Non-standard bone simulation: interactive numerical analysis by computational steering

Abstract

Numerous numerical methods have been developed in an effort to accurately predict stresses in bones. The largest group are variants of the h-version of the finite element method (h-FEM), where low order Ansatz functions are used. By contrast, we3 investigate a combination of high order FEM and a fictitious domain approach, the finite cell method (FCM). While the FCM has been verified and validated in previous publications, this article proposes methods on how the FCM can be made computationally efficient to the extent that it can be used for patient specific, interactive bone simulations. This approach is called computational steering and allows to change input parameters like the position of an implant, material or loads and leads to an almost instantaneous change in the output (stress lines, deformations). This direct feedback gives the user an immediate impression of the impact of his actions to an extent which, otherwise, is hard to obtain by the use of classical non interactive computations. Specifically, we investigate an application to pre-surgical planning of a total hip replacement where it is desirable to select an optimal implant for a specific patient. Herein, optimal is meant in the sense that the expected post-operative stress distribution in the bone closely resembles that before the operation.

This is a preview of subscription content, access via your institution.

References

  1. 1

    Baca V., Horak Z., Mikulenka P., Dzupa V.: Comparison of an inhomogeneous orthotropic and isotropic material models used for fe analyses. Med. Eng. Phys. 30, 924–930 (2008)

    Article  Google Scholar 

  2. 2

    Bongini D., Carfagni M., Governi L.: A semiautomatic computer program for selecting hip prosthesis femoral components. Comput. Methods Programs Biomed. 63, 105–115 (2000)

    Article  Google Scholar 

  3. 3

    Borrmann, A., Wenisch, P., Egger, M., van Treeck, C., Rank, E.: Collaborative computational steering: interactive collaborative design of ventilation and illumination of operating theatres. ICE08, Plymouth (2008)

  4. 4

    Dick, C., Georgii, J., Burgkart, R., Westermann, R.: Computational steering for patient-specific implant planning in orthopedics. In: Proceedings of Visual Computing for Biomedicine, pp. 83–92 (2008)

  5. 5

    Dick C., Georgii J., Burgkart R., Westermann R.: Stress tensor field visualization for implant planning in orthopedics. IEEE Trans. Vis. Comput. Graph. 15, 1399–1406 (2009)

    Article  Google Scholar 

  6. 6

    DiGioia A.M., Simon D., Jaramaz B., Blackwell M.: The value of preoperative planning for total hip arthroplasty. Comput. Assist. Orthop. Surg. Symp. 80, 382 (1995)

    Google Scholar 

  7. 7

    Dongarra J.J., Du Croz J., Duff I.S., Hammarling S.: Algorithm 679: a set of level 3 basic linear algebra subprograms. ACM Trans. Math. Softw. 16, 18–28 (1990)

    Article  MATH  Google Scholar 

  8. 8

    Düster A., Parvizian J., Yang Z., Rank E.: The finite cell method for three-dimensional problems of solid mechanics. Comput. Methods Appl. Mech. Eng. 197, 3768–3782 (2008)

    Article  MATH  Google Scholar 

  9. 9

    Effenberger H., Heiland A., Ramsauer T., Plitz W., Dorn U.: A model for assessing the rotational stability of uncemented femoral implants. Arch. Orthop. Trauma Surg. 121, 60–64 (2000)

    Article  Google Scholar 

  10. 10

    Günter T., Merz B., Mericske-Stern R., Schmitt J., Leppek R., Lengsfeld M.: Testing dental implants with an in vivo finite element model. Biomed. Eng. (Biomedizinische Technik) 45, 272–276 (2000)

    Article  Google Scholar 

  11. 11

    Kak A.C., Slaney M.: Principles of Computerized Tomographic Imaging. Society for Industrial Mathematics, Philadelphia (2001)

    Google Scholar 

  12. 12

    Keyak J.H., Falkinstein Y.: Comparison of in situ and in vitro CT scan-based finite element model predictions of proximal femoral fracture load. Med. Eng. Phys. 25, 781–787 (2003)

    Article  Google Scholar 

  13. 13

    Keyak J.H., Lee I.Y., Skinner H.B.: Correlations between orthogonal mechanical properties and density of trabecular bone: use of different densitometric measures. J. Biomed. Mater. Res. 28(11), 1329–1336 (1994)

    Article  Google Scholar 

  14. 14

    Kuhl E., Balle F.: Computational modeling of hip replacement surgery: total hip replacement vs. hip resurfacing. Technische Mechanik 25, 107–114 (2005)

    Google Scholar 

  15. 15

    MacWilliams B.A., Wilson D.R., DesJardins J.D., Romero J., Chao E.Y.: Hamstrings cocontraction reduces internal rotation, anterior translation, and anterior cruciate ligament load in weight-bearing flexion. J. Orthop. Res. 17, 817–822 (1999)

    Article  Google Scholar 

  16. 16

    McCarthy E.F., Khurana J.S., Zhang P.J.: Essentials in Bone and Soft-Tissue Pathology. Springer, New York (2009)

    Google Scholar 

  17. 17

    Mow V.C., Huiskes R.: Basic Orthopaedic Biomechanics and Mechano-biology. Lippincott Williams & Wilkins, Philadelphia (2005)

    Google Scholar 

  18. 18

    Mulder J., Wijk J., Liere R.: A survey of computational steering environments. Futur. Gener. Comput. Syst. 15(1), 119–129 (1999)

    Article  Google Scholar 

  19. 19

    Niggl, A., Rank, E., Mundani, R.P., Bungartz, H.J.: Organizing a p-Version finite element computation by an octree-based hierarchy. In: Proceedings of the International Conference on Adaptive Modeling and Simulation (2005)

  20. 20

    Parvizian J., Düster A., Rank E.: Finite cell method—h- and p-extension for embedded domain problems in solid mechanics. Comput. Mech. 41, 121–133 (2007)

    MathSciNet  Article  MATH  Google Scholar 

  21. 21

    Riedel, M., Frings, W., Eickermann, T.H., Habbinga, S., Gibbon, P., Mallmann, D., Streit, A., Wolf, F., Lippert, T.H.: Collaborative Interactivity in Parallel HPC Applications. Springer US (2010)

  22. 22

    Rietbergen B.V.: Computational strategies for iterative solutions of large FEM applications employing voxel data. Int. J. Numer. Methods Eng. 39, 2743–2764 (1996)

    Article  MATH  Google Scholar 

  23. 23

    Ruess, M., Tal, D., Trabelsi, N., Yosibash, Z., Rank, E.: The finite cell method for bone simulations: verification and validation. Biomech. Model. Mechanobiol., pp. 1–13 (2011). http://dx.doi.org/10.1007/s10237-011-0322-2

  24. 24

    Saha S., Roychowdhury A.: Application of the finite element method in orthopedic implant design. J. Long-term Eff. Med. Implant. 19[1], 55–82 (2009)

    Google Scholar 

  25. 25

    Schenk O., Gärtner K.: Solving unsymmetric sparse systems of linear equations with PARDISO. J. Futur. Gener. Comput. Syst. 20, 475–487 (2004)

    Article  Google Scholar 

  26. 26

    Schenk O., Gärtner K.: On fast factorization pivoting methods for symmetric indefinite systems. Electron. Trans. Numer. Anal. 23, 158–179 (2006)

    MathSciNet  MATH  Google Scholar 

  27. 27

    Schillinger, D., Rank, E.: An unfitted hp adaptive finite element method based on hierarchical B-splines for interface problems of complex geometry. Comput. Methods Appl. Mech. Eng. (submitted) (2011)

  28. 28

    Süli E., Mayers D.: An Introduction to Numerical Analysis. Cambridge University Press, Cambridge (2003)

    Google Scholar 

  29. 29

    Trabelsi N., Yosibash Z., Wutte C., Augat P., Eberle S.: Patient-specific finite element analysis of the human femu: a double-blinded biomechanical validation. J. Biomech. 44, 1666–1672 (2011)

    Article  Google Scholar 

  30. 30

    Verdonschot N., Huiskes R.: Mechanical effects of stem-cement interface characteristics in total hip replacement. Clin. Orthop. Relat. Res. 329, 326–336 (1996)

    Article  Google Scholar 

  31. 31

    Vetter, J., Schwan, K.: High performance computational steering of physical simulations. In: Proceedings of the 11th International Symposium on Parallel Processing, IPPS 97, pp. 128–132 (1997)

  32. 32

    Weinans H., Huiskes R.: Trends of mechanical consequence and modeling of a fibrous membrane around femoral hip prostheses. IEEE Comput. Sci. Eng. 23, 991–1000 (1990)

    Google Scholar 

  33. 33

    Wenisch P., van Treeck C., Borrmann A., Rank E., Wenisch O.: Computational steering on distributed systems: indoor comfort simulations as a case study of inter-active cfd on supercomputers. Int. J. Parallel Emergent Distrib. Syst. 22, 275–291 (2007)

    MathSciNet  Article  Google Scholar 

  34. 34

    Wolff J.: On the inner architecture of bones and its importance for bone growth. Clin. Orthop. Relat. Res. 468, 1056–1065 (2010)

    Article  Google Scholar 

  35. 35

    Yang, Z.: The finite cell method for geometry-based structural simulation. Ph.D. thesis, Computation in Engineering, Fakultät für Bauingenieur- und Vermessungswesen, Technische Universität München (2011)

  36. 36

    Yosibash Z., Padan R., Joscowicz L., Milgrom C.: A CT-based high-order finite element analysis of the human proximal femur compared to in-vitro experiments. ASME J. Biomech. Eng. 129, 297–309 (2007)

    Article  Google Scholar 

  37. 37

    Yosibash Z., Trabelsi N., Milgrom C.: Reliable simulations of the human proximal femur by high-order finite element analysis validated by experimental observations. J. Biomech. 40, 3688–3699 (2007)

    Article  Google Scholar 

Download references

Author information

Affiliations

Authors

Corresponding author

Correspondence to Stefan Kollmannsberger.

Additional information

Communicated by: Gabriel Wittum.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Yang, Z., Kollmannsberger, S., Düster, A. et al. Non-standard bone simulation: interactive numerical analysis by computational steering. Comput. Visual Sci. 14, 207–216 (2011). https://doi.org/10.1007/s00791-012-0175-y

Download citation

Keywords

  • Surgical planning
  • Computational steering
  • Finite cell method
  • Total hip replacement