Quantification of the uncertainties in resultant joint moments computed in a dynamic activity

Simulation of a control method for active kinesiotherapy with an upper extremity rehabilitation exoskeleton without force sensor

Exoskeleton-aided active rehabilitation is a process that requires sensing and acting upon the motion intentions of the user. Typically, force sensors are used for this. However, they increase the weight and cost of these wearable devices. This paper presents the methodology for detecting users' intentions only with encoders integrated with the drives. It is unique compared to other algorithms, as enables active kinesiotherapy while adding no sensory systems. The method is based on comparing the measured motion with the one computed with the idealised model of the multibody system. The investigation assesses the method's performance and its robustness to model and measurement inaccuracies, as well as patients' unintended motions. Moreover, the PID parameters are selected to provide the optimal regulation based on the dynamics requirements. The research proves the presented concept of the control approach. For all the tests with the final settings, the system reacts to a change in the user's intention below one second and minimises the changes in proportion between the system's acceleration and the generated user's joint torque. The results are comparable to those obtained by EMG-based systems and significantly better than low-cost force sensors.

ISB recommendations on the reporting of intersegmental forces and moments during human motion analysis

The International Society of Biomechanics (ISB) has charged this committee with development of a standard similar in scope to the kinematic standard proposed in Wu et al. (2002) and Wu et al. (2005). Given the variety of purposes for which intersegmental forces and moments are used in biomechanical research, it is not possible to recommend a particular set of analysis standards that will be acceptable in all applications. Instead, it is the purpose of this paper to recommend a set of reporting standards that will result in an understanding of the differences between investigations and the ability to reproduce the research. The end products of this standard are (1) a critical checklist that can be used during submission of manuscripts and abstracts to insure adequate description of methods, and (2) a web based visualization tool that can be used to alter the coordinate system, normalization technique and internal/external perspective of intersegmental forces and moments during walking and running so that the shape and magnitude of the curves can be compared to one's own data.

Influence of body segment parameter estimation on calculated ground reaction forces in highly dynamic movements

The effect of body segment parameter estimation (BSP) on the inverse dynamics modelling results has not yet been demonstrated in specific groups during athletic movements with high segment accelerations. Therefore, the purpose of this study was to analyse this effect in ski-jumpers as representatives of a specific group (i.e. low body mass index) by comparing calculated and measured ground reaction forces during ski-jumping imitation jumps. Full body kinematics and vertical ground reaction forces were recorded of 9 ski-jumpers performing three imitation jumps each. BSP were estimated using three previously published, one individually optimized and one ski-jumper group specific model. Vertical ground reaction forces were calculated using the vertical acceleration of the segments as well as the BSP of the single models in a top-down approach. Statistical analysis revealed a main model effect concerning the root mean square error between the calculated and the measured ground reaction force with deviations between the models of 53%. Individual optimization and the application of the ski-jumper group specific model increased the accuracy of the calculated ground reaction forces by 11 and 7%, respectively, compared to the best performing published model. The results of inverse dynamics modelling are very sensitive to the BSP estimation for specific groups like ski-jumpers during movements incorporating high segment accelerations. This emphasizes the importance of selecting adequate BSP estimation models or methods when analysing specific groups in highly dynamic movements in order to increase the accuracy of the inverse dynamics analyses results.

Test-retest reliability of segment kinetic energy measures in the golf swing

Analyses of segment kinetic energy (KE) can provide the most appropriate means of exploring sequential movements. As the reliability associated with its measurement has not been reported, the aim of this study was to examine the test-retest reliability of segment KE measures in the golf swing. On two occasions, seven male golfers hit five shots with three different clubs. Body segment inertia parameters were estimated for 17 rigid bodies and 3D kinematic data were collected during each swing. The magnitude and timing of peak total, linear and angular kinetic energies were then calculated for each rigid body and for four segment groups. Regardless of club type, KE was measured with high reliability for almost all rigid bodies and segment groups. However, significantly larger magnitudes of peak total (p = 0.039) and linear (p = 0.021) lower body KE were reported in test 2 than in test 1. The high reliability reported in this study provides support for the use of analyses of segment kinetic energy. However, practitioners should pay careful attention to the identification of anatomical landmarks which define the thigh, pelvis and thorax as this was the main cause of variability in repeated measures of segment kinetic energy.

Effects of age and sex on shoulder biomechanics and relative effort during functional tasks

Age-related decline in muscle strength can compromise shoulder function, which could increase the effort needed to perform activities of daily living (ADLs). The purpose of this cross-sectional study was to determine for the first time the relative shoulder effort during ADLs in healthy young and older adults. Ten healthy young adults and ten healthy older adults were tested for maximal isokinetic torque and on a set of ADL tasks. Using inverse dynamics, the shoulder torques during ADLs were referenced to the maximal isokinetic torque and relative effort was determined. Older compared to younger adults had >40% lower isokinetic shoulder abduction strength. The ratio of peak joint torque during six ADLs over the maximal isokinetic torque, i.e., relative effort, was higher in old (∼52%) compared with young adults (∼22%, p < 0.05). Relative effort in older adults was over 40% in overhead activities and particularly high in abduction and reaching tasks, over 60%. Healthy older compared with younger adults perform most ADL tasks involving the shoulder joint with nearly twice the level of relative effort. The concomitant reductions in maximal shoulder isokinetic torque and increases in relative effort may be related to the high prevalence of musculoskeletal pain and shoulder dysfunction in old age reported in epidemiological studies.

Joint torque variability and repeatability during cyclic flexion-extension of the elbow

Background

Joint torques are generally of primary importance for clinicians to analyze the effect of a surgery and to obtain an indicator of functional capability to perform a motion. Given the current need to standardize the functional evaluation of the upper limb, the aim of this paper is to assess (1) the variability of the calculated maximal elbow joint torque during cyclic elbow flexion-extension movements and (2) participant test-retest repeatability in healthy young adults. Calculations were based on an existing non-invasive method including kinematic identification and inverse dynamics processes.

Methods

Twelve healthy young adults (male n = 6) performed 10 elbow flexion-extension movement carrying five different dumbbells (0, 1, 2, 3 and 4 kg) with several flexion-extension frequencies (½, ¹/₃, ¼ Hz) to evaluate peak elbow joint torques.

Results

Whatever the condition, the variability coefficient of trial peak torques remained under 4 %. Bland and Altman plot also showed good test-retest, whatever the frequency conditions for the 0, 1, 2, and 3 kg conditions.

Conclusion

The good repeatability of the flexion-extension peak torques represents a key step to standardize the functional evaluation of the upper limb.

A novel computational framework for deducing muscle synergies from experimental joint moments

Prior experimental studies have hypothesized the existence of a "muscle synergy" based control scheme for producing limb movements and locomotion in vertebrates. Such synergies have been suggested to consist of fixed muscle grouping schemes with the co-activation of all muscles in a synergy resulting in limb movement. Quantitative representations of these groupings (termed muscle weightings) and their control signals (termed synergy controls) have traditionally been derived by the factorization of experimentally measured EMG. This study presents a novel approach for deducing these weightings and controls from inverse dynamic joint moments that are computed from an alternative set of experimental measurements-movement kinematics and kinetics. This technique was applied to joint moments for healthy human walking at 0.7 and 1.7 m/s, and two sets of "simulated" synergies were computed based on two different criteria (1) synergies were required to minimize errors between experimental and simulated joint moments in a musculoskeletal model (pure-synergy solution) (2) along with minimizing joint moment errors, synergies also minimized muscle activation levels (optimal-synergy solution). On comparing the two solutions, it was observed that the introduction of optimality requirements (optimal-synergy) to a control strategy solely aimed at reproducing the joint moments (pure-synergy) did not necessitate major changes in the muscle grouping within synergies or the temporal profiles of synergy control signals. Synergies from both the simulated solutions exhibited many similarities to EMG derived synergies from a previously published study, thus implying that the analysis of the two different types of experimental data reveals similar, underlying synergy structures.

Oscillation and reaction board techniques for estimating inertial properties of a below-knee prosthesis

The purpose of this study was two-fold: (1) demonstrate a technique that can be used to directly estimate the inertial properties of a below-knee prosthesis, and (2) contrast the effects of the proposed technique and that of using intact limb inertial properties on joint kinetic estimates during walking in unilateral, transtibial amputees. An oscillation and reaction board system was validated and shown to be reliable when measuring inertial properties of known geometrical solids. When direct measurements of inertial properties of the prosthesis were used in inverse dynamics modeling of the lower extremity compared with inertial estimates based on an intact shank and foot, joint kinetics at the hip and knee were significantly lower during the swing phase of walking. Differences in joint kinetics during stance, however, were smaller than those observed during swing. Therefore, researchers focusing on the swing phase of walking should consider the impact of prosthesis inertia property estimates on study outcomes. For stance, either one of the two inertial models investigated in our study would likely lead to similar outcomes with an inverse dynamics assessment.

Excessive fluctuations in knee joint moments during early stance in sprinting are caused by digital filtering procedures

Inverse dynamics analyses are commonly used to understand movement patterns in all forms of gait. The aim of this study was to determine the effect of digital filtering procedures on the knee joint moments calculated during sprinting as an example of the possible influence of data analysis processes on interpretation of movement patterns. Data were obtained from three highly trained sprinters who completed a series of 30 m sprints. Ten different combinations of cut-off frequency were applied to the two-dimensional kinematic and kinetic input data with the kinetic cut-off frequency set equal to or higher than the kinematic cut-off frequency. When using the commonly adopted practice of filtering the kinetic data with a higher cut-off frequency than the kinematic data, exaggerated fluctuations in the knee joint moment existed soon after contact. In extreme cases, the knee moved between flexor, extensor and flexor dominance in less than 33 ms and through ranges exceeding 500 Nm. During an inverse dynamics analysis of locomotion, mismatched cut-off frequencies will likely affect the calculated joint moments if the cut-off frequency applied to the kinematic data is less than the true frequency content, particularly during impact phases. In the example of sprinting, exaggerated fluctuations in the knee joint moment appear to be data processing artefact rather than genuine characteristics of the joint kinetics. When the cut-off frequencies, and thus the frequency content of all input data, are matched, the fluctuations after contact are minimal and such a procedure is suggested for inverse dynamics analyses of gait.

The effect of variability in body segment parameters on joint moment using Monte Carlo simulations

This study used Monte Carlo methods to simulate the effects of variability and uncertainty in inertial body segment parameters (BSPs) on joint torques calculated using inverse dynamics. The average and standard deviation values of BSPs from previously published studies were used as inputs into the Monte Carlo simulation. Data from five groups were evaluated: cadaveric subjects; living subjects (Caucasian only); female living subjects (Caucasian only); male living subjects (Caucasian only); and living subjects (non-Caucasian). The differences in BSPs observed between the different groups were statistically significant; however, using BSP variability data from these groups made little difference to the calculated joint torques. This suggests that for slow and repeatable movement such as walking, BSPs have little effect on joint moments, except for the swing phase. Even then, the magnitude of difference in the swing phase due to variability in BSPs is not much greater than the inter-trial variability. As expected, distal BSPs have little effect on proximal joint moment.

Comparative analysis of methods for estimating arm segment parameters and joint torques from inverse dynamics

A common problem in the analyses of upper limb unfettered reaching movements is the estimation of joint torques using inverse dynamics. The inaccuracy in the estimation of joint torques can be caused by the inaccuracy in the acquisition of kinematic variables, body segment parameters (BSPs), and approximation in the biomechanical models. The effect of uncertainty in the estimation of body segment parameters can be especially important in the analysis of movements with high acceleration. A sensitivity analysis was performed to assess the relevance of different sources of inaccuracy in inverse dynamics analysis of a planar arm movement. Eight regression models and one water immersion method for the estimation of BSPs were used to quantify the influence of inertial models on the calculation of joint torques during numerical analysis of unfettered forward arm reaching movements. Thirteen subjects performed 72 forward planar reaches between two targets located on the horizontal plane and aligned with the median plane. Using a planar, double link model for the arm with a floating shoulder, we calculated the normalized joint torque peak and a normalized root mean square (rms) of torque at the shoulder and elbow joints. Statistical analyses quantified the influence of different BSP models on the kinetic variable variance for given uncertainty on the estimation of joint kinematics and biomechanical modeling errors. Our analysis revealed that the choice of BSP estimation method had a particular influence on the normalized rms of joint torques. Moreover, the normalization of kinetic variables to BSPs for a comparison among subjects showed that the interaction between the BSP estimation method and the subject specific somatotype and movement kinematics was a significant source of variance in the kinetic variables. The normalized joint torque peak and the normalized root mean square of joint torque represented valuable parameters to compare the effect of BSP estimation methods on the variance in the population of kinetic variables calculated across a group of subjects with different body types. We found that the variance of the arm segment parameter estimation had more influence on the calculated joint torques than the variance of the kinematics variables. This is due to the low moments of inertia of the upper limb, especially when compared with the leg. Therefore, the results of the inverse dynamics of arm movements are influenced by the choice of BSP estimation method to a greater extent than the results of gait analysis.

Optimal estimation of dynamically consistent kinematics and kinetics for forward dynamic simulation of gait

Forward dynamic simulation provides a powerful framework for characterizing internal loads and for predicting changes in movement due to injury, impairment or surgical intervention. However, the computational challenge of generating simulations has greatly limited the use and application of forward dynamic models for simulating human gait. In this study, we introduce an optimal estimation approach to efficiently solve for generalized accelerations that satisfy the overall equations of motion and best agree with measured kinematics and ground reaction forces. The estimated accelerations are numerically integrated to enforce dynamic consistency over time, resulting in a forward dynamic simulation. Numerical optimization is then used to determine a set of initial generalized coordinates and speeds that produce a simulation that is most consistent with the measured motion over a full cycle of gait. The proposed method was evaluated with synthetically created kinematics and force plate data in which both random noise and bias errors were introduced. We also applied the method to experimental gait data collected from five young healthy adults walking at a preferred speed. We show that the proposed residual elimination algorithm (REA) converges to an accurate solution, reduces the detrimental effects of kinematic measurement errors on joint moments, and eliminates the need for residual forces that arise in standard inverse dynamics. The greatest improvements in joint kinetics were observed proximally, with the algorithm reducing joint moment errors due to marker noise by over 20% at the hip and over 50% at the low back. Simulated joint angles were generally within 1 deg of recorded values when REA was used to generate a simulation from experimental gait data. REA can thus be used as a basis for generating accurate simulations of subject-specific gait dynamics.

Are patient-specific joint and inertial parameters necessary for accurate inverse dynamics analyses of gait?

Variations in joint parameter (JP) values (axis positions and orientations in body segments) and inertial parameter (IP) values (segment masses, mass centers, and moments of inertia) as well as kinematic noise alter the results of inverse dynamics analyses of gait. Three-dimensional linkage models with joint constraints have been proposed as one way to minimize the effects of noisy kinematic data. Such models can also be used to perform gait optimizations to predict post-treatment function given pre-treatment gait data. This study evaluates whether accurate patient-specific JP and IP values are needed in three-dimensional linkage models to produce accurate inverse dynamics results for gait. The study was performed in two stages. First, we used optimization analyses to evaluate whether patient-specific JP and IP values can be calibrated accurately from noisy kinematic data, and second, we used Monte Carlo analyses to evaluate how errors in JP and IP values affect inverse dynamics calculations. Both stages were performed using a dynamic, 27 degrees-of-freedom, full-body linkage model and synthetic (i.e., computer generated) gait data corresponding to a nominal experimental gait motion. In general, JP but not IP values could be found accurately from noisy kinematic data. Root-mean-square (RMS) errors were 3 degrees and 4 mm for JP values and 1 kg, 22 mm, and 74 500 kg * mm2 for IP values. Furthermore, errors in JP but not IP values had a significant effect on calculated lower-extremity inverse dynamics joint torques. The worst RMS torque error averaged 4% bodyweight * height (BW * H) due to JP variations but less than 0.25% (BW * H) due to IP variations. These results suggest that inverse dynamics analyses of gait utilizing linkage models with joint constraints should calibrate the model's JP values to obtain accurate joint torques.

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

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

Determination of patient-specific multi-joint kinematic models through two-level optimization

Dynamic patient-specific musculoskeletal models have great potential for addressing clinical problems in orthopedics and rehabilitation. However, their predictive capability is limited by how well the underlying kinematic model matches the patient's structure. This study presents a general two-level optimization procedure for tuning any multi-joint kinematic model to a patient's experimental movement data. An outer level optimization modifies the model's parameters (joint position and orientations) while repeated inner level optimizations modify the model's degrees of freedom given the current parameters, with the goal of minimizing errors between model and experimental marker trajectories. The approach is demonstrated by fitting a 27 parameter, three-dimensional, 12 degree-of-freedom lower-extremity kinematic model to synthetic and experimental movement data for isolated joint (hip, knee, and ankle) and gait (full leg) motions. For noiseless synthetic data, the approach successfully recovered the known joint parameters to within an arbitrarily tight tolerance. When noise was added to the synthetic data, root-mean-square (RMS) errors between known and recovered joint parameters were within 10.4 degrees and 10 mm. For experimental data, RMS marker distance errors were reduced by up to 62% compared to methods that estimate joint parameters from anatomical landmarks. Optimized joint parameters found using a loaded full-leg gait motion differed significantly from those found using unloaded individual joint motions. In the future, this approach may facilitate the creation of dynamic patient-specific musculoskeletal models for predictive clinical applications.

Balance control during an arm raising movement in bipedal stance: which biomechanical factor is controlled?

In order to obtain new insight into the control of balance during arm raising movements in bipedal stance, we performed a biomechanical analysis of kinematics and dynamical aspects of arm raising movements by combining experimental work, large-scale models of the body, and techniques simulating human behavior. A comparison between experimental and simulated joint kinematics showed that the minimum torque change model yielded realistic trajectories. We then performed an analysis based on computer simulations. Since keeping the center of pressure (CoP) and the projection of the center of mass (CoM) inside the support area is essential for equilibrium, we modeled an arm raising movement where displacement of one or the other variable is limited. For this optimization model, the effects of adding equilibrium constraints on movement trajectories were investigated. The results show that: (a) the choice of the regulated variable influences the strategy adopted by the system and (b) the system was not able to regulate the CoM for very fast movements without compromising its balance. Consequently, we suggest that the system is able to maintain balance while raising the arm by only controlling the CoP. This may be done mainly by using hip mechanisms and controlling net ankle torque.

Biomechanics and muscle coordination of human walking: part II: lessons from dynamical simulations and clinical implications

Principles of muscle coordination in gait have been based largely on analyses of body motion, ground reaction force and EMG measurements. However, data from dynamical simulations provide a cause-effect framework for analyzing these measurements; for example, Part I (Gait Posture, in press) of this two-part review described how force generation in a muscle affects the acceleration and energy flow among the segments. This Part II reviews the mechanical and coordination concepts arising from analyses of simulations of walking. Simple models have elucidated the basic multisegmented ballistic and passive mechanics of walking. Dynamical models driven by net joint moments have provided clues about coordination in healthy and pathological gait. Simulations driven by muscle excitations have highlighted the partial stability afforded by muscles with their viscoelastic-like properties and the predictability of walking performance when minimization of metabolic energy per unit distance is assumed. When combined with neural control models for exciting motoneuronal pools, simulations have shown how the integrative properties of the neuro-musculo-skeletal systems maintain a stable gait. Other analyses of walking simulations have revealed how individual muscles contribute to trunk support and progression. Finally, we discuss how biomechanical models and simulations may enhance our understanding of the mechanics and muscle function of walking in individuals with gait impairments.

Static optimal estimation of joint accelerations for inverse dynamics problem solution

In inverse dynamics computations, the accuracy of the solution strongly depends on the accuracy of the input data. In particular, estimated joint moments are highly sensitive to uncertainties in acceleration data. The aim of the present work was to improve classical inverse dynamics computations by providing an accurate estimation of accelerations. Accelerations are usually calculated from noise-polluted position data using numerical double differentiation, which amplifies measurement noise. The objective of the present paper is to use all available imperfect position and force measurements to extract optimum acceleration estimations. A weighted least-squares optimisation approach is used to provide optimal acceleration distributions most consistent with position and force data, and which account for the propagation of measurement uncertainties. The task chosen for comparing the solution methodology with other classical methods is a typical experimental postural movement, consisting in upper limb swings from an upright stance. The proposed method delivers a set of optimal accelerations well consistent with all available measurements. It also leads to an accurate prediction of ground reactions and it produces no residual moment at the top-most segment.

A sensitivity analysis of the calculation of mechanical output through inverse dynamics: a computer simulation study

The purpose of this study was to systematically determine the effect of experimental errors on the work output calculated using two different methods of inverse dynamics during vertical jumping: (a) the conventional (rotational) method and (b) the translational method. A two-dimensional musculoskeletal model was used to generate precisely known kinematics. Next, the location of each joint center (JC) and the location of each segment's center of mass (CM) were manipulated by +/-10% of segment length to simulate errors in the location of joint centers (delta JC) and errors in the location of segment's center of mass (delta CM), respectively. Work output was subsequently calculated by applying the two methods of inverse dynamics to the manipulated kinematic data. The results showed that the translational method of inverse dynamics was less sensitive (up to 13% error in total work output) to delta JC and delta CM than the rotational method (up to 28% error in total work output). The rotational method of inverse dynamics was particularly sensitive to simulated errors in JC.