Bone Reconstruction and Depth Control During Laser Ablation

  • Uri NahumEmail author
  • Azhar Zam
  • Philippe C. Cattin
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11404)


Cutting bones using laser light has been studied by several groups over the last decades. Yet, the risk of cutting nerves or soft tissues behind the bone is still an untackled problem. When performing tissue ablation such as bone, an acoustic signal is emitted. This paper presents a numerical framework that takes advantage of this acoustic signal to reconstruct not only the structure of the bone but also estimates the current cut position and depth. We employ an inverse problems approach to estimate the bone structure followed by an optimal control step to localize the position and depth of the signal source, i.e. the position of the cut. Besides the methodological description we also present numerical simulations in two dimensions with realistic mixed soft- and hard-tissue objects.


Inverse problems Optimal control Laser ablation Depth control 



This work has been part of the MIRACLE Project funded by the Werner Siemens Foundation, Zug/Switzerland.


  1. 1.
    Burgner, J., Müller, M., Raczkowsky, J., Wörn, H.: Ex vivo accuracy evaluation for robot assisted laser bone ablation. Int. J. Med. Robot. 6(4), 489–500 (2010). Scholar
  2. 2.
    Nguendon, H., et al.: Characterization of ablated porcine bone and muscle using laser-induced acoustic wave method for tissue differentiation. In: Lilge, L. (ed.) Proceedings of European Conferences on Biomedical Optics, Medical Laser Applications and Laser-Tissue Interactions VIII, vol. 10417, p. 104170N. SPIE (2017).
  3. 3.
    Nahum, U.: Adaptive eigenspace for inverse problems in the frequency domain. Ph.D. thesis, University of Basel, Switzerland (2016)Google Scholar
  4. 4.
    Haber, E., Ascher, U., Oldenburg, D.: On optimization techniques for solving nonlinear inverse problems. Inverse Probl. 16(5), 1263 (2000). Scholar
  5. 5.
    Nash, S.: A survey of truncated-Newton methods. J. Comput. Appl. Math. 124(1–2), 45–59 (2000). Scholar
  6. 6.
    Eisenstat, S., Walker, H.: Choosing the forcing terms in an inexact Newton method. SIAM J. Sci. Comput. 17(1), 16–32 (1996). Scholar
  7. 7.
    Métivier, L., Bretaudeau, F., Brossier, R., Operto, S., Virieux, J.: Full waveform inversion and the truncated Newton method: quantitative imaging of complex subsurface structures. Geophys. Prospect. 62(6), 1353–1375 (2014). Scholar
  8. 8.
    Grote, M., Kraym, M., Nahum, U.: Adaptive eigenspace method for inverse scattering problems in the frequency domain. Inverse Probl. 33(2), 025006 (2017). Scholar
  9. 9.
    de Buhan, M., Kray, M.: A new approach to solve the inverse scattering problem for waves: combining the TRAC and the adaptive inversion methods. Inverse Probl. 29(8), 085009 (2013). Scholar
  10. 10.
    Bayliss, A., Turkel, E.: Radiation boundary conditions for wave-like equations. Comm. Pure Appl. Math. 33(6), 707–725 (1980). Scholar
  11. 11.
    Engquist, B., Majda, A.: Absorbing boundary conditions for the numerical simulation of waves. Math. Comput. 31(139), 629–651 (1977). Scholar
  12. 12.
    Grote, M., Keller, J.: Nonreflecting boundary conditions for time-dependent scattering. J. Comput. Phys. 127(1), 52–65 (1996). Scholar
  13. 13.
    Chavent, G.: Nonlinear Least Squares for Inverse Problems. Springer, Heidelberg (1996). Scholar
  14. 14.
    Wirgin, A.: The inverse crime. arXiv:math-ph/0401050 (2004)
  15. 15.
    Operto, S., et al.: Efficient 3-D frequency-domain mono-parameter full-waveform inversion of ocean-bottom cable data: application to Valhall in the visco-acoustic vertical transverse isotropic approximation. Geophys. J. Int. 202(2), 1362–1391 (2015). Scholar

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of Biomedical EngineeringUniversity of BaselBaselSwitzerland

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