Skip to main content

Advertisement

SpringerLink
Log in

Neural dynamics-based Poisson propagation for deformable modelling

  • Original Article
  • Published:
Neural Computing and Applications Aims and scope Submit manuscript

Abstract

This paper presents a new methodology from the standpoint of energy propagation for real-time and nonlinear modelling of deformable objects. It formulates the deformation process of a soft object as a process of energy propagation, in which the mechanical load applied to the object to cause deformation is viewed as the equivalent potential energy based on the law of conservation of energy and is further propagated among masses of the object based on the nonlinear Poisson propagation. Poisson propagation of mechanical load in conjunction with non-rigid mechanics of motion is developed to govern the dynamics of soft object deformation. Further, these two governing processes are modelled with cellular neural networks to achieve real-time computational performance. A prototype simulation system with a haptic device is implemented for real-time simulation of deformable objects with haptic feedback. Simulations, experiments as well as comparisons demonstrate that the proposed methodology exhibits nonlinear force–displacement relationship, capable of modelling large-range deformation. It can also accommodate homogeneous, anisotropic and heterogeneous materials by simply changing the constitutive coefficient value of mass points.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

References

  1. Cover SA, Ezquerra NF, O’Brien JF, Rowe R, Gadacz T, Palm E (1993) Interactively deformable models for surgery simulation. IEEE Comput Graph Appl 13(6):68–75. doi:10.1109/38.252559

    Article  Google Scholar 

  2. CaniGascuel M, Desbrun M (1997) Animation of deformable models using implicit surfaces. IEEE Trans Vis Comput Graph 3(1):39–50. doi:10.1109/2945.582343

    Article  Google Scholar 

  3. Terzopoulos D, Platt J, Barr A, Fleischer K (1987) Elastically deformable models. ACM SIGGRAPH Comput Graph 21(4):205–214. doi:10.1145/37401.37427

    Article  Google Scholar 

  4. Courtecuisse H, Allard J, Kerfriden P, Bordas SPA, Cotin S, Duriez C (2014) Real-time simulation of contact and cutting of heterogeneous soft-tissues. Med Image Anal 18(2):394–410. doi:10.1016/j.media.2013.11.001

    Article  Google Scholar 

  5. Frisken-Gibson SF (1997) 3D ChainMail: a fast algorithm for deforming volumetric objects. In: Proceedings of the symposium on interactive 3D graphics, pp 149–154. doi:10.1145/253284.253324

  6. Zhang J, Zhong Y, Smith J, Gu C (2016) A new ChainMail approach for real-time soft tissue simulation. Bioengineered 7(4):246–252. doi:10.1080/21655979.2016.1197634

    Article  Google Scholar 

  7. Camara M, Mayer E, Darzi A, Pratt P (2016) Soft tissue deformation for surgical simulation: a position-based dynamics approach. Int J Comput Assist Radiol Surg 11(6):919–928. doi:10.1007/s11548-016-1373-8

    Article  Google Scholar 

  8. Misra S, Ramesh KT, Okamura AM (2008) Modeling of tool-tissue interactions for computer-based surgical simulation: a literature review. Presence Teleoper Virtual Environ 17(5):463–491. doi:10.1162/pres.17.5.463

    Article  Google Scholar 

  9. Cotin S, Delingette H, Ayache N (1999) Real-time elastic deformations of soft tissues for surgery simulation. IEEE Trans Vis Comput Graph 5(1):62–73. doi:10.1109/2945.764872

    Article  MATH  Google Scholar 

  10. Wu W, Heng PA (2005) An improved scheme of an interactive finite element model for 3D soft-tissue cutting and deformation. Vis Comput 21(8–10):707–716. doi:10.1007/s00371-005-0310-6

    Article  Google Scholar 

  11. Weber D, Mueller-Roemer J, Altenhofen C, Stork A, Fellner D (2015) Deformation simulation using cubic finite elements and efficient p-multigrid methods. Comput Graph 53:185–195. doi:10.1016/j.cag.2015.06.010

    Article  Google Scholar 

  12. Yang C, Li S, Lan Y, Wang L, Hao A, Qin H (2016) Coupling time-varying modal analysis and FEM for real-time cutting simulation of objects with multi-material sub-domains. Comput Aided Geom Des 43:53–67. doi:10.1016/j.cagd.2016.02.014

    Article  MathSciNet  MATH  Google Scholar 

  13. Huang J, Liu X, Bao H, Guo B, Shum H-Y (2006) An efficient large deformation method using domain decomposition. Comput Graph 30(6):927–935. doi:10.1016/j.cag.2006.08.014

    Article  Google Scholar 

  14. Strbac V, Sloten JV, Famaey N (2015) Analyzing the potential of GPGPUs for real-time explicit finite element analysis of soft tissue deformation using CUDA. Finite Elem Anal Des 105:79–89. doi:10.1016/j.final.2015.07.005

    Article  Google Scholar 

  15. Cotin S, Delingette H, Ayache N (2000) A hybrid elastic model for real-time cutting, deformations, and force feedback for surgery training and simulation. Vis Comput 16(8):437–452. doi:10.1007/Pl00007215

    Article  MATH  Google Scholar 

  16. Zhu B, Gu L (2012) A hybrid deformable model for real-time surgical simulation. Comput Med Imaging Graph 36(5):356–365. doi:10.1016/j.compmedimag.2012.03.001

    Article  Google Scholar 

  17. Zhang GY, Wittek A, Joldes GR, Jin X, Miller K (2014) A three-dimensional nonlinear meshfree algorithm for simulating mechanical responses of soft tissue. Eng Anal Bound Elem 42:60–66. doi:10.1016/j.enganabound.2013.08.014

    Article  MathSciNet  MATH  Google Scholar 

  18. Wittek A, Grosland NM, Joldes GR, Magnotta V, Miller K (2016) 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(1):3–15. doi:10.1007/s10439-015-1469-2

    Article  Google Scholar 

  19. Xu S, Liu X, Zhang H, Hu L (2011) A nonlinear viscoelastic tensor-mass visual model for surgery simulation. IEEE Trans Instrum Meas 60(1):14–20. doi:10.1109/Tim.2010.2065450

    Article  Google Scholar 

  20. Dick C, Georgii J, Westermann R (2011) A real-time multigrid finite hexahedra method for elasticity simulation using CUDA. Simul Model Pract Theory 19(2):801–816. doi:10.1016/j.simpat.2010.11.005

    Article  Google Scholar 

  21. Miller K, Joldes G, Lance D, Wittek A (2007) Total Lagrangian explicit dynamics finite element algorithm for computing soft tissue deformation. Int J Numer Methods Biomed Eng 23(2):121–134. doi:10.1002/cnm.887

    Article  MathSciNet  MATH  Google Scholar 

  22. Goulette F, Chen Z-W (2015) Fast computation of soft tissue deformations in real-time simulation with Hyper-Elastic Mass Links. Comput Methods Appl Mech Eng 295:18–38. doi:10.1016/j.cma.2015.06.015

    Article  MathSciNet  MATH  Google Scholar 

  23. Zhong Y, Shirinzadeh B, Alici G, Smith J (2008) A Poisson-based methodology for deformable object simulation. Int J Model Simul 28(2):156. doi:10.2316/Journal.205.2008.2.205-4551

    Article  Google Scholar 

  24. Sadd MH (2009) Elasticity: theory, applications, and numerics. Academic Press, Cambridge

    Google Scholar 

  25. Selvadurai AP (2013) Partial differential equations in mechanics 2: the biharmonic equation, Poisson’s equation, vol 2. Springer, Berlin

    Google Scholar 

  26. Chua LO, Roska T (1993) The CNN Paradigm. IEEE Trans Circuits Syst I Fundam Theory Appl 40(3):147–156. doi:10.1109/81.222795

    Article  MATH  Google Scholar 

  27. Thiran P, Setti G, Hasler M (1998) An approach to information propagation in 1-D cellular neural networks—part I: local diffusion. IEEE Trans Circuits Syst I Fundam Theory Appl 45(8):777–789. doi:10.1109/81.704819

    Article  MATH  Google Scholar 

  28. Setti G, Thiran P, Serpico C (1998) An approach to information propagation in 1-D cellular neural networks—part II: global propagation. IEEE Trans Circuits Syst I Fundam Theory Appl 45(8):790–811. doi:10.1109/81.704820

    Article  MATH  Google Scholar 

  29. Kozek T, Chua LO, Roska T, Wolf D, Tetzlaff R, Puffer F, Lotz K (1995) Simulating nonlinear waves and partial differential equations via CNN—part II: typical examples. IEEE Trans Circuits Syst I Fundam Theory Appl 42(10):816–820. doi:10.1109/81.473591

    Article  Google Scholar 

  30. Szolgay P, Vörös G, Erőss G (1993) On the applications of the cellular neural network paradigm in mechanical vibrating systems. IEEE Trans Circuits Syst I Fundam Theory Appl 40(3):222–227. doi:10.1109/81.222805

    Article  MATH  Google Scholar 

  31. Roska T, Chua LO, Wolf D, Kozek T, Tetzlaff R, Puffer F (1995) Simulating nonlinear waves and partial differential equations via CNN—part I: basic techniques. IEEE Trans Circuits Syst I Fundam Theory Appl 42(10):807–815. doi:10.1109/81.473590

    Article  Google Scholar 

  32. Chua LO, Yang L (1988) Cellular neural networks: theory. IEEE Trans Circuits Syst 35(10):1257–1272. doi:10.1109/31.7600

    Article  MathSciNet  MATH  Google Scholar 

  33. Vijayan P, Kallinderis Y (1994) A 3D finite-volume scheme for the Euler equations on adaptive tetrahedral grids. J Comput Phys 113(2):249–267. doi:10.1006/jcph.1994.1133

    Article  MathSciNet  MATH  Google Scholar 

  34. Chua LO, Hasler M, Moschytz GS, Neirynck J (1995) Autonomous cellular neural networks: a unified paradigm for pattern formation and active wave propagation. IEEE Trans Circuits Syst I Fundam Theory Appl 42(10):559–577. doi:10.1109/81.473564

    Article  MathSciNet  Google Scholar 

  35. Jingya Z, Jiajun W, Xiuying W, Dagan F (2014) The adaptive FEM elastic model for medical image registration. Phys Med Biol 59(1):97–118. doi:10.1088/0031-9155/59/1/97

    Article  Google Scholar 

  36. Bro-Nielsen M, Cotin S (1996) Real-time volumetric deformable models for surgery simulation using finite elements and condensation. Comput Graph Forum 15(3):57–66. doi:10.1111/1467-8659.1530057

    Article  Google Scholar 

  37. Misra J, Saha I (2010) Artificial neural networks in hardware: a survey of two decades of progress. Neurocomputing 74(1–3):239–255. doi:10.1016/j.neucom.2010.03.021

    Article  Google Scholar 

  38. Ullah Z, Augarde CE (2013) Finite deformation elasto-plastic modelling using an adaptive meshless method. Comput Struct 118(S1):39–52. doi:10.1016/j.compstruc.2012.04.001

    Article  Google Scholar 

  39. Picinbono G, Lombardo JC, Delingette H, Ayache N (2002) Improving realism of a surgery simulator: linear anisotropic elasticity, complex interactions and force extrapolation. J Vis Comput Anim 13(3):147–167. doi:10.1002/vis.257

    Article  MATH  Google Scholar 

  40. Xia P (2016) New advances for haptic rendering: state of the art. Vis Comput. doi:10.1007/s00371-016-1324-y

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Engineering, RMIT University, PO Box 71, Bundoora, VIC, 3083, Australia

    Jinao Zhang, Yongmin Zhong & Chengfan Gu

  2. Department of Surgery, School of Clinical Sciences at Monash Health, Monash University, Clayton, VIC, 3168, Australia

    Julian Smith

Authors
  1. Jinao Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yongmin Zhong
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Julian Smith
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Chengfan Gu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jinao Zhang.

Ethics declarations

Conflict of interest

The authors declare that there is no conflict of interest.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhang, J., Zhong, Y., Smith, J. et al. Neural dynamics-based Poisson propagation for deformable modelling. Neural Comput & Applic 31 (Suppl 2), 1091–1101 (2019). https://doi.org/10.1007/s00521-017-3132-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00521-017-3132-3

Keywords

Search

Navigation