Advertisement

Optimizing Clearance of Bézier Spline Trajectories for Minimally-Invasive Surgery

  • Johannes FauserEmail author
  • Igor Stenin
  • Julia Kristin
  • Thomas Klenzner
  • Jörg Schipper
  • Anirban Mukhopadhyay
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11768)

Abstract

Preoperative planning of nonlinear trajectories is a key element in minimally-invasive surgery. Interpolating between start and goal of an intervention while circumnavigating risk structures provides the necessary feasible solutions for such procedure. While recent research shows that Rapidly-exploring Random Trees (RRT) on Bézier Splines efficiently solve this task, access paths computed by this method do not provide optimal clearance to surrounding anatomy. We propose an approach based on sequential convex optimization that rearranges Bézier Splines computed by an RRT-connect, thereby achieving locally optimal clearance to risk structures. Experiments on real CT data of patients demonstrate the applicability of our approach on two scenarios: catheter insertion through the aorta and temporal bone surgery. We compare distances to risk structures along computed trajectories with the state of the art solution and show that our method results in clinically safer paths.

Keywords

Nonlinear trajectories Convex optimization RRT-connect 

References

  1. 1.
    Patil, S., Burgner, J., Webster, R.J., Alterovitz, R.: Needle steering in 3-d via rapid replanning. IEEE Trans. Rob. 30(4), 853–864 (2014)CrossRefGoogle Scholar
  2. 2.
    Fauser, J., Sakas, G., Mukhopadhyay, A.: Planning nonlinear access paths for temporal bone surgery. Int. J. Comput. Assist. Radiol. Surg. 13(5), 637–646 (2018)CrossRefGoogle Scholar
  3. 3.
    Patil, S., Pan, J., Abbeel, P., Goldberg, K.: Planning curvature and torsion constrained ribbons in 3d with application to intracavitary brachytherapy. IEEE Trans. Autom. Sci. Eng. 12(4), 1332–1345 (2015)CrossRefGoogle Scholar
  4. 4.
    Ganet, F., et al.: Development of a smart guide wire using an electrostrictive polymer: option for steerable orientation and force feedback. Sci. Rep. 5, 18593 (2015)CrossRefGoogle Scholar
  5. 5.
    Fichera, L., et al.: Through the eustachian tube and beyond: a new miniature robotic endoscope to see into the middle ear. IEEE Rob. Autom. Lett. 2(3), 1488–1494 (2017)CrossRefGoogle Scholar
  6. 6.
    Torres, R., Kazmitcheff, G., De Seta, D., Ferrary, E., Sterkers, O., Nguyen, Y.: Improvement of the insertion axis for cochlear implantation with a robot-based system. Eur. Arch. Oto-Rhino-Laryngol. 274(2), 715–721 (2017)CrossRefGoogle Scholar
  7. 7.
    Dahroug, B., Tamadazte, B., Weber, S., Tavernier, L., Andreff, N.: Review on otological robotic systems: Toward microrobot-assisted cholesteatoma surgery. IEEE Rev. Biomed. Eng. 11, 125–142 (2018)CrossRefGoogle Scholar
  8. 8.
    Burgner-Kahrs, J., Rucker, D.C., Choset, H.: Continuum robots for medical applications: a survey. IEEE Trans. Rob. 31(6), 1261–1280 (2015)CrossRefGoogle Scholar
  9. 9.
    Azizi, A., Tremblay, C., Martel, S.: Trajectory planning for vascular navigation from 3d angiography images and vessel centerline data. In: 2017 International Conference on Manipulation, Automation and Robotics at Small Scales (MARSS), pp. 1–6, July 2017Google Scholar
  10. 10.
    Duindam, V., Alterovitz, R., Sastry, S., Goldberg, K.: Skrew-based motion planning for bevel-tip flexible needles in 3D environments with obstacles. In: IEEE Int. Conference on Robotics and Automation, pp. 2483–2488, May 2008Google Scholar
  11. 11.
    Duan, Y., Patil, S., Schulman, J., Goldberg, K., Abbeel, P.: Planning locally optimal, curvature-constrained trajectories in 3D using sequential convex optimization. In: 2014 IEEE International Conference on Robotics and Automation, (ICRA), pp. 5889–5895, May 2014Google Scholar
  12. 12.
    Schulman, J., et al.: Motion planning with sequential convex optimization and convex collision checking. Int. J. Rob. Res. 33(9), 1251–1270 (2014)CrossRefGoogle Scholar
  13. 13.
    Trullo, R., Petitjean, C., Ruan, S., Dubray, B., Nie, D., Shen, D.: Segmentation of organs at risk in thoracic ct images using a sharpmask architecture and conditional random fields. In: 14th IEEE International Symposium on Biomedical Imaging, pp. 1003–1006 (2017)Google Scholar
  14. 14.
    Yang, K., Sukkarieh, S.: 3D smooth path planning for a uav in cluttered natural environments. In: 2008 IEEE/RSJ International Conference on Intelligent Robots and Systems, pp. 794–800, September 2008Google Scholar
  15. 15.
    Boyd, S., Vandenberghe, L.: Convex Optimization. Cambridge University Press, New York (2004)CrossRefGoogle Scholar
  16. 16.
    Valette, S., Chassery, J.M.: Approximated centroidal voronoi diagrams for uniform polygonal mesh coarsening. Comput. Graph. Forum. 23, 381–390 (2004)CrossRefGoogle Scholar
  17. 17.
    Fauser, J., et al.: Toward an automatic preoperative pipeline for image-guided temporal bone surgery. Int. J. Computer. Assist. Radiol. Surg. (2019)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Johannes Fauser
    • 1
    Email author
  • Igor Stenin
    • 2
  • Julia Kristin
    • 2
  • Thomas Klenzner
    • 2
  • Jörg Schipper
    • 2
  • Anirban Mukhopadhyay
    • 1
  1. 1.Department of Computer ScienceTechnische Universität DarmstadtDarmstadtGermany
  2. 2.Department of Oto-Rhino-LaryngologyDüsseldorf University HospitalDüsseldorfGermany

Personalised recommendations