Real-time nonlinear finite element computations on GPU - application to neurosurgical simulation. (English) Zbl 1225.92021

Summary: Application of biomechanical modeling techniques in the area of medical image analysis and surgical simulation implies two conflicting requirements: accurate results and high solution speeds. Accurate results can be obtained only by using appropriate models and solution algorithms. In our previous papers we have presented algorithms and solution methods for performing accurate nonlinear finite element analysis of brain shift (which includes mixed mesh, different non-linear material models, finite deformations and brain – skull contacts) in less than a minute on a personal computer for models having up to 50,000 degrees of freedom. In this paper we present an implementation of our algorithms on a graphics processing unit (GPU) using the new NVIDIA Compute Unified Device Architecture (CUDA) which leads to more than 20 times increase in the computation speed. This makes possible the use of meshes with more elements, which better represent the geometry, are easier to generate, and provide more accurate results.


92C50 Medical applications (general)
92C55 Biomedical imaging and signal processing
68U10 Computing methodologies for image processing
92C10 Biomechanics


Full Text: DOI Link


[1] Ferrant, M.; Nabavi, A.; Macq, B.; Black, P. M.; Jolesz, F. A.; Kikinis, R.; Warfield, S. K., Serial registration of intraoperative MR images of the brain, Med. Image Anal., 6, 4, 337-359 (2002)
[2] Warfield, S. K.; Talos, F.; Tei, A.; Bharatha, A.; Nabavi, A.; Ferrant, M.; Black, P. M.; Jolesz, F. A.; Kikinis, R., Real-time registration of volumetric brain MRI by biomechanical simulation of deformation during image guided surgery, Comput. Visual. Sci., 5, 3-11 (2002) · Zbl 1001.92034
[3] Warfield, S. K.; Haker, S. J.; Talos, I.-F.; Kemper, C. A.; Weisenfeld, N.; Mewes, U. J.; Goldberg-Zimring, D.; Zou, K. H.; Westin, C.-F.; Wells, W. M.; Tempany, C. M.C.; Golby, A.; Black, P. M.; Jolesz, F. A.; Kikinis, R., Capturing intraoperative deformations: research experience at Brigham and Womens’s hospital, Med. Image Anal., 9, 2, 145-162 (2005)
[4] Wittek, A.; Miller, K.; Kikinis, R.; Warfield, S. K., Patient-specific model of brain deformation: application to medical image registration, J. Biomech., 40, 919-929 (2007)
[5] Miller, K.; Joldes, G. R.; Lance, D.; Wittek, A., Total Lagrangian explicit dynamics finite element algorithm for computing soft tissue deformation, Commun. Numer. Methods Engrg., 23, 121-134 (2007) · Zbl 1154.74045
[6] Joldes, G. R.; Wittek, A.; Miller, K., An efficient hourglass control implementation for the uniform strain hexahedron using the total Lagrangian formulation, Commun. Numer. Methods Engrg., 24, 1315-1323 (2008) · Zbl 1153.74044
[7] Joldes, G. R.; Wittek, A.; Miller, K., Non-locking tetrahedral finite element for surgical simulation, Commun. Numer. Methods Engrg., 25, 7, 827-836 (2009) · Zbl 1168.74049
[9] Joldes, G. R.; Wittek, A.; Miller, K., Suite of finite element algorithms for accurate computation of soft tissue deformation for surgical simulation, Med. Image Anal., 13, 6, 912-919 (2009)
[11] Viceconti, M.; Taddei, F., Automatic generation of finite element meshes from computed tomography data, Crit. Rev. Biomed. Engrg., 31, 1, 27-72 (2003)
[12] Owen, S. J., Hex-dominant mesh generation using 3D constrained triangulation, Comput.-Aided Design, 33, 211-220 (2001)
[14] Couteau, B.; Payan, Y.; Lavallée, S., The mesh-matching algorithm: an automatic 3D mesh generator for finite element structures, J. Biomech., 33, 1005-1009 (2000)
[15] Luboz, V.; Chabanas, M.; Swider, P.; Payan, Y., Orbital and maxillofacial computer aided surgery: patient-specific finite element models to predict surgical outcomes, Comput. Methods Biomech. Biomed. Engrg., 8, 4, 259-265 (2005)
[16] Ferrant, M.; Macq, B.; Nabavi, A.; Warfield, S. K., Deformable modeling for characterizing biomedical shape changes, (Discrete Geometry for Computer Imagery: Ninth International Conference (2000), Springer-Verlag: Springer-Verlag Uppsala, Sweden) · Zbl 1043.68795
[17] Clatz, O.; Delingette, H.; Bardinet, E.; Dormont, D.; Ayache, N., Patient specific biomechanical model of the brain: application to Parkinson’s disease procedure, (International Symposium on Surgery Simulation and Soft Tissue Modeling (IS4TM’03) (2003), Springer-Verlag: Springer-Verlag Juan-les-Pins, France)
[18] Clatz, O.; Sermesant, M.; Bondiau, P.-Y.; Delingette, H.; Warfield, S. K.; Malandain, G.; Ayache, N., Realistic simulation of the 3D growth of brain tumors in MR images coupling diffusion with biomechanical deformation, IEEE Trans. Med. Imag., 24, 10, 1334-1346 (2005)
[19] Owens, J. D.; Luebke, D.; Govindaraju, N.; Harris, M.; Krüger, J.; Lefohn, A. E.; Purcell, T. J., A survey of general-purpose computation on graphics hardware, Comput. Graph. Forum, 26, 1, 80-113 (2007)
[20] Taylor, Z. A.; Cheng, M.; Ourselin, S., High-speed nonlinear finite element analysis for surgical simulation using graphics processing units, IEEE Trans. Med. Imag., 27, 5, 650-663 (2008)
[22] Miller, K.; Wittek, A.; Joldes, G.; Horton, A.; Roy, T. D.; Berger, J.; Morriss, L., Modelling brain deformations for computer-integrated neurosurgery, Commun. Numer. Methods Engrg., 26, 1, 117-138 (2009) · Zbl 1180.92042
[23] Joldes, G. R.; Wittek, A.; Miller, K., Computation of intra-operative brain shift using dynamic relaxation, Comput. Methods Appl. Mech. Engrg., 198, 41-44, 3313-3320 (2009) · Zbl 1230.74136
[24] Belytschko, T., An overview of semidiscretization and time integration procedures, (Belytschko, T.; Hughes, T. J.R., Computational Methods for Transient Analysis (1983), North-Holland: North-Holland Amsterdam), 1-66
[25] Bathe, K.-J., Finite Element Procedures (1996), Prentice-Hall: Prentice-Hall New Jersey
[26] Flanagan, D. P.; Belytschko, T., A uniform strain hexahedron and quadrilateral with orthogonal hourglass control, Int. J. Numer. Methods Engrg., 17, 679-706 (1981) · Zbl 0478.73049
[27] Bonet, J.; Burton, A. J., A simple averaged nodal pressure tetrahedral element for incompressible and nearly incompressible dynamic explicit applications, Commun. Numer. Methods Engrg., 14, 437-449 (1998) · Zbl 0906.73060
[28] Bonet, J.; Marriott, H.; Hassan, O., An averaged nodal deformation gradient linear tetrahedral element for large strain explicit dynamic applications, Commun. Numer. Methods Engrg., 17, 551-561 (2001) · Zbl 1154.74307
[29] Zienkiewicz, O. C.; Rojek, J.; Taylor, R. L.; Pastor, M., Triangles and tetrahedra in explicit dynamic codes for solids, Int. J. Numer. Methods Engrg., 43, 565-583 (1998) · Zbl 0939.74073
[30] Dohrmann, C. R.; Heinstein, M. W.; Jung, J.; Key, S. W.; Witkowski, W. R., Node-based uniform strain elements for three-node triangular and four-node tetrahedral meshes, Int. J. Numer. Methods Engrg., 47, 1549-1568 (2000) · Zbl 0989.74067
[31] Hughes, T. J.R., The Finite Element Method: Linear Static and Dynamic Finite Element Analysis (2000), Dover Publications: Dover Publications Mineola, p. 682 · Zbl 1191.74002
[32] Hallquist, J. O., LS-DYNA Theory Manual (2005), Livermore Software Technology Corporation: Livermore Software Technology Corporation Livermore, California
[33] Sauve, R. G.; Morandin, G. D., Simulation of contact in finite deformation problems – algorithm and modelling issues, Int. J. Mech. Mater. Design, 1, 287-316 (2004)
[34] Underwood, P., Dynamic relaxation, (Belytschko, T.; Hughes, T. J.R., Computational Methods for Transient Analysis (1983), New-Holland: New-Holland Amsterdam), 245-265
[35] Miller, K.; Chinzei, K., Constitutive modelling of brain tissue: experiment and theory, J. Biomech., 30, 11/12, 1115-1121 (1997)
[36] Miller, K.; Chinzei, K.; Orssengo, G.; Bednarz, P., Mechanical properties of brain tissue in-vivo: experiment and computer simulation, J. Biomech., 33, 1369-1376 (2000)
[37] Miller, K.; Chinzei, K., Mechanical properties of brain tissue in tension, J. Biomech., 35, 483-490 (2002)
[38] Miga, M. I.; Sinha, T. K.; Cash, D. M.; Galloway, R. I.; Weil, R. J., Cortical surface registration for image-guided neurosurgery using laser-range scanning, IEEE Trans. Med. Imag., 22, 8, 973-985 (2003)
[39] Sun, H.; Farid, H.; Rick, K.; Hartov, A.; Roberts, D. W.; Paulsen, K. D., Estimating cortical surface motion using stereopsis for brain deformation models, (Medical Image Computing and Computer-Assisted Intervention - MICCAI 2003 (2003), Springer: Springer Berlin, Heidelberg), 794-801
[41] Wittek, A.; Hawkins, T.; Miller, K., On the unimportance of constitutive models in computing brain deformation for image-guided surgery, Biomech. Model. Mechanobiol., 8, 1, 77-84 (2009)
[42] Horton, A.; Wittek, A.; Joldes, G. R.; Miller, K., A meshless total Lagrangian explicit dynamics algorithm for surgical simulation, Int. J. Numer. Methods Biomed. Eng. (2010) · Zbl 1193.92056
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.