POD for real-time simulation of hyperelastic soft biological tissue using the point collocation method of finite spheres

Mathematical Problems in Engineering

Volumn 2013, Issue , 2013, Pages

  Banihani, Suleiman ^a   Rabczuk, Timon ^b,c   Almomani, Thakir ^a  

^a HASHEMITE UNIVERSITY   (Jordan)

^b BAUHAUS UNIVERSITY WEIMAR   (Germany)

^c Korea University   (South Korea)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION FUNCTION; MODEL ORDER REDUCTION; NUMERICAL TECHNIQUES; POINT COLLOCATION METHOD; PROPER ORTHOGONAL DECOMPOSITIONS; REAL TIME SIMULATIONS; SOFT BIOLOGICAL TISSUE; VIRTUAL SURGERY SIMULATIONS;

PRINCIPAL COMPONENT ANALYSIS;

COMPUTER SIMULATION;

EID: 84893867956     PISSN: 1024123X     EISSN: 15635147     Source Type: Journal    
DOI: 10.1155/2013/386501     Document Type: Article

References (50)

1. Wagner M. J., Thomas H. A. Jr., Application of the medical knowledge general competency to emergency medicine. Academic Emergency Medicine 2002 9 11 1236 1241 2-s2.0-0036843319 10.1197/aemj.9.11.1236 (Pubitemid 35291556)
2. Lim Y., Physics based digital surgery using the point associated finite field approach [Ph.D. thesis] 2005 Troy, NY, USA Rensselaer Polytechnic Institute
3. Raposio E., Fato M., Schenone A., An "augmented-reality" aid for plastic and reconstructive surgeons. Proceedings of the Medicine Meets Virtual Reality (MMVR '5) 1997 Amsterdam, The Netherlands 232 235
4. Krummel T., Surgical simulation and virtual reality: the coming revolution. Annals of Surgery 1998 228 5 635 637 (Pubitemid 30198307)
5. Levin A., Fewer crashes caused by pilots. 2004 Washington, DC, USA USA Today
6. Frisken-Gibson S. F., Using linked volumes to model object collisions, deformation, cutting, carving, and joining. IEEE Transactions on Visualization and Computer Graphics 1999 5 4 333 348 2-s2.0-0033207125 10.1109/2945.817350 (Pubitemid 30568911)
7. Terzopoulost D., Platt J., Barr A., Fleischert K., Elastically deformable models. 21 Proceedings of the 14th Annual Conference on Computer Graphics and Interactive Techniques (SIGGRAPH '87) July 1987 4 205 214 10.1145/37401.37427
8. Cover S. A., Ezquerra N. F., Rowe R., Gadacz T., O'Brien J. F., Interactively deformable models for surgery simulation. IEEE Computer Graphics and Applications 1993 13 6 68 75 2-s2.0-0027695562 10.1109/38.252559
9. Kühnapfel U. G., Kuhn C., Hübner M., Krumm H. G., Maass H., Neisius B., The Karlsruhe endoscopic surgery trainer as an example for virtual reality in medical education. Minimally Invasive Therapy and Allied Technologies 1997 6 2 122 125 2-s2.0-0030911532 (Pubitemid 27277624)
10. Lee Y., Terzopoulos D., Waters K., Realistic modeling for facial animation. Proceedings of the 22nd Annual ACM Conference on Computer Graphics and Interactive Techniques (SIGGRAPH '95) August 1995 55 62 2-s2.0-0029182694
11. Koch R. M., Gross M. H., Carls F. R., von Buren D. F., Fankhauser G., Parish Y. I. H., Simulating facial surgery using finite element models. Proceedings of the 23rd Annual Conference on Computer Graphics and Interactive Techniques (SIGGRAPH '96) August 1996 421 428 10.1145/237170.237281 2-s2.0-0030409649
12. Kenedi R. M., Gibson T., Evans J. H., Barbenel J. C., Tissue mechanics. Physics in Medicine and Biology 1975 20 5 163 169 10.1088/0031-9155/20/5/00
13. Waters K., Physical model of facial tissue and muscle articulation derived from computer tomography data. 1808 Visualization in Biomedical Computing '92 October 1992 574 583 Proceedings of SPIE 10.1117/12.131110 2-s2.0-0026961256
14. Cotin S., Pignon J., Delinguette H., Subsol G., A craniofacial surgery simulation test-bed. Visualization for Biomedical Computing (VBC '94) October 1994 Rochester, Minn, USA
15. Platt S., Badler N., Animating facial expressions. 15 Proceedings of the 8th Annual Conference on Computer Graphics and Interactive Techniques (SIGGRAPH '81) August 1981 245 252
16. Gelder A., Approximate simulation of elastic membranes by triangulated spring meshes. Journal of Graphic Tools 1998 3 2 21 42 10.1080/10867651.1998. 10487490
17. Bro-Nielsen M., Finite element modeling in surgery simulation. Proceedings of the IEEE 1998 86 3 490 503 2-s2.0-0032021757 10.1109/5.662874 (Pubitemid 128720212)
18. Cotin S., Delingette H., Ayache N., Real-time elastic deformations of soft tissues for surgery simulation. IEEE Transactions on Visualization and Computer Graphics 1999 5 1 62 73 2-s2.0-0032649297 10.1109/2945.764872
19. Delingette H., Ayache N., Cotin S., A hybrid elastic model for real-time cutting, deformations, and force feedback for surgery training and simulation. The Visual Computer 2000 16 8 437 452 2-s2.0-0034315976 10.1007/PL00007215 (Pubitemid 32077030)
20. James D., Pai A., Artdefo: accurate real time deformable objects. Proceedings of the 26th ACM Annual Conference on Computer Graphics and Interactive Techniques (SIGGRAPH '99) August 1999 65 72 10.1145/311535.311542
21. Miller K., Constitutive model of brain tissue suitable for finite element analysis of surgical procedures. Journal of Biomechanics 1999 32 5 531 537 2-s2.0-0032930747 10.1016/S0021-9290(99)00010-X (Pubitemid 29199986)
22. Miller K., Chinzei K., Constitutive modelling of brain tissue: experiment and theory. Journal of Biomechanics 1997 30 11-12 1115 1121 2-s2.0-0031279749 10.1016/S0021-9290(97)00092-4 (Pubitemid 28026501)
23. Miller K., Chinzei K., Mechanical properties of brain tissue in tension. Journal of Biomechanics 2002 35 4 483 490 2-s2.0-0036203451 10.1016/S0021- 9290(01)00234-2 (Pubitemid 34273640)
24. Miller K., Chinzei K., Orssengo G., Bednarz P., Mechanical properties of brain tissue in-vivo: experiment and computer simulation. Journal of Biomechanics 2000 33 11 1369 1376 2-s2.0-0034333768 10.1016/S0021-9290(00)00120- 2 (Pubitemid 30625094)
25. Farshad M., Barbezat M., Flueler P., Schmidlin F., Graber P., Niederer P., Material characterization of the pig kidney in relation with the biomechanical analysis of renal trauma. Journal of Biomechanics 1999 32 4 417 425 2-s2.0-0033118288 10.1016/S0021-9290(98)00180-8 (Pubitemid 29156708)
26. Ayache N., Delingette H., Soft tissue modeling for surgery simulation. Computational Models for the Human Body 2004 Elsevier 453 550
27. Blemker S., Hing V., Fedkiw R., Teran J., Finite volume methods for the simulation of skeletal muscle. Proceedings of the Eurographics/SIGGRAPH Symposium on Computer Animation (SCA '03) 2003 San Diego, Calif, USA 68 74
28. Miller K., Joldes G., Lance D., Wittek A., Total Lagrangian explicit dynamics finite element algorithm for computing soft tissue deformation. Communications in Numerical Methods in Engineering 2007 23 2 121 134 10.1002/cnm.887 MR2291133 ZBL1154.74045 (Pubitemid 46210533)
29. Taylor Z. A., Comas O., Cheng M., Passenger J., Hawkes D. J., Atkinson D., Ourselin S., On modelling of anisotropic viscoelasticity for soft tissue simulation: numerical solution and GPU execution. Medical Image Analysis 2009 13 2 234 244 2-s2.0-62549083431 10.1016/j.media.2008.10.001
30. BaniHani S. M., De S., A comparison of some model order reduction methods for fast simulation of soft tissue response using the point collocation-based method of finite spheres. Engineering with Computers 2009 25 1 37 47 2-s2.0-58549115262 10.1007/s00366-008-0103-4
31. Yoon Y. C., Lee S. H., Belytschko T., Enriched meshfree collocation method with diffuse derivatives for elastic fracture. Computers & Mathematics with Applications 2006 51 8 1349 1366 10.1016/j.camwa.2006.04.010 MR2235832 ZBL1141.74046 (Pubitemid 44041878)
32. Lee S. H., Yoon Y. C., Meshfree point collocation method for elasticity and crack problems. International Journal for Numerical Methods in Engineering 2004 61 1 22 48 2-s2.0-4344616136 10.1002/nme.1053 (Pubitemid 39115799)
33. Puso M. A., Chen J. S., Zywicz E., Elmer W., Meshfree and finite element nodal integration methods. International Journal for Numerical Methods in Engineering 2008 74 3 416 446 10.1002/nme.2181 MR2405049 ZBL1159.74456 (Pubitemid 351516704)
34. De S., Lim Y. J., Manivannan M., Srinivasan M. A., Physically realistic virtual surgery using the point-associated finite field (PAFF) approach. Presence 2006 15 3 294 308 2-s2.0-33745475289 (Pubitemid 43953313)
35. Bathe K. J., Finite Element Procedures 1996 Englewood Cliffs, NJ, USA Prentice-Hall
36. Zienkiewicz O., Taylor R., The Finite Element Method Set 2005 6th London, UK Butterworth-Heinemann
37. Gao Z., Lister K., Desai J. P., Constitutive modeling of liver tissue: experiment and theory. Annals of Biomedical Engineering 2010 38 2 505 516 2-s2.0-77249146357 10.1007/s10439-009-9812-0
38. Ogden R., Non-Linear Elastic Deformations 1984 New York, NY, USA Halsted Press
39. Ogden R., Large deformation isotropic elasticity-on the correlation of theory and experiment for incompressible rubberlike solids. Proceedings of the Royal Society of London A 1972 326 1567 565 584
40. Antoulas A. C., Approximation of Large-Scale Dynamical Systems 2005 Philadelphia, Pa, USA Society for Industrial and Applied Mathematic (SIAM) 10.1137/1.9780898718713 MR2155615
41. Freund R. W., Krylov-subspace methods for reduced-order modeling in circuit simulation. Journal of Computational and Applied Mathematics 2000 123 1-2 395 421 10.1016/S0377-0427(00)00396-4 MR1798535 ZBL0964.65082 (Pubitemid 32027695)
42. Rudnyi E., Korvink J., Review: automatic model reduction for transient simulation of MEMS-based devices. Sensors Update 2002 11 1 3 33 10.1002/seup.200211105
43. Rewienski M., A trajectory piecewise-linear approach to model order reduction of nonlinear dynamical systems [Ph.D. thesis] 2003 Cambridge, Mass, USA MIT
44. Grimme E., Krylov projection methods for model reduction [Ph.D. thesis] 1997 Champaign, Ill, USA University of Illinois at Urbana-Champaign
45. Glover K., All optimal Hankel-norm approximations of linear multivariable systems and their L ∞ -error bounds. International Journal of Control 1984 39 6 1115 1193 10.1080/00207178408933239 MR748558 (Pubitemid 14606446)
46. Liang Y. C., Lee H. P., Lim S. P., Lin W. Z., Lee K. H., Wu C. G., Proper orthogonal decomposition and its applications. I. Theory. Journal of Sound and Vibration 2002 252 3 527 544 10.1006/jsvi.2001.4041 MR1908565 (Pubitemid 35262887)
47. Lumley J., Berkooz G., Holmes P., The proper orthogonal decomposition in the analysis of turbulent flows. Annual Review of Fluid Mechanics 1993 25 539 575
48. Kim T., Frequency-domain Karhunen-Lóeve method and its application to linear dynamic systems. American Institute of Aeronautics and Astronautics Journal 1998 36 11 2117 2123 2-s2.0-0032208939 (Pubitemid 128549440)
49. Holmes P., Lumley J. L., Berkooz G., Turbulence, Coherent Structures, Dynamical Systems and Symmetry 1996 New York, NY, USA Cambridge University Press 10.1017/CBO9780511622700 MR1422658
50. Lumley J. L., Stochastic Tools in Turbulence 1971 New York, NY, USA Academic Press MR0451408