L. Blankevoort

Validation of a three-dimensional model of the knee

Three-dimensional mathematical models of the tibio-femoral joint require input of the geometry of articulating surfaces and ligament insertions, and the mechanical properties of cartilage and ligaments. This paper describes a validation of a knee model through a direct specimen-related comparison between the knee model and the kinematics of four knee joint specimens from which the geometry data were used as input of the model. The knee model is quasi-static and is based on equilibrium of forces and moments. The stiffness properties of the ligaments and articular cartilage were estimated on the basis of data reported in the literature. The so-called reference strains in the ligament bundles for the joint in extension, were determined by using an optimization procedure, minimizing the difference between the kinematics of the model and the kinematics of experimentally obtained flexion motions with an internally or an externally rotated tibia (+/- 3 Nm load). A reasonable to good agreement between the model and the experimental kinematics could be obtained for internal-external rotation laxity and the coupled translations and varus-valgus rotation. The disparity between model and experiment varied from knee to knee, average deviations ranging from close to zero to 8 degrees internal rotation deviation and from 5 mm posterior to 3 mm anterior position deviation. The average anterior-posterior laxities at both 20 degrees and 90 degrees flexion were within the variations reported in the literature, although for each individual joint with some underestimation or overestimation. It was concluded that the optimization procedure compensated for the lack of menisci and capsular structures by higher prestrains, thereby overestimating the ligament forces. Despite the gross simplifications relative to the complex anatomy of the knee, the present knee model can realistically simulate the passive motion characteristics of the human knee joint.

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.

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.

Induction of osteoarthritis by intra-articular injection of collagenase in mice. Strain and sex related differences

To study the effects of strain and sex on the development of injury-induced osteoarthritis (OA) in murine knee joints, two doses of highly purified bacterial collagenase (10 units and 30 units) were injected into male and female mice of two closely related strains, C57BL6 and C57BL10. Frontal histological sections of whole knee joints were made late in the disease process and examined for osteoarthritic lesions. Differences in prevalence of cartilage damage between strains and sexes were observed. Prevalence was higher in C57BL10 (male: almost 100%) than in C57BL6 (male: about 25%), and the prevalence was twice as high in males as in females in both strains. The amount of collagenase (10 or 30 units) did not affect the prevalence of lesions, however, it did influence the severity of the damage. The site of the damage appeared to be dose and strain dependent. Male C57BL6 always showed damage on the medial tibial plateau, independent of dose. In male C57BL10 damage almost always appeared on the lateral tibial plateau with 10 units, while with 30 units the medial plateau also became strongly involved. Since it is known that male mice are more prone to spontaneous OA than female mice and C57BL10 are more prone han C57BL6 mice, it can be concluded that predisposition to spontaneous osteoarthritis increases the risk of developing injury-induced osteoarthritis. Location and severity of the changes will probably be related to joint loading.

In vitro laxity-testers for knee joints of mice☆

The knee joints of mice can be used as a model for studying the effects of interventions on knee laxity. The goal of this study was to quantify knee joint laxity in vitro. Three devices were developed: a positioning- and cementing device, an anterior-posterior (AP) laxity tester and a varus-valgus (VV) laxity tester. The positioning and cementing device was used to position the joint in a reproducible way and to attach clamping pins to the proximal femur and distal tibia using PM MA. The clamping pins were used to fix the joint to the AP- and VV-testers. In both testers the load was applied by means of a spindle-actuated spring while load and displacements were measured simultaneously. The load--displacement data were used to calculate displacement and compliance parameters. The performance of the testers was evaluated by testing 5 normal knee joints of 5 mice. Total AP-translation at + or - 0.8 N was 0.43 (+ or - 0.16 S.D.) mm with compliances of 0.14 (+ or - 0.05 S.D.) mm N(1) and 0.12 ( + or - 10.05 S.D.) mm N(-1) at 0.8 N posterior and anterior force, respectively. Total VV-rotation at + or - 4 Nmm was 17.2 (+ or - 2.6 S.D.) degrees with compliances of 0.9 degrees Nmm(-1) (+ or - 0.2 degrees Nmm(-1) S.D.) and 1.0 Nmm(-1) (+ or - 0.4 degrees Nmm(-1) S.D.) at 4 Nmm valgus and varus moment, respectively. The contributions of the deformations of the bones and the fixtures to the rotations were negligible in the VV-test. In the AP-test they account for approximately 0.07 ( + or - 0.03 S.D.)mm of the total AP-translation. This will not affect the utilization of the device for comparative analysis. It is concluded that in in vitro evaluation of AP- and VV-laxity in knees of mice is feasible with sufficient accuracy for evaluation of changes after ligament damage.