Abstract
The use of multi-body optimisation (MBO) to estimate joint kinematics from stereophotogrammetric data while compensating for soft tissue artefact is still open to debate. Presently used joint models embedded in MBO, such as mechanical linkages, constitute a considerable simplification of joint function, preventing a detailed understanding of it. The present study proposes a knee joint model where femur and tibia are represented as rigid bodies connected through an elastic element the behaviour of which is described by a single stiffness matrix. The deformation energy, computed from the stiffness matrix and joint angles and displacements, is minimised within the MBO. Implemented as a “soft” constraint using a penalty-based method, this elastic joint description challenges the strictness of “hard” constraints. In this study, estimates of knee kinematics obtained using MBO embedding four different knee joint models (i.e., no constraints, spherical joint, parallel mechanism, and elastic joint) were compared against reference kinematics measured using bi-planar fluoroscopy on two healthy subjects ascending stairs. Bland-Altman analysis and sensitivity analysis investigating the influence of variations in the stiffness matrix terms on the estimated kinematics substantiate the conclusions. The difference between the reference knee joint angles and displacements and the corresponding estimates obtained using MBO embedding the stiffness matrix showed an average bias and standard deviation for kinematics of 0.9±3.2° and 1.6±2.3 mm. These values were lower than when no joint constraints (1.1±3.8°, 2.4±4.1 mm) or a parallel mechanism (7.7±3.6°, 1.6±1.7 mm) were used and were comparable to the values obtained with a spherical joint (1.0±3.2°, 1.3±1.9 mm). The study demonstrated the feasibility of substituting an elastic joint for more classic joint constraints in MBO.
Highlights
The in-vivo assessment of lower limb joint kinematics is generally performed using an optoelectronic system and skin markers
Making similar use of “soft” constraints, the objective of the present study is to introduce into the multi-body optimisation (MBO) another tool for modelling the osteoarticular structures: the joint stiffness matrix
Given the acknowledged experimental errors and STA, (a) an improvement of the accuracy of the estimated knee kinematics can be obtained by introducing joint constraints, (b) not those constraints that impede or prescribe joint displacements, and (c) the introduction of “soft” constraints based on a joint stiffness matrix represents an acceptable biofidelic solution
Summary
The in-vivo assessment of lower limb joint kinematics is generally performed using an optoelectronic system and skin markers. It is assumed that these joint constraints can help compensate for the soft tissue artefact (i.e., relative movement between the skin-markers and the underlying bone: STA). As a consequence of the STA, it is commonly admitted that movement analysis using optoelectronic systems and skin markers, and state-of-the art data processing displays a resolution in the order of 5 to 12° and 5 to 17 mm [11,12]. Human joints undergo rotations and translations the amplitude of which may be as small as a few degrees and millimetres This is the case for those degrees of freedom that are stabilised by the passive periarticular structures and, as such, of special interest in clinical applications involving orthopaedic reconstructive procedures [13]. If the objective is motor function assessment, lower resolutions may be acceptable
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