Abstract-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,

Abstract-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 Rdntgcn 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 reconstruc tion of the cruciate ligaments may not be achieved simply by a one-bundle preparation.

It is generally recognized that the mechanical properties of soft connective tissues are affected by their structural components. We documented collagen density distributions in human knee ligaments to quantify differences in density within and between these ligaments. In order to explain the variations in mechanical properties within and between different knee ligaments as described in the literature, the distributions of collagen density were correlated with these biomechanical findings. Human knee ligaments were shown to be nonhomogeneous structures with regard to collagen density. The anterior bundles of all ligaments contained significantly more collagen mass per unit of volume than the posterior bundles did. The percentage differences between the anterior and posterior bundles, in relation to the posterior bundles, were about 25% for the anterior cruciate ligament (ACL) and the collateral ligaments and about 10% for the posterior cruciate ligament (PCL). Along the cruciate ligaments, the central segments had higher collagen densities than did segments adjacent to the ligament insertions (ACL 9%, PCL 24%). The collagen density in the ACL was significantly lower than that in the other ligaments. These variations within and between the ligaments correlate well with the variations in mechanical properties described in the literature; however, other structural differences have to be taken into account to fully explain the variations in mechanical properties from the structural components.

We present a method for the measurement of hydroxyproline density distributions, as an estimate for collagen density distributions, in fibrous tissues such as ligments and tendons. To evaluate this method, a single flexor tendon of a human hand was divided into seven tissue locations. Triplicate determinations of the dry weight tissue mass, volume, and hydroxyproline mass were made at each location: two samples were analyzed at the same time (a and b) and one was analyzed later (c). The intralocation variation is an estimate for the measurement error variance, which indicates both the precision (a compared with b) and the repeatability (b compared with c) of the technique for determination of volume, dry weight tissue mass, hydroxyproline concentration, and hydroxyproline density. The precision was about 5% for all variables, and the repeatability ranged from 1.5–4.3%. In comparison with the interlocation variations, the error variances were small, except for collagen concentration. This indicates that despite the measurement errors, differences in hydroxyproline density can be detected within fibrous tissues with the proposed method. The use of only a single tendon is adequate to evaluate the measurement error of the method, but more tendons should be measured to generalize the absolute values of the variables.

Abstract-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 ( 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,