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]