Effects of data smoothing on the reconstruction of helical axis parameters in human joint kinematics

In biomechanical joint-motion analyses, the continuous motion to be studied is often approximated by a sequence of finite displacements, and the Finite Helical Axis (FHA) or "screw axis" for each displacement is estimated from position measurements on a number of anatomical or artificial landmarks. When FHA parameters are directly determined from raw (noisy) displacement data, both the position and the direction of the FHA are ill-determined, in particular when the sequential displacement steps are small. This implies, that under certain conditions, the continuous pathways of joint motions cannot be adequately described. The purpose of the present experimental study is to investigate the applicability of smoothing (or filtering) techniques, in those cases where FHA parameters are ill-determined. Two different quintic-spline smoothing methods were used to analyze the motion data obtained with Roentgenstereophotogrammetry in two experiments. One concerning carpal motions in a wrist-joint specimen, and one relative to a kinematic laboratory model, in which the axis positions are a priori known. The smoothed and non-smoothed FHA parameter errors were compared. The influences of the number of samples and the size of the sampling interval (displacement step) were investigated, as were the effects of equidistant and nonequidistant sampling conditions and noise invariance.     

Plane of vertebral movement eliciting muscle lengthening history in the low back influences the decrease in muscle spindle responsiveness of the cat

Proprioceptive feedback is thought to play a significant role in controlling both lumbopelvic and intervertebral orientations. In the lumbar spine, a vertebra's positional history along the dorsal-ventral axis has been shown to alter the position, movement, and velocity sensitivity of muscle spindles in the multifidus and longissimus muscles. These effects appear due to muscle history. Because spinal motion segments have up to 6 degrees of freedom for movement, we were interested in whether the axis along which the history is applied differentially affects paraspinal muscle spindles. We tested the null hypothesis that the loading axis, which creates a vertebra's positional history, has no effect on a lumbar muscle spindle's subsequent response to vertebral position or movement. Identical displacements were applied along three orthogonal axes directly at the L(6) spinous process using a feedback motor system under displacement control. Single-unit nerve activity was recorded from 60 muscle spindle afferents in teased filaments from L(6) dorsal rootlets innervating intact longissimus or multifidus muscles of deeply anesthetized cats. Muscle lengthening histories along the caudal-cranial and dorsal-ventral axis, compared with the left-right axis, produced significantly greater reductions in spindle responses to vertebral position and movement. The spinal anatomy suggested that the effect of a lengthening history is greatest when that history had occurred along an axis lying within the anatomical plane of the facet joint. Speculation is made that the interaction between normal spinal mechanics and the inherent thixotropic property of muscle spindles poses a challenge for feedback and feedforward motor control of the lumbar spine.     

Rationalization of kinematic descriptors for three-dimensional hand and finger motion

Modelling joint motion in three dimensions is often based on techniques taken from classical dynamics, each analysis resulting in a set of six parameters describing the relative motion betwen two body segments. The literature on joint kinematics has been difficult to compare due to use of different anatomical landmarks, axis nomenclature, and analytical methods. It is here shown that with care in sequence definition, the three alignment-based systems (Euler, Cardan, floating axis) give identical results for angular parameters. While the equivalent screw displacement axis system can be related simply to the other methods only if the functional axis of motion is aligned with a coordinate axis, the basic matrix for relating rigid body positions before and after a motion can always be reconstructed. Therefore the changes in alignment angles may be obtained from screw displacement parameters, permitting the results of different analyses to be compared. Translation parameters are most difficult to interpret in any system. Examples of the way in which simple planar motions are characterized by the various analytical methods are given.     

Estimation of the axis of a screw motion from noisy data--a new method based on Plücker lines

The problems of estimating the motion and orientation parameters of a body segment from two n point-set patterns are analyzed using the Plücker coordinates of a line (Plücker lines). The aim is to find algorithms less complex than those in conventional use, and thus facilitating more accurate computation of the unknown parameters. All conventional techniques use point transformation to calculate the screw axis. In this paper, we present a novel technique that directly estimates the axis of a screw motion as a Plücker line. The Plücker line can be transformed via the dual-number coordinate transformation matrix. This method is compared with Schwartz and Rozumalski [2005. A new method for estimating joint parameters from motion data. Journal of Biomechanics 38, 107-116] in simulations of random measurement errors and systematic skin movements. Simulation results indicate that the methods based on Plücker lines (Plücker line method) are superior in terms of extremely good results in the determination of the screw axis direction and position as well as a concise derivation of mathematical statements. This investigation yielded practical results, which can be used to locate the axis of a screw motion in a noisy environment. Developing the dual transformation matrix (DTM) from noisy data and determining the screw axis from a given DTM is done in a manner analogous to that for handling simple rotations. A more robust approach to solve for the dual vector associated with DTM is also addressed by using the eigenvector and the singular value decomposition.     

Analysis of the interaction between vertebral lateral deviation and axial rotation in scoliosis

There is a lack of clear biomechanical analyses to explain the interaction of the lateral and axial deformity of the spine in idiopathic scoliosis. A finite element model which represented an isolated ligamentous spine with realistic elastic properties and idealized geometry was used to analyse this interaction. Three variations of this model were used to investigate two different hypotheses about the etiology of scoliosis and to define the forces required to produce a scoliosis deformity. The first hypothesis is that coupling within a motion segment produces the interaction between lateral deviation and axial rotation. The second hypothesis is that posterior tethering by soft tissues in the growing spine produces the observed interaction. Modeling of both hypotheses failed to produce the clinically observed pattern of interaction. Therefore, to find which biomechanical forces were required to produce an idealized scoliosis, prescribed displacements were applied to the model. Production of a double curve scoliosis of 10 degrees Cobb angles required lateral forces on the order of 20 N acting 40 mm anterior to the vertebral body centers. There do not appear to be any anatomic structures capable of producing such forces. Therefore, it seems unlikely that scoliosis deformity can be explained in terms of forces acting on the spine, and understanding of its origins may come from examination of other mechanisms such as asymmetric thoracic growth, or asymmetric vertebral development.     

Minimizing errors associated with calculating the location of the helical axis for spinal motions

One of the more common comparative tools used to quantify the motion of the vertebral joint is the orientation and position of the (finite) helical axis of motion as well as the amount of translation along, and rotation about, this axis. A survey of recent studies that utilize the helical axis of motion to compare motion before and after total disc replacement reveals a lack of concern for the relative errors associated with this metric. Indeed, intrinsic algorithmic and experimental errors that arise when interpreting motion tracking data can easily lead to a misinterpretation of the changes caused by replacement disc devices. While previous studies examining these errors exist, most have overlooked the errors associated with the determination of the location of the helical axis and its intersection with a chosen plane. The purpose of the study presented in this paper was to evaluate the sensitivity and reliability of the helical axis of motion as a comparative tool for kinematically evaluating spinal prostheses devices. To this end, we simulated a typical spine biomechanics testing experiment to investigate the accuracy of calculating the helical axis and its associated parameters using several popular algorithms. The resultant data motivated the development of a new algorithm that is a hybrid of two existing algorithms. The improved accuracy of this hybrid method made it possible to quantify some of the changes to the kinematics of a spinal unit that are induced by distinct placements of a total disc replacement.     

The analysis of golf swing as a kinematic chain using dual Euler angle algorithm

The manner in which anatomical rotation from an individual segment contributes to the position and velocity of the endpoint can be informative in the arena of many athletic events whose goals are to attain the maximal velocity of the most distal segment. This study presents a new method of velocity analysis using dual Euler angles and its application in studying rotational contribution from upper extremity segments to club head speed during a golf swing. Dual Euler angle describes 3D movement as a series of ordered screw motions about each orthogonal axis in a streamlined matrix form-the dual transformation matrix- and allows the translation and rotation component to be described in the same moving frame. Applying this method in biomechanics is a novel idea and the authors have previously applied the methodology to clinical studies on its use in displacement analysis. The focus of this paper is velocity analysis and applications in sports biomechanics. In this study, electrogoniometers (Biometrics, UK) with a frequency of 1000 Hz were attached to a subject during the execution of the swing to obtain the joint angles throughout the motion. The velocity of the club head was then analyzed using the dual velocity which specifies the velocity distribution of a rigid body in screw motion at any point in time as the dual vector. The contributions of each segment to the club-head velocity were also compared. In order to evaluate this method, the calculated position and velocity of the club head were compared to the values obtained from video image analysis. The results indicated that there is good agreement between calculated values and video data, suggesting the suitability of using the Dual Euler method in analyzing a kinematic chain motion.     

Analysis of human mandibular mechanics based on screw theory and in vivo data

In this paper the mechanics of human mandibular function is described in terms of the associated screws. The two distinct, yet related features of jaw mechanics, involving the motion itself as well as the forces, are both functions of the anatomical constraints, namely the contact areas that exist within the temporomandibular joint, and the forces of the muscles and tendons that allow motion to occur. The relationships that exist between these two aspects of jaw-motion are identified in this paper showing that muscle forces can be uniquely represented in terms of the action screw. This new approach to analyzing the mechanics of jaw-motion also incorporates the previously studied motion screw or helical axis. A consistent dynamic model is formulated where the action screw is used to represent the action of the closing muscle forces while the moment arms of the muscle forces are determined about the motion screw representing mandibular kinematics. The action screw formulation is verified using in vivo motion data and MR image information for a single asymptomatic subject. The results confirm the feasibility of the method and its application in dental research. A general increase in the mechanical advantage of most muscles, in the distance between action and motion screws as well as in the expended energy towards the end of the jaw-closing phase was observed. Asymmetries in the distribution of muscle force magnitudes appeared to influence the resultant force and moment of the action screw but had little effect on its spatial location. The method presented is intended to facilitate understanding of mandibular function and dysfunction.     

Evidence for IHA migration during axial rotation of a lumbar spine segment by using a novel high-resolution 6D kinematic tracking system

The biomechanical properties of the lumbar spine have long been studied. However, despite its enormous importance, basic functional and morphological properties have been not well understood and require further experimental analysis since data concerning the spatial instantaneous segmental motions are hardly available. This study describes the theoretical background and the technical properties of an innovative method for tracking the instantaneous 3D motion of human spinal segments in vitro at high spatial resolution. This new acquisition system allows to scrutinise closely the location and alignment of the segmental instantaneous helical axis (IHA) and the respective screw pitch as functions of the absolute rotational angle. The required precision of the measuring device was attained (a) by six highly resolving linear inductive displacement sensors in a special spatially configuration (3-2-1), (b) by a method to apply torque and force independently of each other without counteraction, and (c) by suppression of vibrations. The validity and reliability of the experimental set-up and the numerical method of data analysis were tested by subjects of known mechanical properties. In vitro experiments with a human lumbar segment (L3/L4, autopsy material) demonstrated that (a) the IHA migrated during axial rotation from one segmental articulatio zygapophysialis to the other joint, (b) the IHA tilted medial-laterally, and (c) the pitch of the screw altered linearly as a function of the rotational angle. This phenomenon is traced back to the guidance of the articluationes zygapophysiales. The validation of the method allows to map segments of the entire vertebral column. The results can be used as benchmarks for future models of the human spine.     

Pedicle screw-based posterior dynamic stabilisation of the lumbar spine: in vitro cadaver investigation and a finite element study

Pedicle screw-based dynamic constructs either benefit from a dynamic (flexible) interconnecting rod or a dynamic (hinged) screw. Both types of systems have been reported in the literature. However, reports where the dynamic system is composed of two dynamic components, i.e. a dynamic (hinged) screw and a dynamic rod, are sparse. In this study, the biomechanical characteristics of a novel pedicle screw-based dynamic stabilisation system were investigated and compared with equivalent rigid and semi-rigid systems using in vitro testing and finite element modelling analysis. All stabilisation systems restored stability after decompression. A significant decrease in the range of motion was observed for the rigid system in all loadings. In the semi-rigid construct the range of motion was significantly less than the intact in extension, lateral bending and axial rotation loadings. There were no significant differences in motion between the intact spine and the spine treated with the dynamic system (P>0.05). The peak stress in screws was decreased when the stabilisation construct was equipped with dynamic rod and/or dynamic screws.     

Cervical helical axis characteristics and its center of rotation during active head and upper arm movements-comparisons of whiplash-associated disorders, non-specific neck pain and asymptomatic individuals

The helical axis model can be used to describe translation and rotation of spine segments. The aim of this study was to investigate the cervical helical axis and its center of rotation during fast head movements (side rotation and flexion/extension) and ball catching in patients with non-specific neck pain or pain due to whiplash injury as compared with matched controls. The aim was also to investigate correlations with neck pain intensity. A finite helical axis model with a time-varying window was used. The intersection point of the axis during different movement conditions was calculated. A repeated-measures ANOVA model was used to investigate the cervical helical axis and its rotation center for consecutive levels of 15 degrees during head movement. Irregularities in axis movement were derived using a zero-crossing approach. In addition, head, arm and upper body range of motion and velocity were observed. A general increase of axis irregularity that correlated to pain intensity was observed in the whiplash group. The rotation center was superiorly displaced in the non-specific neck pain group during side rotation, with the same tendency for the whiplash group. During ball catching, an anterior displacement (and a tendency to an inferior displacement) of the center of rotation and slower and more restricted upper body movements implied a changed movement strategy in neck pain patients, possibly as an attempt to stabilize the cervical spine during head movement.     

Structural behavior of human lumbar spinal motion segments

The objectives of this study were to obtain linearized stiffness matrices, and assess the linearity and hysteresis of the motion segments of the human lumbar spine under physiological conditions of axial preload and fluid environment. Also, the stiffness matrices were expressed in the form of an 'equivalent' structure that would give insights into the structural behavior of the spine. Mechanical properties of human cadaveric lumbar L2-3 and L4-5 spinal motion segments were measured in six degrees of freedom by recording forces when each of six principal displacements was applied. Each specimen was tested with axial compressive preloads of 0, 250 and 500 N. The displacements were four slow cycles of +/-0.5mm in anterior-posterior and lateral displacements, +/-0.35 mm axial displacement, +/-1.5 degrees lateral rotation and +/-1 degrees flexion-extension and torsional rotations. There were significant increases with magnitude of preload in the stiffness, hysteresis area (but not loss coefficient) and the linearity of the load-displacement relationship. The mean values of the diagonal and primary off-diagonal stiffness terms for intact motion segments increased significantly relative to values with no preload by an average factor of 1.71 and 2.11 with 250 and 500 N preload, respectively (all eight tests p<0.01). Half of the stiffness terms were greater at L4-5 than L2-3 at higher preloads. The linearized stiffness matrices at each preload magnitude were expressed as an equivalent structure consisting of a truss and a beam with a rigid posterior offset, whose geometrical properties varied with preload. These stiffness properties can be used in structural analyses of the lumbar spine.     

Finite Element Analysis of Interbody Cages in a Human Lumbar Spine

An innovative surgical procedure is vertebral stabilization by interbody cages. It is currently being used to separate and stabilize vertebral bodies and to promote bony fusion of the vertebrae onto or through the cages. This surgery, at some spine levels, can be performed through a laparoscope as an outpatient procedure with low morbidity. Because the procedure is new, little structural information is available on the interbody cages. The objective of this study was to evaluate the human lumbar spine stabilized by interbody cages biomechanically. The finite element method was used to compare cage designs by considering stresses in the cage and in the bone as well as relative displacements between the cage and the adjacent bone at the interface. The biomechanical evaluation considered different bone densities and considered axial, torsional, and bending loads on the lumbar spine. Stress analysis predicts local regions of stress concentration that could be damaging to cancellous bone and will likely require a remodeling response for local damage. This study predicts relative micromotion that could cause the bone resorption and fibrous tissue formation on the contact surfaces of the cage. The geometric constraints caused by the use of two cages will reduce the relative motion and therefore be more likely to allow bone ingrowth at the posterocentral contact region. Finite element analysis suggests that cages are a promising method for separation and stabilization of the vertebral bodies.     

Finite Element Analysis of Interbody Cages in a Human Lumbar Spine

Abstract

An innovative surgical procedure is vertebral stabilization by interbody cages. It is currently being used to separate and stabilize vertebral bodies and to promote bony fusion of the vertebrae onto or through the cages. This surgery, at some spine levels, can be performed through a laparoscope as an outpatient procedure with low morbidity. Because the procedure is new, little structural information is available on the interbody cages. The objective of this study was to evaluate the human lumbar spine stabilized by interbody cages biomechanically. The finite element method was used to compare cage designs by considering stresses in the cage and in the bone as well as relative displacements between the cage and the adjacent bone at the interface. The biomechanical evaluation considered different bone densities and considered axial, torsional, and bending loads on the lumbar spine. Stress analysis predicts local regions of stress concentration that could be damaging to cancellous bone and will likely require a remodeling response for local damage. This study predicts relative micromotion that could cause the bone resorption and fibrous tissue formation on the contact surfaces of the cage. The geometric constraints caused by the use of two cages will reduce the relative motion and therefore be more likely to allow bone ingrowth at the posterocentral contact region. Finite element analysis suggests that cages are a promising method for separation and stabilization of the vertebral bodies.     

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.     

Analysis of the Stress and Displacement Distribution of Inferior Tibiofibular Syndesmosis Injuries Repaired with Screw Fixation: A Finite Element Study

Background

Studies of syndesmosis injuries have concentrated on cadaver models. However, they are unable to obtain exact data regarding the stress and displacement distribution of various tissues, and it is difficult to compare models. We investigated the biomechanical effects of inferior tibiofibular syndesmosis injuries (ITSIs) and screw fixation on the ankle using the finite element (FE) method.

Methodology/Principal Findings

A three-dimensional model of a healthy ankle complex was developed using computed tomography (CT) images. We established models of an ITSI and of screw fixation at the plane 2.5 cm above and parallel to the tibiotalar joint surface of the injured syndesmosis. Simulated loads were applied under three conditions: neutral position with single-foot standing and internal and external rotation of the ankle. ITSI reduced contact forces between the talus and fibula, helped periarticular ankle ligaments withstand more load-resisting movement, and increased the magnitude of displacement at the lower extreme of the tibia and fibula. ITSI fixation with a syndesmotic screw reduced contact forces in all joints, decreased the magnitude of displacement at the lower extreme of the tibia and fibula, and increased crural interosseous membrane stress.

Conclusions/significance

Severe syndesmosis injuries cause stress and displacement distribution of the ankle to change multidirectional ankle instability and should be treated by internal fixation. Though the transverse syndesmotic screw effectively stabilizes syndesmotic diastasis, it also changes stress distribution around the ankle and decreases the joint''s range of motion (ROM). Therefore, fixation should not be performed for a long period of time because it is not physiologically suitable for the ankle joint.     

Porcine models in spinal research: calibration and comparative finite element analysis of various configurations during flexion-extension

This study was conducted to develop and calibrate a detailed 3-dimensional finite element model of the porcine lumbar spine and to compare this model with various configurations in flexion and extension. Computed tomography scans obtained from the L4-L5 lumbar segment of a Landrace x Large White pig were used to generate a solid volume. The various passive components were characterized by using a step-by-step calibration procedure in which the material properties of the anatomic structures were modified to match the corresponding in vitro data set-points retrieved from the literature. The range of motion of the totally assembled intact model was assessed under a 10-Nm flexion-extension moment and compared with data from a bilateral complete and hemifacetectomy configuration. In addition, the results from our porcine model were compared with published data regarding range of motion in a human finite element model in order to predict the configuration of the porcine model that most closely represented the human spine. Both the intact and hemifacetectomy configurations of the porcine model were comparable to the human spine. However, qualitative analysis of the instantaneous axis of rotation revealed a dissimilarity between the intact porcine model and human spine behavior, indicating the hemifacetectomy configuration of the porcine model as the most appropriate for spinal instrumentation studies. The present 3-dimensional finite element porcine model offers an additional tool to improve understanding of the biomechanics of the porcine spine and to decrease the expense of spinal research.