W. Auzinger, H. Schmiedmayer, I. Reichl, E. Weinmüller:
"Reconstructing the knee joint mechnism from kinematic data";
Mathematical and Computer Modelling of Dynamical Systems, 16 (2010), 5; S. 403 - 415.

Kurzfassung englisch:
The interpretation of joint kinematics data in terms of displacements is a product of the type of movement, the measurement technique, and the underlying model of the joint implemented in optimization procedures. Kinematic constraints reducing the number of degrees of freedom (DoF) are expected to compensate for measurement errors and noise, thus, increasing the reproducibility of joint angles. One approach already successfully applied by several groups approximates
the healthy human knee joint as a compound hinge joint with minimal varus/valgus rotation. Most of these optimizations involve an orthogonality constraint. This contribution compares the effect of a model with and without orthogonality constraint on the obtained joint rotation angles. For this purpose kinematic data is simulated without noise and with normally distributed noise of varying size. For small noise the unconstrained model provides more accurate results while for larger noise this is the case for the constrained model. This can be attributed to the shape of the objective function of the unconstrained model near its minimum.

tibiofemoral joint; kinematics; optimization; compound hinge joint; model comparison; sensitivity analysis

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