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A novel hybrid model of the lumbar spine, allowing fast static and dynamic simulations of the disc pressure and the spine mobility, is introduced in this work. Our contribution is to combine rigid bodies, deformable finite elements, articular constraints, and springs into a unique model of the spine. Each vertebra is represented by a rigid body controlling a surface mesh to model contacts on the facet joints and the spinous process. The discs are modeled using a heterogeneous tetrahedral finite element model. The facet joints are represented as elastic joints with six degrees of freedom, while the ligaments are modeled using non-linear one-dimensional elastic elements. The challenge we tackle is to make these different models efficiently interact while respecting the principles of Anatomy and Mechanics. The mobility, the intradiscal pressure, the facet joint force and the instantaneous center of rotation of the lumbar spine are validated against the experimental and theoretical results of the literature on flexion, extension, lateral bending as well as axial rotation. Our hybrid model greatly simplifies the modeling task and dramatically accelerates the simulation of pressure within the discs, as well as the evaluation of the range of motion and the instantaneous centers of rotation, without penalizing precision. These results suggest that for some types of biomechanical simulations, simplified models allow far easier modeling and faster simulations compared to usual full-FEM approaches without any loss of accuracy., {"references":["H. Schmidt, F. Heuer, J. Drumm, Z. Klezl, L. Claes,\nand H.-J. Wilke, \"Application of a calibration method\nprovides more realistic results for a finite element model\nof a lumbar spinal segment.\" Clinical biomechanics\n(Bristol, Avon), vol. 22, no. 4, pp. 377–84, May\n2007. (Online). Available: http://www.ncbi.nlm.nih.gov/\npubmed/17204355","H. Schmidt, F. Heuer, L. Claes, and H.-J. Wilke,\n\"The relation between the instantaneous center of\nrotation and facet joint forces - A finite element\nanalysis.\" Clinical biomechanics (Bristol, Avon), vol. 23,\nno. 3, pp. 270–8, Mar. 2008. (Online). Available:\nhttp://www.ncbi.nlm.nih.gov/pubmed/17997207","H. Schmidt, F. Galbusera, A. Rohlmann, T. Zander,\nand H.-J. Wilke, \"Effect of multilevel lumbar disc\narthroplasty on spine kinematics and facet joint loads\nin flexion and extension: a finite element analysis,\"\nEuropean Spine Journal, vol. 21, no. 5, pp. 663–674,\n2012. (Online). Available: http://dx.doi.org/10.1007/\ns00586-010-1382-1","D. S. Shin, K. Lee, and D. Kim, \"Biomechanical study\nof lumbar spine with dynamic stabilization device using\nfinite element method,\" Comput. Aided Des., vol. 39,\nno. 7, pp. 559–567, Jul. 2007. (Online). Available:\nhttp://dx.doi.org/10.1016/j.cad.2007.03.005","Y. Alapan, C. Demir, T. Kaner, R. Guclu, and\nS. Inceo˘glu, \"Instantaneous center of rotation behavior\nof the lumbar spine with ligament failure.\" Journal of\nneurosurgery. Spine, vol. 18, no. 6, pp. 617–26, Jun.\n2013. (Online). Available: http://www.ncbi.nlm.nih.gov/\npubmed/23600587","T. Zander, A. Rohlmann, and G. Bergmann, \"Influence\nof ligament stiffness on the mechanical behavior of a\nfunctional spinal unit.\" Journal of biomechanics, vol. 37,\nno. 7, pp. 1107–11, Jul. 2004. (Online). Available:\nhttp://www.ncbi.nlm.nih.gov/pubmed/15165881","B. Weisse, a. K. Aiyangar, C. Affolter, R. Gander,\nG. P. Terrasi, and H. Ploeg, \"Determination of the\ntranslational and rotational stiffnesses of an L4-L5\nfunctional spinal unit using a specimen-specific finite\nelement model.\" Journal of the mechanical behavior\nof biomedical materials, vol. 13, pp. 45–61, Sep.\n2012. (Online). Available: http://www.ncbi.nlm.nih.gov/\npubmed/22842275","T. Yoshimura, K. Nakai, and G. Tamaoki, \"Multi-body\ndynamics modelling of seated human body under\nexposure to whole-body vibration.\" Industrial health,\nvol. 43, no. 3, pp. 441–7, Jul. 2005. (Online). Available:\nhttp://www.ncbi.nlm.nih.gov/pubmed/16100921","M. Christophy, N. Faruk Senan, J. Lotz, and O. O'Reilly,\n\"A musculoskeletal model for the lumbar spine,\"\nBiomechanics and Modeling in Mechanobiology, vol. 11,\nno. 1-2, pp. 19–34, 2012. (Online). Available: http:\n//dx.doi.org/10.1007/s10237-011-0290-6\n[10] K. T. Huynh, I. Gibson, B. N. Jagdish, and W. F. Lu,\n\"Development and validation of a discretised multi-body\nspine model in LifeMOD for biodynamic behaviour\nsimulation.\" Computer methods in biomechanics and\nbiomedical engineering, vol. 0, no. June 2013, pp.\n37–41, Apr. 2013. (Online). Available: http://www.ncbi.\nnlm.nih.gov/pubmed/23621475\n[11] E. Sifakis, T. Shinar, G. Irving, and R. Fedkiw, \"Hybrid\nsimulation of deformable solids,\" in Proceedings of\nthe 2007 ACM SIGGRAPH/Eurographics symposium on\nComputer animation. Eurographics Association, 2007,\npp. 81–90.\n[12] S.-H. Lee, E. Sifakis, and D. Terzopoulos,\n\"Comprehensive biomechanical modeling and simulation\nof the upper body,\" ACM Trans. Graph., vol. 28,\nno. 4, pp. 99:1–99:17, Sep. 2009. (Online). Available:\nhttp://doi.acm.org/10.1145/1559755.1559756\n[13] F. Faure, B. Gilles, G. Bousquet, and D. K. Pai, \"Sparse\nmeshless models of complex deformable solids,\" ACM\nTrans. Graph., vol. 30, no. 4, pp. 73:1–73:10, Jul. 2011.\n(Online). Available: http://doi.acm.org/10.1145/2010324.\n1964968\n[14] I. Stavness, J. E. Lloyd, Y. Payan, and S. Fels,\n\"Coupled hard–soft tissue simulation with contact and\nconstraints applied to jaw–tongue–hyoid dynamics,\"\nInternational Journal for Numerical Methods in\nBiomedical Engineering, vol. 27, no. 3, pp. 367–390,\n2011.\n[15] M. Dreischarf, T. Zander, A. Shirazi-Adl, C. Puttlitz,\nC. Adam, C. Chen, V. Goel, A. Kiapour, Y. Kim,\nK. Labus et al., \"Comparison of eight published static\nfinite element models of the intact lumbar spine:\nPredictive power of models improves when combined\ntogether,\" Journal of biomechanics, vol. 47, no. 8, pp.\n1757–1766, 2014.\n[16] N. Mitsuhashi, K. Fujieda, T. Tamura, S. Kawamoto,\nT. Takagi, and K. Okubo, \"Bodyparts3d: 3d structure\ndatabase for anatomical concepts,\" Nucleic Acids\nResearch, vol. 37, no. suppl 1, pp. D782–D785, 2009.\n[17] S. J. Ferguson, K. Ito, and L.-P. Nolte, \"Fluid flow and\nconvective transport of solutes within the intervertebral\ndisc,\" Journal of Biomechanics, vol. 37, no. 2, pp.\n213 – 221, 2004, spinal Biomechanics. (Online).\nAvailable: http://www.sciencedirect.com/science/article/\npii/S0021929003002501\n[18] A. Malandrino, J. A. Planell, and D. Lacroix, \"Statistical\nfactorial analysis on the poroelastic material properties\nsensitivity of the lumbar intervertebral disc under\ncompression, flexion and axial rotation,\" Journal of\nBiomechanics, vol. 42, no. 16, pp. 2780 – 2788,\n2009. (Online). Available: http://www.sciencedirect.com/\nscience/article/pii/S0021929009004679\n[19] A. Shirazi-Adl, A. M. AHMED, and S. C.\nSHRIVASTAVA, \"Mechanical response of a lumbar\nmotion segment in axial torque alone and combined\nwith compression,\" Spine, vol. 11, no. 9, pp. 914–927, 1986.\n[20] J. Chazal, a. Tanguy, M. Bourges, G. Gaurel,\nG. Escande, M. Guillot, and G. Vanneuville,\n\"Biomechanical properties of spinal ligaments and\na histological study of the supraspinal ligament\nin traction.\" Journal of biomechanics, vol. 18,\nno. 3, pp. 167–76, Jan. 1985. (Online). Available:\nhttp://www.ncbi.nlm.nih.gov/pubmed/3997901\n[21] Y. Masharawi, B. Rothschild, G. Dar, S. Peleg,\nD. Robinson, E. Been, and I. Hershkovitz,\n\"Facet Orientation in the Thoracolumbar Spine:\nThree-dimensional Anatomic and Biomechanical\nAnalysis,\" Spine, vol. 29, no. 16, 2004. (Online).\nAvailable: http://journals.lww.com/spinejournal/\nFulltext/2004/08150/Facet\\ Orientation\\ in\\ the\\\nThoracolumbar\\ Spine\\ .9.aspx\n[22] M. Nordin and V. H. V. H. Frankel, Basic biomechanics\nof the musculoskeletal system. Philadelphia (Pa.):\nLippincott Williams & Wilkins, 2001. (Online).\nAvailable: http://opac.inria.fr/record=b1133407\n[23] A. De Luca, \"Feedforward/feedback laws for the control\nof flexible robots,\" in Robotics and Automation, 2000.\nProceedings. ICRA '00. IEEE International Conference\non, vol. 1, 2000, pp. 233–240 vol.1.\n[24] W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P.\nFlannery, Numerical Recipes 3rd Edition: The Art of\nScientific Computing, 3rd ed. New York, NY, USA:\nCambridge University Press, 2007.\n[25] W. M. Park, K. Kim, and Y. H. Kim, \"Effects\nof degenerated intervertebral discs on intersegmental\nrotations, intradiscal pressures, and facet joint forces\nof the whole lumbar spine,\" Computers in biology and\nmedicine, vol. 43, no. 9, pp. 1234–1240, 2013.\n[26] U. M. Ayturk and C. M. Puttlitz, \"Parametric\nconvergence sensitivity and validation of a finite element\nmodel of the human lumbar spine,\" Computer methods in\nbiomechanics and biomedical engineering, vol. 14, no. 8,\npp. 695–705, 2011.\n[27] C.-L. Liu, Z.-C. Zhong, H.-W. Hsu, S.-L. Shih, S.-T.\nWang, C. Hung, and C.-S. Chen, \"Effect of the cord\npretension of the dynesys dynamic stabilisation system\non the biomechanics of the lumbar spine: a finite element\nanalysis,\" European Spine Journal, vol. 20, no. 11, pp.\n1850–1858, 2011.\n[28] J. P. Little, H. De Visser, M. J. Pearcy, and C. J. Adam,\n\"Are coupled rotations in the lumbar spine largely due\nto the osseo-ligamentous anatomy?—a modeling study,\"\nComputer methods in biomechanics and biomedical\nengineering, vol. 11, no. 1, pp. 95–103, 2008.\n[29] A. Shirazi-Adl, \"Biomechanics of the lumbar spine in\nsagittal/lateral moments,\" Spine, vol. 19, no. 21, pp.\n2407–2414, 1994.\n[30] T. Zander, A. Rohlmann, and G. Bergmann, \"Influence\nof different artificial disc kinematics on spine\nbiomechanics,\" Clinical biomechanics, vol. 24, no. 2,\npp. 135–142, 2009.\n[31] A. Kiapour, D. Ambati, R. W. Hoy, and V. K. Goel,\n\"Effect of graded facetectomy on biomechanics of\ndynesys dynamic stabilization system,\" Spine, vol. 37,\nno. 10, pp. E581–E589, 2012.\n[32] M. J. PEARCY and N. BOGDUK, \"Instantaneous\nAxes of Rotation of the Lumbar Intervertebral\nJoints,\" Spine, vol. 13, no. 9, 1988. (Online).\nAvailable: http://journals.lww.com/spinejournal/Fulltext/\n1988/09000/Instantaneous\\ Axes\\ of\\ Rotation\\ of\\\nthe\\ Lumbar.11.aspx\n[33] M.-A. Rousseau, D. S. Bradford, T. M. Hadi, K. L.\nPedersen, and J. C. Lotz, \"The instant axis of rotation\ninfluences facet forces at L5/S1 during flexion/extension\nand lateral bending.\" European spine journal : official\npublication of the European Spine Society, the European\nSpinal Deformity Society, and the European Section\nof the Cervical Spine Research Society, vol. 15,\nno. 3, pp. 299–307, Mar. 2006. (Online). Available:\nhttp://www.pubmedcentral.nih.gov/articlerender.fcgi?\nartid=3489304\\&tool=pmcentrez\\&rendertype=abstract\n[34] P. Bifulco, M. Cesarelli, T. Cerciello, and M. Romano,\n\"A continuous description of intervertebral motion by\nmeans of spline interpolation of kinematic data extracted\nby videofluoroscopy.\" Journal of biomechanics, vol. 45,\nno. 4, pp. 634–41, Feb. 2012. (Online). Available:\nhttp://www.ncbi.nlm.nih.gov/pubmed/22277152\n[35] Faure, F., Duriez, C., Delingette, H., Allard, J., Gilles, B.,\nMarchesseau, S., Talbot, H., Courtecuisse, H., Bousquet,\nG., Peterlik, I. and Cotin S., \"SOFA: A Multi-Model\nFramework for Interactive Physical Simulation,\" Soft\nTissue Biomechanical Modeling for Computer Assisted\nSurgery, vol. 11, pp. 283–321, 2012.\n[36] A. Shirazi-Adl and M. Parnianpour, \"Load-bearing and\nstress analysis of the human spine under a novel\nwrapping compression loading,\" Clinical Biomechanics,\nvol. 15, no. 10, pp. 718–725, 2000."]}

International audience; In this paper, we explore the use of Adaptively Restrained (AR) particles for graphics simulations. Contrary to previous methods, Adaptively Restrained Particle Simulations (ARPS) do not adapt time or space sampling, but rather switch the positional degrees of freedom of particles on and off, while letting their momenta evolve. Therefore, inter-particles forces do not have to be updated at each time step, in contrast with traditional methods that spend a lot of time there. We present the initial formulation of ARPS that was introduced for molecular dynamics simulations, and explore its potential for Computer Graphics applications: We first adapt ARPS to particle-based fluid simulations and propose an efficient incremental algorithm to update forces and scalar fields. We then introduce a new implicit integration scheme enabling to use ARPS for cloth simulation as well. Our experiments show that this new, simple strategy for adaptive simulations can provide significant speedups more easily than traditional adaptive models.

International audience

This thesis is divided in two independent parts, solid animation and image-based surface modeling. A general joint allowing the modeling of surface contact is proposed. Then a new solution strategy for kinematics equations is presented, allowing the handling of an arbitrary number of constraint levels. An extension to dynamics is also presented. We then consider the dynamics approach. A comparison between several popular methods is made, and we propose a new algorithm. It consists in using fast methods for acyclic constraints, and solving the closed loops iteratively using the conjugate gradient algorithm. We finally present two algorithms for real-time solid animation. An iterative global contact force computation is proposed. The other algorithm is an animation loop taking into account collisions and numerical integration correction. The second part of this thesis deals with image-based surface modeling. The first contribution is an algorithm for fast photometric stereo. The second is an iterative error minimization for simultaneous modeling of surface shape and reflectance., Cette thèse se compose de deux parties indépendantes, animation de solides et modélisation de surfaces à base d'images. Un modèle générique d'articulation permettant la représentation de contacts surfaciques est proposé. Puis une nouvelle stratégie de résolution des équations cinématiques est présentée, permettant la prise en compte d'un nombre arbitraire de niveaux de contraintes. Une extension permettant la prise en comte des lois de la dynamique est présentée. Nous considérons ensuite l'approche dynamique. Une comparaison de plusieurs méthodes bien connues est effectuée, et une nouvelle approche est proposée. Elle consiste à tirer parti d'algorithmes rapides pour l'animation de structures acycliques, et de résoudre les cha{î}nes fermées de manière itérative par gradient conjugué. Nous proposons finalement deux algorithmes pour l'animation de solides en temps réel. Une approche pour le calcul des forces de contact par résolution itérative globale est proposée. Le deuxième algorithme est une boucle d'animation permettant la prise en compte de collisions et la correction d'erreurs d'intégration numérique. La deuxième partie de cette thèse porte sur la modélisation automatique de surfaces à base d'images. La première contribution est un algorithme de stéréovision photométrique rapide. La deuxième est une minimisation automatique d'erreur qui permet dans certaines conditions la modélisation simultanée de la géométrie et de la réflectance d'une surface.

International audience; One of the major challenges in physically-based modeling is making simulations efficient. Adaptive models provide an essential solution to these efficiency goals. These models are able to self-adapt in space and time, attempting to provide the best possible compromise between accuracy and speed. This survey reviews the adaptive solutions proposed so far in computer graphics. Models are classified according to the strategy they use for adaptation, from time-stepping and freezing techniques to geometric adaptivity in the form of structured grids, meshes, and particles. Applications range from fluids, through deformable bodies, to articulated solids.

International audience; We present a new method for physically animating deformable shapes using finite element models (FEM). Contrary to commonly used methods based on tetrahedra, our finite elements are the bounding voxels of a given shape at arbitrary resolution. This alleviates the complexities and limitations of tetrahedral volume meshing and results in regular, well-conditionned meshes. We show how to build the voxels and how to set the masses and stiffnesses in order to model the physical properties as accurately as possible at any given resolution. Additionally, we extend a fast and robust tetrahedron-FEM approach to the case of hexahedral elements. This permits simulation of arbitrarily complex shapes at interactive rates in a manner that takes into account the distribution of material within the elements.

International audience; The complexity of most surgical models has not allowed interactive simulations on standard computers. We propose a new framework to finely control the resolution of the models. This allows us to dynamically concentrate the computational force where it is most needed. Given the segmented scan of an object to simulate, we first compute a bounding box and then recursively subdivide it where needed. The cells of this octree structure are labelled with mechanical properties based on material parameters and fill rate. An efficient physical simulation is then performed using hierarchical hexaedral finite elements. The object surface can be used for rendering and to apply boundary conditions. Compared with traditional finite element approaches, our method dramatically simplifies the task of volume meshing in order to facilitate the using of patient specific models, and increases the propagation of the deformations.