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.     

A sensitivity analysis method for the body segment inertial parameters based on ground reaction and joint moment regressor matrices

This paper presents a method allowing a simple and efficient sensitivity analysis of dynamics parameters of complex whole-body human model. The proposed method is based on the ground reaction and joint moment regressor matrices, developed initially in robotics system identification theory, and involved in the equations of motion of the human body. The regressor matrices are linear relatively to the segment inertial parameters allowing us to use simple sensitivity analysis methods. The sensitivity analysis method was applied over gait dynamics and kinematics data of nine subjects and with a 15 segments 3D model of the locomotor apparatus. According to the proposed sensitivity indices, 76 segments inertial parameters out the 150 of the mechanical model were considered as not influent for gait. The main findings were that the segment masses were influent and that, at the exception of the trunk, moment of inertia were not influent for the computation of the ground reaction forces and moments and the joint moments. The same method also shows numerically that at least 90% of the lower-limb joint moments during the stance phase can be estimated only from a force-plate and kinematics data without knowing any of the segment inertial parameters.     

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.     

Static and dynamic optimization solutions for gait are practically equivalent

The proposition that dynamic optimization provides better estimates of muscle forces during gait than static optimization is examined by comparing a dynamic solution with two static solutions. A 23-degree-of-freedom musculoskeletal model actuated by 54 Hill-type musculotendon units was used to simulate one cycle of normal gait. The dynamic problem was to find the muscle excitations which minimized metabolic energy per unit distance traveled, and which produced a repeatable gait cycle. In the dynamic problem, activation dynamics was described by a first-order differential equation. The joint moments predicted by the dynamic solution were used as input to the static problems. In each static problem, the problem was to find the muscle activations which minimized the sum of muscle activations squared, and which generated the joint moments input from the dynamic solution. In the first static problem, muscles were treated as ideal force generators; in the second, they were constrained by their force-length-velocity properties; and in both, activation dynamics was neglected. In terms of predicted muscle forces and joint contact forces, the dynamic and static solutions were remarkably similar. Also, activation dynamics and the force-length-velocity properties of muscle had little influence on the static solutions. Thus, for normal gait, if one can accurately solve the inverse dynamics problem and if one seeks only to estimate muscle forces, the use of dynamic optimization rather than static optimization is currently not justified. Scenarios in which the use of dynamic optimization is justified are suggested.     

Knee moment outcomes using inverse dynamics and the cross product function in moderate knee osteoarthritis gait: A comparison study

Inverse dynamics are the cornerstone of biomechanical assessments to calculate knee moments during walking. In knee osteoarthritis, these outcomes have been used to understand knee pathomechanics, but the complexity of an inverse dynamic model may limit the uptake of joint moments in some clinical and research structures. The objective was to determine whether discrete features of the sagittal and frontal plane knee moments calculated using inverse dynamics compare to knee moments calculated using a cross product function. Knee moments from 74 people with moderate knee osteoarthritis were assessed after ambulating at a self-selected speed on an instrumented dual belt treadmill. Standardized procedures were used for surface marker placement, gait speed determination and data processing. Net external frontal and sagittal plane knee moments were calculated using inverse dynamics and the three-dimensional position of the knee joint center with respect to the center of pressure was crossed with the three-dimensional ground reaction forces in the cross product function. Correlations were high between outcomes of the moment calculations (r > 0.9) and for peak knee adduction moment, knee adduction moment impulse and difference between peak flexion and extension moments, the cross product function resulted in absolute values less than 10% of those calculated using inverse dynamics in this treadmill walking environment. This computational solution may allow the integration of knee moment calculations to understand knee osteoarthritis gait without data collection or computational complexity.     

Comparison of methods for the calculation of energy storage and return in a dynamic elastic response prosthesis

The standard method used to calculate the ankle joint power contains deficiencies when applied to dynamic elastic response prosthetic feet. The standard model, using rotational power and inverse dynamics, assumes a fixed joint center and cannot account for energy storage, dissipation, and return. This study compared the standard method with new analysis models. First, assumptions of inverse dynamics were avoided by directly measuring ankle forces and moments. Second, the ankle center of rotation was corrected by including translational power terms. Analysis with below-knee amputees revealed that the conventional method overestimates ankle forces and moments as well as prosthesis energy storage and return. Results for efficiency of energy return were varied. Large differences between models indicate the standard method may have serious inadequacies in the analysis of certain prosthetic feet. This research is the first application of the new models to prosthetic feet, and suggests the need for additional research in gait analysis with energy-storing prostheses.     

Predicting muscle forces in gait from EMG signals and musculotendon kinematics

An EMG-driven muscle model for determining muscle force-time histories during gait is presented. The model, based on Hill's equation (1938), incorporates morphological data and accounts for changes in musculotendon length, velocity, and the level of muscle excitation for both concentric and eccentric contractions. Musculotendon kinematics were calculated using three-dimensional cinematography with a model of the musculoskeletal system. Muscle force-length-EMG relations were established from slow isokinetic calibrations. Walking muscle force-time histories were determined for two subjects. Joint moments calculated from the predicted muscle forces were compared with moments calculated using a linked segment, inverse dynamics approach. Moment curve correlations ranged from r = 0.72 to R = 0.97 and the root mean square (RMS) differences were from 10 to 20 Nm. Expressed as a relative RMS, the moment differences ranged from a low of 23% at the ankle to a high of 72% at the hip. No single reason for the differences between the two moment curves could be identified. Possible explanations discussed include the linear EMG-to-force assumption and how well the EMG-to-force calibration represented excitation for the whole muscle during gait, assumptions incorporated in the muscle modeling procedure, and errors inherent in validating joint moments predicted from the model to moments calculated using linked segment, inverse dynamics. The closeness with which the joint moment curves matched in the present study supports using the modeling approach proposed to determine muscle forces in gait.     

The effect of perturbing body segment parameters on calculated joint moments and muscle forces during gait

This study examined the effect of body segment parameter (BSP) perturbations on joint moments calculated using an inverse dynamics procedure and muscle forces calculated using computed muscle control (CMC) during gait. BSP (i.e. segment mass, center of mass location (com) and inertia tensor) of the left thigh, shank and foot of a scaled musculoskeletal model were perturbed. These perturbations started from their nominal value and were adjusted to ±40% in steps of 10%, for both individual as well as combined perturbations in BSP. For all perturbations, an inverse dynamics procedure calculated the ankle, knee and hip moments based on an identical inverse kinematics solution. Furthermore, the effect of applying a residual reduction algorithm (RRA) was investigated. Muscle excitations and resulting muscle forces were calculated using CMC. The results show only a limited effect of an individual parameter perturbation on the calculated moments, where the largest effect is found when perturbing the shank com (MS_com,shank, the ratio of absolute difference in torque and relative parameter perturbation, is maximally −7.81 N m for hip flexion moment). The additional influence of perturbing two parameters simultaneously is small (MS_{mass+com,thigh} is maximally 15.2 N m for hip flexion moment). RRA made small changes to the model to increase the dynamic consistency of the simulation (after RRA MS_com,shank is maximally 5.01 N m). CMC results show large differences in muscle forces when BSP are perturbed. These result from the underlying forward integration of the dynamic equations.     

The effect of direct measurement versus cadaver estimates of anthropometry in the calculation of joint moments during above-knee prosthetic gait in pediatrics

Joint reaction forces, moments and powers are important in interpreting gait mechanics and compensatory strategies used by patients walking with above-knee prostheses. Segmental anthropometrics, required to calculate joint moments, are often estimated using data from cadaver studies. However, these values may not be accurate for patients following amputation as prostheses are composed of non-biologic material. The purpose of this study was to compare joint moments using anthropometrics calculated from cadaver studies versus direct measurements of the residual limb and prosthesis for children with an above-knee amputation. Gait data were collected for four subjects with above-knee prostheses walking at preferred and fast speeds. Joint moments were computed using anthropometrics from cadaver studies and direct measurements for each subject. The difference between these two methods primarily affected the inertia couple (Ialpha term) and the inertial effect due to gravity, which comprised a greater percentage of the total joint moment during swing as compared to stance. Peak hip and knee flexor and extensor moments during swing were significantly greater when calculated using cadaver data (p<0.05). These differences were greater while walking fast as compared to slow speeds. A significant difference was not found between these two methods for peak hip and knee moments during stance. A significant difference was found for peak ankle joint moments during stance, but the magnitude was not clinically important. These results support the use of direct measurements of anthropometry when examining above-knee prosthetic gait, particularly during swing.     

Influence of altered gait patterns on the hip joint contact forces

Children who exhibit gait deviations often present a range of bone deformities, particularly at the proximal femur. Altered gait may affect bone growth and lead to deformities by exerting abnormal stresses on the developing bones. The objective of this study was to calculate variations in the hip joint contact forces with different gait patterns. Muscle and hip joint contact forces of four children with different walking characteristics were calculated using an inverse dynamic analysis and a static optimisation algorithm. Kinematic and kinetic analyses were based on a generic musculoskeletal model scaled down to accommodate the dimensions of each child. Results showed that for all the children with altered gaits both the orientation and magnitude of the hip joint contact force deviated from normal. The child with the most severe gait deviations had hip joint contact forces 30% greater than normal, most likely due to the increase in muscle forces required to sustain his crouched stance. Determining how altered gait affects joint loading may help in planning treatment strategies to preserve correct loading on the bone from a young age.     

A physiology-based inverse dynamic analysis of human gait using sequential convex programming: a comparative study

This paper presents an enhanced version of the previously proposed physiological inverse approach (PIA) to calculate musculotendon (MT) forces and evaluates the proposed methodology in a comparative study. PIA combines an inverse dynamic analysis with an optimisation approach that imposes muscle physiology and optimises performance over the entire motion. To solve the resulting large-scale, nonlinear optimisation problem, we neglected muscle fibre contraction speed and an approximate quadratic optimisation problem (PIA-QP) was formulated. Conversely, the enhanced version of PIA proposed in this paper takes into account muscle fibre contraction speed. The optimisation problem is solved using a sequential convex programing procedure (PIA-SCP). The comparative study includes PIA-SCP, PIA-QP and two commonly used approaches from the literature: static optimisation (SO) and computed muscle control (CMC). SO and CMC make simplifying assumptions to limit the computational time. Both methods minimise an instantaneous performance criterion. Furthermore, SO does not impose muscle physiology. All methods are applied to a gait cycle of six control subjects. The relative root mean square error averaged over all subjects, ε(RMS), between the joint torques simulated from the optimised activations and the joint torques obtained from the inverse dynamic analysis was about twice as large for SO (ε(RMS) = 86) as compared with CMC (ε(RMS) = 39) and PIA-SCP (ε(RMS) = 50). ε(RMS) was at least twice as large for PIA-QP (ε(RMS) = 197) than for all other methods. As compared with CMC, muscle activation patterns predicted by PIA-SCP better agree with experimental electromyography (EMG). This study shows that imposing muscle physiology as well as globally optimising performance is important to accurately calculate MT forces underlying gait.     

Influence of body segments' parameters estimation models on inverse dynamics solutions during gait

The purpose of the present study was to examine the influence of anthropometric data on joint kinetics during gait. We particularly focused on the sensitivity of inverse dynamics solutions to the use of models for body segment parameters (BSP) estimation. Six often used estimation models were selected to provide BSP values for the three segments of the lower limb. Kinematics and dynamics were sampled from seven subjects performing barefoot gait at three different speeds. Joint kinetics were estimated with the bottom-up method using BSP values derived from each estimation model as anthropometric inputs. The BSP estimates were highly sensitive to the model used with deviations ranging from at least 9.73% up to 60%. Maximal variations of peak values for the hip joint flexion/extension moment during the swing phase were 20.11%. Hence, our findings suggest that the influence of BSP cannot be neglected. Observed deviations are especially due to the effect of varying simultaneously the mass, moments of inertia and the center of mass location values, according to the underlying relationship of interdependency linking each component. Considering both the differences found in joint kinetics and the level of accuracy of BSP models, evidence is provided that using multiple regression BSP estimation functions derived from Zatsiorsky and Seluyanov should be recommended to assess joint kinetics.     

Differences in lower limb transverse plane joint moments during gait when expressed in two alternative reference frames

When comparing previous studies that have measured the three-dimensional moments acting about the lower limb joints (either external moments or opposing internal joint moments) during able-bodied adult gait, significant variation is apparent in the profiles of the reported transverse plane moments. This variation cannot be explained on the basis of adopted convention (i.e. external versus internal joint moment) or inherent variability in gait strategies. The aim of the current study was to determine whether in fact the frame in which moments are expressed has a dominant effect upon transverse plane moments and thus provides a valid explanation for the observed inconsistency in the literature. Kinematic and ground reaction force data were acquired from nine able-bodied adult subjects walking at a self-selected speed. Three-dimensional hip, knee and ankle joint moments during gait were calculated using a standard inverse dynamics approach. In addition to calculating internal joint moments, the components of the external moment occurring in the transverse plane at each of the lower limb joints were calculated to determine their independent effects. All moments were expressed in both the laboratory frame (LF) as well as the anatomical frame (AF) of the distal segment. With the exception of the ankle rotation moment in the foot AF, lower limb transverse plane joint moments during gait were found to display characteristic profiles that were consistent across subjects. Furthermore, lower limb transverse plane joint moments during gait differed when expressed in the distal segment AF compared to the LF. At the hip, the two alternative reference frames produced near reciprocal joint moment profiles. The components of the external moment revealed that the external ground reaction force moment was primarily responsible for this result. Lower limb transverse plane joint moments during gait were therefore found to be highly sensitive to a change in reference frame. These findings indicate that the different transverse plane joint moment profiles during able-bodied adult gait reported in the literature are likely to be explained on this basis.     

Fatigue effects on the coordinative pattern during cycling: Kinetics and kinematics evaluation

The aim of the present study was to analyze the net joint moment distribution, joint forces and kinematics during cycling to exhaustion. Right pedal forces and lower limb kinematics of ten cyclists were measured throughout a fatigue cycling test at 100% of PO_MAX. The absolute net joint moments, resultant force and kinematics were calculated for the hip, knee and ankle joint through inverse dynamics. The contribution of each joint to the total net joint moments was computed. Decreased pedaling cadence was observed followed by a decreased ankle moment contribution to the total joint moments in the end of the test. The total absolute joint moment, and the hip and knee moments has also increased with fatigue. Resultant force was increased, while kinematics has changed in the end of the test for hip, knee and ankle joints. Reduced ankle contribution to the total absolute joint moment combined with higher ankle force and changes in kinematics has indicated a different mechanical function for this joint. Kinetics and kinematics changes observed at hip and knee joint was expected due to their function as power sources. Kinematics changes would be explained as an attempt to overcome decreased contractile properties of muscles during fatigue.     

Friction in Total Hip Joint Prosthesis Measured In Vivo during Walking

Friction-induced moments and subsequent cup loosening can be the reason for total hip joint replacement failure. The aim of this study was to measure the in vivo contact forces and friction moments during walking. Instrumented hip implants with Al₂O₃ ceramic head and an XPE inlay were used. In vivo measurements were taken 3 months post operatively in 8 subjects. The coefficient of friction was calculated in 3D throughout the whole gait cycle, and average values of the friction-induced power dissipation in the joint were determined. On average, peak contact forces of 248% of the bodyweight and peak friction moments of 0.26% bodyweight times meter were determined. However, contact forces and friction moments varied greatly between individuals. The friction moment increased during the extension phase of the joint. The average coefficient of friction also increased during this period, from 0.04 (0.03 to 0.06) at contralateral toe off to 0.06 (0.04 to 0.08) at contralateral heel strike. During the flexion phase, the coefficient of friction increased further to 0.14 (0.09 to 0.23) at toe off. The average friction-induced power throughout the whole gait cycle was 2.3 W (1.4 W to 3.8 W). Although more parameters than only the synovia determine the friction, the wide ranges of friction coefficients and power dissipation indicate that the lubricating properties of synovia are individually very different. However, such differences may also exist in natural joints and may influence the progression of arthrosis. Furthermore, subjects with very high power dissipation may be at risk of thermally induced implant loosening. The large increase of the friction coefficient during each step could be caused by the synovia being squeezed out under load.     

Subject-specific hip geometry and hip joint centre location affects calculated contact forces at the hip during gait

Hip loading affects the development of hip osteoarthritis, bone remodelling and osseointegration of implants. In this study, we analyzed the effect of subject-specific modelling of hip geometry and hip joint centre (HJC) location on the quantification of hip joint moments, muscle moments and hip contact forces during gait, using musculoskeletal modelling, inverse dynamic analysis and static optimization. For 10 subjects, hip joint moments, muscle moments and hip loading in terms of magnitude and orientation were quantified using three different model types, each including a different amount of subject-specific detail: (1) a generic scaled musculoskeletal model, (2) a generic scaled musculoskeletal model with subject-specific hip geometry (femoral anteversion, neck-length and neck-shaft angle) and (3) a generic scaled musculoskeletal model with subject-specific hip geometry including HJC location. Subject-specific geometry and HJC location were derived from CT. Significant differences were found between the three model types in HJC location, hip flexion–extension moment and inclination angle of the total contact force in the frontal plane. No model agreement was found between the three model types for the calculation of contact forces in terms of magnitude and orientations, and muscle moments. Therefore, we suggest that personalized models with individualized hip joint geometry and HJC location should be used for the quantification of hip loading. For biomechanical analyses aiming to understand modified hip joint loading, and planning hip surgery in patients with osteoarthritis, the amount of subject-specific detail, related to bone geometry and joint centre location in the musculoskeletal models used, needs to be considered.     

An upper extremity inverse dynamics model for pediatric Lofstrand crutch-assisted gait

The objective of this study was to develop an instrumented Lofstrand crutch system, which quantifies three-dimensional (3-D) upper extremity (UE) kinematics and kinetics using an inverse dynamics model. The model describes the dynamics of the shoulders, elbows, wrists, and crutches and is compliant with the International Society of Biomechanics (ISB) recommended standards. A custom designed Lofstrand crutch system with four, six-degree-of-freedom force transducers was implemented with the inverse dynamics model to obtain triaxial UE joint reaction forces and moments. The crutch system was validated statically and dynamically for accuracy of computing joint reaction forces and moments during gait. The root mean square (RMS) error of the system ranged from 0.84 to 5.20%. The system was demonstrated in children with diplegic cerebral palsy (CP), incomplete spinal cord injury (SCI), and type I osteogenesis imperfecta (OI). The greatest joint reaction forces were observed in the posterior direction of the wrist, while shoulder flexion moments were the greatest joint reaction moments. The subject with CP showed the highest forces and the subject with SCI demonstrated the highest moments. Dynamic quantification may help to elucidate UE joint demands in regard to pain and pathology in long-term assistive device users.     

Upper extremity inverse dynamics model for crutch-assisted gait assessment

Current inverse dynamics models of the upper extremity (UE) are limited for the measurement of Lofstrand crutch-assisted gait. The objective of this study is to develop, validate, and demonstrate a three-dimensional (3-D) UE motion assessment system to quantify crutch-assisted gait in children. We propose a novel 3-D dynamic model of the UEs and crutches for quantification of joint motions, forces, and moments during Lofstrand crutch-assisted gait. The model is composed of the upper body (i.e., thorax, upper arms, forearms, and hands) and Lofstrand crutches to determine joint dynamics of the thorax, shoulders, elbows, wrists, and crutches. The model was evaluated and applied to a pediatric subject with myelomeningocele (MM) to demonstrate its effectiveness in the characterization of crutch gait during multiple walking patterns. The model quantified UE dynamics during reciprocal and swing-through crutch-assisted gait patterns. Joint motions and forces were greater during swing-through gait than reciprocal gait. The model is suitable for further application to pediatric crutch-user populations. This study has potential for improving the understanding of the biomechanics of crutch-assisted gait and may impact clinical intervention strategies and therapeutic planning of ambulation.     

Computed tomography-based joint locations affect calculation of joint moments during gait when compared to scaling approaches

Hip joint moments are an important parameter in the biomechanical evaluation of orthopaedic surgery. Joint moments are generally calculated using scaled generic musculoskeletal models. However, due to anatomical variability or pathology, such models may differ from the patient's anatomy, calling into question the accuracy of the resulting joint moments. This study aimed to quantify the potential joint moment errors caused by geometrical inaccuracies in scaled models, during gait, for eight test subjects. For comparison, a semi-automatic computed tomography (CT)-based workflow was introduced to create models with subject-specific joint locations and inertial parameters. 3D surface models of the femora and hemipelves were created by segmentation and the hip joint centres and knee axes were located in these models. The scaled models systematically located the hip joint centre (HJC) up to 33.6 mm too inferiorly. As a consequence, significant and substantial peak hip extension and abduction moment differences were recorded, with, respectively, up to 23.1% and 15.8% higher values in the image-based models. These findings reaffirm the importance of accurate HJC estimation, which may be achieved using CT- or radiography-based subject-specific modelling. However, obesity-related gait analysis marker placement errors may have influenced these results and more research is needed to overcome these artefacts.