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.