J.M.G. Kauer

Characterization of the mechanical behavior of human knee ligaments: A numerical-experimental approach

During knee-joint motions, the fiber bundles of the knee ligaments are nonuniformly loaded in a recruitment pattern, which depends on successive relative orientations of the insertion sites. These fiber bundles vary with respect to length, orientation and mechanical properties. As a result, the stiffness characteristics of the ligaments as a whole are variable during knee-joint motion. The purpose of the present study is to characterize this variable mechanical behavior. It is hypothesized that for this purpose it is essential to consider the ligaments mechanically as multi-bundle structures in which the variability in fiber bundle characteristics is accounted for, rather than as one-dimensional structures. To verify this hypothesis, bone-ligament-bone preparations of the ligaments were subjected to series of unidirectional subfailure tensile tests in which the relative insertion orientations were varied. For each individual test specimen, this series of tensile tests was simulated with a mathematical ligament model. Geometrically, this model consists of multiple line elements, of which the insertions and orientations are anatomically based. In a mathematical optimization process, the unknown stiffness and recruitment parameters of the line elements are identified by fitting the variable stiffness characteristics of the model to those of the test series. Thus, lumped parameters are obtained which describe the mechanical behavior of the ligament as a function of the relative insertion orientation. This method of identification was applied to all four knee ligaments. In all cases, a satisfactory fit between experimental results and computer simulation was obtained, although the residual errors were lower for the cruciate ligaments (1.0-2.4%) than for the collateral ligaments (3.7-8.1%). It was found that models with three or less line elements were very sensitive to geometrical parameters, whereas models with more than 7 line elements suffered from mathematical redundancy. Between 4 and 7 line elements little difference was found. It is concluded that the present ligament models can realistically simulate the variable tensile behavior of human knee ligaments. Hereby the hypothesis is verified that it is essential to consider the ligaments of the knee as multi-bundle structures in order to characterize fully their mechanical behavior.

The effect of variable relative insertion orientation of human knee bone-ligament-bone complexes on the tensile stiffness

In order to evaluate the contribution of the knee ligaments to restrain joint motions, knowledge about their structural properties is required. Due to the variable relative insertion orientation of the ligaments during knee motion, however, different fiber bundles are recruited, each with their specific mechanical properties. Hence, the structural properties vary as a function of knee motion. For this reason, a relationship between the structural tensile properties and the relative insertion orientation is required in order to define the role of the ligaments in knee mechanics. In the present study, this relationship is determined by performing a series of tensile tests in which the relative orientations of the insertion sites of human knee bone-ligament-bone preparations were varied systematically. The experimentally obtained stiffness was significantly affected by the relative orientation of the insertion sites, but more profoundly for the anterior and posterior cruciate ligaments (ACL and PCL) as compared to the medial and lateral collateral ligaments (MCL and LCL). The average decreases in stiffness per 5 degrees tilt of the insertion sites were estimated at -11.6 +/- 3.5 N mm-1 (ACL), -20.9 +/- 2.7 N mm-1 (PCL), -2.6 +/- 0.9 N mm-1 (MCL) and -3.7 +/- 0.3 N mm-1 (LCL). For the PCL and the MCL these changes in stiffness with tilt were rather insensitive to the side of the femoral insertion site which was lifted. The ACL and the LCL, conversely, displayed significant differences in stiffness changes between the different tilt directions.(ABSTRACT TRUNCATED AT 250 WORDS)

AN INVERSE DYNAMICS MODELING APPROACH TO DETERMINE THE RESTRAINING FUNCTION OF HUMAN KNEE LIGAMENT BUNDLES

During knee motion, the fiber bundles of ligaments are nonuniformly loaded in a recruitment pattern which is different for successive knee-joint positions. As a result, the restraining functions of these ligaments are variable. To analyze the relative restraint contributions of the fiber bundles in different knee-joint positions, a new method was developed. Its application was illustrated for the cruciate ligaments of one knee-joint specimen. The methods developed to estimate bundle forces comprise five steps. First, the three-dimensional motions of a knee specimen are measured for anterior-posterior forces, using Röntgen Stereophotogrammetric Analysis. Second, bone-ligament-bone tensile tests are performed to evaluate the mechanical properties of these structures in several relative orientations of the bones. Third, multiple fiber bundles are identified in each ligament, based on the main fiber orientations. Fourth, the nonlinear force-length relationship of each functional bundle, as defined by a stiffness and a recruitment parameter, is determined by combining the multidirectional tensile tests with a multiline-element ligament model. Finally, the information obtained is combined in a whole-joint computer model of the knee, to determine the internal forces in the initial kinematic experiment, using an inverse dynamics approach. The technique appeared to be extremely time consuming and technologically involved. However, it was demonstrated to be useful and effective. The preliminary results reveal that the fiber bundle restraints are extremely sensitive to the knee flexion angle and the restraining forces are highly variable within the ligaments. For both cruciate ligaments, a gradual transition was demonstrated in load transfer from the posterior bundles to the more anteriorly positioned ones during knee flexion. Furthermore, it appeared that relatively high forces were carried by only a few fiber bundles at each flexion angle. Based on these preliminary results, it is concluded that the determination of forces in multiple ligament bundles is important for the understanding of failure mechanisms of ligaments. In particular, alternate loading of different fiber bundles suggests that successful operative reconstruction of the cruciate ligaments may not be achieved simply by a one-bundle preparation.

Carpal Bone Kinematics and Ligament Lengthening Studied for the Full Range of Joint Movement

Present data on carpal kinematics and carpal ligament behaviour are limited to flexion and deviation movements of the hand. These motions do not represent all the wrist-joint motions which are important for the activities of daily living. The goal of this project was to obtain insight into carpal kinematics and carpal ligament behaviour during motions of the hand covering the full range of motion of the wrist joint. The carpals and the ligaments of four wrist-joint specimens were provided with radiopaque markers. These joints were subjected to Röntgenstereophotogrammetric experimentation in a large number of hand positions to determine carpal positions and ligament lengths. The movements of the carpal bones were described by means of finite helical axes (FHA). It was found that the movements of the carpals in the distal row closely resemble those of the hand. Conversely, the motions of the carpals of the proximal row appeared not to be directly proportional to the hand motions and exhibited clear out-of-plane movements. Furthermore, it could be shown that movements of the hand into the ulnodorsal quadrant of the full range of hand motion corresponds to larger helical rotations and translations for most of the carpals than when the hand was moved into any other quadrant. The maximal ligament length changes determined did not exceed the length changes reported for pure flexion and pure deviation movements of the hand.

A GLOBAL VERIFICATION STUDY OF A QUASI-STATIC KNEE MODEL WITH MULTI-BUNDLE LIGAMENTS*

The ligaments of the knee consist of fiber bundles with variable orientations, lengths and mechanical properties. In concept, however, these structures were too often seen as homogeneous structures, which are either stretched or slack during knee motions. In previous studies, we proposed a new structural concept of the ligaments of the knee. In this concept, the ligaments were considered as multi-bundle structures, with nonuniform mechanical properties and zero force lengths. The purpose of the present study was to verify this new concept. For this purpose, laxity characteristics of a human knee joint were compared as measured in an experiment and predicted in a model simulation study. In the experiment, the varus-valgus and anterior-posterior laxities of a knee-joint specimen containing the ligaments and the articular surfaces only, were determined. From this knee-joint, geometric and mechanical parameters were derived to supply the parameters for a three-dimensional quasi-static knee-joint model. These parameters included (i) the three-dimensional insertion points of bundles, defined in the four major knee ligaments, (ii) the mechanical properties of these ligament, as functions of their relative insertion orientations and (iii) three-dimensional representations of the articular surfaces. With this model the experiments were simulated. If knee-model predictions and experimental results agree, then the multi-bundle ligament models are validated, at least with respect to their functional role in anterior-posterior and varus-valgus loading of the joint. The model described the laxity characteristics in AP-translation and VV-rotation of the cadaveric knee-joint specimen reasonably well. Both display the same patterns of laxity changes during knee flexion. Only if a varus moment of 8 N m was applied and if the tibia was posteriorly loaded, did the model predict a slightly higher laxity than that measured experimentally. From the model-experiment comparisons it was concluded that the proposed structural representations of the ligaments and their mechanical property distributions seem to be valid for studying the anterior-posterior and varus-valgus laxity characteristics of the human knee-joint.

Instantaneous Helical Axis Estimation Via Natural, Cross-Validated Splines

In studies of biological joint motion, quantification of translations and rotations by means of a reference point and attitude angles does not provide a clear insight in the relation between kinematics and joint geometry. Because of its geometric simplicity, a better picture can be obtained by means of the Instantaneous Helical Axis (IHA), also known as the instantaneous screw axis, twist axis, or axis of rotation. At each moment in time, joint motion is seen as the movement of one body segment with respect to an adjacent segment (usually distal with respect to proximal), with a translation component along, and a rotation component about a directed line in space which is uniquely determined as long as the rotatory component does not vanish: see Figure 1. The total amounts of translation and rotation along the path of motion can be defined as the time integrals of the instantaneous translation and rotation velocities at the IHA from a given reference time.

A STEREOPHOTOGRAMMETRIC METHOD FOR MEASUREMENTS OF LIGAMENT STRUCTURE

A stereophotogrammetric method is presented to reconstruct the course of a curve in the three-dimensional space. This method is exclusively suitable as a non-destructive tool to determine the surface fiberstructure of ligaments, tendons and other organised collagenous structures. In addition, it is a convenient tool to measure the geometry of articular surfaces and other complicated surface shapes.

An indirect method to assess wrist ligament forces with particular regard to the effect of preconditioning

A method has been developed to calculate the forces that are developed in the ligaments of a joint specimen during motions. This indirect method is needed since direct measurements fail in the case of small ligaments. As an example the small ligaments of the carpal joint are considered. The rationale of the method is that the force generated in a ligament depends on the amount of strain to which it is subjected and on its material characteristics. In the method presented the lengths of the ligaments are determined in vitro at several joint positions by means of röntgenstereophotogrammetry. The zero-force length and the force-elongation relationship are determined on the same ligaments isolated in a materials testing machine. Over a considerable part of the strain range the measurement errors are relatively small compared to the forces determined, less than 10%. The method is applicable to joints in situations where other measuring methods cannot be used. The present analysis shows, however, that the force values determined are susceptible to preconditioning of the ligaments. In preconditioned ligaments the forces could be up to 50% lower than in the non-preconditioned situation. This suggests that ligament forces may vary considerably in vivo, depending on the extent of preconditioning provoked by a particular function.

On the Application of a Smoothing Procedure in the Kinematical Study of the Human Wrist Joint In-Vitro

In most biomechanical studies, the motions of a rigid body (e.g. bone) are described in terms of Euler rotation angles and translation vectors or in terms of helical axis (e.g. axis of rotation, screw axis). Each description has its own benefits. An attractive aspect of the helical axis representation is its illustrative quality, giving a more direct impression of the joint motion. Other advantages are that the helical axis facilitates relating joint kinematics to joint geometry and that the values for translations and rotations are invariant under a co-ordinate system transformation.

Strain of carpal ligaments during wrist-joint motion

To obtain a more accurate apprehension of the mechanics of the wrist-joint, the kinematical behaviour of the carpals and the length changes of the ligaments during hand-motions are determined. These structures are represented by radio-opaque markers. Using X-ray photogrammetric principles the 3D coordinates of those markers are calculated at some fifty positions of a movement-cycle. Clear differences are observed between these 3D, experimentally obtained data and prevailing concepts on ligament behaviour based on 2D kinematics of the carpal bones. It is suggested, based on results, that during some motions the carpal joint is not stabilized by one of the tested ligaments. [Edited author abstract; In English]