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model for brain shift computation. In: Computational Biomechanics for Medicine III, pp. 95–
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62. NVIDIA: NVIDIA’s Next Generation CUDA Compute Architecture: Fermi, http://
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Whitepaper.pdf (2009)
63. Khronos: Open CL https://www.khronos.org/opencl/ (2018)
64. Joldes, G.R., Wittek, A., Miller, K.: Real-time nonlinear finite element computations on GPU -
application to neurosurgical simulation. Comput. Methods Appl. Mech. Eng. 199, 3305–3314
(2010)
65. Comas, O.: Real-time Soft Tissue Modelling on GPU for Medical Simulation. Doctoral School
of Engineering Science, PhD Thesis. Université des Sciences et Technologie de Lille Lille,
France (2011)
66. Courtecuisse, H., Allard, J., Kerfriden, P., Bordas, S.P.A., Cotin, S., Duriez, C.: Real-time
simulation of contact and cutting of heterogeneous soft-tissues. Med. Image Anal. 18, 394–
410 (2014)
67. The American Society of Mechanical Engineers ASME, Standards Committee on Verification
and Validation in Computational Solid Mechanics PTC 60/V&V 10: Guide for Verification and Validation in Computational Solid Mechanics. http://cstools.asme.org/csconnect/pdf/
CommitteeFiles/24816.pdf (2006)
68. Babuska, I., Oden, J.T.: Verification and validation in computational engineering and science:
basic concepts. Comput. Methods Appl. Mech. Eng. 193, 4057–4066 (2004)
69. 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
Eng. 24, 1315 (2007)
70. Waldron, K.J., Kinzel, G.L.: Kinematics, Dynamics, and Design of Machinery. Wiley, New
York (1999)
71. 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)
72. NVIDIA: Quadro on Desktop Workstations https://www.nvidia.com/en-us/designvisualization/quadro-desktop-gpus/
73. Wittek, A., Grosland, N., Joldes, G., Magnotta, V., Miller, K.: From finite element meshes to
clouds of points: a review of methods for generation of computational biomechanics models
for patient-specific applications. Ann. Biomed. Eng. 44, 3–15 (2016)
74. 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. 26, 977–998 (2010)
75. Miller, K., Horton, A., Joldes, G.R., Wittek, A.: Beyond finite elements: a comprehensive,
patient-specific neurosurgical simulation utilizing a meshless method. J. Biomech. 45, 2698–
2701 (2012)
76. Zhang, G.Y., Wittek, A., Joldes, G.R., Jin, X., Miller, K.: A three-dimensional nonlinear
meshfree algorithm for simulating mechanical responses of soft tissue. Eng. Anal. Bound.
Elem. 42, 60–66 (2014)
77. Li, M., Miller, K., Joldes, G.R., Kikinis, R., Wittek, A.: Biomechanical model for computing
deformations for whole-body image registration: A meshless approach. Int. J. Numer. Method
Biomed. Eng. 32, e02771–e02718 (2016)
78. Joldes, G.R., Bourantas, G., Zwick, B., Chowdhury, H., Wittek, A., Agrawal, S., Mountris, K.,
Hyde, D., Warfield, S.K., Miller, K.: Suite of meshless algorithms for accurate computation of
soft tissue deformation for surgical simulation. Med. Image Anal. 56, 152–171 (2019)