Page 182 - Advances in Biomechanics and Tissue Regeneration
P. 182
178 8. TOWARDS THE REAL-TIME MODELING OF THE HEART
[4] T.P. Usyk, I.J. LeGrice, A.D. McCulloch, Computational model of three-dimensional cardiac electromechanics, Comput. Vis. Sci. 4 (4) (2002)
249–257.
[5] B. Baillargeon, N. Rebelo, D.D. Fox, R.L. Taylor, E. Kuhl, The living heart project: a robust and integrative simulator for human heart function,
Eur. J. Mech. A Solids 48 (2014) 38–47.
[6] D.B. Davidson, Computational Electromagnetics for RF and Microwave Engineering, second ed., Cambridge University Press, Cambridge,
2010.
[7] P. Lafortune, R. Arís, M. Vázquez, G. Houzeaux, Coupled electromechanical model of the heart: parallel finite element formulation, Int. J.
Numer. Methods Biomed. Eng. 28 (2012) 72–86.
[8] S. Niederer, N. Smith, The role of the frank-starling law in the transduction of cellular work to whole organ pump function: a computational
modeling analysis, PLoS Comput. Biol. 5 (4) (2009) e1000371, https://doi.org/10.1371/journal.pcbi.1000371.
[9] F.J. Vetter, A.D. McCulloch, Three-dimensional stress and strain in passive rabbit left ventricle: a model study, Ann. Biomed. Eng. 28 (7) (2000)
781–792, https://doi.org/10.1114/1.1289469.
[10] J.C. Walker, M.B. Ratcliffe, P. Zhang, A.W. Wallace, B. Fata, E.W. Hsu, D. Saloner, J.M. Guccione, MRI-based finite-element analysis of left
ventricular aneurysm, Am. J. Physiol. Heart Circ. Physiol. 289 (2) (2005) H692–H700, https://doi.org/10.1152/ajpheart.01226.2004.
[11] S. Cotin, H. Delingette, N. Ayache, Real-time elastic deformations of soft tissues for surgery simulation, IEEE Trans. Vis. Comput. Graph. 5 (1)
(1999) 62–73, https://doi.org/10.1109/2945.764872.
[12] U. Meier, O. López, C. Monserrat, M.C. Juan, M. Alcañiz, Real-time deformable models for surgery simulation: a survey, Comput. Methods
Prog. Biomed. 77 (3) (2005) 183–197, https://doi.org/10.1016/j.cmpb.2004.11.002.
[13] A. Nealen, M. M€ uller, R. Keiser, E. Boxerman, M. Carlson, Physically based deformable models in computer graphics, Comput. Graph. Forum
25 (4) (2006) 809–836, https://doi.org/10.1111/j.1467-8659.2006.01000.x.
[14] L.P. Nedel, D. Thalmann, Real time muscle deformations using mass-spring systems, Proceedings. Computer Graphics International (Cat. No.
98EX149), IEEE Comput. Soc., 1998, pp. 156–165, https://doi.org/10.1109/CGI.1998.694263.
[15] T. Liu, A.W. Bargteil, J.F. O’Brien, L. Kavan, Fast simulation of mass-spring systems, ACM Trans. Graph. 32 (6) (2013) 1–7, https://doi.org/
10.1145/2508363.2508406.
[16] V. Luboz, J. Kyaw-Tun, S. Sen, R. Kneebone, R. Dickinson, R. Kitney, F. Bello, Real-time stent and balloon simulation for stenosis treatment, Vis.
Comput. 30 (3) (2013) 1–9, https://doi.org/10.1007/s00371-013-0859-4.
[17] H. Delingette, Toward realistic soft-tissue modeling in medical simulation, Proc. IEEE 86 (3) (1998) 512–523, https://doi.org/10.1109/5.662876.
[18] Z. Lu, V.S. Arikatla, Z. Han, B.F. Allen, S. De, A physics-based algorithm for real-time simulation of electrosurgery procedures in minimally
invasive surgery, Int. J. Med. Robot. Comput. Assist. Surg. 10 (4) (2014) 495–504, https://doi.org/10.1002/rcs.1561.
[19] J. Berkley, G. Turkiyyah, D. Berg, M. Ganter, S. Weghorst, Real-time finite element modeling for surgery simulation: an application to virtual
suturing, IEEE Trans. Vis. Comput. Graph. 10 (3) (2004) 314–325, https://doi.org/10.1109/TVCG.2004.1272730.
[20] Y.J. Lim, S. De, Real time simulation of nonlinear tissue response in virtual surgery using the point collocation-based method of finite spheres,
Comput. Methods Appl. Mech. Eng. 196 (31–32) (2007) 3011–3024, https://doi.org/10.1016/j.cma.2006.05.015.
[21] H. Courtecuisse, H. Jung, J. Allard, C. Duriez, D.Y. Lee, S. Cotin, GPU-based real-time soft tissue deformation with cutting and haptic feedback,
Prog. Biophys. Mol. Biol. 103 (2–3) (2010) 159–168, https://doi.org/10.1016/j.pbiomolbio.2010.09.016.
[22] P. Holmes, J.L. Lumley, G. Berkooz, Turbulence, Coherent, Structures, Dynamical Systems and Symmetry, first ed., Cambridge University
Press, Cambridge, 1996.
[23] J.S. Hesthaven, G. Rozza, B. Stamm, Certified Reduced Basis Methods for Parametrized Partial Differential Equations, Springer International
Publishing, New York, NY, ISBN: 978-3-319-22469-5, 2015.
[24] F. Chinesta, R. Keunings, A. Leygue, The Proper Generalized Decomposition for Advanced Numerical Simulations, Springer International Pub-
lishing, Cham, ISBN: 978-3-319-02864-4, 2014, https://doi.org/10.1007/978-3-319-02865-1.
[25] T. Tonn, K. Urban, S. Volkwein, Comparison of the reduced-basis and POD a posteriori error estimators for an elliptic linear-quadratic optimal
control problem, Math. Comput. Model. Dyn. Syst. 17 (4) (2011) 355–369, https://doi.org/10.1080/13873954.2011.547678.
[26] M. Boulakia, E. Schenone, J.-F. Gerbeau, Reduced-order modeling for cardiac electrophysiology. Application to parameter identification, Int. J.
Numer. Methods Biomed. Eng. 28 (6–7) (2012) 727–744.
[27] C. Corrado, J. Lassoued, M. Mahjoub, N. Zemzemi, Stability analysis of the POD reduced order method for solving the bidomain model in
cardiac electrophysiology, Math. Biosci. 272 (2016) 81–91.
[28] S. Han, B. Feeny, Application of proper orthogonal decomposition to structural vibration analysis, Mech. Syst. Signal Process. 17 (5) (2003)
989–1001, https://doi.org/10.1006/mssp.2002.1570.
[29] I.T. Georgiou, J. Sansour, Analyzing the finite element dynamics of nonlinear in-plane rods by the method of proper orthogonal decom-
position, in: S. Idelsohn,E. Onate,E.Dvorkin (Eds.),Computational Mechanics, NewTrendsand Applications,CIMNE,Barcelona,
Spain, 1998.
[30] H.V. Ly, H.T. Tran, Modeling and control of physical processes using proper orthogonal decomposition, in: H.T. Banks, K.L. Bowers, J. Lund
(Eds.), Computation and Control VI Proceedings of the Sixth Bozeman Conference, vol. 33, 2001, pp. 223–236, https://doi.org/10.1016/S0895-
7177(00)00240-5.
[31] R.F. Coelho, P. Breitkopf, C. Knopf-Lenoir, P. Villon, Bi-level model reduction for coupled problems. Application to a 3D wing, Struct. Multi-
discip. Optim. 39 (4) (2009) 401–418.
[32] S. Niroomandi, I. Alfaro, E. Cueto, F. Chinesta, Real-time deformable models of non-linear tissues by model reduction techniques, Comput.
Methods Programs Biomed. 91 (3) (2008) 223–231, https://doi.org/10.1016/j.cmpb.2008.04.008.
[33] P. Lancaster, K. Salkauskas, Surfaces generated by moving least squares methods, Math. Comput. 37 (1981) 141–158, https://doi.org/10.1090/
S0025-5718-1981-0616367-1.
[34] R.R. Rama, S. Skatulla, C. Sansour, Real-time modelling of diastolic filling of the heart using the proper orthogonal decomposition with inter-
polation, Int. J. Solids Struct. (2016) 1–12, https://doi.org/10.1016/j.ijsolstr.2016.04.003.
[35] R.R. Rama, S. Skatulla, Towards real-time modelling of passive and active behaviour of the human heart using PODI-based model reduction,
Comput. Struct. (2018), https://doi.org/10.1016/j.compstruc.2018.01.002.
I. BIOMECHANICS