Validation of a model-based inverse kinematics approach based on wearable inertial sensors

Abstract

Wearable inertial measurement units (IMUs) are a promising solution to human motion estimation. Using IMUs 3D orientations, a model-driven inverse kinematics methodology to estimate joint angles is presented. Estimated joint angles were validated against encoder-measured kinematics (robot) and against marker-based kinematics (passive mechanism). Results are promising, with RMS angular errors respectively lower than 3 and 6?deg over a minimum range of motion of 50?deg (robot) and 160?deg (passive mechanism). Moreover, a noise robustness analysis revealed that the model-driven approach reduces the effects of experimental noises, making the proposed technique particularly suitable for application in human motion analysis.     

Temporal-spatial reach parameters derived from inertial sensors correlate to neurodevelopment in toddlers born preterm

Temporal-spatial reach parameters are revealing of upper-limb function in children with motor impairments, but have not been quantified in a toddler population. This work quantitatively characterizes temporal-spatial reach in typically-developing (TD) and very-low-birth-weight (VLBW) preterm toddlers, who are at increased risk of motor impairment. 47 children born VLBW (<1500 g birth-weight; ≤32 weeks gestation) and 22 TD children completed a reaching assessment at 18–22 months of age, adjusted for prematurity. Inertial sensors containing accelerometers, gyroscopes and magnetometers were fixed to toddlers’ wrists while they reached for a cube. Reach time, path length, velocity at contact, peak velocity magnitude and timing, acceleration at contact, and peak acceleration were derived from inertial-sensor and high-speed video data. Preterm children also received the Bayley Scales of Infant Development—3rd Edition (BSID-III). Compared to TD toddlers, preterm toddlers had significantly different reach path length, velocity at contact, peak velocity magnitude and timing, acceleration at contact, and peak acceleration. Among preterm toddlers, decreased reach time (rho = −.346, p = .018), decreased time to peak velocity (r = −.390, p = .007), and increased peak acceleration (r = .298, p = .044) correlated to higher BSID-III fine motor scores. Toddlers with below-average fine motor scores had significantly higher peak and contact velocity. Preterm toddlers demonstrated substantial differences in temporal-spatial reach parameters compared to TD toddlers, and evidence indicated several reach parameters were revealing of function and may be useful as a clinical assessment.     

A smart device inertial-sensing method for gait analysis

The purpose of this study was to establish and cross-validate a method for analyzing gait patterns determined by the center of mass (COM) through inertial sensors embedded in smart devices. The method employed an extended Kalman filter in conjunction with a quaternion rotation matrix approach to transform accelerations from the object onto the global frame. Derived by double integration, peak-to-trough changes in vertical COM position captured by a motion capture system, inertial measurement unit, and smart device were compared in terms of averaged and individual steps. The inter-rater reliability and levels of agreement for systems were discerned through intraclass correlation coefficients (ICC) and Bland–Altman plots. ICCs corresponding to inter-rater reliability were good-to-excellent for position data (ICCs,.80–.95) and acceleration data (ICCs,.54–.81). Levels of agreements were moderate for position data (LOA, 3.1–19.3%) and poor for acceleration data (LOA, 6.8%–17.8%). The Bland–Altman plots, however, revealed a small systematic error, in which peak-to-trough changes in vertical COM position were underestimated by 2.2 mm; the Kalman filter?s accuracy requires further investigation to minimize this oversight. More importantly, however, the study?s preliminary results indicate that the smart device allows for reliable COM measurements, opening up a cost-effective, user-friendly, and popular solution for remotely monitoring movement. The long-term impact of the smart device method on patient rehabilitation and therapy cannot be underestimated: not only could healthcare expenditures be curbed (smart devices being more affordable than today‘s motion sensors), but a more refined grasp of individual functioning, activity, and participation within everyday life could be attained.     

Multi-sensor assessment of dynamic balance during gait in patients with subacute stroke

The capacity to maintain upright balance by minimising upper body oscillations during walking, also referred to as gait stability, has been associated with a decreased risk of fall. Although it is well known that fall is a common complication after stroke, no study considered the role of both trunk and head when assessing gait stability in this population. The primary aim of this study was to propose a multi-sensor protocol to quantify gait stability in patients with subacute stroke using gait quality indices derived from pelvis, sternum, and head accelerations. Second, the association of these indices with the level of walking ability, with traditional clinical scale scores, and with fall events occurring within the six months after patients’ dismissal was investigated. The accelerations corresponding to the three abovementioned body levels were measured using inertial sensors during a 10-Meter Walk Test performed by 45 inpatients and 25 control healthy subjects. A set of indices related to gait stability were estimated and clinical performance scales were administered to each patient. The amplitude of the accelerations, the way it is attenuated/amplified from lower to upper body levels, and the gait symmetry provide valuable information about subject-specific motor strategies, discriminate between different levels of walking ability, and correlate with clinical scales. In conclusion, the proposed multi-sensor protocol could represent a useful tool to quantify gait stability, support clinicians in the identification of patients potentially exposed to a high risk of falling, and assess the effectiveness of rehabilitation protocols in the clinical routine.     

The development and concurrent validity of a real-time algorithm for temporal gait analysis using inertial measurement units

The use of inertial measurement units (IMUs) for gait analysis has emerged as a tool for clinical applications. Shank gyroscope signals have been utilized to identify heel-strike and toe-off, which serve as the foundation for calculating temporal parameters of gait such as single and double limb support time. Recent publications have shown that toe-off occurs later than predicted by the dual minima method (DMM), which has been adopted as an IMU-based gait event detection algorithm. In this study, a real-time algorithm, Noise-Zero Crossing (NZC), was developed to accurately compute temporal gait parameters. Our objective was to determine the concurrent validity of temporal gait parameters derived from the NZC algorithm against parameters measured by an instrumented walkway. The accuracy and precision of temporal gait parameters derived using NZC were compared to those derived using the DMM. The results from Bland-Altman Analysis showed that the NZC algorithm had excellent agreement with the instrumented walkway for identifying the temporal gait parameters of Gait Cycle Time (GCT), Single Limb Support (SLS) time, and Double Limb Support (DLS) time. By utilizing the moment of zero shank angular velocity to identify toe-off, the NZC algorithm performed better than the DMM algorithm in measuring SLS and DLS times. Utilizing the NZC algorithm’s gait event detection preserves DLS time, which has significant clinical implications for pathologic gait assessment.     

A general model for estimating lower extremity inertial properties of individuals with transtibial amputation

Lower extremity joint moment magnitudes during swing are dependent on the inertial properties of the prosthesis and residual limb of individuals with transtibial amputation (TTA). Often, intact limb inertial properties (INTACT) are used for prosthetic limb values in an inverse dynamics model even though these values overestimate the amputated limb’s inertial properties. The purpose of this study was to use subject-specific (SPECIFIC) measures of prosthesis inertial properties to generate a general model (GENERAL) for estimating TTA prosthesis inertial properties. Subject-specific mass, center of mass, and moment of inertia were determined for the shank and foot segments of the prosthesis (n = 11) using an oscillation technique and reaction board. The GENERAL model was derived from the means of the SPECIFIC model. Mass and segment lengths are required GENERAL model inputs. Comparisons of segment inertial properties and joint moments during walking were made using three inertial models (unique sample; n = 9): (1) SPECIFIC, (2) GENERAL, and (3) INTACT. Prosthetic shank inertial properties were significantly smaller with the SPECIFIC and GENERAL model than the INTACT model, but the SPECIFIC and GENERAL model did not statistically differ. Peak knee and hip joint moments during swing were significantly smaller for the SPECIFIC and GENERAL model compared with the INTACT model and were not significantly different between SPECIFIC and GENERAL models. When subject-specific measures are unavailable, using the GENERAL model produces a better estimate of prosthetic side inertial properties resulting in more accurate joint moment measurements for individuals with TTA than the INTACT model.     

Overcoming the limitations of the Harmonic Ratio for the reliable assessment of gait symmetry

The Harmonic Ratio (HR) is an index based on the spectral analysis of lower trunk accelerations that is commonly used to assess the quality of gait. However, it presents several issues concerning reliability and interpretability. As a consequence, the literature provides very different values albeit corresponding to the same populations. In the present work, an improved harmonic ratio (iHR) was defined, relating the power of the intrinsic harmonics (i.e. associated with the symmetric component of gait) to the total power of the signal for each stride, leading to a normalised index ranging from 0 to 100%. The effect of the considered number of harmonics and strides on the estimate of both HR and iHR was assessed. The gait of three groups of volunteers was investigated: young healthy adults, elderly women and male trans-femoral amputees. Both HR and iHR were able to discriminate gait deviations from the gait of young healthy adults. Moreover, iHR proved to be more robust with respect to the number of considered harmonics and strides, and to exhibit a lower inter-stride variability. Additionally, using a normalised index as iHR led to a more straightforward interpretation and improved comparability. The importance of standardised conditions for the index evaluation was unveiled, and, in order to enhance the future comparability of the index, the following guidelines were presented: considering at least 20 harmonics and 20 strides; expressing the acceleration components in a repeatable, anatomical, local system of reference; and evaluating the iHR index, rather than the traditional HR.     

Functional calibration procedure for 3D knee joint angle description using inertial sensors

Measurement of three-dimensional (3D) knee joint angle outside a laboratory is of benefit in clinical examination and therapeutic treatment comparison. Although several motion capture devices exist, there is a need for an ambulatory system that could be used in routine practice. Up-to-date, inertial measurement units (IMUs) have proven to be suitable for unconstrained measurement of knee joint differential orientation. Nevertheless, this differential orientation should be converted into three reliable and clinically interpretable angles. Thus, the aim of this study was to propose a new calibration procedure adapted for the joint coordinate system (JCS), which required only IMUs data. The repeatability of the calibration procedure, as well as the errors in the measurement of 3D knee angle during gait in comparison to a reference system were assessed on eight healthy subjects. The new procedure relying on active and passive movements reported a high repeatability of the mean values (offset<1°) and angular patterns (SD<0.3° and CMC>0.9). In comparison to the reference system, this functional procedure showed high precision (SD<2° and CC>0.75) and moderate accuracy (between 4.0° and 8.1°) for the three knee angle. The combination of the inertial-based system with the functional calibration procedure proposed here resulted in a promising tool for the measurement of 3D knee joint angle. Moreover, this method could be adapted to measure other complex joint, such as ankle or elbow.     

Estimation of manual wheelchair-based activities in the free-living environment using a neural network model with inertial body-worn sensors

Shoulder pain is common in manual wheelchair (MWC) users. Overuse is thought to be a major cause, but little is known about exposure to activities of daily living (ADLs). The study goal was to develop a method to estimate three conditions in the field: (1) non-propulsion activity, (2) MWC propulsion, and (3) static time using an inertial measurement unit (IMU).Upper arm IMU data were collected as ten MWC users performed lab-based MWC-related ADLs. A neural network model was developed to classify data as non-propulsion activity, propulsion, or static, and validated for the lab-based data collection by video comparison. Six of the participants’ free-living IMU data were collected and the lab-based model was applied to estimate daily non-propulsion activity, propulsion, and static time.The neural network model yielded lab-based validity measures ≥0.87 for differentiating non-propulsion activity, propulsion, and static time. A quasi-validation of one participant’s field-based data yielded validity measures ≥0.66 for identifying propulsion. Participants’ estimated mean daily non-propulsion activity, propulsion, and static time ranged from 158 to 409, 13 to 25, and 367 to 609 min, respectively. The preliminary results suggest the model may be able to accurately identify MWC users’ field-based activities. The inclusion of field-based IMU data in the model could further improve field-based classification.     

A constrained extended Kalman filter for the optimal estimate of kinematics and kinetics of a sagittal symmetric exercise

This paper presents a method for real-time estimation of the kinematics and kinetics of a human body performing a sagittal symmetric motor task, which would minimize the impact of the stereophotogrammetric soft tissue artefacts (STA). The method is based on a bi-dimensional mechanical model of the locomotor apparatus the state variables of which (joint angles, velocities and accelerations, and the segments lengths and inertial parameters) are estimated by a constrained extended Kalman filter (CEKF) that fuses input information made of both stereophotogrammetric and dynamometric measurement data. Filter gains are made to saturate in order to obtain plausible state variables and the measurement covariance matrix of the filter accounts for the expected STA maximal amplitudes. We hypothesised that the ensemble of constraints and input redundant information would allow the method to attenuate the STA propagation to the end results. The method was evaluated in ten human subjects performing a squat exercise. The CEKF estimated and measured skin marker trajectories exhibited a RMS difference lower than 4 mm, thus in the range of STAs. The RMS differences between the measured ground reaction force and moment and those estimated using the proposed method (9 N and 10 N m) were much lower than obtained using a classical inverse dynamics approach (22 N and 30 N m). From the latter results it may be inferred that the presented method allows for a significant improvement of the accuracy with which kinematic variables and relevant time derivatives, model parameters and, therefore, intersegmental moments are estimated.     

Classification of deadlift biomechanics with wearable inertial measurement units

The deadlift is a compound full-body exercise that is fundamental in resistance training, rehabilitation programs and powerlifting competitions. Accurate quantification of deadlift biomechanics is important to reduce the risk of injury and ensure training and rehabilitation goals are achieved. This study sought to develop and evaluate deadlift exercise technique classification systems utilising Inertial Measurement Units (IMUs), recording at 51.2 Hz, worn on the lumbar spine, both thighs and both shanks. It also sought to compare classification quality when these IMUs are worn in combination and in isolation. Two datasets of IMU deadlift data were collected. Eighty participants first completed deadlifts with acceptable technique and 5 distinct, deliberately induced deviations from acceptable form. Fifty-five members of this group also completed a fatiguing protocol (3-Repition Maximum test) to enable the collection of natural deadlift deviations. For both datasets, universal and personalised random-forests classifiers were developed and evaluated. Personalised classifiers outperformed universal classifiers in accuracy, sensitivity and specificity in the binary classification of acceptable or aberrant technique and in the multi-label classification of specific deadlift deviations. Whilst recent research has favoured universal classifiers due to the reduced overhead in setting them up for new system users, this work demonstrates that such techniques may not be appropriate for classifying deadlift technique due to the poor accuracy achieved. However, personalised classifiers perform very well in assessing deadlift technique, even when using data derived from a single lumbar-worn IMU to detect specific naturally occurring technique mistakes.     

A novel method for assessing the 3-D orientation accuracy of inertial/magnetic sensors

A novel method for assessing the accuracy of inertial/magnetic sensors is presented. The method, referred to as the “residual matrix” method, is advantageous because it decouples the sensor's error with respect to Earth's gravity vector (attitude residual error: pitch and roll) from the sensor's error with respect to magnetic north (heading residual error), while remaining insensitive to singularity problems when the second Euler rotation is close to ±90°. As a demonstration, the accuracy of an inertial/magnetic sensor mounted to a participant's forearm was evaluated during a reaching task in a laboratory. Sensor orientation was measured internally (by the inertial/magnetic sensor) and externally using an optoelectronic measurement system with a marker cluster rigidly attached to the sensor's enclosure. Roll, pitch and heading residuals were calculated using the proposed novel method, as well as using a common orientation assessment method where the residuals are defined as the difference between the Euler angles measured by the inertial sensor and those measured by the optoelectronic system. Using the proposed residual matrix method, the roll and pitch residuals remained less than 1° and, as expected, no statistically significant difference between these two measures of attitude accuracy was found; the heading residuals were significantly larger than the attitude residuals but remained below 2°. Using the direct Euler angle comparison method, the residuals were in general larger due to singularity issues, and the expected significant difference between inertial/magnetic sensor attitude and heading accuracy was not present.     

Statistical method for prediction of gait kinematics with Gaussian process regression

We propose a novel methodology for predicting human gait pattern kinematics based on a statistical and stochastic approach using a method called Gaussian process regression (GPR). We selected 14 body parameters that significantly affect the gait pattern and 14 joint motions that represent gait kinematics. The body parameter and gait kinematics data were recorded from 113 subjects by anthropometric measurements and a motion capture system. We generated a regression model with GPR for gait pattern prediction and built a stochastic function mapping from body parameters to gait kinematics based on the database and GPR, and validated the model with a cross validation method. The function can not only produce trajectories for the joint motions associated with gait kinematics, but can also estimate the associated uncertainties. Our approach results in a novel, low-cost and subject-specific method for predicting gait kinematics with only the subject's body parameters as the necessary input, and also enables a comprehensive understanding of the correlation and uncertainty between body parameters and gait kinematics.     

Compensation for inertial and gravity effects in a moving force platform

Force plates for human movement analysis provide accurate measurements when mounted rigidly on an inertial reference frame. Large measurement errors occur, however, when the force plate is accelerated, or tilted relative to gravity. This prohibits the use of force plates in human perturbation studies with controlled surface movements, or in conditions where the foundation is moving or not sufficiently rigid. Here we present a linear model to predict the inertial and gravitational artifacts using accelerometer signals. The model is first calibrated with data collected from random movements of the unloaded system and then used to compensate for the errors in another trial. The method was tested experimentally on an instrumented force treadmill capable of dynamic mediolateral translation and sagittal pitch. The compensation was evaluated in five experimental conditions, including platform motions induced by actuators, by motor vibration, and by human ground reaction forces. In the test that included all sources of platform motion, the root-mean-square (RMS) errors were 39.0 N and 15.3 N m in force and moment, before compensation, and 1.6 N and 1.1 N m, after compensation. A sensitivity analysis was performed to determine the effect on estimating joint moments during human gait. Joint moment errors in hip, knee, and ankle were initially 53.80 N m, 32.69 N m, and 19.10 N m, and reduced to 1.67 N m, 1.37 N m, and 1.13 N m with our method. It was concluded that the compensation method can reduce the inertial and gravitational artifacts to an acceptable level for human gait analysis.     

Real-time inverse kinematics and inverse dynamics for lower limb applications using OpenSim

Real-time estimation of joint angles and moments can be used for rapid evaluation in clinical, sport, and rehabilitation contexts. However, real-time calculation of kinematics and kinetics is currently based on approximate solutions or generic anatomical models. We present a real-time system based on OpenSim solving inverse kinematics and dynamics without simplifications at 2000 frame per seconds with less than 31.5 ms of delay. We describe the software architecture, sensitivity analyses to minimise delays and errors, and compare offline and real-time results. This system has the potential to strongly impact current rehabilitation practices enabling the use of personalised musculoskeletal models in real-time.     

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 a novel gait retraining device on lower limb kinematics and muscle activation in healthy adults

The Re-Link Trainer (RLT) is a modified walking frame with a linkage system designed to apply a non-individualized kinematic constraint to normalize gait trajectory of the left limb. The premise behind the RLT is that a user’s lower limb is constrained into a physiologically normal gait pattern, ideally generating symmetry across gait cycle parameters and kinematics. This pilot study investigated adaptations in the natural gait pattern of healthy adults when using the RLT compared to normal overground walking. Bilateral lower limb kinematic and electromyography data were collected while participants walked overground at a self-selected speed, followed by walking in the RLT. A series of 2-way analyses of variance examined between-limb and between-condition differences. Peak hip extension and knee flexion were reduced bilaterally when walking in the RLT. Left peak hip extension occurred earlier in the gait cycle when using the RLT, but later for the right limb. Peak hip flexion was significantly increased and occurred earlier for the constrained limb, while peak plantarflexion was significantly reduced. Peak knee flexion and plantarflexion in the right limb occurred later when using the RLT. Significant bilateral reductions in peak electromyography amplitude were evident when walking in the RLT, along with a significant shift in when peak muscle activity was occurring. These findings suggest that the RLT does impose a significant constraint, but generates asymmetries in lower limb kinematics and muscle activity patterns. The large interindividual variation suggests users may utilize differing motor strategies to adapt their gait pattern to the imposed constraint.     

Tibiofemoral kinematics and condylar motion during the stance phase of gait

Accurate knowledge of the dynamic knee motion in-vivo is instrumental for understanding normal and pathological function of the knee joint. However, interpreting motion of the knee joint during gait in other than the sagittal plane remains controversial. In this study, we utilized the dual fluoroscopic imaging technique to investigate the six-degree-of-freedom kinematics and condylar motion of the knee during the stance phase of treadmill gait in eight healthy volunteers at a speed of 0.67 m/s. We hypothesized that the 6DOF knee kinematics measured during gait will be different from those reported for non-weightbearing activities, especially with regards to the phenomenon of femoral rollback. In addition, we hypothesized that motion of the medial femoral condyle in the transverse plane is greater than that of the lateral femoral condyle during the stance phase of treadmill gait. The rotational motion and the anterior–posterior translation of the femur with respect to the tibia showed a clear relationship with the flexion–extension path of the knee during the stance phase. Additionally, we observed that the phenomenon of femoral rollback was reversed, with the femur noted to move posteriorly with extension and anteriorly with flexion. Furthermore, we noted that motion of the medial femoral condyle in the transverse plane was greater than that of the lateral femoral condyle during the stance phase of gait (17.4±2.0 mm vs. 7.4±6.1 mm, respectively; p<0.01). The trend was opposite to what has been observed during non-weightbearing flexion or single-leg lunge in previous studies. These data provide baseline knowledge for the understanding of normal physiology and for the analysis of pathological function of the knee joint during walking. These findings further demonstrate that knee kinematics is activity-dependent and motion patterns of one activity (non-weightbearing flexion or lunge) cannot be generalized to interpret a different one (gait).