In vivo determination of the anatomical axes of the ankle joint complex: An optimization approach

This study investigates the feasibility of a subject-specific three-dimensional model of the ankle joint complex for kinematic and dynamic analysis of movement. The ankle joint complex was modelled as a three-segment system, connected by two ideal highe joints: the talocrural and the subtalar joint. A mathematical formulation was developed to express the three-dimensional translation and rotation between the foot and shank segments as a function of the two joint angles, and 12 model parameters describing the locations of the joint axes. An optimization method was used to fit the model parameters to three-dimensional kinematic data of foot and shank markers, obtained during test movements throughout the entire physiological range of motion of the ankle joint. The movement of the talus segment, which cannot be measured non-invasively, is not necessary for the analysis.

This optimization method was used to determine the position and orientation of the joint axes in 14 normal subjects. After optimization, the discrepancy between the best fitting model and actual marker kinematics was between 1 and 3 mm for all subjects. The predicted inclination of the subtalar joint axis from the horizontal plane was 37.4±2.7°, and the medial deviation was 18.0±16.2°. The lateral side of the talucrural axis was directed slightly posteriorly (6.8±8.1°), and inclined downward by 7.0±5.4°. These results are similar to previously reported typical results from anatomical, in vitro, studies. Reproducibility was evaluated by repeated testing of one subject, which resulted in variations of about one-fifth of the standard deviation within the group, the inclination of the subtalar joint axis was significantly correlated to the arch height and a radiographic ‘tarsal index’. It is concluded that this optimization method provides the opportunity to incorporate inter-individual anatomical differences into kinematic and dynamic analysis of the ankle joint complex. This allows a more functional interpretation of kinematic data, and more realistic estimates of internal forces.     

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.     

Comparison of three local frame definitions for the kinematic analysis of the fingers and the wrist

Because the hand is a complex poly-articular limb, numerous methods have been proposed to investigate its kinematics therefore complicating the comparison between studies and the methodological choices. With the objective of overcoming such issues, the present study compared the effect of three local frame definitions on local axis orientations and joint angles of the fingers and the wrist. Three local frames were implemented for each segment. The “Reference” frames were aligned with global axes during a static neutral posture. The “Landmark” frames were computed using palpated bony landmarks. The “Functional” frames included a flexion–extension axis estimated during functional movements. These definitions were compared with regard to the deviations between obtained local segment axes and the evolution of joint (Cardan) angles during two test motions. Each definition resulted in specific local frame orientations with deviations of 15° in average for a given local axis. Interestingly, these deviations produced only slight differences (below 7°) regarding flexion–extension Cardan angles indicating that there is no preferred method when only interested in finger flexion–extension movements. In this case, the Reference method was the easiest to implement, but did not provide physiological results for the thumb. Using the Functional frames reduced the kinematic cross-talk on the secondary and tertiary Cardan angles by up to 20° indicating that the Functional definition is useful when investigating complex three-dimensional movements. Globally, the Landmark definition provides valuable results and, contrary to the other definitions, is applicable for finger deformities or compromised joint rotations.     

Globographic visualisation of three dimensional joint angles

Three different methods for describing three dimensional joint angles are commonly used in biomechanics. The joint coordinate system and Cardan/Euler angles are conceptually quite different but are known to represent the same underlying mathematics. More recently the globographic method has been suggested as an alternative and this has proved particularly attractive for the shoulder joint. All three methods can be implemented in a number of ways leading to a choice of angle definitions. Very recently Rab has demonstrated that the globographic method is equivalent to one implementation of the joint coordinate system. This paper presents a rigorous analysis of the three different methods and proves their mathematical equivalence. The well known sequence dependence of Cardan/Euler is presented as equivalent to configuration dependence of the joint coordinate system and orientation dependence of globographic angles. The precise definition of different angle sets can be easily visualised using the globographic method using analogues of longitude, latitude and surface bearings with which most users will already be familiar. The method implicitly requires one axis of the moving segment to be identified as its principal axis and this can be extremely useful in helping define the most appropriate angle set to describe the orientation of any particular joint. Using this technique different angle sets are considered to be most appropriate for different joints and examples of this for the hip, knee, ankle, pelvis and axial skeleton are outlined.     

The load-bearing area in the knee joint

Measurements were made of the location and size of the contact areas in cadaver knee joints, for a load of 150 Kgf applied for 5 sec down the long axis of the tibia. Results were obtained from a total of 4 knees, considering flexion angles from 0 to 120°. The methods used were to measure directly from castings of the joint cavity; and to calculate from measurements of radii of curvature and joint deflection. Average contact areas for lateral and medial condyles were 1·4 and 1·8 cm² respectively. Areas for the medial condyle were greater than for the lateral condyle and also the areas diminished as flexion angle increased. The implications of the results to contact stresses, joint lubrication and ‘condylar replacement’ knee prosthesis design were discussed.     

Acetabular morphology and resurfacing design

The bony surfaces of 18 archaeological hemipelves were scanned using a 3D laser surface scanner and CyDir™ software on a Silicon Graphics workstation. The acetabular area was selected and point data from the approximately spherical bone surface saved. These data were input to a MATLAB routine that calculated the radius and centre of the best-fit sphere. The goodness of fit was estimated using the mean and standard deviation of the distance of the bone surface points from the sphere surface. Eight points, at approximately equal distances around the acetabular rim, were selected with reference to bony landmarks. A plane containing three of these points served as an orientation reference plane. The vectors joining the eight rim points to the centre of the best-fit sphere were found. The angles between these vectors and the normal to the reference plane were calculated. Paired angles were summed to give the angle subtended by the acetabular rim in four directions. The overall mean angle was 158° (range of mean angles 145°–173°). The largest individual angles, some exceeding 180°, were in the superior–inferior direction, while the mean angle in the anterior–posterior direction, i.e. that controlling flexion-extension, was 152°. Males had larger subtended angles than females, although the difference was not statistically significant. Simulated reaming increased all angles by approximately 10°. The subtended angles are important parameters in the design of the acetabular component of a hip replacement and particularly important in resurfacing hip replacement when the volume available is tightly constrained.     

The ichthyosaur integument: skin fibers, a means for a strong, flexible and smooth skin

The ichthyosaur skin is examined in order to further our understanding of the adaptation of these animals to the aquatic medium and their locomotory efficiency. Softtissue structures in two excellently preserved specimens of the ichthyosaur Stenopterygius quadricissus and in a partial skull of Ichthyosaurus provide unique data on the integument of advanced or tunniform ichthyosaurs. A system of fibers of three classes based on thickness and in different levels of the integument covered almost the entire surface of the body. The thickest fibers are located deepest in the skin and the thinnest outermost. The latter consist of at least two superimposed layers of fine fibers that extend in opposing directions to form a lattice or orthogonal meshwork. The angles of these fibers vary between 25 ° and 75 ° to the long axis of the animals, depending on their location in the body. The fibers of the two other size classes, lying deeper in the tissue, were observed in single layers. The thickest fibers extend in near parallel rows approximately 60 °-80 ° to the long axis of the animal in the area near the midpoint of the body and 90 ° in the post-dorsal fin region. The intermediate-sized fibers were apparently oriented at ca. 50 °-75 ° to the animal's long axis and were regularly spaced. Of considerable interest is their attachment dorsally to longitudinal fibers. This contrasts with the general condition of helically arranged fibers in fast-swimming marine vertebrates such as tuna and sharks, but compares with the condition in sirenians. Fibers were observed in the dorsal and caudal fins but not in the limbs. The fibers in ichthyosaurs are the thickest so far noted in marine vertebrates. The presence of a complex system of fibers, which includes an orthogonal meshwork of the finest of these, suggests that creasing of the skin would have been minimized, a condition highly important in reducing drag during the locomotion of marine animals.     

Polarised absorption spectroscopy of chlorophyll-lipid membranes

A technique has been developed for measuring visible absorption spectra of chlorophyll in lipid membranes. An expression is derived which enables the directions of the transition moments of the different absorption bands to be determined from polarisation data. It is found that the transition moments of the principal blue and red absorption bands of chlorophyll a make angles of 26° and 36.5° respectively with the plane of the membrane. On the assumption that these two transitions lie in the plane of the porphyrin ring and are mutually perpendicular, it may be deduced that the plane of the porphyrin ring is tilted at approx. 48° to the membrane surface. For chlorophyll b the transition moments of the blue and red bands are found to make angles of 29.5° and 36.5° with the plane of the bilayer, giving an angle of tilt of the porphyrin ring of approx. 51°.

These results are compared with measurements of dichroism in vivo.     

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.     

Three-dimensional measurement of rearfoot motion during running

Excessive ranges of motion during running have been speculated to be connected to injuries to the lower extremities. Movement of the foot and lower leg has commonly been studied with two-dimensional techniques. However, differences in the alignment of the longitudinal axis of the foot with the camera axis will produce measurement errors for projected angles of the lower extremities. A three-dimensional approach would not have this limitation. The purpose of this study is to present a three-dimensional model for calculation of angles between lower leg and foot, lower leg and ground, and foot and ground, and to compare results from treadmill running derived from this model with results derived from a two-dimensional model for different alignment angles between foot axis and camera axis. A two camera Selspot system was used to obtain three-dimensional information on motion of the studied segments. It was found that several two-dimensional variables measured from a posterior view are very sensitive to the alignment angle between the foot and the camera axis. Some variables change as much as 1 degrees for every 2 degrees of change of the alignment angle. The large influence of rotations other than the measured one in two-dimensional measurements makes advisable the use of a three-dimensional model when studying motion between foot and lower leg during running.     

Influence of patella alta on knee extensor mechanics

The purpose of this study was to compare the knee extensor mechanics in persons with and without patella alta. Thirteen subjects with patella alta and 14 subjects with normal patellar position participated in the study. Sagittal and axial MR images of the knee were acquired at 0°, 20°, 40°, and 60° of knee flexion. Measurements of actual moment arm, patellar ligament/quadriceps tendon force ratio, quadriceps effective moment arm, and joint reaction force/quadriceps force ratio were obtained. There were no differences between groups in terms of actual moment arm. However, subjects with patella alta had significantly larger patellar ligament/quadriceps tendon force ratios (1.04±0.02 vs. 0.92±0.02) and quadriceps effective moment arms (4.40±0.09 vs. 4.00±0.09 cm) when averaged across the range of knee flexion angles tested. There was no difference in the joint reaction force/quadriceps force ratio between groups. The observed differences in knee extensor mechanics suggest that individuals with patella alta have a more efficient knee extensor mechanism and would be expected to generate similar joint reaction forces per unit quadriceps force compared to subjects with normal patellar position. Therefore, persons with patella alta may experience less patellofemoral joint reaction force to overcome the same knee flexion moment in the range of 0°–60° of knee flexion.     

Intrinsic and extrinsic contributions to the passive moment at the metacarpophalangeal joint

The purpose of this investigation was to determine whether the passive range of motion at the finger joints is restricted more by intrinsic tissues (cross a single joint) or by extrinsic tissues (cross multiple joints). The passive moment at the metacarpophalangeal (MP) joint of the index finger was modeled as the sum of intrinsic and extrinsic components. The intrinsic component was modeled only as a function of MP joint angle. The extrinsic component was modeled as a function of MP joint angle and wrist angle. With the wrist fixed in seven different positions the passive moment at the MP joint of eight subjects was recorded as the finger was rotated through its range at a constant rate. The moment-angle data were fit by the model and the extrinsic and intrinsic components were calculated for a range of MP joint angles and wrist positions. With the MP joint near its extension limit, the median percent extrinsic contribution was 94% with the wrist extended 60° and 14% with the wrist flexed 60°. These percentages were 40 and 88%, respectively, with the MP joint near its flexion limit. Our findings indicate that at most wrist angles the extrinsic tissues offer greater restraint at the limits of MP joint extension and flexion than the intrinsic tissues. The intrinsic tissues predominate when the wrist is flexed or extended enough to slacken the extrinsic tissues. Additional characteristics of intrinsic and extrinsic tissues can be deduced by examining the parameter values calculated by the model.     

Accuracy of intramedullary alignment in total knee replacement

The accuracy of a system of intramedullary alignment using 6 mm rods was assessed in 100 patients undergoing total knee replacements. Post-operative, full length weight-bearing X-rays were used; the mechanical axis from head was used as the reference axis. The method of calculating the errors produced by flexion and rotation of the limb in relation to the X-ray beam is described, the mean deviation from the mechanical axis in 100 cases being 0.67° valgus with a standard deviation of 2.47°. The maximum error was 6.68° valgus and 4.62° varus. The purpose of this study is twofold, first to assess the accuracy of this system of intramedullary alignment and, second, to develop a method of correcting for apparent radiological misalignment using standard radiographic equipment.     

The role of the biceps brachii in shoulder elevation.

The biceps brachii is a bi-articular muscle affecting motion at the shoulder and elbow. While its' action at the elbow is well documented, its role in shoulder elevation is less clear. Therefore, the purpose of this project was to investigate the influence of shoulder and elbow joint angles on the shoulder elevation function of the biceps brachii. Twelve males and 18 females were tested on a Biodex dynamometer with the biceps brachii muscle selectively stimulated at a standardized level of voltage. The results indicated that both shoulder and elbow joint angles influence the shoulder joint elevation moment produced by the biceps brachii. Further analysis revealed that the elevation moment was greatest with the shoulder joint at 0 degrees and the elbow flexed 30 degrees or less. The greatest reduction in the elevation moment occurred between shoulder angles of 0 degrees and 30 degrees . The shoulder elevation moment was near zero when shoulder elevation reached or exceeded 60 degrees regardless of elbow angle. These results clarify the role of the biceps in shoulder elevation, as a dynamic stabilizer, and suggest that it is a decelerator of the arm during the throwing motion.     

The effects of alignment of an articulated ankle-foot orthosis on lower limb joint kinematics and kinetics during gait in individuals post-stroke

Mechanical tuning of an ankle-foot orthosis (AFO) is important in improving gait in individuals post-stroke. Alignment and resistance are two factors that are tunable in articulated AFOs. The aim of this study was to investigate the effects of changing AFO ankle alignment on lower limb joint kinematics and kinetics with constant dorsiflexion and plantarflexion resistance in individuals post-stroke. Gait analysis was performed on 10 individuals post-stroke under four distinct alignment conditions using an articulated AFO with an ankle joint whose alignment is adjustable in the sagittal plane. Kinematic and kinetic data of lower limb joints were recorded using a Vicon 3-dimensional motion capture system and Bertec split-belt instrumented treadmill. The incremental changes in the alignment of the articulated AFO toward dorsiflexion angles significantly affected ankle and knee joint angles and knee joint moments while walking in individuals post-stroke. No significant differences were found in the hip joint parameters. The alignment of the articulated AFO was suggested to play an important role in improving knee joint kinematics and kinetics in stance through improvement of ankle joint kinematics while walking in individuals post-stroke. Future studies should investigate long-term effects of AFO alignment on gait in the community in individuals post-stroke.     

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.     

A correction for axis misalignment in the joint angle curves representing knee movement in gait analysis

This paper derives a simple mathematical model relating changes in the orientations of the two Cartesian coordinate systems involved in recording knee movement and the varus-valgus and the internal-external rotation angles for describing the knee's motion. Rotation matrices are given for changing the orientations of the two Cartesian coordinate systems in such a way that the quadratic variations in the varus-valgus and in the external-internal angles are minimal. These estimated rotation matrices are used to correct for axis misalignment. The correction is calibrated by considering the impact of the new orientation of the thigh Cartesian coordinate system on the hip joint angles. The procedure is applied to kinematic data collected on normal subjects. The uncertainty about the specification of the thigh Cartesian coordinate system is shown to explain some of the between subject variability in the varus-valgus and in the internal-external rotation angles curves.     

Influence of kinematic analysis methods on detecting ankle and subtalar joint instability

Patients with subtalar joint instability may be misdiagnosed with ankle instability, which may lead to chronic instability at the subtalar joint. Therefore, it is important to understand the difference in kinematics after ligament sectioning and differentiate the changes in kinematics between ankle and subtalar instability. Three methods may be used to determine the joint kinematics; the Euler angles, the Joint Coordinate System (JCS) and the helical axis (HA). The purpose of this study was to investigate the influence of using either method to detect subtalar and ankle joints instability. 3D kinematics at the ankle and subtalar joint were analyzed on 8 cadaveric specimens while the foot was intact and after sequentially sectioning the anterior talofibular ligament (ATFL), the calcaneofibular ligament (CFL), the cervical ligament and the interosseous talocalcaneal ligament (ITCL). Comparison in kinematics calculated from sensor and anatomical landmarks was conducted as well as the influence of Euler angles and JCS rotation sequence (between ISB recommendation and previous research) on the subtalar joint. All data showed a significant increase in inversion when the ITCL was sectioned. There were differences in the data calculated using sensors coordinate systems vs. anatomic coordinate systems. Anatomic coordinate systems were recommended for these calculations. The Euler angle and JCS gave similar results. Differences in Euler angles and JCS sequence lead to the same conclusion in detecting instability at the ankle and subtalar joint. As expected, the HA detected instability in plantarflexion at the ankle joint and in inversion at the subtalar joint.