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

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

Elbow helical axes of motion are not the same in physiologic and kinetic joint simulators

Physiologic and kinetic joint simulators have been widely used for investigations of joint mechanics. The two types of simulator differ in the way joint motion is achieved; through prescribed motions and/or forces in kinetic joint simulators and by tendon loads in physiologic joint simulators. These two testing modalities have produced important insights, as in elucidating the importance of soft tissue structures to joint stability. However, the equivalence of the modalities has not been tested. This study sequentially tested five cadaveric elbows using both a physiologic simulator and a robot/6DOF system. Using position data from markers on the humerus and ulna, we calculated and compared the helical axes of motion of the specimens as the elbows were flexed from full extension. Six step size increments were used in the helical axis calculation. Marker position data at each test's full extension and full flexion point were also used to calculate a datum (overall) helical axis. The angles between the datum axis and step-wise movements were computed and stored. Increasing step size monotonically decreased the variability and the average conical angle encompassing the helical axes; a repeated measures ANOVA using test type (robot or physiologic simulator) and step size found that both type and step caused statistically significant differences (p<0.001). The large changes in helical axis angle observed for small changes in elbow flexion angle, especially in the robot tests, are a caveat for investigators using similar control algorithms. Controllers may need to include increased joint compliance and/or C(1) continuity to reduce variability.     

Impact of enzyme motion on activity

Experimental and theoretical data imply that enzyme motion plays an important role in enzymatic reactions. Enzyme motion can influence both the activation free energy barrier and the degree of barrier recrossing. A hybrid theoretical approach has been developed for the investigation of the relation between enzyme motion and activity. This approach includes both electronic and nuclear quantum effects. It distinguishes between thermally averaged promoting motions that influence the activation free energy barrier and dynamical motions that influence the barrier recrossings. Applications to hydride transfer in liver alcohol dehydrogenase and dihydrofolate reductase resulted in the identification and characterization of important enzyme motions. These applications have also led to the proposal of a network of coupled promoting motions in enzymatic reactions. These concepts have important implications for protein engineering and drug design.     

Assessment of the functional method of hip joint center location subject to reduced range of hip motion

Motion analysis of the lower extremities usually requires determination of the location of the hip joint center. The results of several recent studies have suggested that kinematic and kinetic variables calculated from motion analysis data are highly sensitive to errors in hip joint center location. "Functional" methods in which the location of the hip joint center is determined from the relative motion of the thigh and pelvis, rather than from the locations of bony landmarks, are promising but may be ineffective when motion is limited. The aims of the present study were to determine whether the accuracy of the functional method is compromised in young and elderly subjects when limitations on hip motion are imposed and to investigate the possibility of locating the hip joint center using data collected during commonly studied motions (walking, sit-to-stand, stair ascent, stair descent) rather than using data from an ad hoc trial in which varied hip motions are performed. The results of the study suggested that functional methods would result in worst-case hip joint center location errors of 26mm (comparable to the average errors previously reported for joint center location based on bony landmarks) when available hip motion is substantially limited. Much larger errors ( approximately 70mm worst-case), however, resulted when hip joint centers were located from data collected during commonly performed motions, perhaps because these motions are, for the most part, restricted to the sagittal plane. It appears that the functional method can be successfully implemented when range of motion is limited but still requires collection of a special motion trial in which hip motion in both the sagittal and frontal planes is recorded.     

Effect of plant interaction on wind-induced crop motion

Plant motion due to wind affects plant growth, a phenomenon called thigmomorphogenesis. Despite intensive studies of the turbulence over plant canopies, the study of plant motion induced by wind has often been limited to individual trees or cereal plants. Few models of global canopy motions are available. Moreover the numerical analysis of models that are based on individual stems becomes time consuming when dealing with crops. A model of motion within the canopies is proposed here using a wave propagation equation within a homogenized continuous medium, and a forcing function representing turbulent gusts advected over the canopy. This model is derived from a discrete model of a set of plant shoots represented as individual oscillators, including elastic contacts between shoots. Such contacts induce nonlinearities into the wave equation. A new experimental method to measure stem dynamical properties and elastic collision properties is presented with an illustration on alfalfa stems. Results obtained modeling plant motions in an alfalfa crop are presented.     

Importance of nonlinear and multivariable flexibility coefficients in the prediction of human cervical spine motion

The flexibility matrix currently forms the basis for multibody dynamics models of cervical spine motion. While studies have aimed to determine cervical motion segment behavior, their accuracy and utility have been limited by both experimental and analytical assumptions. Flexibility terms have been primarily represented as constants despite the spine's nonlinear stiffening response. Also, nondiagonal terms, describing coupled motions, of the matrices are often omitted. Currently, no study validates the flexibility approach for predicting vertebral motions; nor have the effects of matrix approximations and simplifications been quantified. Therefore, the purpose of this study is to quantify flexibility relationships for cervical motion segments, examine the importance of nonlinear components of the flexibility matrix, and determine the extent to which multivariable relationships may alter motion prediction. To that end, using unembalmed human cervical spine motion segments, a full battery of flexibility tests were performed for a neutral orientation and also following an axial pretorque. Primary and coupled matrix components were described using linear and piecewise nonlinear incremental constants. A third matrix approach utilized multivariable incremental relationships. Measured motions were predicted using structural flexibility methods and evaluated using RMS error between predicted and measured responses. A full set of flexibility relationships describe primary and coupled motions for C3-C4 and C5-C6. A flexibility matrix using piecewise incremental responses offers improved predictions over one using linear methods (p<0.01). However, no significant improvement is obtained using nonlinear terms represented by a multivariable functional approach (p<0.2). Based on these findings, it is suggested that a multivariable approach for flexibility is more demanding experimentally and analytically while not offering improved motion prediction.     

Segmental motion of forefoot and hindfoot as a diagnostic tool

Segmental motions derived from non-invasive motion analysis are being used to investigate the intrinsic functional behavior of the foot and ankle in health and disease. The goal of this research was to examine the ability of a generic segmented model of the foot to capture and differentiate changes in internal skeletal kinematics due to neuromuscular disease and/or trauma. A robotic apparatus that reproduces the kinematics and kinetics of gait in cadaver lower extremities was employed to produce motion under normal and aberrant neuromuscular activation patterns of tibialis posterior and/or tibialis anterior. Stance phase simulations were conducted on 10 donor limbs while recording three-dimensional kinematic trajectories of (1) skin-mounted markers used clinically to construct segmented foot models, and (2) bone-mounted marker clusters to capture actual internal bone motion as the gold standard for comparison. The models constructed from external marker data were able to differentiate the kinematic behaviors elicited by different neuromuscular conditions in a manner similar to that using the bone-derived data. Measurable differences between internal and externally measured kinematics were small, variable and random across the three axes of rotation and neuromuscular conditions, with a tendency toward more differences noted during early and late stance. Albeit slightly different, three-dimensional motion profiles of the hindfoot and forefoot segments correlated well with internal skeletal motion under all neuromuscular conditions, thereby confirming the utility of measuring segmental motions as a valid means of clinical assessment.     

Collective motions in glucosamine-6-phosphate synthase: influence of ligand binding and role in ammonia channelling and opening of the fructose-6-phosphate binding site

The large protein motions of the bacterial enzyme glucosamine-6-phosphate synthase have been addressed using full atom normal modes analysis for the empty, the glucose-6-phosphate and the glucose-6-phosphate + glutamate bound proteins. The approach that was used involving energy minimizations along the normal modes coordinates identified functional motions of the protein, some of which were characterized earlier by X-ray diffraction studies. This method made it possible for the first time to highlight significant energy differences according to whether none, only one or both of the active sites of the protein were occupied. Our data favoured a specific motion of the glutamine binding domain following the fixation of fructose-6-phosphate and suggested a rigidified structure with both sites occupied. Here, we show that most of the collective large amplitude motions of glucosamine-6-phosphate synthase that are modulated by ligand binding are crucial for the enzyme catalytic cycle, as they strongly modify the geometry of both the ammonia channel and the C-tail, demonstrating their role in ammonia transfer and ligand binding.     

Fast and reliable analysis of molecular motion using proximity relations and dimensionality reduction

The analysis of molecular motion starting from extensive sampling of molecular configurations remains an important and challenging task in computational biology. Existing methods require a significant amount of time to extract the most relevant motion information from such data sets. In this work, we provide a practical tool for molecular motion analysis. The proposed method builds upon the recent ScIMAP (Scalable Isomap) method, which, by using proximity relations and dimensionality reduction, has been shown to reliably extract from simulation data a few parameters that capture the main, linear and/or nonlinear, modes of motion of a molecular system. The results we present in the context of protein folding reveal that the proposed method characterizes the folding process essentially as well as ScIMAP. At the same time, by projecting the simulation data and computing proximity relations in a low-dimensional Euclidean space, it renders such analysis computationally practical. In many instances, the proposed method reduces the computational cost from several CPU months to just a few CPU hours, making it possible to analyze extensive simulation data in a matter of a few hours using only a single processor. These results establish the proposed method as a reliable and practical tool for analyzing motions of considerably large molecular systems and proteins with complex folding mechanisms.     

Differential motion dynamics of synaptic vesicles undergoing spontaneous and activity-evoked endocytosis

Synaptic vesicle exo- and endocytosis are usually driven by neuronal activity but can also occur spontaneously. The identity and differences between vesicles supporting evoked and spontaneous neurotransmission remain highly debated. Here we combined nanometer-resolution imaging with a transient motion analysis approach to examine the dynamics of individual synaptic vesicles in hippocampal terminals under physiological conditions. We found that vesicles undergoing spontaneous and stimulated endocytosis differ in their dynamic behavior, particularly in the ability to engage in directed motion. Our data indicate that such motional differences depend on the myosin family of motor proteins, particularly myosin II. Analysis of synaptic transmission in the presence of myosin II inhibitor confirmed a specific role for myosin II in evoked, but not spontaneous, neurotransmission and also suggested a functional role of myosin II-mediated vesicle motion in supporting vesicle mobilization during neural activity.     

Immunoglobulin structure exhibits control over CDR motion

Motions of the IgG structure are evaluated using normal mode analysis of an elastic network model to detect hinges, the dominance of low frequency modes, and the most important internal motions. One question we seek to answer is whether or not IgG hinge motions facilitate antigen binding. We also evaluate the protein crystal and packing effects on the experimental temperature factors and disorder predictions. We find that the effects of the protein environment on the crystallographic temperature factors may be misleading for evaluating specific functional motions of IgG. The extent of motion of the antigen binding domains is computed to show their large spatial sampling. We conclude that the IgG structure is specifically designed to facilitate large excursions of the antigen binding domains. Normal modes are shown as capable of computationally evaluating the hinge motions and the spatial sampling by the structure. The antigen binding loops and the major hinge appear to behave similarly to the rest of the structure when we consider the dominance of the low frequency modes and the extent of internal motion. The full IgG structure has a lower spectral dimension than individual F(ab) domains, pointing to more efficient information transfer through the antibody than through each domain. This supports the claim that the IgG structure is specifically constructed to facilitate antigen binding by coupling motion of the antigen binding loops with the large scale hinge motions.     

The accuracy of measuring glenohumeral motion with a surface humeral cuff

Conclusions about normal and pathologic shoulder motion are frequently made from studies using skin surface markers, yet accuracy of such sensors representing humeral motion is not well known. Nineteen subjects were investigated with flock of birds electromagnetic sensors attached to transcortical pins placed into the scapula and humerus, and a thermoplastic cuff secured on the arm. Subjects completed two repetitions of raising and lowering the arm in the sagittal, scapular and coronal planes, as well as shoulder internal and external rotation with the elbow at the side and abducted to 90°. Humeral motion was recorded simultaneously from surface and bone fixed sensors. The average magnitude of error was calculated for the surface and bone fixed measurements throughout the range of motion. ANOVA tested for differences across angles of elevation, raising and lowering, and differences in body mass index. For all five motions tested, the plane of elevation rotation average absolute error ranged from 0-2°, while the humeral elevation rotation average error ranged from 0-4°. The axial rotation average absolute error was much greater, ranging from 5° during elevation motions to approaching 30° at maximum excursion of internal/external rotation motions. Average absolute error was greater in subjects with body mass index greater than 25. Surface sensors are an accurate way of measuring humeral elevation rotations and plane of elevation rotations. Conversely, there is a large amount of average error for axial rotations when using a humeral cuff to measure glenohumeral internal/external rotation as the primary motion.     

Interocular motion combination for dichoptic moving stimuli

When gratings moving in different directions are presented separately to the two eyes, we typically perceive periods of the combination of motion in the two eyes as well as periods of one or the other monocular motions. To investigate whether such interocular motion combination is determined by the intersection-of-constraints (IOC) or vector average mechanism, we recorded both optokinetic nystagmus eye movements (OKN) and perception during dichoptic presentation of moving gratings and random-dot patterns with various differences of interocular motion direction. For moving gratings, OKN alternately tracks not only the direction of the two monocular motions but also the direction of their combined motion. The OKN in the combined motion direction is highly correlated with the perceived direction of combined motion; its velocity complies with the IOC rule rather than the vector average of the dichoptic motion stimuli. For moving random-dot patterns, both OKN and perceived motion alternate only between the directions of the two monocular motions. These results suggest that interocular motion combination in dichoptic gratings is determined by the IOC and depends on their form.     

Time-correlation analysis of simulated water motion in flexible and rigid gramicidin channels.

Molecular dynamics simulations have been done on a system consisting of the polypeptide membrane channel former gramicidin, plus water molecules in the channel and caps of waters at the two ends of the channel. In the absence of explicit simulation of the surrounding membrane, the helical form of the channel was maintained by artificial restraints on the peptide motion. The characteristic time constant of the artificial restraint was varied to assess the effect of the restraints on the channel structure and water motions. Time-correlation analysis was done on the motions of individual channel waters and on the motions of the center of mass of the channel waters. It is found that individual water molecules confined in the channel execute higher frequency motions than bulk water, for all degrees of channel peptide restraint. The center-of-mass motion of the chain of channel waters (which is the motion that is critical for transmembrane transport, due to the mandatory single filing of water in the channel) does not exhibit these higher frequency motions. The mobility of the water chain is dramatically reduced by holding the channel rigid. Thus permeation through the channel is not like flow through a rigid pipe; rather permeation is facilitated by peptide motion. For the looser restraints we used, the mobility of the water chain was not very much affected by the degree of restraint. Depending on which set of experiments is considered, the computed mobility of our water chain in the flexible channel is four to twenty times too high to account for the experimentally measured resistance of the gramicidin channel to water flow. From this result it appears likely that the peptide motions of an actual gramicidin channel embedded in a lipid membrane may be more restrained than in our flexible channel model, and that these restraints may be a significant modulator of channel permeability. For the completely rigid channel model the "trapping" of the water molecules in preferred positions throughout the molecular dynamics run precludes a reasonable assessment of mobility, but it seems to be quite low.     

A kinematic approach for efficient and robust simulation of the cardiac beating motion

Computer simulation techniques for cardiac beating motions potentially have many applications and a broad audience. However, most existing methods require enormous computational costs and often show unstable behavior for extreme parameter sets, which interrupts smooth simulation study and make it difficult to apply them to interactive applications. To address this issue, we present an efficient and robust framework for simulating the cardiac beating motion. The global cardiac motion is generated by the accumulation of local myocardial fiber contractions. We compute such local-to-global deformations using a kinematic approach; we divide a heart mesh model into overlapping local regions, contract them independently according to fiber orientation, and compute a global shape that satisfies contracted shapes of all local regions as much as possible. A comparison between our method and a physics-based method showed that our method can generate motion very close to that of a physics-based simulation. Our kinematic method has high controllability; the simulated ventricle-wall-contraction speed can be easily adjusted to that of a real heart by controlling local contraction timing. We demonstrate that our method achieves a highly realistic beating motion of a whole heart in real time on a consumer-level computer. Our method provides an important step to bridge a gap between cardiac simulations and interactive applications.     

Thermodynamic dissection of large‐scale domain motions coupled with ligand binding of enzyme I

Domain motions are central to the biological functions of many proteins. The energetics of the motions, however, is often difficult to characterize when motions are coupled with the ligand binding. Here, we determined the thermodynamic parameters of individual domain motions and ligand binding of enzyme I (EI) using strategic domain-deletion mutants that selectively removed particular motions. Upon ligand binding, EI employs two large-scale domain motions, the hinge motion and the swivel motion, to switch between conformational states of distinct domain−domain orientations. Calorimetric analysis of the EI mutants separated the free energy changes of the binding and motions, demonstrating that the unfavorable hinge motion (ΔG = 1.5 kcal mol⁻¹) was driven by the favorable swivel motion (ΔG = −5.2 kcal mol⁻¹). The large free energy differences could be explained by the physicochemical nature of the domain interfaces associated with the motions; the hinge motion employed much narrower interface than the swivel motion without any hydrogen bonds or salt bridges. The small heat capacity further suggested that the packing of the domain interfaces associated with the hinge motion was less compact than that commonly observed in proteins. Lastly, thermodynamic analysis of phosphorylated EI suggests that the domain motions are regulated by the ligand binding and the phosphorylation states. Taken together, the thermodynamic dissection approach illustrates how multiple motions and ligand binding are energetically connected during the functional cycle of EI.     

A musculo-skeletal model of rat ankle motion and its experimental test on rat

A biomechanical musculo-skeletal model of functional electrical stimulation (FES)-induced rat ankle motion was implemented and tested in rat experiments. The muscle model is a new Hill-based model which includes established physiological relations of force-velocity and force-length-frequency. However, the series-elastic component and the activation component of previous Hill-based models are replaced by a new component which accounts for dynamic time delays and recruitment that occur in real muscle force generation during limb movements. The skeletal model includes gravity and dynamic forces that occur in real rat ankle motions. In computer simulations, various FES patterns were applied to the tibialis anterior (TA) and soleus (SO) model muscles to produce walk-like ankle motions. In lab experiments, the same stimulation patterns were applied by epimysial electrodes implanted in the TA and SO muscles of live rats cordotomized at level T7. The resulting rat motions were recorded by video camera. Video data was converted to ankle angle-vs-time files for comparison with corresponding model angle-vs-time files. Over a physiologically significant range of ankle motions, model parameters were adjustable to yield model motions that agreed with rat motions to within 2 degrees (root mean square differences of rat and model ankle angles). This is shown in plots of model and rat motions presented here for representative cases of FES. The accuracy of our model in reproducing real ankle motions supports the hypothesis that our new muscle model generates correct muscle forces over a useful range of limb motions. It suggests that the model may be useful in the design of FES neural prostheses.     

Design of a marker-based human motion tracking system

In this paper a complete design of a high speed optical motion analyzer system has been described. The main core of the image processing unit has been implemented by the differential algorithm procedure. Some intelligent and conservative procedures that facilitate the search algorithm have also been proposed and implemented for the processing of human motions. Moreover, an optimized modified direct linear transformation (MDLT) method has been used to reconstruct 3D markers positions which are used for deriving kinematic characteristics of the motion. Consequently, a set of complete tests using some simple mechanical devices were conducted to verify the system outputs. Considering the system verification for human motion analysis, we used the system for gait analysis and the results including joint angles showed good compatibility with other investigations. Furthermore, a sport application example of the system has been quantitatively presented and discussed for Iranian National Karate-kas. The low computational cost, the high precision in detecting and reconstructing marker position with 2.39 mm error, and the capability of capturing from any number of cameras to increase the domain of operation of the subject, has made the proposed method a reliable approach for real-time human motion analysis. No special environment limitation, portability, low cost hardware and built in units for simulations and kinematic analysis are the other significant specifications of this system.     

Bias-free separation of internal and overall motion of biomolecules

Collective internal motions are known to be important for the function of biological macromolecules. It has been discussed in the past whether the application of superimposing algorithms to remove the overall motion from a structural ensemble introduces artificial correlations between distant atoms. Here we present a new method to eliminate residual rotation and translation from cartesian modes derived from a normal mode analysis or from a principal component analysis. Bias-free separation is based on the idea that the addition of modes of pure rotation/translation can compensate the residual overall motion. Removal of overall motion must reduce the "total amount of motion" (TAM) in the mode. Our algorithm allows to back-calculate revised covariance matrices. The approach was applied to two model systems that show residual overall motion, when analyzed using all atoms as reference for the superimposing algorithm. In both cases, our algorithm was capable of eliminating residual covariances caused by the overall motion, while retaining internal covariances even for very distant atoms. A structural ensemble obtained for a 13-ns molecular dynamics simulation of the protein Ribonuclease T1 showed a covariance matrix of the corrected modes with significantly sharper contours after applying the bias-free separation.