0
Technical Brief

Helical Axis Data Visualization and Analysis of the Knee Joint Articulation

[+] Author and Article Information
Ricardo Manuel Millán Vaquero

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

Alexander Vais

Welfenlab,
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

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

Karl-Ingo Friese

Welfenlab,
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

Welfenlab,
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.

FIGURES IN THIS ARTICLE
<>
Copyright © 2016 by ASME
Your Session has timed out. Please sign back in to continue.

References

Hollister, A. M. , Jatana, S. , Singh, A. K. , Sullivan, W. W. , and Lupichuk, A. G. , 1993, “ The Axes of Rotation of the Knee,” Clin. Orthop. Relat. Res., 290, pp. 259–268. [PubMed]
Chasles, M. , 1830, “ Note sur les propriétés générales du système de deux corps semblables entr'eux et placés d'une manière quelconque dans l'espace; et sur le déplacement fini ou infiniment petit d'un corps solide libre,” Bull. Sci. Math., Férussac, 14, pp. 321–326.
Woltring, H. , De Lange, A. , Kauer, J. , and Huiskes, R. , 1987, “ Instantaneous Helical Axis Estimation via Natural, Cross-Validated Splines,” Biomechanics: Basic and Applied Research, Springer, Berlin, pp. 121–128.
Blankevoort, L. , Huiskes, R. , and Lange, A. D. , 1990, “ Helical Axes of Passive Knee Joint Motions,” J. Biomech., 23(12), pp. 1219–1229. [CrossRef] [PubMed]
Woltring, H. , Huiskes, R. , De Lange, A. , and Veldpaus, F. , 1985, “ Finite Centroid and Helical Axis Estimation From Noisy Landmark Measurements in the Study of Human Joint Kinematics,” J. Biomech., 18(5), pp. 379–389. [CrossRef] [PubMed]
Metzger, M. , Faruk Senan, N. , O'Reilly, O. , and Lotz, J. , 2010, “ Minimizing Errors Associated With Calculating the Location of the Helical Axis for Spinal Motions,” J. Biomech., 43(14), pp. 2822–2829. [CrossRef] [PubMed]
Hart, R. , Mote, C. , and Skinner, H. , 1991, “ A Finite Helical Axis as a Landmark for Kinematic Reference of the Knee,” ASME J. Biomech. Eng., 113(2), pp. 215–222. [CrossRef]
Manal, K. , McClay, I. , Stanhope, S. , Richards, J. , and Galinat, B. , 2000, “ Comparison of Surface Mounted Markers and Attachment Methods in Estimating Tibial Rotations During Walking: An In Vivo Study,” Gait Posture, 11(1), pp. 38–45. [CrossRef] [PubMed]
van den Bogert, A. J. , Reinschmidt, C. , and Lundberg, A. , 2008, “ Helical Axes of Skeletal Knee Joint Motion During Running,” J. Biomech., 41(8), pp. 1632–1638. [CrossRef] [PubMed]
Murray, R. M. , Li, Z. , Sastry, S. S. , and Sastry, S. S. , 1994, A Mathematical Introduction to Robotic Manipulation, CRC Press, Boca Raton, FL.
Wu, W.-L. , Su, F.-C. , Cheng, Y.-M. , Huang, P.-J. , Chou, Y.-L. , and Chou, C.-K. , 2000, “ Gait Analysis After Ankle Arthrodesis,” Gait Posture, 11(1), pp. 54–61. [CrossRef] [PubMed]
Besier, T. F. , Sturnieks, D. L. , Alderson, J. A. , and Lloyd, D. G. , 2003, “ Repeatability of Gait Data Using a Functional Hip Joint Centre and a Mean Helical Knee Axis,” J. Biomech., 36(8), pp. 1159–1168. [CrossRef] [PubMed]
Van Sint Jan, S. L. , Clapworthy, G. J. , and Rooze, M. , 1998, “ Visualization of Combined Motions in Human Joints,” IEEE Comput. Graphics Appl., 18(6), pp. 10–14. [CrossRef]
Van Sint Jan, S. , Salvia, P. , Hilal, I. , Sholukha, V. , Rooze, M. , and Clapworthy, G. , 2002, “ Registration of 6-DOFs Electrogoniometry and CT Medical Imaging for 3D Joint Modeling,” J. Biomech., 35(11), pp. 1475–1484. [CrossRef] [PubMed]
Millán Vaquero, R. M. , Lynch, S. D. , Fleischer, B. , Rzepecki, J. , Friese, K.-I. , Hurschler, C. , and Wolter, F.-E. , 2015, “ Enhanced Visualization of Knee Joint Functional Articulation Based on Helical Axis Method,” Bildverarbeitung für die Medizin 2015. Informatik aktuell, Springer, New York, pp. 449–454.
Friese, K.-I. , and Wolter, F.-E. , 2000, “ Local and Global Geometric Methods for Analysis, Interrogation, Reconstruction, Modification, and Design of Shape,” Computer Graphics International, Welfenlab Report No. 3, pp. 137–151.
Serra, J. , 1984, Image Analysis and Mathematical Morphology, Vol. 1, Academic Press, Orlando, FL.
Kanamiya, T. , Naito, M. , Hara, M. , and Yoshimura, I. , 2002, “ The Influences of Biomechanical Factors on Cartilage Regeneration After High Tibial Osteotomy for Knees With Medial Compartment Osteoarthritis,” Arthroscopy, 18(7), pp. 725–729. [CrossRef] [PubMed]
Houard, X. , Goldring, M. B. , and Berenbaum, F. , 2013, “ Homeostatic Mechanisms in Articular Cartilage and Role of Inflammation in Osteoarthritis,” Curr. Rheumatol. Rep., 15(11), pp. 1–10. [CrossRef]
Gehlenborg, N. , O'Donoghue, S. I. , Baliga, N. S. , Goesmann, A. , Hibbs, M. A. , Kitano, H. , Kohlbacher, O. , Neuweger, H. , Schneider, R. , Tenenbaum, D. , and Gavin, A.-C. , 2010, “ Visualization of Omics Data for Systems Biology,” Nat. Methods, 7 (Suppl. 3), pp. S56–S68. [CrossRef] [PubMed]
O'Donoghue, S. I. , Gavin, A.-C. , Gehlenborg, N. , Goodsell, D. S. , Hériché, J.-K. , Nielsen, C. B. , North, C. , Olson, A. J. , Procter, J. B. , Shattuck, D. W. , Walter, T. , and Wong, B. , 2010, “ Visualizing Biological Data—Now and in the Future,” Nat. Methods, 7 (Suppl. 3), pp. S2–S4. [CrossRef] [PubMed]
Hunter, P. , Coveney, P. V. , de Bono, B. , Diaz, V. , Fenner, J. , Frangi, A. F. , Harris, P. , Hose, R. , Kohl, P. , Lawford, P. , McCormack, K. , Mendes, M. , Omholt, S. , Quarteroni, A. , Shublaq, N. , Skår, J. , Stroetmann, K. , Tegner, J. , Thomas, S. R. , Tollis, I. , Tsamardinos, I. , van Beek, J. H. G. M. , and Viceconti, M. , 2010, “ A Vision and Strategy for the Virtual Physiological Human in 2010 and Beyond,” Philos. Trans. R. Soc. London A, 368(1920), pp. 2595–2614. [CrossRef]
Rossman, W. , 2002, Lie Groups: An Introduction Through Linear Groups, Oxford University Press, New York.
Jinkerson, R. A. , Abrams, S. L. , Bardis, L. , Chryssostomidis, C. , Clément, A. , Patrikalakis, N. M. , and Wolter, F.-E. , 1993, “ Inspection and Feature Extraction of Marine Propellers,” J. Ship Prod., 9, pp. 88–106.
Visser, M. , Stramigioli, S. , and Heemskerk, C. , 2006, “ Cayley–Hamilton for Roboticists,” International Conference on Intelligent Robots and Systems, Beijing, China, Oct. 9–15, pp. 4187–4192.
Woltring, H. , 1994, “ 3-D Attitude Representation of Human Joints: A Standardization Proposal,” J. Biomech., 27(12), pp. 1399–1414. [CrossRef] [PubMed]
Grassia, F. S. , 1998, “ Practical Parameterization of Rotations Using the Exponential Map,” J. Graphics Tools, 3(3), pp. 29–48. [CrossRef]
Šenk, M. , and Chèze, L. , 2006, “ Rotation Sequence as an Important Factor in Shoulder Kinematics,” Clin. Biomech., 21 (Suppl. 1), pp. 3–8. [CrossRef]
Gutschke, M. , Vais, A. , and Wolter, F.-E. , 2015, “ Differential Geometric Methods for Examining the Dynamics of Slow-Fast Vector Fields,” Visual Comput., 31(2), pp. 169–186. [CrossRef]
Thielhelm, H. , Vais, A. , and Wolter, F.-E. , 2015, “ Geodesic Bifurcation on Smooth Surfaces,” Visual Comput., 31(2), pp. 187–204. [CrossRef]
Wolter, F.-E. , and Tuohy, S. T. , 1992, “ Curvature Computations for Degenerate Surface Patches,” Comput. Aided Geom. Des, 9(4), pp. 241–270. [CrossRef]
Rodrigues, O. , 1840, “ Des lois géometriques qui regissent les déplacements d’ un systéme solide dans l' espace, et de la variation des coordonnées provenant de ces déplacement considerées indépendent des causes qui peuvent les produire,” J. Math. Pures Appl., 5, pp. 380–400.
Ostermeier, S. , Hurschler, C. , and Stukenborg-Colsman, C. , 2004, “ Quadriceps Function After TKA—An In Vitro Study in a Knee Kinematic Simulator,” Clin. Biomech., 19(3), pp. 270–276. [CrossRef]
Wu, G. , Siegler, S. , Allard, P. , Kirtley, C. , Leardini, A. , Rosenbaum, D. , Whittle, M. , D'Lima, D. D. , Cristofolini, L. , Witte, H. , Schmid, O. , and Stokes, I. , 2002, “ ISB Recommendation on Definitions of Joint Coordinate System of Various Joints for the Reporting of Human Joint Motion—Part I: Ankle, Hip, and Spine,” J. Biomech., 35(4), pp. 543–548. [CrossRef] [PubMed]
Spoor, C. , and Veldpaus, F. , 1980, “ Rigid Body Motion Calculated From Spatial Co-Ordinates of Markers,” J. Biomech., 13(4), pp. 391–393. [CrossRef] [PubMed]
Belta, C. , and Kumar, V. , 2002, “ Euclidean Metrics for Motion Generation on se (3),” Proc. Inst. Mech. Eng., Part C, 216(1), pp. 47–60. [CrossRef]
Borg, I. , and Groenen, P. J. , 2005, Modern Multidimensional Scaling: Theory and Applications, Springer, Berlin.
Cox, T. F. , and Cox, M. A. , 2000, Multidimensional Scaling, CRC Press, Boca Raton, FL.
Reuter, M. , Wolter, F.-E. , and Peinecke, N. , 2006, “ Laplace–Beltrami Spectra as Shape-DNA of Surfaces and Solids,” Comput. Aided Des., 38(4), pp. 342–366. [CrossRef]
Peinecke, N. , Wolter, F.-E. , and Reuter, M. , 2007, “ Laplace Spectra as Fingerprints for Image Recognition,” Comput. Aided Des., 39(6), pp. 460–476. [CrossRef]
Reuter, M. , Niethammer, M. , Wolter, F.-E. , Bouix, S. , and Shenton, M. , 2007, “ Global Medical Shape Analysis Using the Volumetric Laplace Spectrum,” International Conference on Cyberworlds 2007 (NASAGEM), IEEE Hannover, Germany, Oct. 24–26, pp. 417–426.
Friese, K.-I. , Blanke, P. , and Wolter, F.-E. , 2011, “ YaDiV—An Open Platform for 3D Visualization and 3D Segmentation of Medical Data,” Visual Comput., 27(2), pp. 129–139. [CrossRef]
Vlasov, R. , Friese, K.-I. , and Wolter, F.-E. , 2013, “ Haptic Rendering of Volume Data With Collision Detection Guarantee Using Path Finding,” Transactions on Computational Science XVIII (Lecture Notes in Computer Science), Vol. 7848, Springer, Berlin/Heidelberg, pp. 212–231.
Goldring, M. B. , 2012, “ Articular Cartilage Degradation in Osteoarthritis,” HSS J., 8(1), pp. 7–9. [CrossRef] [PubMed]
Ondrésik, M. , Correia, C. , Sousa, R. , Oliveira, J. , and Reis, R. , 2014, “ Understanding Cellular Behaviour in Early and Late Stage of MSD,” J. Tissue Eng. Regener Med., 8, p. 412.
Astephen, J. L. , Deluzio, K. J. , Caldwell, G. E. , Dunbar, M. J. , and Hubley-Kozey, C. L. , 2008, “ Gait and Neuromuscular Pattern Changes are Associated With Differences in Knee Osteoarthritis Severity Levels,” J. Biomech., 41(4), pp. 868–876. [CrossRef] [PubMed]
Chen, J. , Dougherty, E. , Demir, S. , Friedman, C. , Li, C.-S. , and Wong, S. , 2005, “ Grand Challenges for Multimodal Bio-Medical Systems,” IEEE Circuits Syst. Mag., 5(2), pp. 46–52. [CrossRef]
McFarlane, N. J. , Ma, X. , Clapworthy, G. J. , Bessis, N. , and Testi, D. , 2012, “ A Survey and Classification of Visualisation in Multiscale Biomedical Applications,” 16th International Conference on Information Visualisation, Montpellier, France, July 11–13, pp. 561–566.
Millán Vaquero, R. M. , Rzepecki, J. , Friese, K.-I. , and Wolter, F.-E. , 2014, “ Visualization and User Interaction Methods for Multiscale Biomedical Data,” 3D Multiscale Physiological Human, Springer, Berlin, pp. 107–133.
Hauser, H. , 2006, “ Generalizing Focus+Context Visualization,” Scientific Visualization: The Visual Extraction of Knowledge From Data (Mathematics and Visualization), Springer, Berlin, Heidelberg, pp. 305–327.
Agibetov, A. , Millán Vaquero, R. M. , Friese, K.-I. , Patanè, G. , Spagnuolo, M. , and Wolter, F.-E. , 2014, “ Integrated Visualization and Analysis of a Multi-Scale Biomedical Knowledge Space,” EuroVis Workshop on Visual Analytics, The Eurographics Association, Goslar, Germany, pp. 25–29.
Rzepecki, J. , Millán Vaquero, R. M. , Vais, A. , Friese, K.-I. , and Wolter, F.-E. , 2014, “ Multimodal Approach for Natural Biomedical Multi-Scale Exploration,” Advances in Visual Computing, Springer, Berlin, pp. 620–631.
Higgins, T. , 2010, “ Unity—3d Game Engine,” Unity Technologies, San Francisco, CA, accessed May 1, 2016, http://unity3d.com/
Millán Vaquero, R. M. , Agibetov, A. , Rzepecki, J. , Ondrésik, M. , Vais, A. , Oliveira, J. M. , Patanè, G. , Friese, K.-I. , Reis, R. L. , Spagnuolo, M. , and Wolter, F.-E. , 2015, “ A Semantically Adaptable Integrated Visualization and Natural Exploration of Multi-Scale Biomedical Data,” 19th International Conference on Information Visualisation, Barcelona, Spain, July 22–24, pp. 543–552.
Dennis, D. A. , Komistek, R. D. , Kim, R. H. , and Sharma, A. , 2010, “ Gap Balancing Versus Measured Resection Technique for Total Knee Arthroplasty,” Clin. Orthop. Relat. Res., 468(1), pp. 102–107. [CrossRef] [PubMed]
Zhang, X.-L. , Zhang, W. , and Shao, J.-J. , 2012, “ Rotational Alignment in Total Knee Arthroplasty: Nonimage-Based Navigation System Versus Conventional Technique,” Chin. Med. J., 125(2), pp. 236–243. [PubMed]
Guan, S. , Gray, H. , Keynejad, F. , and Pandy, M. , 2016, “ Mobile Biplane X-Ray Imaging System for Measuring 3D Dynamic Joint Motion During Overground Gait,” IEEE Trans. Med. Imaging, 35(1), pp. 326–336. [CrossRef] [PubMed]

Figures

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. 4

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

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. 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)

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).

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In