Abstract
Modelling of interactions of soft tissues with surgical tools is a fundamental issue in interactive surgical simulation. This paper presents a new methodology for modelling of nonlinear characteristics of soft tissue deformation for interactive surgical simulation. The proposed methodology formulates soft tissue deformation as a process of energy propagation; the mechanical load applied to soft tissues to cause deformation is treated as the equivalent thermal energy according to the conservation law of energy and further distributed among masses of soft tissues in the manner of heat conduction. Heat conduction of mechanical load and non-rigid mechanics of motion are combined to conduct soft tissue deformation. To obtain real-time computational performance, cellular neural networks are developed for both propagation of mechanical load and non-rigid mechanical dynamics, leading to novel neural network models embedded with deformation mechanics and physical dynamics for interactive soft tissue simulation. Real-time force interaction is also achieved with an integration of a haptic device via force input, soft tissue deformation, and force feedback. Simulations and experimental results demonstrate the proposed methodology exhibits the typical mechanical behaviour of soft tissues and accepts nonlinear soft tissue deformation. It can also accommodate isotropic and homogeneous, anisotropic, and heterogeneous materials by a simple modification of thermal conductivity values of mass points.
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References
Miller, K.: Computational biomechanics for patient-specific applications. Ann. Biomed. Eng. 44, 1–2 (2016)
Zhang, J., Zhong, Y., Gu, C.: Deformable models for surgical simulation: a survey. IEEE Rev. Biomed. Eng. (2018). https://doi.org/10.1109/RBME.2017.2773521
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)
Lim, Y.-J., De, S.: 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, 3011–3024 (2007)
Kerdok, A.E., Cotin, S.M., Ottensmeyer, M.P., Galea, A.M., Howe, R.D., Dawson, S.L.: Truth cube: establishing physical standards for soft tissue simulation. Med. Image Anal. 7, 283–291 (2003)
Sederberg, T.W., Parry, S.R.: Free-form deformation of solid geometric models. ACM SIGGRAPH Comput. Graph. 20, 151–160 (1986)
Cover, S.A., Ezquerra, N.F., O’Brien, J.F., Rowe, R., Gadacz, T., Palm, E.: Interactively deformable models for surgery simulation. IEEE Comput. Graph. Appl. 13, 68–75 (1993)
Duan, Y., Huang, W., Chang, H., Chen, W., Zhou, J., Teo, S.K., Su, Y., Chui, C.K., Chang, S.: Volume preserved mass–spring model with novel constraints for soft tissue deformation. IEEE J. Biomed. Health Inform. 20, 268–280 (2016)
Hammer, P.E., Sacks, M.S., Del Nido J, P., Howe, R.D.: Mass-spring model for simulation of heart valve tissue mechanical behavior. Ann. Biomed. Eng. 39, 1668–1679 (2011)
Nealen, A., Müller, M., Keiser, R., Boxerman, E., Carlson, M.: Physically based deformable models in computer graphics. Comput. Graph Forum 25, 809–836 (2006)
Meier, U., Lopez, O., Monserrat, C., Juan, M.C., Alcaniz, M.: Real-time deformable models for surgery simulation: a survey. Comput. Methods Progr. Biomed. 77, 183–197 (2005)
Delingette, H.: Toward realistic soft-tissue modeling in medical simulation. Proc. IEEE 86, 512–523 (1998)
Gibson, S.F., Mirtich, B.: A survey of deformable modeling in computer graphics. Technical Report, Mitsubishi Electric Research Laboratories (1997)
Frisken-Gibson, S.F.: 3D ChainMail: a fast algorithm for deforming volumetric objects. In: Proceedings of the Symposium on Interactive 3D graphics, pp. 149–154 (1997)
Gibson, S., Fyock, C., Grimson, E., Kanade, T., Kikinis, R., Lauer, H., McKenzie, N., Mor, A., Nakajima, S., Ohkami, H., Osborne, R., Samosky, J., Sawada, A.: Volumetric object modeling for surgical simulation. Med. Image Anal. 2, 121–132 (1998)
Zhang, J., Zhong, Y., Smith, J., Gu, C.: A new ChainMail approach for real-time soft tissue simulation. Bioengineered 7, 246–252 (2016)
Zhang, J., Zhong, Y., Gu, C.: Ellipsoid bounding region-based ChainMail algorithm for soft tissue deformation in surgical simulation. Int. J. Interact. Des. Manuf. (IJIDeM) (2017). https://doi.org/10.1007/s12008-017-0437-5
Zhang, J., Zhong, Y., Smith, J., Gu, C.: ChainMail based neural dynamics modeling of soft tissue deformation for surgical simulation. Technol. Health Care 25, 231–239 (2017)
Bro-Nielsen, M., Cotin, S.: Real-time volumetric deformable models for surgery simulation using finite elements and condensation. Comput. Graph Forum 15, 57–66 (1996)
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)
Cotin, S., Delingette, H., Ayache, N.: A hybrid elastic model for real-time cutting, deformations, and force feedback for surgery training and simulation. Vis. Comput. 16, 437–452 (2000)
Miller, K., Joldes, G., Lance, D., Wittek, A.: Total Lagrangian explicit dynamics finite element algorithm for computing soft tissue deformation. Int. J. Numer. Methods Biomed. Eng. 23, 121–134 (2007)
Monserrat, C., Meier, U., Alcaniz, M., Chinesta, F., Juan, M.C.: A new approach for the real-time simulation of tissue deformations in surgery simulation. Comput. Methods Progr. Biomed. 64, 77–85 (2001)
Zhu, B., Gu, L.: A hybrid deformable model for real-time surgical simulation. Comput. Med. Imaging Graph. 36, 356–365 (2012)
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)
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)
Aras, R., Shen, Y., Audette, M.: An analytic meshless enrichment function for handling discontinuities in interactive surgical simulation. Adv. Eng. Softw. 102, 40–48 (2016)
Zou, Y., Liu, P.X.: A high-resolution model for soft tissue deformation based on point primitives. Comput. Methods Progr. Biomed. 148, 113–121 (2017)
Palyanov, A., Khayrulin, S., Larson, S.D.: Application of smoothed particle hydrodynamics to modeling mechanisms of biological tissue. Adv. Eng. Softw. 98, 1–11 (2016)
Rausch, M.K., Karniadakis, G.E., Humphrey, J.D.: Modeling soft tissue damage and failure using a combined particle/continuum approach. Biomech. Model. Mechanobiol. 16, 1–13 (2016)
De, S., Kim, J., Lim, Y.-J., Srinivasan, M.A.: The point collocation-based method of finite spheres (PCMFS) for real time surgery simulation. Comput. Struct. 83, 1515–1525 (2005)
Payan, Y.: Soft Tissue Biomechanical Modeling for Computer Assisted Surgery. Springer, Berlin (2012)
Picinbono, G., Delingette, H., Ayache, N.: Non-linear anisotropic elasticity for real-time surgery simulation. Graph. Models 65, 305–321 (2003)
Xu, S., Liu, X., Zhang, H., Hu, L.: A nonlinear viscoelastic tensor-mass visual model for surgery simulation. IEEE T Instrum. Meas. 60, 14–20 (2011)
Courtecuisse, H., Jung, H., Allard, J., Duriez, C., Lee, D.Y., Cotin, S.: GPU-based real-time soft tissue deformation with cutting and haptic feedback. Progr. Biophys. Mol. Biol. 103, 159–168 (2010)
Plantefève, R., Peterlik, I., Haouchine, N., Cotin, S.: Patient-specific biomechanical modeling for guidance during minimally-invasive hepatic surgery. Ann. Biomed. Eng. 44, 139–153 (2016)
Schwartz, J.-M., Denninger, M., Rancourt, D., Moisan, C., Laurendeau, D.: Modelling liver tissue properties using a non-linear visco-elastic model for surgery simulation. Med. Image Anal. 9, 103–112 (2005)
Zhong, Y., Shirinzadeh, B., Smith, J., Gu, C.: Thermal–mechanical-based soft tissue deformation for surgery simulation. Adv. Robot. 24, 1719–1739 (2010)
Holzapfel, G.A.: Nonlinear Solid Mechanics. Wiley Chichester, Chichester (2000)
Zhang, J., Zhong, Y., Gu, C.: Energy balance method for modelling of soft tissue deformation. Comput. Aided Des. 93, 15–25 (2017)
Sadd, M.H.: Elasticity: Theory, Applications, and Numerics. Academic Press, Cambridge (2009)
Olsrud, J., Friberg, B., Ahlgren, M., Persson, B.R.R.: Thermal conductivity of uterine tissue in vitro. Phys. Med. Biol. 43, 2397–2406 (1998)
Khaled, A.R.A., Vafai, K.: The role of porous media in modeling flow and heat transfer in biological tissues. Int. J. Heat Mass Transf. 46, 4989–5003 (2003)
Chua, L.O., Roska, T.: The CNN paradigm. IEEE T Circuits I 40, 147–156 (1993)
Thiran, P., Setti, G., Hasler, M.: An approach to information propagation in 1-D cellular neural networks - part i: local diffusion. IEEE Trans. Circuits Syst. I Fundam. Theory Appl. 45, 777–789 (1998)
Setti, G., Thiran, P., Serpico, C.: An approach to information propagation in 1-D cellular neural networks - part ii: global propagation. IEEE Trans. Circuits Syst. I Fundam. Theory Appl. 45, 790–811 (1998)
Kozek, T., Chua, L.O., Roska, T., Wolf, D., Tetzlaff, R., Puffer, F., Lotz, K.: Simulating nonlinear waves and partial differential equations via CNN-part II: typical examples. IEEE Trans. Circuits Syst. I Fundam. Theory Appl. 42, 816–820 (1995)
Szolgay, P., Vörös, G., Erőss, G.: On the applications of the cellular neural network paradigm in mechanical vibrating systems. IEEE Trans. Circuits Syst. I Fundam. Theory Appl. 40, 222–227 (1993)
Roska, T., Chua, L.O., Wolf, D., Kozek, T., Tetzlaff, R., Puffer, F.: Simulating nonlinear waves and partial differential equations via CNN-part I: basic techniques. IEEE Trans. Circuits Syst. I Fundam. Theory Appl. 42, 807–815 (1995)
Chua, L.O., Yang, L.: Cellular neural networks: theory. IEEE T Circuits Syst. 35, 1257–1272 (1988)
Chua, L.O., Hasler, M., Moschytz, G.S., Neirynck, J.: Autonomous Cellular neural networks: a unified paradigm for pattern formation and active wave propagation. IEEE Trans. Circuits Syst. I Fundam. Theory Appl. 42, 559–577 (1995)
DiMaio, S.P., Salcudean, S.E.: Needle insertion modeling and simulation. IEEE Trans. Robot. Autom. 19, 864–875 (2003)
Sparks, J.L., Vavalle, N.A., Kasting, K.E., Long, B., Tanaka, M.L., Sanger, P.A., Schnell, K., Conner-Kerr, T.A.: Use of silicone materials to simulate tissue biomechanics as related to deep tissue injury. Adv. Skin Wound Care 28, 59–68 (2015)
Misra, J., Saha, I.: Artificial neural networks in hardware A survey of two decades of progress. Neurocomputing 74, 239–255 (2010)
Ullah, Z., Augarde, C.E.: Finite deformation elasto-plastic modelling using an adaptive meshless method. Comput. Struct. 118, 39–52 (2013)
Picinbono, G., Lombardo, J.C., Delingette, H., Ayache, N.: Improving realism of a surgery simulator: linear anisotropic elasticity, complex interactions and force extrapolation. J. Vis. Comput. Anim. 13, 147–167 (2002)
Choi, K.-S., Sun, H., Heng, P.-A.: An efficient and scalable deformable model for virtual reality-based medical applications. Artif. Intell. Med. 32, 51–69 (2004)
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Zhang, J., Shin, J., Zhong, Y. et al. Heat conduction-based methodology for nonlinear soft tissue deformation. Int J Interact Des Manuf 13, 147–161 (2019). https://doi.org/10.1007/s12008-018-0486-4
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DOI: https://doi.org/10.1007/s12008-018-0486-4