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.     

Kinematics of lower limbs during walking are emulated by springy walking model with a compliantly connected,off-centered curvy foot

The dynamics of the center of mass (CoM) during walking and running at various gait conditions are well described by the mechanics of a simple passive spring loaded inverted pendulum (SLIP). Due to its simplicity, however, the current form of the SLIP model is limited at providing any further information about multi-segmental lower limbs that generate oscillatory CoM behaviors and their corresponding ground reaction forces. Considering that the dynamics of the CoM are simply achieved by mass-spring mechanics, we wondered whether any of the multi-joint motions could be demonstrated by simple mechanics. In this study, we expand a SLIP model of human locomotion with an off-centered curvy foot connected to the leg by a springy segment that emulates the asymmetric kinematics and kinetics of the ankle joint. The passive dynamics of the proposed expansion of the SLIP model demonstrated the empirical data of ground reaction forces, center of mass trajectories, ankle joint kinematics and corresponding ankle joint torque at various gait speeds. From the mechanically simulated trajectories of the ankle joint and CoM, the motion of lower-limb segments, such as thigh and shank angles, could be estimated from inverse kinematics. The estimation of lower limb kinematics showed a qualitative match with empirical data of walking at various speeds. The representability of passive compliant mechanics for the kinetics of the CoM and ankle joint and lower limb joint kinematics implies that the coordination of multi-joint lower limbs during gait can be understood with a mechanical framework.     

A neuromusculoskeletal tracking method for estimating individual muscle forces in human movement

A neuromusculoskeletal tracking (NMT) method was developed to estimate muscle forces from observed motion data. The NMT method combines skeletal motion tracking and optimal neuromuscular tracking to produce forward simulations of human movement quickly and accurately. The skeletal motion tracker calculates the joint torques needed to actuate a skeletal model and track observed segment angles and ground forces in a forward simulation of the motor task. The optimal neuromuscular tracker resolves the muscle redundancy problem dynamically and finds the muscle excitations (and muscle forces) needed to produce the joint torques calculated by the skeletal motion tracker. To evaluate the accuracy of the NMT method, kinematics and ground forces obtained from an optimal control (parameter optimization) solution for maximum-height jumping were contaminated with both random and systematic noise. These data served as input observations to the NMT method as well as an inverse dynamics analysis. The NMT solution was compared to the input observations, the original optimal solution, and a simulation driven by the inverse dynamics torques. The results show that, in contrast to inverse dynamics, the NMT method is able to produce an accurate forward simulation consistent with the optimal control solution. The NMT method also requires 3 orders-of-magnitude less CPU time than parameter optimization. The speed and accuracy of the NMT method make it a promising new tool for estimating muscle forces using experimentally obtained kinematics and ground force data.     

A closed-loop cadaveric foot and ankle loading model

Investigations of human foot and ankle biomechanics rely chiefly on cadaver experiments. The application of proper force magnitudes to the cadaver foot and ankle is essential to obtain valid biomechanical data. Data for external ground reaction forces are readily available from human motion analysis. However, determining appropriate forces for extrinsic foot and ankle muscles is more problematic. A common approach is the estimation of forces from muscle physiological cross-sectional areas and electromyographic data. We have developed a novel approach for loading the Achilles and posterior tibialis tendons that does not prescribe predetermined muscle forces. For our loading model, these muscle forces are determined experimentally using independent plantarflexion and inversion angle feedback control. The independent (input) parameters -- calcaneus plantarflexion, calcaneus inversion, ground reaction forces, and peroneus forces -- are specified. The dependent (output) parameters -- Achilles force, posterior tibialis force, joint motion, and spring ligament strain -- are functions of the independent parameters and the kinematics of the foot and ankle. We have investigated the performance of our model for a single, clinically relevant event during the gait cycle. The instantaneous external forces and foot orientation determined from human subjects in a motion analysis laboratory were simulated in vitro using closed-loop feedback control. Compared to muscle force estimates based on physiological cross-sectional area data and EMG activity at 40% of the gait cycle, the posterior tibialis force and Achilles force required when using position feedback control were greater.     

Reflections on clinical gait analysis

Clinical gait analysis allows the measurement and assessment of walking biomechanics, which facilitates the identification of abnormal characteristics and the recommendation of treatment alternatives. The predominant methods for this analysis currently include the tracking of external markers placed on the patient, the monitoring of patient/ground interaction (e.g. ground reaction forces), and the recording of muscle electromyographic (EMG) activity, all during gait. These data allow the computation of stride and temporal parameters, joint/segment kinematics, joint kinetics, and EMG plots that are used to gain a better understanding of a patient's walking difficulties. Gait interpretation involves a systemic evaluation of each of these types of data, noting both corroborating and conflicting information while identifying functionally significant deviations from the normal. Understanding the etiology of these abnormalities allows the formulation of a treatment plan that may involve physical therapy, bracing, and/or surgery. This process is challenging because of the complexity of the motion, neuromuscular involvement of the patient (e.g. dynamic spasticity), variability of treatment outcome, and on occasion, uncertainty about the quality of the gait data. The experience of the interpretation team with respect to gait biomechanics, a particular patient population, and the effectiveness of different treatment modalities is the principal determinant of the success of this approach. The clinical gait analysis process continues to evolve positively. It has become more comprehensive and meaningful because of an improved understanding of normal gait biomechanics and more rigorous data collection/reduction protocols that complement accumulated clinically relevant experience.     

Improving joint torque calculations: optimization-based inverse dynamics to reduce the effect of motion errors

The accuracy of joint torques calculated from inverse dynamics methods is strongly dependent upon errors in body segment motion profiles, which arise from two sources of noise: the motion capture system and movement artifacts of skin-mounted markers. The current study presents a method to increase the accuracy of estimated joint torques through the optimization of the angular position data used to describe these segment motions. To compute these angular data, we formulated a constrained nonlinear optimization problem with a cost function that minimizes the difference between the known ground reaction forces (GRFs) and the GRF calculated via a top-down inverse dynamics solution. To evaluate this approach, we constructed idealized error-free reference movements (of squatting and lifting) that produced a set of known “true” motions and associated true joint torques and GRF. To simulate real-world inaccuracies in motion data, these true motions were perturbed by artificial noise. We then applied our approach to these noise-induced data to determine optimized motions and related joint torques. To evaluate the efficacy of the optimization approach compared to traditional (bottom-up or top-down) inverse dynamics approaches, we computed the root mean square error (RMSE) values of joint torques derived from each approach relative to the expected true joint torques. Compared to traditional approaches, the optimization approach reduced the RMSE by 54% to 79%. Average reduction due to our method was 65%; previous methods only achieved an overall reduction of 30%. These results suggest that significant improvement in the accuracy of joint torque calculations can be achieved using this approach.     

A pilot study investigating motor adaptations when learning to walk with a whole-body powered exoskeleton

Evidence is emerging on how whole-body powered exoskeleton (EXO) use impacts users in basic occupational work scenarios, yet our understanding of how users learn to use this complex technology is limited. We explored how novice users adapted to using an EXO during gait. Six novices and five experienced users completed the study. Novices completed an initial training/familiarization gait session, followed by three subsequent gait sessions using the EXO, while experienced users completed one gait session with the EXO. Spatiotemporal gait measures, pelvis and lower limb joint kinematics, muscle activities, EXO torques, and human-EXO interaction forces were measured. Adaptations among novices were most pronounced in spatiotemporal gait measures, followed by joint kinematics, with smaller changes evident in muscle activity and EXO joint torques. Compared to the experienced users, novices exhibited a shorter step length and walked with significantly greater anterior pelvic tilt and less hip extension. Novices also used lower joint torques from the EXO at the hip and knee, and they had greater biceps femoris activity. Overall, our results may suggest that novices exhibited clear progress in learning, but they had not yet adopted motor strategies similar to those of experienced users after the three sessions. We suggest potential future directions to enhance motor adaptations to powered EXO in terms of both training protocols and human-EXO interfaces.     

The influence of soft tissue movement on ground reaction forces, joint torques and joint reaction forces in drop landings

The aim of this study was to determine the effects that soft tissue motion has on ground reaction forces, joint torques and joint reaction forces in drop landings. To this end a four body-segment wobbling mass model was developed to reproduce the vertical ground reaction force curve for the first 100 ms of landing. Particular attention was paid to the passive impact phase, while selecting most model parameters a priori, thus permitting examination of the rigid body assumption on system kinetics. A two-dimensional wobbling mass model was developed in DADS (version 9.00, CADSI) to simulate landing from a drop of 43 cm. Subject-specific inertia parameters were calculated for both the rigid links and the wobbling masses. The magnitude and frequency response of the soft tissue of the subject to impulsive loading was measured and used as a criterion for assessing the wobbling mass motion. The model successfully reproduced the vertical ground reaction force for the first 100 ms of the landing with a peak vertical ground reaction force error of 1.2% and root mean square errors of 5% for the first 15 ms and 12% for the first 40 ms. The resultant joint forces and torques were lower for the wobbling mass model compared with a rigid body model, up to nearly 50% lower, indicating the important contribution of the wobbling masses on reducing system loading.     

Shoulder joint loadings in post total hip replacement surgery patients during assisted walking: The influence of the crutch setup

A crutch is prescribed to permit the patient to walk safely and independently immediately after total hip replacement (THR) surgery. Purpose of this study is to evaluate the influence of the crutch setup on upper limbs biomechanics, including shoulder joint kinematics and kinetics parameters that will be evaluated to detect possible differences related to the crutch length.Thirty patients were randomly assigned to elbow flexed (EF) or elbow extended (EE) forearm crutch setup. Subjects were asked to walk on the laboratory path, instrumented with motion tracking system and force platforms. Spatiotemporal gait parameters, crutch ground reaction force (GRF) and crutch displacement (measured as the relative distance between the crutch position on the floor and the shoulder joint center), were evaluated. A three-dimensional (3D) biomechanical model was implemented to determine shoulder joint kinematics and kinetics during crutch walking.Results showed that the stride length significantly decreased, and base of support width increased for the EF group when compared to the EE group. Crutch forces and distance to the body significantly decreased in the EE group. Furthermore, shoulder joint moments in all planes of motion, vertical and lateral forces were significantly reduced in the EE group.The present study showed that crutch setup influenced performance and upper limb loading during walking, with EE setup allowing a more stable walking and reducing stress on the shoulder joint when compared to the EF setup. Results may help therapists in rationalizing crutch length adjustments for patients after THR surgery.     

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.     

Higher medially-directed joint reaction forces are a characteristic of dysplastic hips: A comparative study using subject-specific musculoskeletal models

Acetabular dysplasia is a known cause of hip osteoarthritis. In addition to abnormal anatomy, changes in kinematics, joint reaction forces (JRFs), and muscle forces could cause tissue damage to the cartilage and labrum, and may contribute to pain and fatigue. The objective of this study was to compare lower extremity joint angles, moments, hip JRFs and muscle forces during gait between patients with symptomatic acetabular dysplasia and healthy controls. Marker trajectories and ground reaction forces were measured in 10 dysplasia patients and 10 typically developing control subjects. A musculoskeletal model was scaled in OpenSim to each subject and subject-specific hip joint centers were determined using reconstructions from CT images. Joint kinematics and moments were calculated using inverse kinematics and inverse dynamics, respectively. Muscle forces and hip JRFs were estimated with static optimization. Inter-group differences were tested for statistical significance (p ≤ 0.05) and large effect sizes (d ≥ 0.8). Results demonstrated that dysplasia patients had higher medially directed JRFs. Joint angles and moments were mostly similar between the groups, but large inter-group effect sizes suggested some restriction in range of motion by patients at the hip and ankle. Higher medially-directed JRFs and inter-group differences in hip muscle forces likely stem from lateralization of the hip joint center in dysplastic patients. Joint force differences, combined with reductions in range of motion at the hip and ankle may also indicate compensatory strategies by patients with dysplasia to maintain joint stability.     

Finger joint coordination during tapping

We investigated finger joint coordination during tapping by characterizing joint kinematics and torques in terms of muscle activation patterns and energy profiles. Six subjects tapped with their index finger on a computer keyswitch as if they were typing on the middle row of a keyboard. Fingertip force, keyswitch position, kinematics of the metacarpophalangeal (MCP) and the proximal and distal interphalangeal (IP) joints, and intramuscular electromyography of intrinsic and extrinsic finger muscles were measured simultaneously. Finger joint torques were calculated based on a closed-form Newton–Euler inverse dynamic model of the finger. During the keystroke, the MCP joint flexed and the IP joints extended before and throughout the loading phase of the contact period, creating a closing reciprocal motion of the finger joints. As the finger lifted, the MCP joint extended and the interphalangeal (IP) joints flexed, creating an opening reciprocal motion. Intrinsic finger muscle and extrinsic flexor activities both began after the initiation of the downward finger movement. The intrinsic finger muscle activity preceded both the IP joint extension and the onset of extrinsic muscle activity. Only extrinsic extensor activity was present as the finger was lifted. While both potential energy and kinetic energy are present and large enough to overcome the work necessary to press the keyswitch, the motor control strategies utilize the muscle forces and joint torques to ensure a successful keystroke.     

A review of biomechanical models

This paper surveys biomechanical models of the nonimpact type, involving the musculo-skeletal system. Models of bones, joints and body segments, including human gait and motion of the whole body are discussed. In particular, stress analysis of bone, calculation of ligament and muscle forces across joints and the kinetics and kinematics of locomotion are discussed. The models are described in terms of the method of formulation, the method of solution and the realism of the results obtained. There is a need for more data on material properties of various body tissues and more experimental research to develop techniques for validating many of the models. Further work on the selection of appropriate objective functions for indeterminate problems is also required.     

Using computed muscle control to generate forward dynamic simulations of human walking from experimental data

The objective of this study was to develop an efficient methodology for generating muscle-actuated simulations of human walking that closely reproduce experimental measures of kinematics and ground reaction forces. We first introduce a residual elimination algorithm (REA) to compute pelvis and low back kinematic trajectories that ensure consistency between whole-body dynamics and measured ground reactions. We then use a computed muscle control (CMC) algorithm to vary muscle excitations to track experimental joint kinematics within a forward dynamic simulation. CMC explicitly accounts for delays in muscle force production resulting from activation and contraction dynamics while using a general static optimization framework to resolve muscle redundancy. CMC was used to compute muscle excitation patterns that drove a 21-degrees-of-freedom, 92 muscle model to track experimental gait data of 10 healthy young adults. Simulated joint kinematics closely tracked experimental quantities (mean root-mean-squared errors generally less than 1 degrees), and the time histories of muscle activations were similar to electromyographic recordings. A simulation of a half-cycle of gait could be generated using approximately 30 min of computer processing time. The speed and accuracy of REA and CMC make it practical to generate subject-specific simulations of gait.     

Proprioception, gait kinematics, and rate of loading during walking: are they related?

The cyclic nature of walking can lead to repetitive stress and associated complications due to the rate of loading (ROL) experienced by the body at the initial contact of the foot with the ground. An individual's gait kinematics at initial contact has been suggested to give rise to the ROL, and a repetitive, high ROL may lead to several disorders, including osteoarthritis. Additionally, proprioception, the feedback signaling of limb position and movement, may play a role in how the foot strikes the ground and thus, the ROL. Our goal was to explore the relationship between proprioception, gait kinematics and ROL. Thirty-eight women were recruited for gait analysis, and the gait characteristics 50 ms prior to and at initial contact were examined. Two proprioception tests, joint angle reproduction and threshold to detect passive motion were used to examine the subject's proprioceptive acuity. Our results indicate that individuals with a larger knee angle (i.e., greater extension) 50 ms prior to initial contact (IC) experience a higher ROL during gait and have poorer proprioceptive scores. However, it remains unclear whether poor proprioception causes a high ROL or if a high ROL damages the mechanoreceptors involved in proprioception, but the apparent relationship is significant and warrants further investigation.     

Muscle work is biased toward energy generation over dissipation in non-level running

This study tested the hypothesis that skeletal muscles generate more mechanical energy in gait tasks that raise the center of mass compared to the mechanical energy they dissipate in gait tasks that lower the center of mass despite equivalent changes in total mechanical energy. Thirteen adults ran on a 10° decline and incline surface at a constant average velocity. Three-dimensional (3D) joint powers were calculated from ground force and 3D kinematic data using inverse dynamics. Joint work was calculated from the power curves and assumed to be due to skeletal muscle–tendon actuators. External work was calculated from the kinematics of the pelvis through the gait cycle. Incline vs. decline running was characterized with smaller ground forces that operated over longer lever arms causing larger joint torques and work from these torques. Total lower extremity joint work was 28% greater in incline vs. decline running (1.32 vs. −1.03 J/kg m, p<0.001). Total lower extremity joint work comprised 86% and 71% of the total external work in incline (1.53 J/kg m) and decline running (−1.45 J/kg m), which themselves were not significantly different (p<0.180). We conjectured that the larger ground forces in decline vs. incline running caused larger accelerations of all body tissues and initiated a greater energy-dissipating response in these tissues compared to their response in incline running. The runners actively lowered themselves less during decline stance and descended farther as projectiles than they lifted themselves during incline stance and ascended as projectiles. These data indicated that despite larger ground forces in decline running, the reduced displacement during downhill stance phases limited the work done by muscle contraction in decline compared to incline running.     

An analytical model for the ergometer rowing: inverse multibody dynamics analysis

A model for the ergometer rowing exercise is presented in this paper. From the quantitative observations of a particular trajectory (motion), the model is used to determine the moment of the forces produced by the muscles about each joint. These forces are evaluated according to the continuous system of equations of motion. An inverse dynamics analysis is performed in order to predict the joint torques developed by the muscles during the execution of the task. An elementary multibody mechanical system is used as an example to discuss the assumptions and procedures adopted.     

Performance assessment of the Terry Fox jogging prosthesis for above-knee amputees

The Terry Fox jogging (TFJ) prosthesis was developed at Chedoke-McMaster Hospital to alleviate the asymmetric jogging pattern experienced by above-knee amputees when attempting to jog with conventional walking prostheses. This prosthesis features a spring-loaded, telescoping shank designed to eliminate any vaulting action and control the trunk motion during stance. The spring is intended to attenuate the impact forces and release its stored energy at push-off to provide momentum transfer to the jogger. This prosthesis was comprehensively assessed in the gait laboratory, by evaluating the kinematics, energy and power flow patterns of an above-knee amputee jogger wearing the TFJ prosthesis. Included in the assessment is the ability of the prosthesis to satisfy a set of relevant design criteria that have been established from non-amputee jogging patterns. An increased swing phase time for the prosthetic limb and the need to have the knee hyperextended throughout the stance phase contributed to an asymmetric jogging style. The telescoping action did lower the amputee's centre of mass, thereby reducing the vaulting effect. However, the spring only imparted a lifting action to the jogger and the ground reaction forces were double those of a non-amputee jogger. These findings clearly indicate a need to redesign the TFJ prosthesis and are being incorporated in the design of a new physiological jogging prosthesis.     

The effects of alignment of an articulated ankle-foot orthosis on lower limb joint kinematics and kinetics during gait in individuals post-stroke

Mechanical tuning of an ankle-foot orthosis (AFO) is important in improving gait in individuals post-stroke. Alignment and resistance are two factors that are tunable in articulated AFOs. The aim of this study was to investigate the effects of changing AFO ankle alignment on lower limb joint kinematics and kinetics with constant dorsiflexion and plantarflexion resistance in individuals post-stroke. Gait analysis was performed on 10 individuals post-stroke under four distinct alignment conditions using an articulated AFO with an ankle joint whose alignment is adjustable in the sagittal plane. Kinematic and kinetic data of lower limb joints were recorded using a Vicon 3-dimensional motion capture system and Bertec split-belt instrumented treadmill. The incremental changes in the alignment of the articulated AFO toward dorsiflexion angles significantly affected ankle and knee joint angles and knee joint moments while walking in individuals post-stroke. No significant differences were found in the hip joint parameters. The alignment of the articulated AFO was suggested to play an important role in improving knee joint kinematics and kinetics in stance through improvement of ankle joint kinematics while walking in individuals post-stroke. Future studies should investigate long-term effects of AFO alignment on gait in the community in individuals post-stroke.     

Attempts to optimise functional electrical stimulation of antagonistic muscles by mathematical modelling

The mathematical relationship between the kinetic data of joint motion and the functional electrical stimulation (FES) voltage of the corresponding antagonistic pair of muscles is given on the basis of a dynamic ankle joint model. The mathematical model is solved with the aid of state variables, while the resulting electrical stimulation voltage is found as a solution of the Volterra integral equation. The calculated stimulation voltage was applied to the plantar and dorsiflexors of the ankle joint of a hemiplegic patient. The measured ground reaction forces and goniograms during walking with and without electrical stimulation showed a significant improvement of the patient's gait. The problems of low saturation muscle force during FES, the need for individual determination of model parameters, nonlinearities of the system and the variability of gait are discussed.