A subject specific multibody model of the knee with menisci

Abstract

The menisci of the knee play an important role in joint function and our understanding of knee mechanics and tissue interactions can be enhanced through computational models of the tibio-menisco-femoral structure. Several finite element models of the knee that include meniscus–cartilage contact exist, but these models are typically limited to simplified boundary conditions. Movement simulation and musculoskeletal modeling can predict muscle forces, but are typically performed using the multibody method with simplified representation of joint structures. This study develops a subject specific computational model of the knee with menisci that can be incorporated into neuromusculoskeletal models within a multibody framework. Meniscus geometries from a 78-year-old female right cadaver knee were divided into 61 discrete elements (29 medial and 32 lateral) that were connected through 6 × 6 stiffness matrices. An optimization and design of experiments approach was used to determine parameters for the 6 × 6 stiffness matrices such that the force–displacement relationship of the meniscus matched that of a linearly elastic transversely isotropic finite element model for the same cadaver knee. Similarly, parameters for compliant contact models of tibio-menisco-femoral articulations were derived from finite element solutions. As a final step, a multibody knee model was developed and placed within a dynamic knee simulator model and the tibio-femoral and patello-femoral kinematics compared to an identically loaded cadaver knee. RMS errors between finite element displacement and multibody displacement after parameter optimization were 0.017 mm for the lateral meniscus and 0.051 mm for the medial meniscus. RMS errors between model predicted and experimental cadaver kinematics during a walk cycle were less than 11 mm translation and less than 7° orientation. A small improvement in kinematics, compared to experimental measurements, was seen when the menisci were included versus a model without the menisci. With the menisci the predicted tibio-femoral contact force was significantly reduced on the lateral side (937 N peak force versus 633 N peak force), but no significant reduction was seen on the medial side.