Three-dimensional Joint Rotations Research Articles

Beyond Inverse Dynamics: Methods for Assessment of Individual Muscle Function during Gait.

Three-dimensional motion analysis performed in the modern gait analysis laboratory provides a wealth of information about the kinematics and kinetics of human locomotion, but standard gait analysis is largely restricted to joint-level measures. Three-dimensional joint rotations, joint moments, and joint powers tell us a great deal about gait mechanics, but it is often of interest to know about the roles that muscles play. This narrative review surveys work that has been done, largely over the past four decades, to augment standard gait analysis with muscle-level assessments of function. Often, these assessments have incorporated additional technology such as ultrasound imaging, or complex modeling and simulation techniques. The review discusses measurements of muscle moment arm during walking along with assessment of muscle mechanical advantage, muscle-tendon lengths, and the use of induced acceleration analysis to determine muscle roles. In each section of the review, examples are provided of how the auxiliary analyses have been used to gain potentially useful information about normal and pathological human walking. While this work highlights the potential benefits of adding various measures to gait analysis, it is acknowledged that challenges to implementation remain, such as the need for specialized knowledge and the potential for bias introduced by model choices.

Rear-foot, mid-foot and fore-foot motion during the stance phase of gait

This paper proposes a new protocol designed to track a large number of foot segments during the stance phase of gait with the smallest possible number of markers, with particular clinical focus on coronal plane alignment of the rear-foot, transverse and sagittal plane alignment of the metatarsal bones, and changes at the medial longitudinal arch. The shank, calcaneus, mid-foot and metatarsus were assumed to be 3D rigid bodies. The longitudinal axis of the first, second and fifth metatarsal bones and the proximal phalanx of the hallux were also tracked independently. Skin markers were mounted on bony prominences or joint lines, avoiding the course of main tendons. Trajectories of the 14 markers were collected by an eight-camera motion capture system at 100 Hz on a population of 10 young volunteers. Three-dimensional joint rotations and planar angles were calculated according to anatomically based reference frames. The marker set was well visible throughout the stance phase of gait, even in a camera configuration typical of gait analysis of the full body. The time-histories of the joint rotations and planar angles were well repeatable among subjects and consistent with clinical and biomechanical knowledge. Several dynamic measurements were originally taken, such as elevation/drop of the medial longitudinal arch and of three metatarsal bones, rear-foot to fore-foot rotation and transverse plane deformation of the metatarsus. The information obtained from this protocol, consistent with previous clinical knowledge, enhanced our understanding of the dynamics of the human foot during stance.

Direct comparison of kinematic data collected using an electromagnetic tracking system versus a digital optical system

The purpose of this study was to quantify the dynamic accuracy of kinematics measured by a digital optical motion analysis system in a gait analysis laboratory (capture volume approximately 20 m 3) compared to a standard range direct-current electromagnetic (EM) tracking device (capture volume approximately 1 m 3). This is a subset of a larger effort to establish an appropriate marker set for the optical system to quantify upperlimb kinematics simultaneously with gait, in comparison to previous studies of isolated upperlimb movements that have employed EM tracking devices. Rigid clusters of spherical reflective markers and EM sensors were attached to a mechanical articulator that mimicked three-dimensional joint rotations, similar to the elbow. As the articulator was moved through known ranges of motion (i.e. gold standard), kinematic data were collected simultaneously using both tracking systems. Both systems were tended to underestimate the range of motion; however, the application of post hoc smoothing and least-squares correction algorithms reduced these effects. When smoothing and correction algorithms were used, the magnitude of the mean difference between the gold standard and either the EM or optical system did not exceed 2° for any of the compound motions performed. This level of agreement suggests that the measurements obtained from either system are clinically comparable, provided appropriate smoothing and correction algorithms are employed.

A new non-orthogonal decomposition method to determine effective torques for three-dimensional joint rotation

This paper describes a new non-orthogonal decomposition method to determine effective torques for three-dimensional (3D) joint rotation. A rotation about a joint coordinate axis (e.g. shoulder internal/external rotation) cannot be explained only by the torque about the joint coordinate axis because the joint coordinate axes usually deviate from the principal axes of inertia of the entire kinematic chain distal to the joint. Instead of decomposing torques into three orthogonal joint coordinate axes, our new method decomposes torques into three “non-orthogonal effective axes” that are determined in such a way that a torque about each effective axis produces a joint rotation only about one of the joint coordinate axes. To demonstrate the validity of this new method, a simple internal/external rotation of the upper arm with the elbow flexed at 90° was analyzed by both orthogonal and non-orthogonal decomposition methods. The results showed that only the non-orthogonal decomposition method could explain the cause-effect mechanism whereby three angular accelerations at the shoulder joint are produced by the gravity torque, resultant joint torque, and interaction torque. The proposed method would be helpful for biomechanics and motor control researchers to investigate the manner in which the central nervous system coordinates the gravity torque, resultant joint torque, and interaction torque to control 3D joint rotations.

Joint rotation between two attitudes in the spherical rotation coordinate system

Three-dimensional joint rotation between two attitudes rather than starting from neutral position is the most common pattern of human movement. This paper presents a method for determining the joint rotations starting from a non-neutral attitude in the spherical rotation coordinate system based on a two-step rotation method. The method uses three spherical rotation angles that are consistent with clinical description of joint rotations and are mathematically proved to be sequence independent. The method can be easily understood by clinicians and applied in clinical practice. Two numerical examples of humeral rotations are presented to demonstrate the effectiveness of the method in dealing with different patterns of three-dimensional joint rotations between two attitudes.

A spherical rotation coordinate system for the description of three-dimensional joint rotations.

Three-dimensional joint rotations in human movement analysis have been mainly described by Euler/Cardan angles. Due to sequence dependence, each combination of three Euler/Cardan angles defines a single pattern of joint rotation. When the rotation pattern is unknown, it needs to be considered using a particular sequence of Euler/Cardan angles to represent joint rotations. In this paper a spherical rotation coordinate system is developed for describing three-dimensional joint rotations using a method of rotation involving two steps: a long axis rotation and a pure axial rotation. Two angles of the classical spherical coordinate system--longitude and latitude--are used to describe long axis rotations in this newly proposed coordinate system. The spherical rotation coordinate system uses a radial rotation angle to describe pure axial rotation of a limb segment whereas the classical spherical coordinate system uses a radial displacement to describe motion of a point. An application of the spherical rotation coordinate system is given to define three-dimensional rotations of the glenohumeral joint. A mathematical proof shows that the long axis rotation and axial rotation are sequence independent. Two numerical examples are investigated which demonstrate that the spherical rotation angles can be uniquely determined in both forward and inverse kinematics without considering sequences rotations.

A three-dimensional definition for the flexion/extension and abduction/adduction angles.

Flexion/extension and abduction/adduction, two major parameters for the description of joint rotations, are used to define planer anatomical orientations of body segments. These two-dimensional definitions have been used extensively in the biomechanical literature for reporting and representing both two-dimensional and three-dimensional joint rotations. Whether these traditional two-dimensional measurements represent true joint rotations in three dimensions has not been investigated. A quantitative error analysis is presented to show how large an error can be produced in the flexion/extension and abduction/adduction angles when using two-dimensional measurements to represent three-dimensional joint rotations. The results indicate that for an out-of-plane flexion the error in abduction angle measured by previous methods increases with both flexion and initial abduction angle and become very sensitive when the flexion angle exceeds 40 degrees. Although the error can be less than 2 degrees for flexion below 20 degrees when the initial abduction angle is at 30 degrees, it can be as large as 9 degrees for 60 degrees of flexion with an initial 10 degrees of abduction; nearly double the real abduction angle. Therefore, two-dimensional measurements of flexion/extension and abduction/adduction can be erroneous and overestimated for a three-dimensional joint rotation. To overcome the problem new definitions are proposed for the true flexion/extension and abduction/adduction angles as two independent parameters for three-dimensional joint rotation.

Methodological considerations for using inductive sensors (3space isotrak) to monitor 3-D orthopaedic joint motion

Objective. To assess and improve methodological constraints of the 3 space isotrak. Design. Several data sets were used to evaluate the following constraints: the performance is adversely affected by close proximity of metallic objects or electromagnetic fields; the 3 space field contaminates electromyography recordings; and cross-talk from one axis to the other two occurs if the Euler rotation sequence is not matched to the orthopaedic description and function of the joint in question. Background. The 3 space isotrak is one of the few instruments suitable for measurement of relative three-dimensional joint rotation, however several methodological constraints exist. Results and Conclusions. Generally, accuracy can be maintained by restricting offending objects from the sensitive zone between the transmitter and sensor and using long leads to afford the subject distance from computers and other electrical instrumentation; while contamination of EMG amplitude in the time domain can be minimized by using quality instrumentation, and on occasion modifying electrode orientation. Contamination of the EMG frequency content appears unavoidable at low levels of muscle contraction; and cross-talk between axes is minimized by matching the first Euler rotation with the axis of the joint that is characterized by the greatest expected angular displacement.

An inverse dynamics model for the analysis, reconstruction and prediction of bipedal walking

Walking is a constrained movement which may best be observed during the double stance phase when both feet contact the floor. When analyzing a measured movement with an inverse dynamics model, a violation of these constrains will always occur due to measuring errors and deviations of the segments model from reality, leading to inconsistent results. Consistency is obtained by implementing the constraints into the model. This makes it possible to combine the inverse dynamics model with optimization techniques in order to predict walking patterns or to reconstruct non-measured rotations when only a part of the three-dimensional joint rotations is measured. In this paper the outlines of the extended inverse dynamics method are presented, the constraints which define walking are defined and the optimization procedure is described. The model is applied to analyze a normal walking pattern of which only the hip, knee and ankle flexions/extensions are measured. This input movement is reconstructed to a kinematically and dynamically consistent three-dimensional movement, and the joint forces (including the ground reaction forces) and joint moments of force, needed to bring about this movement are estimated.

Kinematic analysis of human movement.

Understanding the kinematics of human movement is of both a basic and an applied value in medicine and biology. Motion measurement can be used to evaluate functional performance of limbs under normal and abnormal conditions. Kinematic knowledge is also essential for proper diagnosis and surgical treatment of joint disease and the design of prosthetic devices to restore function. In general, kinematic analysis of human movement can be categorized into two main areas: 1) Gross movement of the limb segments interconnected by joints, where the relative three-dimensional joint rotation is described by adopting the Eulerian angle system. With proper selection of axes of rotation between two bone segments, the associated finite rotation is sequence independent. This concept is particularly useful, since it matches precisely the clinical definition of joint motion. 2) Detailed analysis of joint articulating surface motion, where generalized three-dimensional, unconstrained rotation and translation are described utilizing the concept of the screw displacement axis. Knowing the surface geometry and soft-tissue constraints, the movement of an articulating joint can be analyzed to provide basic information for lubrication and wear studies. In addition, with appropriate numerical differentiation, velocity and acceleration can be obtained from the displacement information described by the above two methods. Currently available measurement techniques of human movement can be classified into three categories: 1) electrical linkage methods; 2) stereometric methods and biplanar roentgenographic methods; and 3) accelerometric methods. Each system has its unique advantages and limitations in terms of the operational principle, instruments required, data reduction, and type of information produced. Representative analyses of human upper and lower extremity movement will be included as illustrative examples.