Orthotropic Thin Shell Elasticity Estimation for Surface Registration

  • Qingyu Zhao
  • Stephen Pizer
  • Ron Alterovitz
  • Marc Niethammer
  • Julian Rosenman
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10265)

Abstract

Elastic physical models have been widely used to regularize deformations in different medical object registration tasks. Traditional approaches usually assume uniform isotropic tissue elasticity (a constant regularization weight) across the whole domain, which contradicts human tissue elasticity being not only inhomogeneous but also anisotropic. We focus on producing more physically realistic deformations for the task of surface registration. We model the surface as an orthotropic elastic thin shell, and we propose a novel statistical framework to estimate inhomogeneous and anisotropic shell elasticity parameters only from a group of known surface deformations. With this framework we show that a joint estimation of within-patient surface deformations and the shell elasticity parameters can improve groupwise registration accuracy. The method is tested in the context of endoscopic reconstruction-surface registration.

Notes

Acknowledgement

This work was supported by NIH grant R01 CA158925. We thank Dr. Bhisham Chera from the Department of Radiation Oncology for providing the endoscopy data.

References

  1. 1.
    Bajcsy, R., Kovačič, S.: Multiresolution elastic matching. Comput. Vis. Graph. Image Process. 46(1), 1–21 (1989)CrossRefGoogle Scholar
  2. 2.
    Christensen, G., Rabbitt, R., Miller, M.: Deformable templates using large deformation kinematics. Comput. Vis. Graph. Image Process. 5(10), 1435–1447 (1996)Google Scholar
  3. 3.
    Thirion, J.: Image matching as a diffusion process: an analogy with Maxwells demons. Med. Image Anal. 2(3), 243–260 (1998)CrossRefGoogle Scholar
  4. 4.
    Beg, M., Miller, M., Trouvé, A., Younes, L.: Computing large deformation metric mappings via geodesic flows of diffeomorphisms. Int. J. Comput. Vis. 61(2), 139–157 (2005)CrossRefGoogle Scholar
  5. 5.
    Miga, M.: A new approach to elastography using mutual information and finite elements. Phys. Med. Biol. 48(4), 467–480 (2003)CrossRefGoogle Scholar
  6. 6.
    Kroon, M., Holzapfel, G.A.: Estimation of the distributions of anisotropic, elastic properties and wall stresses of saccular cerebral aneurysms by inverse analysis. Proc. R. Soc. Lond. A: Math. Phys. Eng. Sci. 464(2092), 807–825 (2008)MathSciNetCrossRefMATHGoogle Scholar
  7. 7.
    Schneider, R., Faust, G., Hindenlang, U., Helwig, P.: Inhomogeneous, orthotropic material model for the cortical structure of long bones modeled on the basis of clinical CT or density data. Comput. Methods Appl. Mech. Eng. 198(27–29), 2167–2174 (2009)CrossRefMATHGoogle Scholar
  8. 8.
    Yang, S., Jojic, V., Lian, J., Chen, R., Zhu, H., Lin, M.C.: Classification of prostate cancer grades and t-stages based on tissue elasticity using medical image analysis. In: Ourselin, S., Joskowicz, L., Sabuncu, M.R., Unal, G., Wells, W. (eds.) MICCAI 2016. LNCS, vol. 9900, pp. 627–635. Springer, Cham (2016). doi:10.1007/978-3-319-46720-7_73 CrossRefGoogle Scholar
  9. 9.
    Freiman, M., Voss, S.D., Warfield, S.K.: Demons registration with local affine adaptive regularization: application to registration of abdominal structures. In: IEEE International Symposium on Biomedical Imaging, pp. 1219–1222 (2011)Google Scholar
  10. 10.
    Gerig, T., Shahim, K., Reyes, M., Vetter, T., Lüthi, M.: Spatially varying registration using gaussian processes. In: Golland, P., Hata, N., Barillot, C., Hornegger, J., Howe, R. (eds.) MICCAI 2014. LNCS, vol. 8674, pp. 413–420. Springer, Cham (2014). doi:10.1007/978-3-319-10470-6_52 Google Scholar
  11. 11.
    Vialard, F.-X., Risser, L.: Spatially-varying metric learning for diffeomorphic image registration: a variational framework. In: Golland, P., Hata, N., Barillot, C., Hornegger, J., Howe, R. (eds.) MICCAI 2014. LNCS, vol. 8673, pp. 227–234. Springer, Cham (2014). doi:10.1007/978-3-319-10404-1_29 Google Scholar
  12. 12.
    Davatzikos, C.: Spatial transformation and registration of brain images using elastically deformable models. Comput. Methods Appl. Mech. Eng. 66(2), 207–222 (1997)Google Scholar
  13. 13.
    Alterovitz, R., Goldberg, K., Pouliot, J., Hsu, I.C.J., Kim, Y., Noworolski, S.M., Kurhanewicz, J.: Registration of MR prostate images with biomechanical modeling and nonlinear parameter estimation. Med. Phys. 33(2), 446–454 (2006)CrossRefGoogle Scholar
  14. 14.
    Misra, S., Ramesh, R., Okamura, A.: Modelling of non-linear elastic tissues for surgical simulation. Comput. Methods Appl. Mech. Eng. 13(6), 811–818 (2010)Google Scholar
  15. 15.
    Green, M., Geng, G., Qin, E., Sinkus, R., Gandevia, S., Bilston, L.: Measuring anisotropic muscle stiffness properties using elastography. NMR Biomed. 26(11), 1387–1394 (2013)CrossRefGoogle Scholar
  16. 16.
    Risholm, P., Ross, J., Washko, G.R., Wells, W.M.: Probabilistic elastography: estimating lung elasticity. In: Székely, G., Hahn, H.K. (eds.) IPMI 2011. LNCS, vol. 6801, pp. 699–710. Springer, Heidelberg (2011). doi:10.1007/978-3-642-22092-0_57 CrossRefGoogle Scholar
  17. 17.
    Bauer, M., Bruveris, M., Michor, P.W.: Overview of the geometries of shape spaces and diffeomorphism groups. J. Math. Imaging Vis. 50(1), 60–97 (2014)MathSciNetCrossRefMATHGoogle Scholar
  18. 18.
    Schulz, J., Pizer, S.M., Marron, J., Godtliebsen, F.: Nonlinear hypothesis testing of geometrical object properties of shapes applied to Hippocampi. J. Math. Imaging Vis. 54(1), 15–34 (2015)CrossRefMATHGoogle Scholar
  19. 19.
    Ventsel, E., Krauthammer, T.: Thin Plates and Shells: Theory: Analysis, and Applications. CRC Press, Boca Raton (2001)CrossRefGoogle Scholar
  20. 20.
    Gingold, Y., Secord, A., Han, J.Y., Grinspun, E., Zorin, D.: A discrete modelfor inelastic deformation of thin shells. Technical report, Courant Institute of Mathematical Sciences (2004)Google Scholar
  21. 21.
    Zhao, Q., Price, J.T., Pizer, S., Niethammer, M., Alterovitz, R., Rosenman, J.: Surface registration in the presence of topology changes and missing patches. In: Medical Image Understanding and Analysis, pp. 8–13 (2015)Google Scholar
  22. 22.
    Arsigny, V., Fillard, P., Pennec, X., Ayache, N.: Log-euclidean metrics for fast and simple calculus on diffusion tensors. Phys. Med. Biol. 56(2), 411–421 (2006)Google Scholar
  23. 23.
    Crane, K., Desbrun, M., Schröder, P.: Trivial connections on discrete surfaces. In: Symposium on Geometry Processing, vol. 29 (2010)Google Scholar
  24. 24.
    Zhao, Q., Price, T., Pizer, S., Niethammer, M., Alterovitz, R., Rosenman, J.: The endoscopogram: a 3D model reconstructed from endoscopic video frames. In: Ourselin, S., Joskowicz, L., Sabuncu, M.R., Unal, G., Wells, W. (eds.) MICCAI 2016. LNCS, vol. 9900, pp. 439–447. Springer, Cham (2016). doi:10.1007/978-3-319-46720-7_51 CrossRefGoogle Scholar
  25. 25.
    Price, T., Zhao, Q., Rosenman, J., Pizer, S., Frahm, J.M.: Shape from motion and shading in uncontrolled environments. Technical report, Department of Computer Science, University of North Carolina at Chapel Hill (2016)Google Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Qingyu Zhao
    • 1
  • Stephen Pizer
    • 1
    • 2
  • Ron Alterovitz
    • 1
  • Marc Niethammer
    • 1
  • Julian Rosenman
    • 1
    • 2
  1. 1.Computer ScienceUNC Chapel HillChapel HillUSA
  2. 2.Radiation OncologyUNC Chapel HillChapel HillUSA

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