Inertial compensation for belt acceleration in an instrumented treadmill

Instrumented treadmills provide a convenient means for applying horizontal perturbations during gait or standing. However, varying the treadmill belt speed introduces inertial artifacts in the sagittal plane moment component of the ground reaction force. Here we present a compensation method based on a second-order dynamic model that predicts inertial pitch moment from belt acceleration. The method was tested experimentally on an unloaded treadmill at a slow belt speed with small random variations (1.20±0.10 m/s) and at a faster belt speed with large random variations (2.00±0.50 m/s). Inertial artifacts of up to 12 Nm (root-mean-square, RMS) and 30 Nm (peak) were observed. Coefficients of the model were calibrated on one trial and then used to predict and compensate the pitch moment of another trial with different random variations. Coefficients of determination (R²$R^2$) were 72.08% and 96.75% for the slow and fast conditions, respectively. After compensation, the root-mean-square (RMS) of the inertial artifact was reduced by 47.37% for the slow speed and 81.98% for fast speed, leaving only 1.5 Nm and 2.1 Nm of artifact uncorrected, respectively. It was concluded that the compensation technique reduced inertial errors substantially, thereby improving the accuracy in joint moment calculations on an instrumented treadmill with varying belt speed.     

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.     

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

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

Correction of the inertial effect resulting from a plate moving under low-friction conditions

The purpose of the present study was to develop a set of equations that can be employed to remove the inertial effect introduced by the movable platform upon which a person stands during a slip induced in gait; this allows the real ground reaction force (GRF) and its center of pressure (COP) to be determined. Analyses were also performed to determine how sensitive the COP offsets were to the changes of the parameters in the equation that affected the correction of the inertial effect. In addition, the results were verified empirically using a low friction movable platform together with a stationary object, a pendulum, and human subjects during a slip induced during gait. Our analyses revealed that the amount of correction required for the inertial effect due to the movable component is affected by its mass and its center of mass (COM) position, acceleration, the friction coefficient, and the landing position of the foot relative to the COM. The maximum error in the horizontal component of the GRF was close to 0.09 (body weight) during the recovery from a slip in walking. When uncorrected, the maximum error in the COP measurement could reach as much as 4 cm. Finally, these errors were magnified in the joint-moment computation and propagated proximally, ranging from 0.2 to 1.0 Nm/body mass from the ankle to the hip.     

Validity of the top-down approach of inverse dynamics analysis in fast and large rotational trunk movements

This study investigated the validity of the top-down approach of inverse dynamics analysis in fast and large rotational movements of the trunk about three orthogonal axes of the pelvis for nine male collegiate students. The maximum angles of the upper trunk relative to the pelvis were approximately 47°, 49°, 32°, and 55° for lateral bending, flexion, extension, and axial rotation, respectively, with maximum angular velocities of 209°/s, 201°/s, 145°/s, and 288°/s, respectively. The pelvic moments about the axes during the movements were determined using the top-down and bottom-up approaches of inverse dynamics and compared between the two approaches. Three body segment inertial parameter sets were estimated using anthropometric data sets (Ae et al., Biomechanism 11, 1992; De Leva, J Biomech, 1996; Dumas et al., J Biomech, 2007). The root-mean-square errors of the moments and the absolute errors of the peaks of the moments were generally smaller than 10 N·m. The results suggest that the pelvic moment in motions involving fast and large trunk movements can be determined with a certain level of validity using the top-down approach in which the trunk is modeled as two or three rigid-link segments.     

1-D blood flow modelling in a running human body

In this paper an attempt was made to simulate blood flow in a mobile human arterial network, specifically, in a running human subject. In order to simulate the effect of motion, a previously published immobile 1-D model was modified by including an inertial force term into the momentum equation. To calculate inertial force, gait analysis was performed at different levels of speed. Our results show that motion has a significant effect on the amplitudes of the blood pressure and flow rate but the average values are not effected significantly.     

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.     

Kinematic and kinetic changes in obese gait in bariatric surgery-induced weight loss

This study examines the effects of a radical bariatric surgery-induced weight loss on the gait of obese subjects. We performed a three-dimensional motion analysis of lower limbs, and collected force platform data in the gait laboratory to calculate knee and hip joint moments. Subjects (n=13) performed walking trials in the laboratory before and 8.8 months (SD 4.2) after the surgical procedure at two gait speeds (1.2m/s and 1.5m/s). The average weight loss was 26.7kg (SD 9.2kg), corresponding to 21.5% (SD 6.8%) of the initial weight. We observed a decrease in step width at both gait speeds, but no changes in relative double support or swing time or stride length. A significant decrease was noted in the absolute values of peak knee abductor, peak knee flexor and peak hip extensor moments. However, the moment values normalized by the body weight and height remained unchanged in most cases. Thus, we conclude that weight loss reduces hip and knee joint moments in proportion to the amount of weight lost.     

Increased hip internal abduction moment and reduced speed are the gait strategies used by women with knee osteoarthritis

The purpose of this study was to identify the gait strategies in women with mild and moderate knee osteoarthritis (OA). Forty women diagnosed with OA of the knee and 40 healthy women participated in the study. Toe-out progression angle, trunk lateral lean, hip internal abduction moment and gait speed were measured using Qualisys ProReflex System and two force plates. Principal component analysis was applied to extract features from the gait waveforms data that characterized the waveforms main modes of temporal variation. Discriminant analysis with a stepwise model was conducted to determine which strategies could best discriminate groups. According to the discriminant model, the PC2 of the internal abduction moment of the hip and the gait speed were the most discriminatory variables between the groups. The OA group showed decreased gait speed, decreased hip internal abduction moment during the loading response phase, and increased hip internal abduction moment during the mid and terminal stance phases. Interventions that may increase hip internal abduction moment, such as the strengthening of the hip abductors muscles, may benefit women with knee OA. Training slower than normal gait speeds must be considered in light of potential adverse implications on overall physical function, daily tasks, and safety.     

The relationship between joint kinetic factors and the walk-run gait transition speed during human locomotion

The primary purpose of this project was to examine whether lower extremity joint kinetic factors are related to the walk-run gait transition during human locomotion. Following determination of the preferred transition speed (PTS), each of the 16 subjects walked down a 25-m runway, and over a floor-mounted force platform at five speeds (70, 80, 90, 100, and 110% of the PTS), and ran over the force platform at three speeds (80, 100, and 120% of the PTS) while being videotaped (240 Hz) from the right sagittal plane. Two-dimensional kinematic data were synchronized with ground reaction force data (960 Hz). After smoothing, ankle and knee joint moments and powers were calculated using standard inverse dynamics calculations. The maximum dorsiflexor moment was the only variable tested that increased as walking speed increased and then decreased when gait changed to a run at the PTS, meeting the criteria set to indicate that this variable influences the walk-run gait transition during human locomotion. This supports previous research suggesting that an important factor in changing gaits at the PTS is the prevention of undue stress in the dorsiflexor muscles.     

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.     

A simple method to estimate force plate inertial components in a moving surface

Support surface perturbations are a common paradigm for the study of balance and postural control. Forces and moments acquired from force plates mounted on, or within, the moving surface will contain components resulting from the inertia of the force plate itself. These force plate inertial components must be removed in order to accurately estimate forces resulting from contact with the force plate. This is particularly important when these contact forces are to be used in further calculations, such as an inverse dynamics analysis of joint kinetics. An estimate of the FPIC can be derived using the kinematics of the moving surface and the inertial properties of the force plate. This technique allowed for a reduction of up to 85% of the peak and integrated FPIC acquired from AMTI (OR6-7) force plates during translations of 0.1m, and surface rotations of 10 degrees, using a ramp stimulus of 150 ms duration.     

Cross-validation of a portable,six-degree-of-freedom load cell for use in lower-limb prosthetics research

The iPecs™ load cell is a lightweight, six-degree-of-freedom force transducer designed to fit easily into an endoskeletal prosthesis via a universal mounting interface. Unlike earlier tethered systems, it is capable of wireless data transmission and on-board memory storage, which facilitate its use in both clinical and real-world settings. To date, however, the validity of the iPecs™ load cell has not been rigorously established, particularly for loading conditions that represent typical prosthesis use. The aim of this study was to assess the accuracy of an iPecs™ load cell during in situ human subject testing by cross-validating its force and moment measurements with those of a typical gait analysis laboratory. Specifically, the gait mechanics of a single person with transtibial amputation were simultaneously measured using an iPecs™ load cell, multiple floor-mounted force platforms, and a three-dimensional motion capture system. Overall, the forces and moments measured by the iPecs™ were highly correlated with those measured by the gait analysis laboratory (r>0.86) and RMSEs were less than 3.4% and 5.2% full scale output across all force and moment channels, respectively. Despite this favorable comparison, however, the results of a sensitivity analysis suggest that care should be taken to accurately identify the axes and instrumentation center of the load cell in situations where iPecs™ data will be interpreted in a coordinate system other than its own (e.g., inverse dynamics analysis).     

Novel approach to ambulatory assessment of human segmental orientation on a wearable sensor system

A new method using a double-sensor difference based algorithm for analyzing human segment rotational angles in two directions for segmental orientation analysis in the three-dimensional (3D) space was presented. A wearable sensor system based only on triaxial accelerometers was developed to obtain the pitch and yaw angles of thigh segment with an accelerometer approximating translational acceleration of the hip joint and two accelerometers measuring the actual accelerations on the thigh. To evaluate the method, the system was first tested on a 2° of freedom mechanical arm assembled out of rigid segments and encoders. Then, to estimate the human segmental orientation, the wearable sensor system was tested on the thighs of eight volunteer subjects, who walked in a straight forward line in the work space of an optical motion analysis system at three self-selected speeds: slow, normal and fast. In the experiment, the subject was assumed to walk in a straight forward way with very little trunk sway, skin artifacts and no significant internal/external rotation of the leg. The root mean square (RMS) errors of the thigh segment orientation measurement were between 2.4° and 4.9° during normal gait that had a 45° flexion/extension range of motion. Measurement error was observed to increase with increasing walking speed probably because of the result of increased trunk sway, axial rotation and skin artifacts. The results show that, without integration and switching between different sensors, using only one kind of sensor, the wearable sensor system is suitable for ambulatory analysis of normal gait orientation of thigh and shank in two directions of the segment-fixed local coordinate system in 3D space. It can then be applied to assess spatio-temporal gait parameters and monitoring the gait function of patients in clinical settings.     

Estimation of stride length in level walking using an inertial measurement unit attached to the foot: a validation of the zero velocity assumption during stance

In a variety of applications, inertial sensors are used to estimate spatial parameters by double integrating over time their coordinate acceleration components. In human movement applications, the drift inherent to the accelerometer signals is often reduced by exploiting the cyclical nature of gait and under the hypothesis that the velocity of the sensor is zero at some point in stance. In this study, the validity of the latter hypothesis was investigated by determining the minimum velocity of progression of selected points of the foot and shank during the stance phase of the gait cycle while walking at three different speeds on level ground. The errors affecting the accuracy of the stride length estimation resulting from assuming a zero velocity at the beginning of the integration interval were evaluated on twenty healthy subjects. Results showed that the minimum velocity of the selected points on the foot and shank increased as gait speed increased. Whereas the average minimum velocity of the foot locations was lower than 0.011 m/s, the velocity of the shank locations were up to 0.049 m/s corresponding to a percent error of the stride length equal to 3.3%. The preferable foot locations for an inertial sensor resulted to be the calcaneus and the lateral aspect of the rearfoot. In estimating the stride length, the hypothesis that the velocity of the sensor can be set to zero sometimes during stance is acceptable only if the sensor is attached to the foot.     

The differences in sagittal plane whole-body angular momentum during gait between patients with hemiparesis and healthy people

Regulation of whole-body angular momentum (WBAM) is essential for maintaining dynamic balance during gait. Patients with hemiparesis frequently fall toward the anterior direction; however, whether this is due to impaired WBAM control in the sagittal plane during gait remains unknown. The present study aimed to investigate the differences in WBAM in the sagittal plane during gait between patients with hemiparesis and healthy individuals. Thirty-three chronic stroke patients with hemiparesis and twenty-two age- and gender-matched healthy controls walked along a 7-m walkway while gait data were recorded using a motion analysis system and force plates. WBAM and joint moment were calculated in the sagittal plane during each gait cycle. The range of WBAM in the sagittal plane in the second half of the paretic gait cycle was significantly larger than that in the first and second halves of the right gait cycle in the controls (P = 0.015 and P = 0.011). Furthermore, multiple regression analysis revealed the slower walking speed (P < 0.001) and larger knee extension moment on the non-paretic side (P = 0.003) contributed to the larger range of WBAM in the sagittal plane in the second half of the paretic gait cycle. Our findings suggest that dynamic stability in the sagittal plane is impaired in the second half of the paretic gait cycle. In addition, the large knee extension moment on the non-paretic side might play a role in the dynamic instability in the sagittal plane during gait in patients with hemiparesis.     

Knee Adduction Moment and Medial Contact Force – Facts about Their Correlation during Gait

The external knee adduction moment is considered a surrogate measure for the medial tibiofemoral contact force and is commonly used to quantify the load reducing effect of orthopedic interventions. However, only limited and controversial data exist about the correlation between adduction moment and medial force. The objective of this study was to examine whether the adduction moment is indeed a strong predictor for the medial force by determining their correlation during gait. Instrumented knee implants with telemetric data transmission were used to measure tibiofemoral contact forces in nine subjects. Gait analyses were performed simultaneously to the joint load measurements. Skeletal kinematics, as well as the ground reaction forces and inertial parameters, were used as inputs in an inverse dynamics approach to calculate the external knee adduction moment. Linear regression analysis was used to analyze the correlation between adduction moment and medial force for the whole stance phase and separately for the early and late stance phase. Whereas only moderate correlations between adduction moment and medial force were observed throughout the whole stance phase (R² = 0.56) and during the late stance phase (R² = 0.51), a high correlation was observed at the early stance phase (R² = 0.76). Furthermore, the adduction moment was highly correlated to the medial force ratio throughout the whole stance phase (R² = 0.75). These results suggest that the adduction moment is a surrogate measure, well-suited to predicting the medial force ratio throughout the whole stance phase or medial force during the early stance phase. However, particularly during the late stance phase, moderate correlations and high inter-individual variations revealed that the predictive value of the adduction moment is limited. Further analyses are necessary to examine whether a combination of other kinematic, kinetic or neuromuscular factors may lead to a more reliable prediction of the force magnitude.     

Ensemble averaging and multiple statistical testing of EMG activities of cyclically repeated body motions. A tool for muscle function analysis in experimental and clinical orthopaedics.

Coupled with suitable computerized signal recording and processing methods surface electromyography can be a powerful tool for the analysis of muscle activity in specific body movements. It can be used for this purpose in experimental and in clinical diagnostic orthopaedics as well as in physiotherapy. We describe in this paper a motion analysis system comprising this feature. It has been employed for the diagnosis of the basic angular kinematics and muscle function in human gait and other cyclically repeatable movements of the human locomotive system. Changes in the temporal characteristics of the movements and the muscle activity due to changed physical or experimental conditions can be systematically investigated this way. Such changes can be the result of surgical and/or conservative orthopaedic therapy, a long term physiotherapeutic program, or modified walking conditions as in experimental orthopaedics. They are displayed and validated by signal ensemble averaging and subsequent multiple statistical testing (e.g. by a suitably adapted Bonferroni criterion). The efficiency of the system is demonstrated by an exemplary gait analysis of selected kinematic and muscular effects caused by an experimental simulation of a leg length inequality.     

Whole body inverse dynamics over a complete gait cycle based only on measured kinematics

This paper presents a three-dimensional (3D) whole body multi-segment model for inverse dynamics analysis over a complete gait cycle, based only on measured kinematic data. The sequence of inverse dynamics calculations differs significantly from the conventional application of inverse dynamics using force plate data. A new validated "Smooth Transition Assumption" was used to solve the indeterminacy problem in the double support phase. Kinematic data is required for all major body segments and, hence, a whole body gait measurement protocol is presented. Finally, sensitivity analyses were conducted to evaluate the effects of digital filtering and body segment parameters on the accuracy of the prediction results. The model gave reasonably good estimates of sagittal plane ground forces and moment; however, the estimates in the other planes were less good, which we believe is largely due to their small magnitudes in comparison to the sagittal forces and moment. The errors observed are most likely caused by errors in the kinematic data resulting from skin movement artefact and by errors in the estimated body segment parameters. A digital filtering cut-off frequency of 4.5Hz was found to produce the best results. It was also shown that errors in the mass properties of body segments can play a crucial role, with changes in properties sometimes having a disproportionate effect on the calculated ground reactions. The implication of these results is that, even when force plate data is available, the estimated joint forces are likely to suffer from similar errors.     

Keep on your toes: gait initiation from toe-standing

Gait initiation from toe-standing is common in patients with upper motor neurone (UMN) pathology as well as in able-bodied subjects during certain dance and athletic situations. It is unclear whether balance problems in patients who toe-walk are due to the underlying pathology, or due to initiating gait from toe-standing. The aim of this study was to compare the biomechanics of gait initiation from toe-standing to that from heel-toe standing in healthy able-bodied subjects. Data were collected for three seconds prior to, and three seconds after, a visual signal to initiate gait. Ground reaction force and centre of pressure (COP) data were collected with an AMTI force platform, and electromyographic and kinematic data were collected from each limb with a Vicon motion analysis system. When initiating gait from toe-standing, there was a smaller backward displacement of the COP compared to heel-toe standing. In addition, greater forward momentum was generated, and there was an increase in gastrocnemius, rectus femoris and biceps femoris muscle activity. There were no differences in COP displacement or momentum generated in the mediolateral direction for the two conditions. Thus, initiating gait from toe-standing allows one to generate greater amounts of forward momentum but not at the expense of generating excessive stance-side momentum. This may be an advantageous method of initiating movement for dancers and athletes in certain situations. This work also suggests that balance problems in patients with UMN pathology are likely due to the underlying pathology and are not due to initiating gait from toe-standing.