A constraint-based approach to modelling the mobility of the human knee joint.

A model of knee mobility able to predict the range and pattern of movement in the unloaded joint was proposed by Wilson et al. (J. Biomech. 31 (1998) 1127-1136). The articular surfaces in the lateral and medial compartments and isometric fascicles in three of the knee ligaments were represented as five constraints on motion between the femur and tibia in a single degree-of-freedom parallel spatial mechanism. The path of movement of the bones during passive flexion was found by solving the forward kinematics of the mechanism using an iterative method. The present paper shows that such a mechanism-based solution approach can lead to an underestimation of the flexion range. This is due to the mechanism reaching a 'stationary configuration' and 'locking'. A new, constraint-based approach to the solution of the model joint displacement is proposed. It avoids the representation of ligaments and articular surfaces by kinematically equivalent chains of one degree-of-freedom pairs which are prone to singularities. It relies instead on a numerical solution of five non-linear constraint equations to find the relative positions of the bones at a series of flexion angles. The method is successful both in its ability to predict motion through a physiological range and in its efficiency with a solution rate forty times faster than the original algorithm. The new approach may be extended to include more complex joint surface geometry, allowing a study of the effects of articular surface shape and ligament arrangement on joint kinematics

The components of passive knee movement are coupled to flexion angle.

Movement of the unloaded knee has been described in several studies by an "envelope of passive flexion", a description that does not describe or explain the widely reported coupling of internal tibial rotation to flexion. The objective of the current study was to show that the envelope of passive knee flexion can be reduced to a coupled path. Two hypotheses were tested: (1) in normal knees flexed passively, internal/external rotation, abduction/adduction and all three components of translation are coupled to flexion angle, and (2) the tibia rotates internally as the knee is flexed passively. Fifteen cadaver knees were flexed in a rig designed to apply minimal resistance to knee movement while three-dimensional kinematics of the femur relative to the tibia were measured with an electromagnetic tracking system. Each specimen displayed internal tibial rotation and posterior, proximal and medial displacement of a reference point with flexion, while a range of ab/adduction behaviour was observed. Mean absolute differences between the flexing and extending paths in normal specimens were under 2 and 0.2 degrees for internal/external tibial rotation and ab/adduction, respectively. Deviation from the movement path was resisted: when released after being displaced, the femur of each normal joint sprang back to its original position on the motion path. It was concluded that passive knee flexion can be described by a coupled path. Although the exact shape of the path is very sensitive to load and varies between knees, knee rotations and translations were always coupled to flexion, and internal tibial rotation with flexion was always observed

Helical axis calculation based on Burmester theory: experimental comparison with traditional techniques for human tibiotalar joint motion

In prosthetics and orthotics design, it is sometimes necessary to approximate the multiaxial motion of several human joints to a simple rotation about a single fixed axis. A new technique for the calculation of this axis is proposed, originally based on Burmester’s theory. This was compared with traditional approaches based on the mean and finite helical axes. The three techniques were assessed by relevant optimal axis estimation in in vitro measurements of tibiotalar joint motion. A standard jig and radiostereometry were used in two anatomical specimens to obtain accurate measurements of joint flexion. The performance of each technique was determined by comparing the motion based on the resulting axis with the experimental data. Random noise with magnitude typically similar to that of the skin motion was also added to the measured motion. All three techniques performed well in identifying a single rotation axis for tibiotalar joint motion. Burmester’s theory provides an additional method for human joint motion analysis, which is particularly robust when experimental data are considerably error affected

Multibody Optimisations: From Kinematic Constraints to Knee Contact Forces and Ligament Forces. In : Biomechanics of Anthropomorphic Systems

Musculoskeletal models are widely used in biomechanics today to better understand muscle and joint function. Musculo-tendon forces as well as joint contact forces and ligament forces can be estimated within an inverse dynamics computational framework. Using a musculoskeletal model of the lower limb, this chapter presents the different optimisations required to drive the model with experimental data and to compute these forces and their interactions. In these optimisations, the development of anatomical constraints representing, for example, the medial and lateral tibiofemoral contacts or the cruciate ligaments is crucial both to inverse kinematics and to inverse dynamics. Some emblematic results are presented for knee contact forces and ligament forces during gait, illustrating the couplings between joint degrees of freedom and the interactions between forces acting both in muscles and in joints