A meshless Total Lagrangian explicit dynamics algorithm for surgical simulation

International Journal for Numerical Methods in Biomedical Engineering

Volumn 26, Issue 8, 2010, Pages 977-998

  Horton, Ashley ^a   Wittek, Adam ^a   Joldes, Grand Roman ^a   Miller, Karol ^a  

^a UNIVERSITY OF WESTERN AUSTRALIA   (Australia)

Author keywords

Biomechanics; Explicit dynamics; Meshless methods; Total Lagrangian formulation

Indexed keywords

AUTOMATIC MODELS; CENTRAL DIFFERENCE METHOD; EXPLICIT DYNAMICS; EXPLICIT TIME INTEGRATION; FINITE ELEMENT SIMULATIONS; GEOMETRIC INTEGRATION; GEOMETRICALLY NONLINEAR; MESH-LESS METHODS; MESHLESS; NEO-HOOKEAN MATERIAL; NODE PLACEMENT; REAL TIME SIMULATIONS; SURGICAL SIMULATION; TOTAL LAGRANGIAN; TOTAL LAGRANGIAN FORMULATION; VERY SOFT TISSUE;

BIOMECHANICS; COMPUTER SIMULATION; DEFORMATION; LAGRANGE MULTIPLIERS;

FINITE ELEMENT METHOD;

EID: 77956463006     PISSN: 20407939     EISSN: 20407947     Source Type: Journal    
DOI: 10.1002/cnm.1374     Document Type: Article

References (31)

1. Cotin S, Delingette H, Ayache N. Real-time elastic deformations of soft tissues for surgery simulation. IEEE Transactions on Visualization and Computer Graphics 1999; 5:62-73.
2. Bathe KJ. Finite Element Procedures. Prentice-Hall: NJ, 1996.
3. Szekely G, Brechbuhler C, Hutter R, Rhomberg A, Ironmonger N, Schmid P. Modelling of soft tissue deformation for laparoscopic surgery simulation. Medical Image Analysis 2000; 4:57-66.
4. Picinbono G, Delingette H, Ayache N. Non-linear anisotropic elasticity for real-time surgery simulation. Graphical Models 2003; 65:305-321.
5. Luboz V, Chabanas M, Swider P, Payan Y. Orbital and maxillofacial computer aided surgery: patient-specific finite element models to predict surgical outcomes. Computer Methods in Biomechanics and Biomedical Engineering 2005; 8:259-265.
6. Wittek A, Miller K, Kikinis R, Warfield S. Patient-specific model of brain deformation: application to medical image registration. Journal of Biomechanics 2007; 40(4):919-929.
7. 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.
8. Wittek A, Hawkins T, Miller K. On the unimportance of constitutive models in computing brain deformation for image-guided surgery. Biomechanics in Modeling and Mechanobiology 2009; 8(1):77-84.
9. Melenk JM, Babuska I. Partition of unity finite element method: basic theory and applications. Computer Methods in Applied Mechanics and Engineering 1996; 139(1):289-314.
10. Babuska I, Melenk JM. Partition of unity method. International Journal for Numerical Methods in Engineering 1997; 40(4):727-758.
11. Liu GR. Mesh Free Methods; Moving Beyond the Finite Element Method. CRC Press: Boca Raton, 1996.
12. Li S, Liu WK. Meshfree Particle Methods. Springer: Berlin, 2004.
13. Horton A, Wittek A, Miller K. Computer simulation of brain shift using an element free Galerkin method. Seventh International Symposium on Computer Methods in Biomechanics and Biomedical Engineering, Antibes, 2006; 906-911.
14. Belytschko T, Lu YY, Gu L. Element-free galerkin methods. International Journal for Numerical Methods in Engineering 1994; 37(2):229-256.
15. Belytschko T, Krongauz Y, Organ D, Fleming M, Krysl P. Meshless methods: an overview and recent developments. Computer Methods in Applied Mechanics and Engineering 1996; 139(1):3-47.
16. Chen JS, Wu CT, Yoon S, You Y. A stabilized conforming nodal integration for Galerkin mesh-free methods. International Journal for Numerical Methods in Engineering 2001; 50:435-466.
17. Lancaster P, Salkauskas K. Surfaces generated by moving least squares methods. Mathematics of Computation 1981; 37:141-158.
18. Nayroles B, Touzot G, Villon P. Generalizing the finite element method: diffuse approximation and diffuse elements. Computational Mechanics 1992; 10(5):307-318.
19. Fleming M, Chu YA, Moran B, Belytschko T. Enriched element-free Galerkin methods for crack tip fields. International Journal for Numerical Methods in Engineering 1997; 40(8):1483-1504.
20. Daux C, Mos N, Dolbow J, Sukumar N, Belytschko T. Arbitrary branched and intersecting cracks with the extended finite element method. International Journal for Numerical Methods in Engineering 2000; 48(12):1741-1760.
21. Hughes TJR. The Finite Element Method: Linear Static and Dynamic Finite Element Analysis. Prentice-Hall: Englewood Cliffs, 2004.
22. Ogden RW. Non-Linear Elastic Deformations. Ellis Horwood Ltd.: Chichester, 1984.
23. Taylor Z, Cheng M, Ourselin S. Real-time nonlinear finite element analysis for surgical simulation using graphics processing units. Lecture Notes in Computer Science, vol. 4791. Springer: Berlin, 2007; 701-708.
24. Flanagan DP, Belytschko T. Eigenvalues and stable times steps for the uniform strain hexahedron and quadrilateral. Journal of Applied Mechanics 1984; 51:35-40.
25. Miller K. Biomechanics of Brain for Computer Integrated Surgery. Publishing House of the Warsaw University of Technology: Warsaw, 2002.
26. ABAQUS online documentation, version 6.5, 2007. Available from: http://129.25.16.135:2080/v6.5/.
27. Guangyao L, Belytschko T. Element-free Galerkin method for contact problems in metal forming analysis. Engineering Computations 2001; 18:62-78.
28. Liu GR, Gu YT. A local radial point interpolation method (LRPIM) for free vibration analyses of 2-D solids. Journal of Sound and Vibration 2001; 246:29-46.
29. Liu GR, Dai KY, Lim KM, Gu YT. A radial point interpolation method for simulation of two-dimensional piezoelectric structures. Smart Materials and Structures 2003; 12:171-180.
30. Hoover WM, Hoover CG, Merritt EC. Smooth-particle applied mechanics: conservation of angular momentum with tensile stability and velocity averaging. Physical Review E 2004; 69(1):016702.
31. Hieber SE, Koumoutsakos P. A Lagrangian particle method for the simulation of linear and nonlinear elastic models of soft tissue. Journal of Computational Physics 2008; 227(21):9195-9215.