Abstract
Modelling of the cartilage within the acetabulum is necessary for determination of stresses in preoperative simulation of femoral acetabular impingement (FAI), a condition that is considered a primary cause of osteoarthritis. Presented is a previously proven method for elastic solid deformation using smoothed particle hydrodynamics (SPH). Smoothed particle hydrodynamics is a mesh-free method that has advantages in computational speed and accuracy over other graphical methods and as such is attractive for medical simulations that require high degrees of precision and real-time operability. A complete formulation of the method of polar decomposition as devised for smoothed particle hydrodynamics is outlined with the inclusion of a corotational formulation for accurate rotation handling. Modifications to the existing method include boundary and collision handling using an adapted virtual particle method, as well as an algorithm for parallel implementation on the GPU using NVIDIA’s CUDA framework. The method is verified through testing with a range of material parameters within the provided elastic solid framework. Employing CUDA for calculations is found to dramatically increase the computational speed of the simulation. The results of an indenter analysis of cartilage modelled as a purely elastic solid are presented and evaluated, with the conclusion that with further refinement the presented method is promising for use in cartilage simulations.
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Martin, D.E., Tashman, S.: The biomechanics of femoroacetabular impingement. Oper. Tech. Orthop. 20, 248–254 (2010)
Tannast, M., Goricki, D., Beck, M., Murphy, S.B., Siebenrock, K.A.: Hip damage occurs at the zone of femoroacetabular impingement. Clin. Orthop. Relat. Res. 466, 273–280 (2008)
Krekel, P.R., Vochteloo, A.J.H., Bloem, R.M., Nelissen, R.G.: Femoroacetabular impingement and its implications on range of motion: a case report. J. Med. Case Rep. 5, 143 (2011)
Asheesh, B., et al.: Surgical treatment of femoroacetabular impingement improves hip kinematics: a computer-assisted model. Am. J. Sports Med. 39, 43S–49S (2011)
Terzopoulos, D., Platt, J., Barr, A., Fleischer, K.: Elastically deformable models. Com Graph 21, 205–214 (1987)
Molino, N., Bridson, R., Teran, J., Fedkiw, R.: A crystalline, red green strategy for meshing highly deformable objects with tetrahedra. In: Proceedings of 12th IMR 103-114 (2003)
Maciel, A., Boulic, R., Thalmann, D.: Deformable tissue parameterized by properties of real biological tissue. Surg. Sim. Soft Tissue Model 2673, 74–87 (2003)
Lloyd, B.A., Szekely, G., Harders, M.: Identification of spring parameters for deformable object simulation. IEEE Trans. Vis. Comp. Graph. 13, 1081–1094 (2007)
James, D.L., Pai, D.K.: ArtDefo: accurate real time deformable objects. SIGGRAPH 1999, 65–72 (1999)
MeieMollemans, W., Schutyser, F., Najmi, N., Maes, F., Suetens, P.: Predicting soft tissue deformations for a maxillofacial surgery planning system: from computational strategies to a complete clinical validation. Med. Image Anal. 11, 282–301 (2007)
Cotin, S., Delingette, H., Ayache, N.: A hybrid elastic model allowing real-time cutting, deformations and force-feedback for surgery training and simulation. In: Proceedings on Computer Animation, pp, 70–81 (2000)
Niroomandi, S., Alfaro, I., Cueto, E., Chinesta, F.: Accounting for large deformations in real-time simulations of soft tissues based on reduced-order models. Comput. Methods Programs Biomed. 105, 1–12 (2012)
Bro-Nielsen, M.: Finite element modeling in surgery simulation. Proc. IEEE 86, 490–503 (1998)
Cotin, S., Delingette, H., Ayache, N.: Real-time elastic deformations of soft tissues for surgery simulation. IEEE Trans. Vis. Comput. Graph 5, 62–73 (1999)
Meier, U., López, O., Monserrat, C., Juan, M.C., Alcañiz, M.: Real-time deformable models for surgery simulation: a survey. Comput. Methods Programs Biomed. 77, 183–197 (2005)
Monaghan, J.J.: Smoothed Particle Hydrodynamics. Rep. Prog. Phys. 68, 1703–1759 (2005)
Hieber, S.E., Koumoutsakos, P.: A Lagrangian particle method for the simulation of linear and nonlinear elastic models of soft tissue. J. Comput. Phys. 227, 9195–9215 (2008)
Müller, M., Chentanez, N.: Solid simulation with oriented particles. ACM Trans. Graph. 30(92), 1–9 (2011)
Gingold, R.A., Monaghan, J.J.: Smoothed particle hydrodynamics—theory and application to non-spherical stars. Mon. Not. R. Astron. Soc. 181, 375–389 (1977)
Müller, M., Charypar, D., Gross, M.: Particle-Based Fluid Simulation for Interactive Applications. In: Eurograph/SIGGRAPH Symposium on Computer Animation, pp. 154–159 (2003)
Bao, K., Zhang, H., Zheng, L., Wu, E.: Pressure corrected SPH for fluid animation. Comput. Animat. Virtual Worlds 20, 311–320 (2009)
Lenaerts, T., Adams, B., Dutré, P.: Porous Flow in Particle-Based Fluid Simulations. ACM Trans. Graph. 49, 1–8 (2008)
Cleary, P.W., Das, R.: The potential for SPH modelling of solid deformation and fracture. In: IUTAM Symposium on Theoretical, Computational and Modelling Aspects of Inelastic Media, pp. 287–296 (2008)
Gray, J.P., Monaghan, J.J., Swift, R.P.: SPH elastic dynamics. Comp. Methods Appl. Mech. Eng. 190, 6641–6662 (2001)
Qin, J., Pang, W.M., Nguyen, B.P., Ni, D., Chui, C.K.: Particle-based Simulation of blood flow and vessel wall interactions in virtual surgery. In: SolCT, pp. 128–133 (2010)
Mesit, J., Guha, R.K.: Experimenting with real time simulation parameters for fluid model of soft bodies. In: Proceedings of SpringSim, pp. 1–8 (2010)
Hieber, S.E., Walther, J.H., Koumoutsakos, P.: Remeshed smoothed particle hydrodynamics simulation of the mechanical behavior of human organs. Technol. Health Care 12, 305–314 (2004)
Solenthaler, B., Schläfli, J., Pajarola, R.: A unified particle model for fluid-solid interactions. Comput. Animat. Virtual Worlds 18, 69–82 (2007)
Becker, M., Ihmsen, M., Teschner, M.: Corotated SPH for deformable solids. In: Proceedings of the 5th Eurographics Conference on Natural Phenomena, pp. 27–34 (2009)
Mow, V.C., Holmes, M.H., Lai, M.W.: Fluid transport and mechanical properties of articular cartilage: a review. J. Biomech. 17, 377–394 (1984)
Korhonen, R.K., et al.: Fibril reinforced poroelastic model predicts specifically mechanical behavior of normal, proteoglycan depleted and collagen degraded articular cartilage. J. Biomech. 36, 1373–1379 (2003)
Wilson, W., Huyghe, J.M., van Donkelaar, C.C.: Depth-dependent compressive equilibrium properties of articular cartilage explained by its composition. Biomech. Model. Mechanobiol. 6, 43–53 (2007)
Schmedding, R., Teschner, M.: Inversion handling for stable deformable modeling. Vis. Comp. 24, 625–633 (2008)
Jin, H., Lewis, J.L.: Determination of Poisson’s ratio of articular cartilage by indentation using different-sized indenters. J. Biomech. Eng. 126, 138–145 (2004)
Müller, M. et al.: Point based animation of elastic, plastic and melting objects. In: Proceedings of SIGGRAPH Symposium on Computer Animation, pp. 141–151 (2004)
Liu, M.B., Liu, G.R.: Smoothed particle hydrodynamics (SPH): an overview and recent developments. Arch. Comput. Methods Eng. 17, 25–76 (2010)
Desbrun, M., Gascuel, M.P.: Smoothed particles: A new paradigm for animating highly deformable bodies. In: Proceedings of EG Workshop on Animation and Simulation, pp. 61–76 (1996)
Lu, X.L., Wan, L.Q., Guo, X.E., Mow, V.C.: A linearized formulation of triphasic mixture theory for articular cartilage, and its application to indentation analysis. J. Biomech. 43, 673–679 (2010)
Macklin, M., Müller, M.: Position based fluids. ACM Trans. Graph. 32(104), 1–5 (2013)
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Boyer, P., LeBlanc, S., Joslin, C. (2015). Smoothed Particle Hydrodynamics Applied to Cartilage Deformation. In: Cai, Y., See, S. (eds) GPU Computing and Applications. Springer, Singapore. https://doi.org/10.1007/978-981-287-134-3_10
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DOI: https://doi.org/10.1007/978-981-287-134-3_10
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