Tracking Knee Joint Functional Axes through Tikhonov Filtering and Plűcker Coordinates

Wangdo Kim

doi:10.4172/2165-7025.s4-001

Abstract

Researchers have reported several compensation methods to estimate bone and joint position from a cluster of skin-mounted markers as influenced by Soft Tissue Artifacts (STA). Tikhonov Regularization Filtering (TRF) as a means to estimate Instantaneous Screw Axes (ISA) was introduced here as a means to reduce the displacement of a rigid body to its simplest geometric form. Recent studies have suggested that the ISA of the knee, i.e., Knee Functional Axes (KFA), might be closely connected to the estimation of constraint forces such as those due to medial and lateral connective tissues. The estimations of ISAs were known to be highly sensitive to noisy data, which may be mathematically ill-posed, requiring smoothing such as that conducted by regularization. The main contribution in this work was to establish the reciprocal connection between the KFA and Ground Reaction Forces (GRF) as a means to estimate joint constraint forces. Presented results compare the computational performance with published kinetic and kinematic joint data generated from an instrumented total knee replacement. Implications of these preliminary findings with respect to dynamic alignment as a functional anatomic metric are discussed.

Highlights

The strategies for minimizing modelling errors such as those produced by Soft Tissue Artifacts (STAs) have received much attention from both researchers and practitioners [1,2]
This technique is based on the analogy that the inertial tensor about the Centre of Mass (COM) of a Three-Dimensional (3D) rigid body is related to the covariance matrix of the trivariate random vectors, whose Probability Density Function (PDF) is proportional to the point-wise density of the rigid body itself
It was found that the ordinary process of estimation of b could not be applied to the optimal generation of knee instantaneous axes

Summary

Introduction

The strategies for minimizing modelling errors such as those produced by Soft Tissue Artifacts (STAs) have received much attention from both researchers and practitioners [1,2]. The Centre of Mass (COM) and the inertial tensor of the marker-clusters are calculated at each time frame This technique is based on the analogy that the inertial tensor about the COM of a Three-Dimensional (3D) rigid body is related to the covariance matrix of the trivariate random vectors, whose PDF is proportional to the point-wise density of the rigid body itself. The global optimization treats each body segment in holistic terms, i.e., a structure that is undergoing transformation as a whole, rather than in terms of separate segments each with imposition constraints at the joint [5] This process has been defined by minimizing the weighted sums-of-squares distance between simulation and model-determined marker positions

Objectives

Methods

Results

Conclusion