Development of a planar multibody model of the human knee joint

Abstract

International audienceThe aim of this work is to develop a dynamic model for the biological human knee joint. The model is formulated in the framework of multibody systems methodologies, as a system of two bodies, the femur and the tibia. For the purpose of describing the formulation, the relative motion of the tibia with respect to the femur is considered. Due to their higher stiffness compared to that of the articular cartilages, the femur and tibia are considered as rigid bodies. The femur and tibia cartilages are considered to be deformable structures with specific material characteristics. The rotation and gliding motions of the tibia relative to the femur cannot be modeled with any conventional kinematic joint, but rather in terms of the action of the knee ligaments and potential contact between the bones. Based on medical imaging techniques, the femur and tibia profiles in the sagittal plane are extracted and used to define the interface geometric conditions for contact. When a contact is detected, a continuous nonlinear contact force law is applied which calculates the contact forces developed at the interface as a function of the relative indentation between the two bodies. The four basic cruciate and collateral ligaments present in the knee are also taken into account in the proposed knee joint model, which are modeled as nonlinear elastic springs. The forces produced in the ligaments, together with the contact forces, are introduced into the system's equations of motion as external forces. In addition, an external force is applied on the center of mass of the tibia, in order to actuate the system mimicking a normal gait motion. Finally, numerical results obtained from computational simulations are used to address the assumptions and procedures adopted in this study

On the continuous contact force models for soft materials in multibody dynamics

“…The general motivation for this work comes from current interest in developing mathematical models for the dynamics of constrained multibody systems involving contact events between soft materials, such as in the case of biomechanical systems and bushing elements made with polymer materials [35][36][37][38][39][40][41]. In fact, modeling contacts with a high degree of energy dissipation plays a crucial role in the analysis, design and control of many mechanical systems in the measure that soft materials are characterized by low or medium values of the coefficient of restitution.…”

Influence of the contact model on the dynamic response of the human knee joint

“…This section deals with the fundamental issues of the mathematical human knee model used in this study, which has been developed under the framework of MBS methodologies [2]. The knee model is composed by two rigid bodies, the tibia and the femur, which describe a general planar motion in the sagittal plane.…”

“…The absolute rotation angles of the local coordinate systems of bodies i and j are denoted by i and j , respectively. The Cartesian coordinates of centres of mass and inertia properties of the femur and tibia used in this study correspond to a male subject of weight 76 kg and height 1.8 m [2].…”

“…In order to compute the contact distance, the position, orientation, and contact geometry of potential contact bodies have to be known. In short, three main ingredients have to be considered to perform a dynamic contact-impact analysis, namely the definition of the contact geometry, the contact detection approach, and the application of the constitutive contact force law [1][2][3].…”

Modeling of the condyle elements within a biomechanical knee model

“…A possible reason is that much biomechanical simulation is based upon inverse dynamics, where movement of all degrees-offreedom is input to the analysis leading to a presumption of simple joint kinematics. For most applications concerning simple joints, such as the hip joint [27], this is a reasonable assumption, but for detailed investigations of more complex and incongruent joints, such as the knee joint [28], is it not. The purpose of this paper is to present a biomechanics model capturing some of the complexity of the knee joint while retaining the computational efficiency of inverse dynamics analysis.…”