A. Huson

A three-dimensional mathematical model of the knee-joint

Abstract A three-dimensional analytical model of the knee-joint is presented, taking into account the geometry of the joint surfaces as well as the geometry and material properties of the ligaments and capsule. The position of a large number of points on the joint surfaces is measured and the geometry of these surfaces is then approximated by polynomials in space. The ligaments and capsule are represented by a number of non-linear springs, with material properties selected from the literature. For a given three-dimensional loading (forces as well as moments) at various flexion-extension angles, the location of contact points, magnitude and direction of contact forces, magnitude of ligament elongation and ligament forces can be calculated. In the results presented in this paper special attention is given to the anterior-posterior laxity of a joint. A sensitivity study was undertaken to evaluate the model response due to some of the model parameters and to gain a better understanding of the function of the elements in the model. It is concluded that the predictions of the model agree well with experiments described in the literature.

Estimation of instantaneous moment arms of lower-leg muscles

Muscle moment arms at the human knee and ankle were estimated from muscle length changes measured as a function of joint flexion angle in cadaver specimens. Nearly all lower-leg muscles were studied: extensor digitorum longus, extensor hallucis longus, flexor digitorum longus, flexor hallucis longus, gastrocnemius lateralis, gastrocnemius medialis, peroneus brevis, peroneus longus, peroneus tertius, plantaris, soleus, tibialis anterior, and tibialis posterior. Noise in measured muscle length was filtered by means of quintic splines. Moment arms of the mm. gastrocnemii appear to be much more dependent on joint flexion angles than was generally assumed by other investigators. Some consequences for earlier analyses are mentioned.

Confined compression of canine annulus fibrosus under chemical and mechanical loading

Uniaxial confined compression and swelling experiments on cylindrical specimens taken either in an axial or in a radial direction from a canine lumbar annulus fibrosus are presented. The loading protocol consisted of a combination of stepwise mechanical and chemical loading. Swelling and consolidation curves of normalized displacement versus square root of normalized time did not show a dependence on site or orientation of the specimen. All stages in which height increases, namely, conditioning, swelling, and desolidation show only slight differences in these normalized curves. Consolidation is initially faster, and later slower. The transport coefficient for axial specimens is higher than for radial specimens, for consolidation e.g., 3.14 +/- 1.56 10(-10) m2s(-1) and 1.11 +/- 0.33 10(-10) m2s(-1) respectively, the biphasic aggregate moduli are 1.01 +/- 0.31 MPa and 0.66 +/- 0.30 MPa, respectively.

Nonhomogeneous permeability of canine anulus fibrosus.

Study Design This report examines the permeability coefficient and aggregate modulus of slices of anulus cut from canine lumbar intervertebral discs. Objectives To examine the influence of radial position on the properties of these materials, including outer samples with intact anulus edge. Summary of Background Data The outer edge of anulus fibrosus shows radial bulge during axial compression of motion segments. The radial bulge increases monotonically when the axial compression is sustained for several hours, until a plateau is reached. Triphasic modeling of axial compression shows that this time course of radial bulge can not be obtained using a uniform permeability coefficient according to values in the literature. Methods Confined consolidation experiments (controlled load) were designed to measure the time course of uniaxial deformation of samples of anulus that were 4 mm in diameter and 1 mm tall. The rotation symmetry axis of the samples was defined in the radial direction of the disc. The radial permeability coefficient and the aggregate modulus were determined using the consolidation data and the linear biphasic theory. Results The permeability coefficient was lower at the periphery than in deeper layers of the anulus. Outer samples with outer surfaces that were 0.0‐0.5 mm from the anulus edge had an average permeability coefficient of (1.02 ± 0.57) × 10‐16 m4/Ns (n = 24). Inner samples that were 2.0‐2.5 mm from the anulus edge had an average permeability coefficient of (2.81 ± 0.98) × 10‐16 m4/Ns (n = 13). The aggregate modulus HA of outer samples was significantly higher (HA = 1.56 ± 0.34 MPa) than that of inner samples (HA = 1.31 ± 0.47 MPa). Conclusions The fact that the outer anulus is less permeable than the inner anulus may explain why radial bulge of anulus fibrosus increases monotonically in time to an equilibrium value during sustained axial compression of a motion segment.

A model study of muscle forces and joint-force direction in normal and dysplastic neonatal hips

Orthopaedic treatment of congenital hip dysplasia does not always give the desired result. With the present model, prediction of the effects of various treatments on the force direction in the hip joint could help to improve and select treatment (the force direction is presumed to control the collum growth direction). The model contains three-dimensional mathematical descriptions of all muscles passing the hip joint, for various degrees of femoral dysplasia, and for various hip postures. Muscles run straight or curve round some skeletal parts. Muscle forces (all isometric) are calculated from muscle mass, density, pennation angle, mean fibre length, muscle elongation, and assumed activation levels. The latter serve as parameters for optimization. Resting lengths are taken from an assumed fetal posture, and from the observed neonatal posture. Differences between force directions before and after birth, as calculated with the model, agree with collum direction changes described by von Lanz and Mayet (1953).

Nonlinear dynamic behavior of the human knee joint--Part II: Time-domain analyses: effects of structural damage in postmortem experiments.

A description is given of the results obtained for step excitation for two human knee joint specimens using a time-domain analysis technique. As was expected from the results of a previous study, the magnitude of the dynamic load applied has a marked influence upon the stiffness and damping values for the two observed vibration modes. Deliberate damaging of selected joint elements also yields a well observable change in the dynamic behavior of the joint although these changes are difficult to interpret. Here the use of a nonlinear dynamic numerical model of the knee joint seems indispensable. An important observation is, however, that the experimental method discussed here enables to quantify the behavior of the joint and therefore may provide a valuable tool for validation of such a model.

An experimental approach to evaluate the dynamic behavior of the human knee

An experimental approach for an in vitro investigation of some aspects of dynamic force transmission through the human knee joint is presented. Essentially, the behavior of the joint was analyzed by measuring the responses to low level random excitation of the tibia while the femur was clamped. A global equilibrium position of the joint was attained by exerting static forces on the tibia via three tendinous muscle attachments. The responses to the applied dynamic loads were measured using a multi-channel dynamic measuring system and quantified by means of transfer function analysis techniques. Some preliminary experimental results are presented to illustrate the effects of variation of the direction and the magnitude of the applied dynamic and static loads.

Perspectives in Human-Joint Kinematics

To-day human joint kinematics can be studied with scientific tools which reach far beyond the power of earlier workers in this field. Indeed, several sophisticated methods to trace three-dimensional movements have become available with steadily increasing accuracy. But undoubtedly, the storage and processing of large amounts of data has made the most impressive advance thanks to modern computing facilities.

AN EXPERIMENTAL SETUP FOR THE MEASUREMENT OF FORCES ON A HUMAN CADAVERIC FOOT DURING INVERSION

An experimental setup was developed for statically measuring seven vertical and three horizontal reaction forces on the foot. In the setup, the leg can be simultaneously loaded (1) by a vertical force, (2) by an externally applied axial moment, and (3) by simulated muscle forces. The foot is free to invert under influence of the external loads. Statical analysis and test experiments were used for evaluation. The setup can be used in combination with Roentgen photogrammetry to measure bone positions simultaneously with forces.

A simplified quasi-static model of the human knee joint based on a general two-body-system theory

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