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.     

In vivo tests of an improved method for functional location of the subtalar joint axis

The subtalar joint is important in frontal plane movement and posture of the hindfoot. Abnormal subtalar joint moments caused by muscle forces and the ground reaction force acting on the foot are thought to play a role in various foot deformities. Calculating joint moments typically requires knowledge of the location of the joint axis; however, location of the subtalar axis from measured movement is difficult because the talus cannot be tracked using skin-mounted markers. The accuracy of a novel technique for locating the subtalar axis was assessed in vivo using magnetic resonance imaging. The method was also tested with skin-mounted markers and video motion analysis. The technique involves applying forces to the foot that cause pure subtalar joint motion (with negligible talocrural joint motion), and then using helical axis decomposition of the resulting tibiocalcaneal motion. The resulting subtalar axis estimates differed by 6° on average from the true best-fit subtalar axes in the MRI tests. Motion was found to have been applied primarily about the subtalar joint with an average of only 3° of talocrural joint motion. The proposed method provides a potential means for obtaining subject-specific subtalar axis estimates which can then be used in inverse dynamic analyses and subject-specific musculoskeletal models.     

Study of the joint configuration of the knee using a morpho-functional analysis

Skin marker motion analyses are the most widespread techniques to study human movements. Nevertheless, trajectories obtained through such methods are biased because of soft tissue artifacts and lead, consequently, to false collisions and dislocations when bone motion is under investigation. It's an open challenge to enhance kinematics curves particularly for the knee joint involved in the mechanics of gait. The kinematics of flexion/extension of the knee is classically modeled by a rotation around a fixed axis. However, the trend of current biomechanical studies is to improve this modeling by introducing a morphological knowledge such as ligament constraints. In this paper, we propose to highlight the morpho-functionnal link on this joint thanks to two contributions. The first one consists in proposing a method capable of extracting a kinematics of flexion/extension of the knee from a unique CT scan. This method is based on the determination of a mobile axis capable of keeping the information of rolling/sliding. The second one consists in a qualitative and quantitative temporal analysis of the position of the bones during the movement. We compare the results of the two kinematics (static and mobile axis) using original figures of articular coherence and an associated index.     

Can one angle be simply subtracted from another to determine range of motion in three-dimensional motion analysis?

To determine the range of motion of a joint between an initial orientation and a final orientation, it is convenient to subtract initial joint angles from final joint angles, a method referred to as the vectorial approach. However, for three-dimensional movements, the vectorial approach is not mathematically correct. To determine the joint range of motion, the rotation matrix between the two orientations should be calculated, and angles describing the range of motion should be extracted from this matrix, a method referred to as the matrical approach. As the matrical approach is less straightforward to implement, it is of interest to identify situations in which the vectorial approach leads to insubstantial errors. In this study, the vectorial approach was compared to the matrical approach, and theoretical justification was given for situations in which the vectorial approach can reasonably be used. The main findings are that the vectorial approach can be used if (1) the motion is planar (Woltring HJ. 1994. 3-D attitude representation of human joints: a standardization proposal. J Biomech 27(12): 1399–1414), (2) the angles between the final and the initial orientation are small (Woltring HJ. 1991. Representation and calculation of 3-D joint movement. Hum Mov Sci 10(5): 603–616), (3) the angles between the initial orientation of the distal segment and the proximal segment are small and finally (4) when only one large angle occurs between the initial orientation of the distal segment and the proximal segment and the angle sequence is chosen in such a way that this large angle occurs on the first axis of rotation. These findings provide specific criteria to consider when choosing the angle sequence to use for movement analysis.     

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.     

A new method for estimating the axis of rotation and the center of rotation.

A new method is presented for estimating the parameters of two different models of a joint. The two models are: (1) A rotational joint with a fixed axis of rotation, also referred to as a hinge joint and (2) a ball and socket model, corresponding to a spherical joint. Given the motion of a set of markers, it is shown how the parameters can be estimated, utilizing the whole data set. The parameters are estimated from motion data by minimizing two objective functions. The method does not assume a rigid body motion, but only that each marker rotates around the same fixed axis of rotation or center of rotation. Simulation results indicate that in situations where the rigid body assumption is valid and when measurement noise is present, the proposed method is inferior to methods that utilize the rigid body assumption. However, when there are large skin movement artefacts, simulation results show the proposed method to be more robust.     

Tactile efficiency of insect antennae with two hinge joints

Antennae are the main organs of the arthropod tactile sense. In contrast to other senses that are capable of retrieving spatial information, e.g. vision, spatial sampling of tactile information requires active movement of the sense organ. For a quantitative analysis of basic principles of active tactile sensing, we use a generic model of arbitrary antennae with two hinge joints (revolute joints). This kind of antenna is typical for Orthoptera and Phasmatodea, i.e. insect orders that contain model species for the study of antennal movements, including cricket, locust and stick insect. First, we analyse the significance of morphological properties on workspace and sampling acuity. It is shown how joint axis orientation determines areas out of reach while affecting acuity in the areas within reach. Second, we assume a parametric set of movement strategies, based on empirical data on the stick insect Carausius morosus, and investigate the role of each strategy parameter on tactile sampling performance. A stochastic environment is used to measure sampling density, and a viscous friction model is assumed to introduce energy consumption and, thus, a measure of tactile efficiency. Up to a saturation level, sampling density is proportional to the range or frequency of joint angle modulation. The effect of phase shift is strong if joint angle modulation frequencies are equal, but diminishes for other frequency ratios. Speed of forward progression influences the optimal choice of movement strategy. Finally, for an analysis of environmental effects on tactile performance, we show how efficiency depends on predominant edge direction. For example, with slanted and non-orthogonal joint axis orientations, as present in the stick insect, the optimal sampling strategy is less sensitive to a change from horizontal to vertical edge predominance than with orthogonal and non-slanted joint axes, as present in a cricket.Electronic Supplementary Material Supplementary material is available in the online version of this article at     

Leg-to-body geometry determines eyestalk reactions to substrate til

Summary The effect of oscillatory movement of single legs (about C-B axis) on compensatory eyestalk reactions and on leg counterforce as normally produced by substrate tilt has been investigated with the legs at different states of flexion (M-C joint) and leg-to-body orientation (T-C joint). Eye response and force reaction released by standard C-B movement increase with increasing angle of M-C (Figs. 2, 4) and decrease with decrease of T-C angle (Fig. 3). The effects demonstrate a multiplying influence of M-C signal and T-C signal on C-B signals. The stump of an autotomized leg releases eye responses of similar magnitude to unimpaired single legs (Fig. 5).The data are discussed in relation to neurophysiological findings and with respect to the geometrical implications for the mechanism of substrate orientation (Fig. 6).We wish to give thanks to the Max-Planck-Institut (FS, DMN) and to the Carnegie Trust (DMN) for financial support. We thank Renate Alton for technical assistance and Dorothee Maier for her help with the data analysis. Particular thanks should be expressed to the Istituto di Zoologia, Universita di Firenze (Director: Prof. Dr. L. Pardi) for promoting this research.     

An integrated approach to the characterization of cell movement.

BACKGROUND: Most phenomena in developmental biology involve or depend upon cell migration. This article describes a comprehensive framework for the characterization and analysis of trajectories defined by cell movement. The following two perspectives are considered: (a) the behavior of each individual cell and (b) interactions between neighboring pairs of cells. METHODS: The measurements considered for individual trajectories include the velocity magnitude and orientation, maximum spatial dispersion, displacement effectiveness, and displacement entropies. Interactions between two trajectories are characterized by comparing the respective velocities. RESULTS: The potential of the overall framework is illustrated using data of moving cells in different biological environments. The work shows that it is possible to use the new algorithm presented here to characterize cell motility. CONCLUSIONS: The features of the algorithm were successful in determining the motility changes under different experimental conditions.     

Influence of substrate modification and C-terminal truncation on the active site structure of substrate-bound heme oxygenase from Neisseriae meningitidis. A 1H NMR study

Heme oxygenase (HO), from the pathogenic bacterium N. meningitidis(NmHO), which secures host iron, shares many properties with mammalian HOs but also exhibits some key differences. The crystal structure appears more compact, and the crystal-undetected C-terminus interacts with substrate in solution. The unique nature of substrate-protein, specifically pyrrole-I/II-helix-2, peripheral interactions in NmHO are probed by 2D (1)H NMR to reveal unique structural features controlling substrate orientation. The thermodynamics of substrate orientational isomerism are mapped for substrates with individual vinyl → methyl → hydrogen substitutions and with enzyme C-terminal deletions. NmHO exhibits significantly stronger orientational preference, reflecting much stronger and selective pyrrole-I/II interactions with the protein matrix, than in mammalian HOs. Thus, replacing bulky vinyls with hydrogens results in a 180° rotation of substrate about the α,γ-meso axis in the active site. A "collapse" of the substrate pocket as substrate size decreases is reflected in movement of helix-2 toward the substrate as indicated by significant and selective increased NOESY cross-peak intensity, increase in steric Fe-CN tilt reflected in the orientation of the major magnetic axis, and decrease in steric constraints controlling the rate of aromatic ring reorientation. The active site of NmHO appears "stressed" for native protohemin, and its "collapse" upon replacing vinyls by hydrogen leads to a factor ~10(2) increase in substrate affinity. Interaction of the C-terminus with the active site destabilizes the crystallographic protohemin orientation by ~0.7 kcal/mol, which is consistent with optimizing the His207-Asp27 H-bond. Implications of the active site "stress" for product release are discussed.     

A new method for estimating joint parameters from motion data

Joint centers and axes of rotation (joint parameters) are central to all branches of movement analysis. In gait analysis, the standard protocol used to determine hip and knee joint parameters is prone to errors arising from palpation, anthropometric regression equations, and misplaced alignment devices. Several alternative methods have been proposed, but to date none have been shown to be accurate and reliable enough for use in the clinical setting. This article describes a new method for joint parameter estimation. The new method can be summarized as follows: (i) the motions of two adjacent segments spanning a single joint are tracked, (ii) the axis of rotation between every pair of observed segment configurations is computed, (iii) the most likely intersection of all axes (effective joint center) and most likely orientation of the axes (effective joint axis) is found. Initial validation of the method was conducted on a hinged mechanical analog and a single healthy adult subject. For the analog, the center was found to be within 3.8 mm of the geometric center and 2.0 degrees of the geometric axis (standard deviation). For the adult subject, hip centers varied on the order of 1-3 mm, knee centers by 3-9 mm, and knee axes by 2.0 degrees. The results suggest that the new method is an objective, precise, and practical alternative to the standard clinical approach.     

Kinematics of primate midfoot flexibility

This study describes a unique assessment of primate intrinsic foot joint kinematics based upon bone pin rigid cluster tracking. It challenges the assumption that human evolution resulted in a reduction of midfoot flexibility, which has been identified in other primates as the “midtarsal break.” Rigid cluster pins were inserted into the foot bones of human, chimpanzee, baboon, and macaque cadavers. The positions of these bone pins were monitored during a plantarflexion‐dorsiflexion movement cycle. Analysis resolved flexion‐extension movement patterns and the associated orientation of rotational axes for the talonavicular, calcaneocuboid, and lateral cubometatarsal joints. Results show that midfoot flexibility occurs primarily at the talonavicular and cubometatarsal joints. The rotational magnitudes are roughly similar between humans and chimps. There is also a similarity among evaluated primates in the observed rotations of the lateral cubometatarsal joint, but there was much greater rotation observed for the talonavicular joint, which may serve to differentiate monkeys from the hominines. It appears that the capability for a midtarsal break is present within the human foot. A consideration of the joint axes shows that the medial and lateral joints have opposing orientations, which has been associated with a rigid locking mechanism in the human foot. However, the potential for this same mechanism also appears in the chimpanzee foot. These findings demonstrate a functional similarity within the midfoot of the hominines. Therefore, the kinematic capabilities and restrictions for the skeletal linkages of the human foot may not be as unique as has been previously suggested. Am J Phys Anthropol 155:610–620, 2014. © 2014 Wiley Periodicals, Inc.     

A motion-decomposition approach to address gimbal lock in the 3-cylinder open chain mechanism description of a joint coordinate system at the glenohumeral joint

In this study, the standard-sequence properties of a joint coordinate system were implemented for the glenohumeral joint by the use of a set of instantaneous geometrical planes. These are: a plane that is bound by the humeral long axis and an orthogonal axis that is the cross product of the scapular anterior axis and this long axis, and a plane that is bounded by the long axis of the humerus and the cross product of the scapular lateral axis and this long axis. The relevant axes are updated after every decomposition of a motion component of a humeral position. Flexion, abduction and rotation are then implemented upon three of these axes and are applied in a step-wise uncoupling of an acquired humeral motion to extract the joint coordinate system angles. This technique was numerically applied to physiological kinematics data from the literature to convert them to the joint coordinate system and to visually reconstruct the motion on a set of glenohumeral bones for validation.     

Bau und Bewegung der Antennen von Calliphora erythrocephala

Summary The anatomy of the four antennal joints of Calliphora erythrocephala and their significance in the total movement of the antenna were investigated. Both the head-scapus joint (1) and the funiculus-arista joint (4) are virtually rigid and do not participate in the active movements of the antenna. The pedicellus can be moved actively about two axes in the scapus-pedicellus joint (2), a horizontal and a vertical one. Prior to flight the antenna is raised into flight position by rotating the pedicellus about the horizontal axis of the scapus-pedicellus joint (2). During flight drag from frontal air currents on the arista rotates the funiculus with respect to the pedicellus about the longitudinal axis common to the funiculus and the pedicellus-funiculus joint (3). This passive movement of the funiculus is probably perceived by receptors in the pedicellus: the organ of Johnston and a large sensillum campaniforme. Also during flight the pedicellus is rotated actively about the vertical (second) axis of the scapus-pedicellus joint (2). This active movement is opposite to the passive rotation of the funiculus and thus changes the angle of attack for the air currents acting on the arista.

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Mit Unterstützung der Deutschen Forschungsgemeinschaft.     

JAWS coordinates chondrogenesis and synovial joint positioning

Properly positioned synovial joints are crucial to coordinated skeletal movement. Despite their importance for skeletal development and function, the molecular mechanisms that underlie joint positioning are not well understood. We show that mice carrying an insertional mutation in a previously uncharacterized gene, which we have named Jaws (joints abnormal with splitting), die perinatally with striking skeletal defects, including ectopic interphalangeal joints. These ectopic joints develop along the longitudinal axis and persist at birth, suggesting that JAWS is uniquely required for the orientation and consequent positioning of interphalangeal joints within the endochondral skeleton. Jaws mutant mice also exhibit severe chondrodysplasia characterized by delayed and disorganized maturation of growth plate chondrocytes, together with impaired chondroitin sulfation and abnormal metabolism of the chondroitin sulfate proteoglycan aggrecan. Our findings identify JAWS as a key regulator of chondrogenesis and synovial joint positioning required for the restriction of joint formation to discrete stereotyped locations in the embryonic skeleton.