On the estimation of joint kinematics during gait.

In gait analysis, the concepts of Euler and helical (screw) angles are used to define the three-dimensional relative joint angular motion of lower extremities. Reliable estimation of joint angular motion depends on the accurate definition and construction of embedded axes within each body segment. In this paper, using sensitivity analysis, we quantify the effects of uncertainties in the definition and construction of embedded axes on the estimation of joint angular motion during gait. Using representative hip and knee motion data from normal subjects and cerebral palsy patients, the flexion-extension axis is analytically perturbed +/- 15 degrees in 5 degrees steps from a reference position, and the joint angles are recomputed for both Euler and helical angle definitions. For the Euler model, hip and knee flexion angles are relatively unaffected while the ab/adduction and rotation angles are significantly affected throughout the gait cycle. An error of 15 degrees in the definition of flexion-extension axis gives rise to maximum errors of 8 and 12 degrees for the ab/adduction angle, and 10-15 degrees for the rotation angles at the hip and knee, respectively. Furthermore, the magnitude of errors in ab/adduction and rotation angles are a function of the flexion angle. The errors for the ab/adduction angles increase with increasing flexion angle and for the rotation angle, decrease with increasing flexion angle. In cerebral palsy patients with flexed knee pattern of gait, this will result in distorted estimation of ab/adduction and rotation. For the helical model, similar results are obtained for the helical angle and associated direction cosines.(ABSTRACT TRUNCATED AT 250 WORDS)     

Orientation and location of the finite helical axis of the equine forelimb joints

To reduce anatomically unrealistic limb postures in a virtual musculoskeletal model of a horse's forelimb, accurate knowledge on forelimb joint constraints is essential. The aim of this cadaver study is to report all orientation and position changes of the finite helical axes (FHA) as a function of joint angle for different equine forelimb joints. Five horse cadaver forelimbs with standardized cuts at the midlevel of each segment were used. Bone pins with reflective marker triads were drilled into the forelimb bones. Unless joint angles were anatomically coupled, each joint was manually moved independently in all three rotational degrees of freedom (flexion–extension, abduction–adduction, internal–external rotation). The 3D coordinates of the marker triads were recorded using a six infra-red camera system. The FHA and its orientational and positional properties were calculated and expressed against joint angle over the entire range of motion using a finite helical axis method. When coupled, joint angles and FHA were expressed in function of flexion–extension angle. Flexion–extension movement was substantial in all forelimb joints, the shoulder allowed additional considerable motion in all three rotational degrees of freedoms. The position of the FHA was constant in the fetlock and elbow and a constant orientation of the FHA was found in the shoulder. Orientation and position changes of the FHA over the entire range of motion were observed in the carpus and the interphalangeal joints. We report FHA position and orientation changes as a function of flexion–extension angle to allow for inclusion in a musculoskeletal model of a horse to minimize calculation errors caused by incorrect location of the FHA.     

Sensitivity of the knee joint kinematics calculation to selection of flexion axes

Various flexion axes have been used in the literature to describe knee joint kinematics. This study measured the passive knee kinematics of six cadaveric human knee specimens using two widely accepted flexion axes; transepicondylar axis and the geometric center axis. These two axes were found to form an angle of 4.0 degrees +/- 0.8 degrees. The tibial rotation calculated using the transepicondylar axis was significantly different than the rotation obtained using the geometric center axis for the same knee motion. At 90 degrees of flexion, the tibial rotation obtained using the transepicondylar axis was 4.8 degrees +/- 9.4 degrees whereas the rotation recorded using the geometric center axis at the same flexion angle was 13.8 degrees +/- 10.2 degrees. At 150 degrees of knee flexion, the rotations obtained from the transepicondylar and the geometric center axes were 7.2 degrees +/- 5.7 degrees and 19.9 degrees +/- 6.9 degrees, respectively. The data suggest that a clear definition of the flexion axis is necessary when reporting knee joint kinematics.     

Measurement of the screw-home motion of the knee is sensitive to errors in axis alignment

Measurements of joint angles during motion analysis are subject to error caused by kinematic crosstalk, that is, one joint rotation (e. g., flexion) being interpreted as another (e.g., abduction). Kinematic crosstalk results from the chosen joint coordinate system being misaligned with the axes about which rotations are assumed to occur. The aim of this paper is to demonstrate that measurement of the so-called "screw-home" motion of the human knee, in which axial rotation and extension are coupled, is especially prone to errors due to crosstalk. The motions of two different two-segment mechanical linkages were examined to study the effects of crosstalk. The segments of the first linkage (NSH) were connected by a revolute joint, but the second linkage (SH) incorporated gearing that caused 15 degrees of screw-home rotation to occur with 90 degrees knee flexion. It was found that rotating the flexion axis (inducing crosstalk) could make linkage NSH appear to exhibit a screw-home motion and that a different rotation of the flexion axis could make linkage SH apparently exhibit pure flexion. These findings suggest that the measurement of screw-home rotation may be strongly influenced by errors in the location of the flexion axis. The magnitudes of these displacements of the flexion axis were consistent with the inter-observer variability seen when five experienced observers defined the flexion axis by palpating the medial and lateral femoral epicondyles. Care should be taken when interpreting small internal-external rotations and abduction-adduction angles to ensure that they are not the products of kinematic crosstalk.     

Repeatability of gait data using a functional hip joint centre and a mean helical knee axis

Repeatability of traditional kinematic and kinetic models is affected by the ability to accurately locate anatomical landmarks (ALs) to define joint centres and anatomical coordinate systems. Numerical methods that define joint centres and axes of rotation independent of ALs may also improve the repeatability of kinematic and kinetic data. The purpose of this paper was to compare the repeatability of gait data obtained from two models, one based on ALs (AL model), and the other incorporating a functional method to define hip joint centres and a mean helical axis to define knee joint flexion/extension axes (FUN model). A foot calibration rig was also developed to define the foot segment independent of ALs. The FUN model produced slightly more repeatable hip and knee joint kinematic and kinetic data than the AL model, with the advantage of not having to accurately locate ALs. Repeatability of the models was similar comparing within-tester sessions to between-tester sessions. The FUN model may also produce more repeatable data than the AL model in subject populations where location of ALs is difficult. The foot calibration rig employed in both the AL and FUN model provided an easy alternative to define the foot segment and obtain repeatable data, without accurately locating ALs on the foot.     

A joint coordinate system proposal for the study of the trapeziometacarpal joint kinematics

The International Society of Biomechanics (ISB) has recommended a standardisation for the motion reporting of almost all human joints. This study proposes an adaptation for the trapeziometacarpal joint.

The definition of the segment coordinate system of both trapezium and first metacarpal is based on functional anatomy. The definition of the joint coordinate system (JCS) is guided by the two degrees of freedom of the joint, i.e. flexion–extension about a trapezium axis and abduction–adduction about a first metacarpal axis. The rotations obtained using three methods are compared on the same data: the fixed axes sequence proposed by Cooney et al., the mobile axes sequence proposed by the ISB and our alternative mobile axes sequence. The rotation amplitudes show a difference of 9° in flexion–extension, 2° in abduction–adduction and 13° in internal–external rotation.

This study emphasizes the importance of adapting the JCS to the functional anatomy of each particular joint.     

A novel methodology to reproduce previously recorded six-degree of freedom kinematics on the same diarthrodial joint

The objective of this study was to develop a novel method to more accurately reproduce previously recorded 6-DOF kinematics of the tibia with respect to the femur using robotic technology. Furthermore, the effect of performing only a single or multiple registrations and the effect of robot joint configuration were investigated. A single registration consisted of registering the tibia and femur with respect to the robot at full extension and reproducing all kinematics while multiple registrations consisted of registering the bones at each flexion angle and reproducing only the kinematics of the corresponding flexion angle. Kinematics of the knee in response to an anterior (134 N) and combined internal/external (+/-10 N m) and varus/valgus (+/-5 N m) loads were collected at 0 degrees , 15 degrees , 30 degrees , 60 degrees , and 90 degrees of flexion. A six axes, serial-articulated robotic manipulator (PUMA Model 762) was calibrated and the working volume was reduced to improve the robot's accuracy. The effect of the robot joint configuration was determined by performing single and multiple registrations for three selected configurations. For each robot joint configuration, the accuracy in position of the reproduced kinematics improved after multiple registrations (0.7+/-0.3, 1.2+/-0.5, and 0.9+/-0.2 mm, respectively) when compared to only a single registration (1.3+/-0.9, 2.0+/-1.0, and 1.5+/-0.7 mm, respectively) (p<0.05). The accuracy in position of each robot joint configuration was unique as significant differences were detected between each of the configurations. These data demonstrate that the number of registrations and the robot joint configuration both affect the accuracy of the reproduced kinematics. Therefore, when using robotic technology to reproduce previously recorded kinematics, it may be necessary to perform these analyses for each individual robotic system and for each diarthrodial joint, as different joints will require the robot to be placed in different robot joint configurations.     

Helical axes of skeletal knee joint motion during running

The purpose of this study was to determine the changes in the axis of rotation of the knee that occur during the stance phase of running. Using intracortical pins, the three-dimensional skeletal kinematics of three subjects were measured during the stance phase of five running trials. The stance phase was divided into equal motion increments for which the position and orientation of the finite helical axes (FHA) were calculated relative to a tibial reference frame. Results were consistent within and between subjects. At the beginning of stance, the FHA was located at the midepicondylar point and during the flexion phase moved 20mm posteriorly and 10mm distally. At the time of peak flexion, the FHA shifted rapidly by about 10-20mm in proximal and posterior direction. The angle between the FHA and the tibial transverse plane increased gradually during flexion, to about 15 degrees of medial inclination, and then returned to zero at the start of the extension phase. These changes in position and orientation of FHA in the knee should be considered in analyses of muscle function during human movement, which require moment arms to be defined relative to a functional rotation axis. The finding that substantial changes in axis of rotation occurred independent of flexion angle suggests that musculoskeletal models must have more than one kinematic degree-of-freedom at the knee. The same applies to the design of knee prostheses, if the goal is to restore normal muscle function.     

On intrinsic equivalences of the finite helical axis,the instantaneous helical axis,and the SARA approach. A mathematical perspective

Accurate determination of joint axes is essential for understanding musculoskeletal function. Whilst numerous algorithms to compute such axes exist, the conditions under which each of the methods performs best remain largely unknown. Typically, algorithms are evaluated for specific conditions only limiting the external validity of conclusions regarding their performance. We derive exact mathematical relationships between three commonly used algorithms for computing joint axes from motion data: finite helical axes (FHA), instantaneous helical axes (IHA) and SARA (symmetrical axis of rotation approach), including relationships for an extension to the mean helical axes methods that facilitate determining joint centres and axes. Through the derivation of a sound mathematical framework to objectively compare the algorithms we demonstrate that the FHA and SARA approach are equivalent for the analysis of two time frames. Moreover, we show that the position of a helical axis derived from the IHA using positional data is affected by a systematic error perpendicular to the true axis direction, whereas the axis direction is identical to those computed with either the FHA or SARA approach (true direction). Finally, with an appropriate choice of weighting factors the mean FHA (MFHA) method is equivalent to the Symmetrical Centre of Rotation Estimation (SCoRE) algorithm for determination of a Centre of Rotation (CoR), and similarly, equivalent to the SARA algorithm for determination of an Axis of Rotation (AoR). The deep understanding of the equivalences between methods presented here enables readers to choose numerically efficient, robust methods for determining AoRs and CoRs with confidence.     

Functional knee axis based on isokinetic dynamometry data: Comparison of two methods, MRI validation, and effect on knee joint kinematics

This paper compares geometry-based knee axes of rotation (transepicondylar axis and geometric center axis) and motion-based functional knee axes of rotation (fAoR). Two algorithms are evaluated to calculate fAoRs: Gamage and Lasenby's sphere fitting algorithm (GL) and Ehrig et al.'s axis transformation algorithm (SARA). Calculations are based on 3D motion data acquired during isokinetic dynamometry. AoRs are validated with the equivalent axis based on static MR-images. We quantified the difference in orientation between two knee axes of rotation as the angle between the projection of the axes in the transversal and frontal planes, and the difference in location as the distance between the intersection points of the axes with the sagittal plane. Maximum differences between fAoRs resulting from GL and SARA were 5.7° and 15.4mm, respectively. Maximum differences between fAoRs resulting from GL or SARA and the equivalent axis were 5.4°/11.5mm and 8.6°/12.8mm, respectively. Differences between geometry-based axes and EA are larger than differences between fAoR and EA both in orientation (maximum 10.6°).and location (maximum 20.8mm). Knee joint angle trajectories and the corresponding accelerations for the different knee axes of rotation were estimated using Kalman smoothing. For the joint angles, the maximum RMS difference with the MRI-based equivalent axis, which was used as a reference, was 3°. For the knee joint accelerations, the maximum RMS difference with the equivalent axis was 20°/s(2). Functional knee axes of rotation describe knee motion better than geometry-based axes. GL performs better than SARA for calculations based on experimental dynamometry.     

Improved single- and multi-contact life-time testing of dental restorative materials using key characteristics of the human masticatory system and a force/position-controlled robotic dental wear simulator

This paper presents a new in vitro wear simulator based on spatial parallel kinematics and a biologically inspired implicit force/position hybrid controller to replicate chewing movements and dental wear formations on dental components, such as crowns, bridges or a full set of teeth. The human mandible, guided by passive structures such as posterior teeth and the two temporomandibular joints, moves with up to 6 degrees of freedom (DOF) in Cartesian space. The currently available wear simulators lack the ability to perform these chewing movements. In many cases, their lack of sufficient DOF enables them only to replicate the sliding motion of a single occlusal contact point by neglecting rotational movements and the motion along one Cartesian axis. The motion and forces of more than one occlusal contact points cannot accurately be replicated by these instruments. Furthermore, the majority of wear simulators are unable to control simultaneously the main wear-affecting parameters, considering abrasive mechanical wear, which are the occlusal sliding motion and bite forces in the constraint contact phase of the human chewing cycle. It has been shown that such discrepancies between the true in vivo and the simulated in vitro condition influence the outcome and the quality of wear studies. This can be improved by implementing biological features of the human masticatory system such as tooth compliance realized through the passive action of the periodontal ligament and active bite force control realized though the central nervous system using feedback from periodontal preceptors. The simulator described in this paper can be used for single- and multi-occlusal contact testing due to its kinematics and ability to exactly replicate human translational and rotational mandibular movements with up to 6 DOF without neglecting movements along or around the three Cartesian axes. Recorded human mandibular motion and occlusal force data are the reference inputs of the simulator. Experimental studies of wear using this simulator demonstrate that integrating the biological feature of combined force/position hybrid control in dental material testing improves the linearity and reduces the variability of results. In addition, it has been shown that present biaxially operated dental wear simulators are likely to provide misleading results in comparative in vitro/in vivo one-contact studies due to neglecting the occlusal sliding motion in one plane which could introduce an error of up to 49% since occlusal sliding motion D and volumetric wear loss V(loss) are proportional.     

Quantifying translations in the radiohumeral joint: application of a floating axis analysis

The purpose of this study was to apply the Floating Axis analysis technique to the elbow joint, and to verify its ability to quantify clinically relevant radiohumeral translation in vitro using an electromagnetic tracking device. Of particular interest was the ability to quantify changes in anterior-posterior radial head translation, which is associated with the clinical condition of posterolateral rotatory instability of the elbow. Following the method proposed by Grood and Suntay to determine motions in the knee, an elbow coordinate system with axes representing the flexion-extension axis of the humerus, the long axis of the radius, and their mutual perpendicular, was developed. The algorithm was tested using a mechanical articulator that modeled the Floating Axis approach. Translation errors using this articulator were 0.1+/-0.1mm. The algorithm was applied to kinematic data collected from 12 cadaveric elbows that underwent a pivot shift test prior and subsequent to transection of the lateral collateral ligament. Anterior-posterior radiohumeral translation increased significantly in these elbows following the ligament sectioning (p<0.0001), with the average magnitude of posterior translation increasing from 0.9 to 19.8mm at 90 degrees of flexion. This approach will provide valuable information related to alterations in elbow motion pathways, especially for studies aimed at quantifying changes in joint stability.     

A finite helical axis as a landmark for kinematic reference of the knee

Reference coordinates based on the finite helical axis for flexion of the knee from 0 to 90 deg are proposed. Six degree-of-freedom tracking allows the use of such a helical axis as a kinematic landmark for knee motion representation. Data from five human subjects in vivo are presented as a path of finite helical axes for flexion of the knee from 20 to 80 deg. The finite helical axis rotates by an average of 11.4 deg, the centrode translates an average of 19.8 mm, and the total axial translation averages 0.1 mm during flexion from 20 to 80 deg. Error due to the transducer was measured on a fixed-pivot pendulum and found to be 1.0 deg and 1.9 mm rms for the helical axis orientation and position, respectively, and 0.1 mm for the axial translation. Reproducibility and soft tissue effects on the measurements were repeatable to 4.0 deg and 2.7 mm rms in orientation and position, respectively, and 0.1 mm for the axial translations. Soft tissue errors averaged 4.9 deg and 3.6 mm in position and orientation, and 0.3 mm in the axial translations.     

Joint gap kinematics in posterior-stabilized total knee arthroplasty measured by a new tensor with the navigation system

BACKGROUND: The management of soft tissue balance during surgery is essential for the success of total knee arthroplasty (TKA) but remains difficult, leaving it much to the surgeon's feel. Previous assessments for soft tissue balance have been performed under unphysiological joint conditions, with patellar eversion and without the prosthesis only at extension and 90 deg of flexion. We therefore developed a new tensor for TKA procedures, enabling soft tissue balance assessment throughout the range of motion while reproducing postoperative joint alignment with the patellofemoral (PF) joint reduced and the tibiofemoral joint aligned. Our purpose in the present study was to clarify joint gap kinematics using the tensor with the CT-free computer assisted navigation system. METHOD OF APPROACH: Joint gap kinematics, defined as joint gap change during knee motion, was evaluated during 30 consecutive, primary posterior-stabilized (PS) TKA with the navigation system in 30 osteoarthritic patients. Measurements were performed using a newly developed tensor, which enabled the measurement of the joint gap throughout the range of motion, including the joint conditions relevant after TKA with PF joint reduced and trial femoral component in place. Joint gap was assessed by the tensor at full extension, 5 deg, 10 deg, 15 deg, 30 deg, 45 deg, 60 deg, 90 deg, and 135 deg of flexion with the patella both everted and reduced. The navigation system was used to obtain the accuracy of implantations and to measure an accurate flexion angle of the knee during the intraoperative joint gap measurement. RESULTS: Results showed that the joint gap varied depending on the knee flexion angle. Joint gap showed an accelerated decrease during full knee extension. With the PF joint everted, the joint gap increased throughout knee flexion. In contrast, the joint gap with the PF joint reduced increased with knee flexion but decreased after 60 deg of flexion. CONCLUSIONS: We clarified the characteristics of joint gap kinematics in PS TKA under physiological and reproducible joint conditions. Our findings can provide useful information for prosthetic design and selection and allow evaluation of surgical technique throughout the range of knee motion that may lead to consistent clinical outcomes after TKA.     

Design and construction of a simulator for testing finger joint replacements.

A simulator for testing finger joint replacements was developed. Movement intervals of 15 degrees at flexion and extension plain can be set using an adjustable crank drive. The maximum range of motion is 105 degrees, 90 degrees being the maximum flexion and 15 degrees the extension. Thus, the simulator is also suitable for impingement tests. A constant joint load is infinitely variable from 20 N to 500 N. Test frequency is also infinitely variable from 0.2 Hz to 2 Hz. A modular assembly of the components of the prosthesis means that these can be positioned as required, and that any type of prosthesis may be tested. The design and the material allow for an all-round lubrication at a heat up to 37 degrees C. The equipment is designed for permanent operation. Pre-clinical quality assurance for finger joint replacements can be considerably improved by the implementation of the present simulator.     

In-vivo range of motion of the subtalar joint using computed tomography

Understanding in vivo subtalar joint kinematics is important for evaluation of subtalar joint instability, the design of a subtalar prosthesis and for analysing surgical procedures of the ankle and hindfoot. No accurate data are available on the normal range of subtalar joint motion. The purpose of this study was to introduce a method that enables the quantification of the extremes of the range of motion of the subtalar joint in a loaded state using multidetector computed tomography (CT) imaging. In 20 subjects, an external load was applied to a footplate and forced the otherwise unconstrained foot in eight extreme positions. These extreme positions were foot dorsiflexion, plantarflexion, eversion, inversion and four extreme positions in between the before mentioned positions. CT images were acquired in a neutral foot position and each extreme position separately. After bone segmentation and contour matching of the CT data sets, the helical axes were determined for the motion of the calcaneus relative to the talus between four pairs of opposite extreme foot positions. The helical axis was represented in a coordinate system based on the geometric principal axes of the subjects’ talus. The greatest relative motion between the calcaneus and the talus was calculated for foot motion from extreme eversion to extreme inversion (mean rotation about the helical axis of 37.3±5.9°, mean translation of 2.3±1.1 mm). A consistent pattern of range of subtalar joint motion was found for motion of the foot with a considerable eversion and inversion component.     

On the estimate of the two dominant axes of the knee using an instrumented spatial linkage

This article presents the validation of a technique to assess the appropriateness of a 2 degree-of-freedom model for the human knee, and, in which case, the dominant axes of flexion/extension and internal/external longitudinal rotation are estimated. The technique relies on the use of an instrumented spatial linkage for the accurate detection of passive knee kinematics, and it is based on the assumption that points on the longitudinal rotation axis describe nearly circular and planar trajectories, whereas the flexion/extension axis is perpendicular to those trajectories through their centers of rotation. By manually enforcing a tibia rotation while bending the knee in flexion, a standard optimization algorithm is used to estimate the approximate axis of longitudinal rotation, and the axis of flexion is estimated consequently. The proposed technique is validated through simulated data and experimentally applied on a 2 degree-of-freedom mechanical joint. A procedure is proposed to verify the fixed axes assumption for the knee model. The suggested methodology could be possibly valuable in understanding knee kinematics, and in particular for the design and implant of customized hinged external fixators, which have shown to be effective in knee dislocation treatment and rehabilitation.     

In vitro assessment of a motion-based optimization method for locating the talocrural and subtalar joint axes

The locations of the joint axes of the ankle complex vary considerably between subjects, yet no noninvasive method with demonstrated accuracy exists for locating these axes. The moments of muscle and ground reaction forces about the joint axes are dependent on axis locations, making knowledge of these locations critical to accurate musculoskeletal modeling of the foot and ankle. The accuracy of a computational optimization method that fits a two-revolute model to measured motion was assessed using computer-generated data, a two-revolute mechanical linkage, and three lower-leg cadaver specimens. Motions were applied to cadaver specimens under axial load while bone-mounted markers attached to the tibia, talus, and calcaneus were tracked using a video-based motion analysis system. Estimates of the talocrural and subtalar axis locations were computed from motions of the calcaneus relative to the tibia using the optimization method. These axes were compared to mean helical axes computed directly from tibia, talus, and calcaneus motions. The optimization method performed well when the motions were computer-generated or measured in the mechanical linkage, with angular differences between optimization and mean helical axes ranging from 1 deg to 5 deg. In the cadaver specimens, however, these differences exceeded 20 deg. Optimization methods that locate the anatomical joint axes of the ankle complex by fitting two revolute joints to measured tibia-calcaneus motions may be limited because of problems arising from non-revolute behavior.     

Calculating the axes of rotation for the subtalar and talocrural joints using 3D bone reconstructions

Orientation of the subtalar joint axis dictates inversion and eversion movements of the foot and has been the focus of evolutionary and clinical studies for a number of years. Previous studies have measured the subtalar joint axis against the axis of the whole foot, the talocrural joint axis and, recently, the principal axes of the talus. The present study introduces a new method for estimating average joint axes from 3D reconstructions of bones and applies the method to the talus to calculate the subtalar and talocrural joint axes. The study also assesses the validity of the principal axes as a reference coordinate system against which to measure the subtalar joint axis. In order to define the angle of the subtalar joint axis relative to that of another axis in the talus, we suggest measuring the subtalar joint axis against the talocrural joint axis. We present corresponding 3D vector angles calculated from a modern human skeletal sample. This method is applicable to virtual 3D models acquired through surface-scanning of disarticulated 'dry' osteological samples, as well as to 3D models created from CT or MRI scans.