 76.9 ± 19.6 kg) walked and ran at different speeds (2–14 km·h−1) on a force plate–instrumented treadmill while wearing accelerometers at their ankle, lower back and hip. Regression equations were developed to predict pGRF and pLR from accelerometry data. Leave-one-out cross-validation was used to calculate prediction accuracy and Bland–Altman plots. Our pGRF prediction equation was compared with a reference equation previously published. Body mass and peak acceleration were included for pGRF prediction and body mass and peak acceleration rate for pLR prediction. All pGRF equation coefficients of determination were above 0.96, and a good agreement between actual and predicted pGRF was observed, with a mean absolute percent error (MAPE) below 7.3%. Accuracy indices from our equations were better than previously developed equations. All pLR prediction equations presented a lower accuracy compared to those developed to predict pGRF. Walking and running pGRF can be predicted with high accuracy by accelerometry-based equations, representing an easy way to determine mechanical loading in free-living conditions. The pLR prediction equations yielded a somewhat lower prediction accuracy compared with the pGRF equations.

American Academy of Sports Physical Therapy Platform Presentation Abstracts SPL1–SPL82

American Academy of Sports Physical Therapy Platform Presentation Abstracts SPL1–SPL82

IMU sensors beneath walking surface for ground reaction force prediction in gait

Objective : Utilization of inertial measurement units (IMU) data for ground reaction force (GRF) prediction has been widely studied and documented when these sensors attach to the body segments. However, it was inconvenient and required people’s cooperation. A novel approach of the current study was setting IMU sensors mounted underneath the walking surface to measure footstep induced structural vibration. We aimed to conduct the force plate to validate the prediction accuracy of this approach. Methods : Fifteen hundred steps were recorded from five individuals. Twenty-four measured features from four IMU sensors were treated as inputs to the long short-term memory model for multidimensional GRF predictions. The GRF data from the force plate were considered as the ground truth for comparisons. The accuracy performance was determined by the normalized root mean square error (NRMSE) method. Results : The averaged NRMSE was 6.05%, 3.93%, and 4.37% for Fx, Fy, and Fz, respectively. Conclusion : The accuracy was comparable with IMU sensors attached to the body, particularly in the vertical direction. The current study demonstrated the feasibility of this approach and successfully predicted ground reaction force with high accuracy. Significance : The validation of IMU sensors mounted underneath the walking surface for GRF prediction provides an alternative method for biometrics in gait.

Improving the ground reaction force prediction accuracy using one-axis plantar pressure: Expansion of input variable for neural network

In this study, we describe a method to predict 6-axis ground reaction forces based solely on plantar pressure (PP) data obtained from insole type measurement devices free of space limitations. Because only vertical force is calculable from PP data, a wavelet neural network derived from a non-linear mapping function was used to obtain 3-axis ground reaction force in medial-lateral (GRFML), anterior-posterior (GRFAP) and vertical (GRFV) and 3-axis ground reaction moment in sagittal (GRFS), frontal (GRFF) and transverse (GRFT) data for the remaining axes and planes. As the prediction performance of nonlinear models depends strongly on input variables, in this study, three input variables – accumulated PP with respect to time, center of pressure (COP) pattern, and measurements of the opposite foot, which are calculable only with a PP device – were considered in order to improve prediction performance. To conduct this study, the golf swing motions of 80 subjects were characterized as unilateral movement and GRF patterns as functions of individual characteristics. The prediction model was verified with 5-fold cross-validation utilizing the measured values of two force plates. As a result, prediction model (correlation coefficient, r=0.73–0.97) utilized accumulated PP and PP data of the opposite foot and showed the highest prediction accuracy in left-foot GRFV, GRMF, GRMT and right-foot GRFAP, GRFML, GRMF, GRMT. Likewise, another prediction model (r=0.83–0.98) utilized accumulated PP and COP patterns as input and showed the best accuracy in left-foot GRFAP, GRFML, GRMS and right-foot GRFV, GRMS. New methods based on the findings of the present study are expected to help resolve problems such as spatial limitation and limited analyzable motions in existing GRF measurement processes.

Intervertebral reaction force prediction using an enhanced assembly of OpenSim models

OpenSim offers a valuable approach to investigating otherwise difficult to assess yet important biomechanical parameters such as joint reaction forces. Although the range of available models in the public repository is continually increasing, there currently exists no OpenSim model for the computation of intervertebral joint reactions during flexion and lifting tasks. The current work combines and improves elements of existing models to develop an enhanced model of the upper body and lumbar spine. Models of the upper body with extremities, neck and head were combined with an improved version of a lumbar spine from the model repository. Translational motion was enabled for each lumbar vertebrae with six controllable degrees of freedom. Motion segment stiffness was implemented at lumbar levels and mass properties were assigned throughout the model. Moreover, body coordinate frames of the spine were modified to allow straightforward variation of sagittal alignment and to simplify interpretation of results. Evaluation of model predictions for level L1–L2, L3–L4 and L4–L5 in various postures of forward flexion and moderate lifting (8 kg) revealed an agreement within 10% to experimental studies and model-based computational analyses. However, in an extended posture or during lifting of heavier loads (20 kg), computed joint reactions differed substantially from reported in vivo measures using instrumented implants. We conclude that agreement between the model and available experimental data was good in view of limitations of both the model and the validation datasets. The presented model is useful in that it permits computation of realistic lumbar spine joint reaction forces during flexion and moderate lifting tasks. The model and corresponding documentation are now available in the online OpenSim repository.

A Nonlinear Leg Damping Model for the Prediction of Running Forces and Stability

Despite the neuromechanical complexity underlying animal locomotion, the steady-state center-of-mass motions and ground reaction forces of animal running can be predicted by simple spring-mass models such as the canonical spring-loaded inverted pendulum (SLIP) model. Such SLIP models have been useful for the fields of biomechanics and robotics in part because ground reaction forces are commonly measured and readily available for comparing with model predictions. To better predict the stability of running, beyond the canonical conservative SLIP model, more recent extensions have been proposed and investigated with hip actuation and linear leg damping (e.g., hip-actuated SLIP). So far, these attempts have gained improved prediction of the stability of locomotion but have led to a loss of the ability to accurately predict ground reaction forces. Unfortunately, the linear damping utilized in current models leads to an unrealistic prediction of damping force and ground reaction force with a large nonzero magnitude at touchdown (TD). Here, we develop a leg damping model that is bilinear in leg length and velocity in order to yield improved damping force and ground reaction force prediction. We compare the running ground reaction forces, small and large perturbation stability, parameter sensitivity, and energetic cost resulting from both the linear and bilinear damping models. We found that bilinear damping helps to produce more realistic, smooth vertical ground reaction forces, thus fixing the current problem with the linear damping model. Despite large changes in the damping force and power loss profile during the stance phase, the overall dynamics and energetics on a stride-to-stride basis of the two models are largely the same, implying that the integrated effect of damping over a stride is what matters most to the stability and energetics of running. Overall, this new model, an actuated SLIP model with bilinear damping, can provide significantly improved prediction of ground reaction forces as well as stability and energetics of locomotion.

Crossflow Vortices of a Jet Injected into a Supersonic Crossflow

Numerous investigations of the fluid mechanics of the transverse jet injected into a supersonic flow (TJISF) flowfield have been motivated by the study of supersonic combustor fuel injection, thrust vector control of rocket nozzles, and jet reaction force prediction. Early studies presented detailed qualitative discussions of the structure of the TJISF flowfield. A few studies have provided either quantitative or semiquantitative measurements of the velocity fields of underexpanded jets injected into a supersonic flow. Despite these investigations, there is a dearth of nonintrusive, quantitative mean velocity and turbulence measurements in the TJISF flowfield. This note uses laser Doppler velocimetry (LDV) measurements of the mean velocity fields to study development of the crossflow vortices of a sonic, underexpanded transverse jet injected into a Mach 1.6 crossflow.

Velocity Measurements of a Jet Injected into a Supersonic Crossflow

This paper presents a quantitative, experimental study of a single, sonic, underexpanded, transverse, round jet injected into a Mach 1.6 crosse ow. This investigation is applicable to studies of supersonic combustors, thrust vector control of rocket nozzles, the cooling of nozzle walls, and jet reaction force prediction. Schlieren/shadowgraph photography and two-component, frequency preshifted laser Doppler velocimetry are used to visualize the e ow and to measure three mean velocity components, e ve of the six kinematic Reynolds stresses, and turbulent kinetic energy at over 4000 locations throughout the e owe eld. The study focuses on the transverse, midline plane and on two crosse ow planes. These measurements are used to study the size and orientation of the recirculation regions upstream and downstream of the jet; the structure and strength of the bow shock, barrel shock, and Mach disk; the structure, strength, and development of the kidney-shaped, counter-rotating vortex pair; the growth of the annular shear layer between the jet plume and the crosse ow; and the growth of the boundary layer beneath the jet. In addition, the present study provides validation data for analytical and numerical predictions of the transverse jet e owe eld.

The prediction of reaction forces from gait data

A computer analysis of gait data has been performed to determine the translational and angular accelerations of the limb segment during normal locomotion. Using anthropometric data, the appropriate mass moments of inertia of the limb segments have been applied to allow a prediction of hip and knee moments and floor reaction forces. It was found that the phase of the head-arms-trunk system with respect to the hip-thigh-shank system is important in determining hip moments. The floor reaction force and knee moment data are then applied to the problem of the design of an external prosthetic polycentric knee joint.