Technical Brief

Helical Axis Data Visualization and Analysis of the Knee Joint Articulation

[+] Author and Article Information
Ricardo Manuel Millán Vaquero

Division of Computer Graphics,
Leibniz University of Hannover,
Welfengarten 1,
Hannover D-30167, Germany
e-mail: rmillan@welfenlab.de

Alexander Vais

Division of Computer Graphics,
Leibniz University of Hannover,
Welfengarten 1,
Hannover D-30167, Germany
e-mail: vais@welfenlab.de

Sean Dean Lynch

Laboratory for Biomechanics and Biomaterials,
Orthopaedic Department,
Hannover Medical School,
Haubergstr. 3,
Hannover D-30625, Germany
e-mail: Lynch.Sean@mh-hannover.de

Jan Rzepecki

Division of Computer Graphics,
Leibniz University of Hannover,
Welfengarten 1,
Hannover D-30167, Germany
e-mail: jrzepecki@welfenlab.de

Karl-Ingo Friese

Division of Computer Graphics,
Leibniz University of Hannover,
Welfengarten 1,
Hannover D-30167, Germany
e-mail: kif@welfenlab.de

Christof Hurschler

Laboratory for Biomechanics and Biomaterials,
Orthopaedic Department,
Hannover Medical School,
Haubergstr. 3,
Hannover D-30625, Germany
e-mail: Hurschler.Christof@mh-hannover.de

Franz-Erich Wolter

Division of Computer Graphics,
Leibniz University of Hannover,
Welfengarten 1,
Hannover D-30167, Germany
e-mail: few@welfenlab.de

Manuscript received August 7, 2015; final manuscript received June 18, 2016; published online July 22, 2016. Assoc. Editor: Kenneth Fischer.

J Biomech Eng 138(9), 094501 (Jul 22, 2016) (9 pages) Paper No: BIO-15-1397; doi: 10.1115/1.4034005 History: Received August 07, 2015; Revised June 18, 2016

We present processing methods and visualization techniques for accurately characterizing and interpreting kinematical data of flexion–extension motion of the knee joint based on helical axes. We make use of the Lie group of rigid body motions and particularly its Lie algebra for a natural representation of motion sequences. This allows to analyze and compute the finite helical axis (FHA) and instantaneous helical axis (IHA) in a unified way without redundant degrees of freedom or singularities. A polynomial fitting based on Legendre polynomials within the Lie algebra is applied to provide a smooth description of a given discrete knee motion sequence which is essential for obtaining stable instantaneous helical axes for further analysis. Moreover, this allows for an efficient overall similarity comparison across several motion sequences in order to differentiate among several cases. Our approach combines a specifically designed patient-specific three-dimensional visualization basing on the processed helical axes information and incorporating computed tomography (CT) scans for an intuitive interpretation of the axes and their geometrical relation with respect to the knee joint anatomy. In addition, in the context of the study of diseases affecting the musculoskeletal articulation, we propose to integrate the above tools into a multiscale framework for exploring related data sets distributed across multiple spatial scales. We demonstrate the utility of our methods, exemplarily processing a collection of motion sequences acquired from experimental data involving several surgery techniques. Our approach enables an accurate analysis, visualization and comparison of knee joint articulation, contributing to the evaluation and diagnosis in medical applications.

Copyright © 2016 by ASME
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Grahic Jump Location
Fig. 1

Description of a rigid body transformation in terms of a screw

Grahic Jump Location
Fig. 2

(a) Experimental setup, with passive reflective markers tools fixed to the knee joint. (b) Scheme of relevant coordinate systems.

Grahic Jump Location
Fig. 3

Helical axis configuration for the flexion of tibia with respect to femur. Hα is given by the point of rotation pα and the unit vector ωα for each angle α.

Grahic Jump Location
Fig. 5

Comparison of helical axis between the proposed method (continuous curves) and based on FHA [9] (samples)

Grahic Jump Location
Fig. 8

Multiscale environment for exploration of patient-specific knee joint related data. Helical axes visualizations (behavioral scale) are explored together with other related data sets for a complete analysis of knee-joint diseases with a multiscale nature. In the example, the environment incorporates views of the cartilage (organ scale), including a femoral cartilage thickness map and a 3D reconstruction of a micro-CT scan from a cartilage sample, with some structural characteristics represented by an InfoVis visualization placed in the neighborhood of the latter, and histological images of cross sections (cellular scale).

Grahic Jump Location
Fig. 4

Representation of a sampled motion sequence withinthe Lie algebra se(3) with a third order polynomial approximation

Grahic Jump Location
Fig. 6

Patient-specific anatomical visualization of the helical axis, (a) with the proposed method and (b) based on FHA [9]

Grahic Jump Location
Fig. 7

Analysis of similarity between helical axis sequences on a subject in a pre- (denoted by N) and postoperative state (P)



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