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.     

MRI-derived body segment parameters of children differ from age-based estimates derived using photogrammetry

Body segment parameters are required when researching joint kinetics using inverse dynamics models. However, the only regression equations for estimating pediatric body segment parameters across a wide age range were developed, using photogrammetry, based on 12 boys and have not been validated to date (Jensen, R.K., 1986. Body segment mass, radius and radius of gyration proportions of children. Journal of Biomechanics 19, 359–368). To assess whether these equations could validly be applied to girls, we asked whether body segment parameters estimated by the equations differ from parameters measured using a validated magnetic resonance imaging (MRI) method. If so, do the differences cause significant differences in joint kinetics during normal gait? Body segment parameters were estimated from axial MRIs of the left thigh and shank of 10 healthy girls (9.6±0.9 years) and compared to those from Jensen's equations. Kinematics and kinetics were collected for 10 walking trials. Extrema in hip and knee moments and powers were compared between the two sets of body segment parameters. With the exception of the shank mass center and radius of gyration, body segment parameters measured using MRI were significantly different from those estimated using regression equations. These systematic differences in body segment parameters resulted in significant differences in sagittal-plane joint moments and powers during gait. Nevertheless, it is doubtful that even the greatest differences in kinetics are practically meaningful (0.3%BW×HT and 0.7%BW×HT/s for moments and power at the hip, respectively). Therefore, body segment parameters estimated using Jensen's regression equations are a suitable substitute for more detailed anatomical imaging of 8–10-year-old girls when quantifying joint kinetics during gait.     

Realistic loading conditions for upper body bending

Different modes of load applications are used to simulate flexion and extension of the upper body. It is not clear which loading modes deliver realistic results and allow the comparison of different studies.In a numerical study, a validated finite element model of the lumbar spine, ranging from the vertebra L1 to the disc L5–S1 was employed. Each of six different loading modes was studied for simulating flexion and extension, including pure moments, an eccentric axial force, using a wedged fixture, and applying upper body weight plus follower load plus muscle forces. Intersegmental rotations, intradiscal pressures and facet joint contact forces were calculated. Where possible, results were compared to data measured in vivo.The results of the loading modes studied show a large variance for some values. Outcome measures such as flexion angle and intradiscal pressure differed at a segment by up to 44% and 88%, respectively, related to their maximum values. Intradiscal pressure is mainly determined by the magnitude of the applied compressive force. For flexion maximum contact forces between 0 and 69 N are predicted in each facet joint for different loading modes. For both flexion and extension, applying upper body weight plus follower load plus muscle forces as well as a follower load together with a bending moment delivers results which agreed well with in vivo data from the literature.Choosing an adequate loading mode is important in spine biomechanics when realistic results are required for intersegmental rotations, intradiscal pressure and facet joint contact forces. Only then will results of different studies be comparable.     

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.     

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.     

Joint axes of rotation and body segment parameters of pig limbs

To enable a quantification of net joint moments and joint reaction forces, indicators of joint loading, this study aimed to locate the mediolateral joint axes of rotation and establish the body segment parameters of the limbs of pigs (Sus scrofa). To locate the joint axes of rotation the scapulohumeral, humeroradial, carpal complex, metacarpophalangeal, coxofemoral, femorotibial, tarsal, and metatarsophalangeal joints from 12 carcasses were studied. The joints were photographed in three positions, bisecting lines drawn at fixed landmarks with their intersection marking the joint axes of rotation. The body segment parameters, i.e. the segment mass, center of mass and moment of inertia were measured on the humerus, radius/ulna, metacarpus, forepastern, foretoe, femur, tibia, metatarsus, hindpastern, and hindtoe segments from five carcasses. The segments were weighed, and their center of mass was found by balancing them. The moments of inertia of the humerus, radius/ulna, femur and tibia were found by rotating the segments. The moments of inertia of the remaining segments were calculated. Generally, the joint axes of rotation were near the attachment site of the lateral collateral ligaments. The forelimb, with segments taken as one, was significantly lighter and shorter than the hindlimb (P < 0.001). In all segments the center of mass was located 31 to 50% distal to the proximal segment end. The segment mass decreased with distance from the trunk, as did the segment moment of inertia. The results may serve as reference on the location of the joint axes of rotation and on the body segment parameters for inverse dynamic modeling of pigs.     

The influence of limb alignment on the gait of above-knee amputees.

Biomechanical gait tests on above-knee amputees were conducted in which the alignment of the prosthesis was changed systematically. An eight-segment biomechanical model of the above-knee amputee was developed to analyse and present the three-dimensional kinematic and kinetic data obtained. The effects of alignment changes on the above-knee amputees' gait were studied in terms of the angular displacements of the lower limbs, ground reactions and intersegmental moments. It was found that following the alignment changes the angular displacement at the hip joint on the prosthetic side showed compensatory actions by the amputee. The ground reaction force was sensitive to alignment changes, and in particular, the changes in the characteristics of the fore-aft component of the ground force could be related to the alignment changes. The antero-posterior intersegmental moments at the prosthetic ankle and knee joints were evidently influenced by alignment.     

Discrepancies in knee joint moments using common anatomical frames defined by different palpable landmarks

The aim was to investigate the effects of three anatomical frames using palpable anatomical landmarks of the knee on the net knee joint moments. The femoral epicondyles, femoral condyles, and tibial ridges were used to define the different anatomical frames and the segment end points of the distal femur and proximal tibia, which represent the origin of the tibial coordinate system. Gait data were then collected using the calibrated anatomical system technique (CAST), and the external net knee joint moments in the sagittal, coronal, and transverse planes were calculated based upon the three anatomical frames. Peak knee moments were found to be significantly different in the sagittal plane by approximately 25% (p 相似文献   

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.     

Are Subject-Specific Musculoskeletal Models Robust to the Uncertainties in Parameter Identification?

Subject-specific musculoskeletal modeling can be applied to study musculoskeletal disorders, allowing inclusion of personalized anatomy and properties. Independent of the tools used for model creation, there are unavoidable uncertainties associated with parameter identification, whose effect on model predictions is still not fully understood. The aim of the present study was to analyze the sensitivity of subject-specific model predictions (i.e., joint angles, joint moments, muscle and joint contact forces) during walking to the uncertainties in the identification of body landmark positions, maximum muscle tension and musculotendon geometry. To this aim, we created an MRI-based musculoskeletal model of the lower limbs, defined as a 7-segment, 10-degree-of-freedom articulated linkage, actuated by 84 musculotendon units. We then performed a Monte-Carlo probabilistic analysis perturbing model parameters according to their uncertainty, and solving a typical inverse dynamics and static optimization problem using 500 models that included the different sets of perturbed variable values. Model creation and gait simulations were performed by using freely available software that we developed to standardize the process of model creation, integrate with OpenSim and create probabilistic simulations of movement. The uncertainties in input variables had a moderate effect on model predictions, as muscle and joint contact forces showed maximum standard deviation of 0.3 times body-weight and maximum range of 2.1 times body-weight. In addition, the output variables significantly correlated with few input variables (up to 7 out of 312) across the gait cycle, including the geometry definition of larger muscles and the maximum muscle tension in limited gait portions. Although we found subject-specific models not markedly sensitive to parameter identification, researchers should be aware of the model precision in relation to the intended application. In fact, force predictions could be affected by an uncertainty in the same order of magnitude of its value, although this condition has low probability to occur.     

Patellofemoral joint forces

In this review of patellofemoral joint forces as they might apply to implant design, methodologies for estimating forces on the patella and estimates of the forces, as reported in the literature, are summarized. Two methodologies exist for studying joint loads; one that measures kinematics in-vivo and uses analysis to estimate the joint loads and another that measures ground reaction forces and uses analysis to estimate the joint loads. In both these analyses many assumptions are required with varying degrees of uncertainty; here, those assumptions are examined with data from the published literature. The topics covered include: relationships between quadriceps forces and patellofemoral forces or patella ligament forces, relationships between knee joint moments and quadriceps forces, knee joint moments in various gaits, relationships between patellofemoral forces and lateral subluxation forces, and relationships between patella forces and inferior-superior forces. In many cases, there is little data on patella forces during normal activities, in other cases, there are some discrepancies in reported patella forces, i.e. during squat.     

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.     

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.     

Estimation of foot joint kinetics in three and four segment foot models using an existing proportionality scheme: Application in paediatric barefoot walking

Recent studies which estimated foot segment kinetic patterns were found to have inconclusive data on one hand, and did not dissociate the kinetics of the chopart and lisfranc joint. The current study aimed therefore at reproducing independent, recently published three-segment foot kinetic data (Study 1) and in a second stage expand the estimation towards a four-segment model (Study 2).Concerning the reproducibility study, two recently published three segment foot models (Bruening et al., 2014; Saraswat et al., 2014) were reproduced and kinetic parameters were incorporated in order to calculate joint moments and powers of paediatric cohorts during gait. Ground reaction forces were measured with an integrated force/pressure plate measurement set-up and a recently published proportionality scheme was applied to determine subarea total ground reaction forces. Regarding Study 2, moments and powers were estimated with respect to the Instituto Ortopedico Rizzoli four-segment model. The proportionality scheme was expanded in this study and the impact of joint centre location on kinetic data was evaluated.Findings related to Study 1 showed in general good agreement with the kinetic data published by Bruening et al. (2014). Contrarily, the peak ankle, midfoot and hallux powers published by Saraswat et al. (2014) are disputed. Findings of Study 2 revealed that the chopart joint encompasses both power absorption and generation, whereas the Lisfranc joint mainly contributes to power generation.The results highlights the necessity for further studies in the field of foot kinetic models and provides a first estimation of the kinetic behaviour of the Lisfranc joint.     

Analysis of the influence of disc degeneration on the mechanical behaviour of a lumbar motion segment using the finite element method

Compared to a healthy intervertebral disc, the geometry and the material properties of the involved tissues are altered in a degenerated disc. It is not completely understood how this affects the mechanical behaviour of a motion segment. In order to study the influence of disc degeneration on motion segment mechanics a three-dimensional, nonlinear finite element model of the L3/L4 functional unit was used. Different grades of disc degeneration were simulated by varying disc height and bulk modulus of the nucleus pulposus. The model was loaded with pure moments of 10Nm in the three main anatomic planes. The finite element model predicted the same trends for intersegmental rotation and intradiscal pressure as described in the literature for in vitro studies. A comparison between calculated intersegmental rotation and experimental data showed a mean difference of 1.9 degrees while the mean standard deviation was 2.5 degrees . A mildly degenerated disc increases intersegmental rotation for all loading cases. With further increasing disc degeneration intersegmental rotation is decreased. For axial rotation the decrease takes place in the final stage. Intradiscal pressure is lower while facet joint force and maximum von Mises stress in the annulus are higher in a degenerated compared to a healthy disc.     

The effects of electromyography-assisted modelling in estimating musculotendon forces during gait in children with cerebral palsy

Neuro-musculoskeletal modelling can provide insight into the aberrant muscle function during walking in those suffering cerebral palsy (CP). However, such modelling employs optimization to estimate muscle activation that may not account for disturbed motor control and muscle weakness in CP. This study evaluated different forms of neuro-musculoskeletal model personalization and optimization to estimate musculotendon forces during gait of nine children with CP (GMFCS I-II) and nine typically developing (TD) children. Data collection included 3D-kinematics, ground reaction forces, and electromyography (EMG) of eight lower limb muscles. Four different optimization methods estimated muscle activation and musculotendon forces of a scaled-generic musculoskeletal model for each child walking, i.e. (i) static optimization that minimized summed-excitation squared; (ii) static optimization with maximum isometric muscle forces scaled to body mass; (iii) an EMG-assisted approach using optimization to minimize summed-excitation squared while reducing tracking errors of experimental EMG-linear envelopes and joint moments; and (iv) EMG-assisted with musculotendon model parameters first personalized by calibration. Both static optimization approaches showed a relatively low model performance compared to EMG envelopes. EMG-assisted approaches performed much better, especially in CP, with only a minor mismatch in joint moments. Calibration did not affect model performance significantly, however it did affect musculotendon forces, especially in CP. A model more consistent with experimental measures is more likely to yield more physiologically representative results. Therefore, this study highlights the importance of calibrated EMG-assisted modelling when estimating musculotendon forces in TD children and even more so in children with CP.     

Influence of the 3D inverse dynamic method on the joint forces and moments during gait

The joint forces and moments are commonly used in gait analysis. They can be computed by four different 3D inverse dynamic methods proposed in the literature, either based on vectors and Euler angles, wrenches and quaternions, homogeneous matrices, or generalized coordinates and forces. In order to analyze the influence of the inverse dynamic method, the joint forces and moments were computed during gait on nine healthy subjects. A ratio was computed between the relative dispersions (due to the method) and the absolute amplitudes of the gait curves. The influence of the inverse dynamic method was negligible at the ankle (2%) but major at the knee and the hip joints (40%). This influence seems to be due to the dynamic computation rather than the kinematic computation. Compared to the influence of the joint center location, the body segment inertial parameter estimation, and more, the influence of the inverse dynamic method is at least of equivalent importance. This point should be confirmed with other subjects, possibly pathologic, and other movements.     

Change in knee contact force with simulated change in body weight

The relationship between obesity, weight gain and progression of knee osteoarthritis is well supported, suggesting that excessive joint loading may be a mechanism responsible for cartilage deterioration. Examining the influence of weight gain on joint compressive forces is difficult, as both muscles and ground reaction forces can have a significant impact on the forces experienced during gait. While previous studies have examined the relationship between body weight and knee forces, these studies have used models that were not validated using experimental data. Therefore, the objective of this study was to evaluate the relationship between changes in body weight and changes in knee joint contact forces for an individual's gait pattern using musculoskeletal modeling that is validated against known internal compressive forces. Optimal weighting constants were determined for three subjects to generate valid predictions of knee contact forces (KCFs) using in vivo data collection with instrumented total knee arthroplasty. A total of five simulations per walking trial were generated for each subject, from 80% to 120% body weight in 10% increments, resulting in 50 total simulations. The change in peak KCF with respect to body weight was found to be constant and subject-specific, predominantly determined by the peak force during the baseline condition at 100% body weight. This relationship may be further altered by any change in kinematics or body mass distribution that may occur as a result of a change in body weight or exercise program.     

Estimating the muscle forces generated in the human lower extremity when walking: a physiological solution

A model capable of estimating individual muscle activity during human lower extremity activity has been developed. This model was implemented and applied to normal gait. Both 3D cinematography and force platform records were collected to define the kinematics of the lower limb segments and the ground reaction forces. From these data the lengths, velocities, and moment arms of the muscles and the net muscle moments were calculated. These data were then used to estimate the output from a set of pattern generators which specified the neural input to and hence the force generated in each muscle. Results were obtained which demonstrate that it is feasible to construct a hierarchical physiological model which will estimate individual muscle forces. This statement must be tempered somewhat in that better anatomical and neurophysiological data must be made available and that this model, and all others attempting to estimate individual muscle forces, must be rigorously tested before being applied in a research, sports, or clinical setting.