A Novel Method for Quantifying Uncertainty in the Unified Envelope of Constraint in the Passive Knee Joint

Abstract

The Experimental Joint Biomechanics Research Lab at the University of Kansas created the unified envelope (UE) of constraint as a means for describing the overall laxity of the passive knee joint. The UE is currently calculated with the use of a radial basis function (RBF), which has been shown to provide a useful approximation of the multidimensional relationship between applied forces and observed kinematics. However, the UE does not provide any information regarding its certainty in the approximation at any given position, making comparisons between UEs more difficult. The main objective of this thesis was to create an estimate for the uncertainty of the UE, specific to each point within the UE. Secondary objectives included reducing the effect of the investigator on the UE and determining the optimal protocol for loading during laxity evaluations. To determine if the proposed method was able to meet the objectives, three different investigators performed manual laxity evaluations on one cadaveric specimen. Data from these evaluations were sequentially downsampled and used to create many slightly different UEs. The variance of these UEs at each point were combined with a general measure of variance, found by calculating the variance of the error when RBFs use the sequentially downsampled data to approximate known data. This estimate appeared to perform well throughout the envelope, providing a standard deviation consistent with measurements from previous studies. Results also showed a decrease in the median absolute difference between investigators of 18.3% in VV°, 15.6% in IE°, and 16.2% in AP position (mm) when compared to the previous method. The importance of collecting both uniaxial and multiaxial loading trials during the laxity evaluation was also verified. The following chapters provide further information on methods and results, along with future applications.