Use of dual Euler angles to quantify the three-dimensional joint motion and its application to the ankle joint complex

This paper presents a modified Euler angles method, dual Euler angles approach, to describe general spatial human joint motions. In dual Euler angles approach, the three-dimensional joint motion is considered as three successive screw motions with respect to the axes of the moving segment coordinate system; accordingly, the screw motion displacements are represented by dual Euler angles. The algorithm for calculating dual Euler angles from coordinates of markers on the moving segment is also provided in this study. As an example, the proposed method is applied to describe motions of ankle joint complex during dorsiflexion–plantarflexion. A Flock of Birds electromagnetic tracking device (FOB) was used to measure joint motion in vivo. Preliminary accuracy tests on a gimbal structure demonstrate that the mean errors of dual Euler angles evaluated by using source data from FOB are less than 1° for rotations and 1 mm for translations, respectively. Based on the pilot study, FOB is feasible for quantifying human joint motions using dual Euler angles approach.     

Knee joint secondary motion accuracy improved by quaternion-based optimizer with bony landmark constraints

Skin marker-based motion analysis has been widely used in biomechanical studies and clinical applications. Unfortunately, the accuracy of knee joint secondary motions is largely limited by the nonrigidity nature of human body segments. Numerous studies have investigated the characteristics of soft tissue movement. Utilizing these characteristics, we may improve the accuracy of knee joint motion measurement. An optimizer was developed by incorporating the soft tissue movement patterns at special bony landmarks into constraint functions. Bony landmark constraints were assigned to the skin markers at femur epicondyles, tibial plateau edges, and tibial tuberosity in a motion analysis algorithm by limiting their allowed position space relative to the underlying bone. The rotation matrix was represented by quaternion, and the constrained optimization problem was solved by Fletcher's version of the Levenberg-Marquardt optimization technique. The algorithm was validated by using motion data from both skin-based markers and bone-mounted markers attached to fresh cadavers. By comparing the results with the ground truth bone motion generated from the bone-mounted markers, the new algorithm had a significantly higher accuracy (root-mean-square (RMS) error: 0.7 ± 0.1 deg in axial rotation and 0.4 ± 0.1 deg in varus-valgus) in estimating the knee joint secondary rotations than algorithms without bony landmark constraints (RMS error: 1.7 ± 0.4 deg in axial rotation and 0.7 ± 0.1 deg in varus-valgus). Also, it predicts a more accurate medial-lateral translation (RMS error: 0.4 ± 0.1 mm) than the conventional techniques (RMS error: 1.2 ± 0.2 mm). The new algorithm, using bony landmark constrains, estimates more accurate secondary rotations and medial-lateral translation of the underlying bone.     

Modeling of control and learning in a stepping motion

In a previous study (Beuter et al. 1986) the authors modeled a stepping motion using a three-body linkage with four degrees of freedom. Stepping was simulated by using three task parameters (i.e., step height, length, and duration) and sinusoidal joint angular velocity profiles. The results supported the concept of a hierarchical control structure with open-loop control during normal operation. In this study we refine the dynamic model and improve the simulation technique by incorporating the dynamics of the leg after landing, adding a foot segment to the model, and preprogramming the complete step motion using cycloids. The equations of the forces and torques developed on the ground by the foot during the landing phase are derived using the Lagrangian method. Simulation results are compared to experimental data collected on a subject stepping four times over an obstacle using a Selspot motion analysis system. A hierarchical control model that incorporates a learning process is proposed. The model allows an efficient combination of open and closed loop control strategies and involves hardwired movement segments. We also test the hypothesis of cycloidal velocity profiles in the joint programs against experimental data using a novel curve-fitting procedure based on analytical rather than numerical differentiation. The results suggest multiob-jective optimization of the joint's motion. The control and learning model proposed here will help the understanding of the mechanisms responsible for assembling selected movement segments into goaldirected movement sequences in humans.     

Kinematics of lower limbs during walking are emulated by springy walking model with a compliantly connected,off-centered curvy foot

The dynamics of the center of mass (CoM) during walking and running at various gait conditions are well described by the mechanics of a simple passive spring loaded inverted pendulum (SLIP). Due to its simplicity, however, the current form of the SLIP model is limited at providing any further information about multi-segmental lower limbs that generate oscillatory CoM behaviors and their corresponding ground reaction forces. Considering that the dynamics of the CoM are simply achieved by mass-spring mechanics, we wondered whether any of the multi-joint motions could be demonstrated by simple mechanics. In this study, we expand a SLIP model of human locomotion with an off-centered curvy foot connected to the leg by a springy segment that emulates the asymmetric kinematics and kinetics of the ankle joint. The passive dynamics of the proposed expansion of the SLIP model demonstrated the empirical data of ground reaction forces, center of mass trajectories, ankle joint kinematics and corresponding ankle joint torque at various gait speeds. From the mechanically simulated trajectories of the ankle joint and CoM, the motion of lower-limb segments, such as thigh and shank angles, could be estimated from inverse kinematics. The estimation of lower limb kinematics showed a qualitative match with empirical data of walking at various speeds. The representability of passive compliant mechanics for the kinetics of the CoM and ankle joint and lower limb joint kinematics implies that the coordination of multi-joint lower limbs during gait can be understood with a mechanical framework.     

Representation of planar motion of complex joints by means of rolling pairs. Application to neck motion

We propose to model planar movements between two human segments by means of rolling-without-slipping kinematic pairs. We compute the path traced by the instantaneous center of rotation (ICR) as seen from the proximal and distal segments, thus obtaining the fixed and moving centrodes, respectively. The joint motion is then represented by the rolling-without-slipping of one centrode on the other. The resulting joint kinematic model is based on the real movement and accounts for nonfixed axes of rotation; therefore it could improve current models based on revolute pairs in those cases where joint movement implies displacement of the ICR. Previous authors have used the ICR to characterize human joint motion, but they only considered the fixed centrode. Such an approach is not adequate for reproducing motion because the fixed centrode by itself does not convey information about body position. The combination of the fixed and moving centrodes gathers the kinematic information needed to reproduce the position and velocities of moving bodies. To illustrate our method, we applied it to the flexion-extension movement of the head relative to the thorax. The model provides a good estimation of motion both for position variables (mean R(pos)=0.995) and for velocities (mean R(vel)=0.958). This approach is more realistic than other models of neck motion based on revolute pairs, such as the dual-pivot model. The geometry of the centrodes can provide some information about the nature of the movement. For instance, the ascending and descending curves of the fixed centrode suggest a sequential movement of the cervical vertebrae.     

Auditory motion information drives visual motion perception

Background

Vision provides the most salient information with regard to the stimulus motion. However, it has recently been demonstrated that static visual stimuli are perceived as moving laterally by alternating left-right sound sources. The underlying mechanism of this phenomenon remains unclear; it has not yet been determined whether auditory motion signals, rather than auditory positional signals, can directly contribute to visual motion perception.

Methodology/Principal Findings

Static visual flashes were presented at retinal locations outside the fovea together with a lateral auditory motion provided by a virtual stereo noise source smoothly shifting in the horizontal plane. The flash appeared to move by means of the auditory motion when the spatiotemporal position of the flashes was in the middle of the auditory motion trajectory. Furthermore, the lateral auditory motion altered visual motion perception in a global motion display where different localized motion signals of multiple visual stimuli were combined to produce a coherent visual motion perception.

Conclusions/Significance

These findings suggest there exist direct interactions between auditory and visual motion signals, and that there might be common neural substrates for auditory and visual motion processing.     

Motion segmentation method for hybrid characteristic on human motion

Motion segmentation and analysis are used to improve the process of classification of motion and information gathered on repetitive or periodic characteristic. The classification result is useful for ergonomic and postural safety analysis, since repetitive motion is known to be related to certain musculoskeletal disorders. Past studies mainly focused on motion segmentation on particular motion characteristic with certain prior knowledge on static or periodic property of motion, which narrowed method's applicability. This paper attempts to introduce a method to tackle human joint motion without having prior knowledge. The motion is segmented by a two-pass algorithm. Recursive least square (RLS) is firstly used to estimate possible segments on the input human-motion set. Further, period identification and extra segmentation process are applied to produce meaningful segments. Each of the result segments is modeled by a damped harmonic model, with frequency, amplitude and duration produced as parameters for ergonomic evaluation and other human factor studies such as task safety evaluation and sport analysis. Experiments show that the method can handle periodic, random and mixed characteristics on human motion, which can also be extended to the usage in repetitive motion in workflow and irregular periodic motion like sport movement.     

Tracking the motion of hidden segments using kinematic constraints and Kalman filtering

Motion capture for biomechanical applications involves in almost all cases sensors or markers that are applied to the skin of the body segments of interest. This paper deals with the problem of estimating the movement of connected skeletal segments from 3D position data of markers attached to the skin. The use of kinematic constraints has been shown previously to reduce the error in estimated segment movement that are due to skin and muscles moving with respect to the underlying segment. A kinematic constraint reduces the number of degrees of freedom between two articulating segments. Moreover, kinematic constraints can help reveal the movement of some segments when the 3D marker data otherwise are insufficient. Important cases include the human ankle complex and the phalangeal segments of the horse, where the movement of small segments is almost completely hidden from external observation by joint capsules and ligaments. This paper discusses the use of an extended Kalman filter for tracking a system of connected segments. The system is modeled using rigid segments connected by simplified joint models. The position and orientation of the mechanism are specified by a set of generalized coordinates corresponding to the mechanism's degrees of motion. The generalized coordinates together with their first time derivatives can be used as the state vector of a state space model governing the kinematics of the mechanism. The data collected are marker trajectories from skin-mounted markers, and the state vector is related to the position of the markers through a nonlinear function. The Jacobian of this function is derived. The practical use of the method is demonstrated on a model of the distal part of the limb of the horse. Monte Carlo simulations of marker data for a two-segment system connected by a joint with three degrees of freedom indicate that the proposed method gives significant improvement over a method, which does not make use of the joint constraint, but the method requires that the model is a good approximation of the true mechanism. Applying the method to data on the movement of the four distal-most segments of the horse's limb shows good between trial consistency and small differences between measured marker positions and marker positions predicted by the model.     

The mechanisms that enable arm motion to enhance vertical jump performance-a simulation study

The reasons why using the arms can increase standing vertical jump height are investigated by computer simulations. The human models consist of four/five segments connected by frictionless joints. The head-trunk-arms act as a fourth segment in the first model while the arms become a fifth segment in the second model. Planar model movement is actuated by joint torque generators. Each joint torque is the product of three variable functions of activation level, angular velocity dependence, and maximum isometric torque varying with joint angle. Simulations start from a balanced initial posture and end at jump takeoff. Jump height is maximized by finding the optimal combination of joint activation timings. Arm motion enhances jumping performance by increasing mass center height and vertical takeoff velocity. The former and latter contribute about 1/3 and 2/3 to the increased height, respectively. Durations in hip torque generation and ground contact period are lengthened by swinging the arms. Theories explaining the performance enhancement caused by arms are examined. The force transmission theory is questionable because shoulder joint force due to arm motion does not precisely reflect the change in vertical ground reaction force. The joint torque/work augmentation theory is acceptable only at the hips but not at the knees and ankles because only hip joint work is considerably increased. The pull/impart energy theory is also acceptable because shoulder joint work is responsible for about half of the additional energy created by arm swings.     

Load-displacement properties of lower cervical spine motion segments

The load-displacement behavior of 35 fresh adult cervical spine motion segments was measured in compression, shear, flexion, extension, lateral bending and axial torsion tests. Motion segments were tested both intact and with posterior elements removed. Applied forces ranged to 73.6 N in compression and to 39 N in shear, while applied moments ranged to 2.16 Nm. For each mode of loading, principal and coupled motions were measured and stiffnesses were calculated. The effect of disc degeneration on motion segment stiffnesses and the moments required for motion segment failure were also measured. In compression, the stiffnesses of the cervical motion segments were similar to those of thoracic and lumbar motion segments. In other modes of loading, cervical stiffnesses were considerably smaller than thoracic or lumbar stiffnesses. Removal of the posterior elements decreased cervical motion segment stiffnesses by as much as 50%. Degenerated cervical discs were less stiff in compression and stiffer in shear than less degenerated discs, but in bending or axial torsion, no statistically significant differences were evident. Bending moments causing failure were an order of magnitude lower than those for lumbar segments.     

Interaction torque contributes to planar reaching at slow speed

Background

How the central nervous system (CNS) organizes the joint dynamics for multi-joint movement is a complex problem, because of the passive interaction among segmental movements. Previous studies have demonstrated that the CNS predictively compensates for interaction torque (INT) which is arising from the movement of the adjacent joints. However, most of these studies have mainly examined quick movements, presumably because the current belief is that the effects of INT are not significant at slow speeds. The functional contribution of INT for multijoint movements performed in various speeds is still unclear. The purpose of this study was to examine the contribution of INT to a planer reaching in a wide range of motion speeds for healthy subjects.

Methods

Subjects performed reaching movements toward five targets under three different speed conditions. Joint position data were recorded using a 3-D motion analysis device (50 Hz). Torque components, muscle torque (MUS), interaction torque (INT), gravity torque (G), and net torque (NET) were calculated by solving the dynamic equations for the shoulder and elbow. NET at a joint which produces the joint kinematics will be an algebraic sum of torque components; NET = MUS - G - INT. Dynamic muscle torque (DMUS = MUS-G) was also calculated. Contributions of INT impulse and DMUS impulse to NET impulse were examined.

Results

The relative contribution of INT to NET was not dependent on speed for both joints at every target. INT was additive (same direction) to DMUS at the shoulder joint, while in the elbow DMUS counteracted (opposed to) INT. The trajectory of reach was linear and two-joint movements were coordinated with a specific combination at each target, regardless of motion speed. However, DMUS at the elbow was opposed to the direction of elbow movement, and its magnitude varied from trial to trial in order to compensate for the variability of INT.

Conclusion

Interaction torque was important at slow speeds. Muscle torques at the two joints were not directly related to each other to produce coordinated joint movement during a reach. These results support Bernstein's idea that coordinated movement is not completely determined by motor command in multi-joint motion. Based on the data presented in this study and the work of others, a model for the connection between joint torques (muscle and passive torques including interaction torque) and joint coordination is proposed.     

The impact of adding trunk motion to the interpretation of the role of joint moments during normal walking

Biomechanical model assumptions affect the interpretation of the role of the muscle or joint moments to the segmental power estimated by induced acceleration analysis (IAA). We evaluated the effect of modeling the pelvis and trunk segments as two separate segments (8 SM) versus as a single segment (7 SM) on the segmental power, support of the body, knee and hip extension acceleration produced by the joint moments during the stance phase of normal walking. Significant differences were observed in the contribution of the stance hip abductor and extensor moments to support, ipsilateral knee and hip acceleration, and ipsilateral thigh and upper body power. The primary finding was that the role of the stance hip moment in generating ipsilateral thigh and upper body power differed based on degrees of freedom in the model. Secondarily, the magnitude of contributions also differed. For example, the hip abductor and extensor moments showed greater contribution to support, hip and knee acceleration in the 8 SM. IAA and segment power analysis are sensitive to the degrees of freedom between the pelvis and trunk. There is currently no gold standard by which to evaluate the accuracy of IAA predictions. However, modeling the pelvis and trunk as separate segments is closer to the anatomical architecture of the body. An 8 SM appears to be more appropriate for estimating the role of joint moments, particularly to motion of more proximal segments during normal walking.     

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.     

Measurement of a spinal motion segment stiffness matrix

The six-degrees-of-freedom elastic behavior of spinal motion segments can be approximated by a stiffness matrix. A method is described to measure this stiffness matrix directly with the motion segment held under physiological conditions of axial preload and in an isotonic fluid bath by measuring the forces and moments associated with each of the six orthogonal translations and rotations. The stiffness matrix was obtained from the load-displacement measurements by linear least squares assuming a symmetric matrix. Results from a pig lumbar spinal motion segment in an isotonic bath, with and without a 500 N axial preload, showed a large stiffening effect with axial preload.     

Effect of a pedicle-screw-based motion preservation system on lumbar spine biomechanics: A probabilistic finite element study with subsequent sensitivity analysis

Pedicle-screw-based motion preservation systems are often used to support a slightly degenerated disc. Such implants are intended to reduce intradiscal pressure and facet joints forces, while having a minimal effect on the motion patterns.In a probabilistic finite element study with subsequent sensitivity analysis, the effects of 10 input parameters, such as elastic modulus and diameter of the elastic rod, distraction of the segment, level of bridged segments, etc. on the output parameters intervertebral rotations, intradiscal pressures, and facet joint forces were determined. A validated finite element model of the lumbar spine was employed. Probabilistic studies were performed for seven loading cases: upright standing, flexion, extension, left and right lateral bending and left and right axial rotation.The simulations show that intervertebral rotation angles, intradiscal pressures and facet joint forces are in most cases reduced by a motion preservation system. The influence on intradiscal pressure is small, except in extension. For many input parameter combinations, the values for intervertebral rotations and facet joint forces are very low, which indicates that the implant is too stiff in these cases. The output parameters are affected most by the following input parameters: loading case, elastic modulus and diameter of the elastic rod, distraction of the segment, and angular rigidity of the connection between screws and rod.The designated functions of a motion preservation system can best be achieved when the longitudinal rod has a low stiffness, and when the connection between rod and pedicle screws is rigid.     

Quantifying biomechanical motion using Procrustes motion analysis

The ability to quantify and compare the movements of organisms is a central focus of many studies in biology, anthropology, biomechanics, and ergonomics. However, while the importance of functional motion analysis has long been acknowledged, quantitative methods for identifying differences in motion have not been widely developed. In this article, we present an approach to the functional analysis of motion and quantification of motion types. Our approach, Procrustes Motion Analysis (PMA) can be used to distinguish differences in cyclical, repeated, or goal-directed motions. PMA exploits the fact that any motion can be represented by an ordered sequence of postures exhibited throughout the course of a motion. Changes in posture from time step to time step form a trajectory through a multivariate data space, representing a specific motion. By evaluating the size, shape, and orientation of these motion trajectories, it is possible to examine variation in motion type within and among groups or even with respect to continuous variables. This represents a significant analytical advance over current approaches. Using simulated and digitized data representing cyclical, repeated and goal-directed motions, we show that PMA correctly identifies distinct motion tasks in these data sets.     

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.     

Role of endplates in contributing to compression behaviors of motion segments and intervertebral discs

The purpose of this study was to gain an improved understanding of the mechanical behavior of the intervertebral disc in the presence and absence of the vertebral endplates. Mechanical behaviors of rat caudal motion segments, vertebrae and isolated disc explants under two different permeability conditions were investigated and viscoelastic behaviors were evaluated using a stretched-exponential function to describe creep and recovery behaviors. The results demonstrated that both vertebrae and discs underwent significant deformations in the motion segment even under relatively low-loading conditions. Secondly, disruption of the collagenous network had minimal impact on equilibrium deformations of disc explants as compared to disc deformations occurring in the motion segments provided that vertebral deformations were accounted for; however, differences in endplate permeability conditions had a significant effect on viscoelastic behaviors. Creep occurred more quickly than recovery for motion segment and explant specimens. In addition, disc explants and motion segments both exhibited non-recoverable deformations under axial compression under low- and high-loading conditions. Results have important implications for interpreting the role of vertebral endplates in contributing to disc mechanical behaviors and direct application to mechanobiology studies involving external loading to rodent tail intervertebral discs.