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Visiting a Sequence of Points with a Bevel-Tip Needle

Conference paper
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Part of the Lecture Notes in Computer Science book series (LNCS, volume 6034)

Abstract

Many surgical procedures could benefit from guiding a bevel-tip needle along circular arcs to multiple treatment points in a patient. At each treatment point, the needle can inject a radioactive pellet into a cancerous region or extract a tissue sample. Our main result is an algorithm to steer a bevel-tip needle through a sequence of treatment points in the plane while minimizing the number of times that the needle must be reoriented. This algorithm is related to [6] and takes quadratic time when consecutive points in the sequence are sufficiently separated. We can also guide a needle through an arbitrary sequence of points in the plane by accounting for a lack of optimal substructure.

Keywords

Needle Steering Link Distance Brachytherapy Biopsy 

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References

  1. 1.
    Agarwal, P.K., Biedl, T., Lazard, S., Robbins, S., Suri, S., Whitesides, S.: Curvature-constrained shortest paths in a convex polygon. In: 14th Symposium on Computational Geometry (SoCG), pp. 392–401 (1998)Google Scholar
  2. 2.
    Alterovitz, R., Branicky, M., Goldberg, K.: Motion planning under uncertainty for image-guided medical needle steering. International Journal of Robotics Research 27(1361) (2008)Google Scholar
  3. 3.
    Alterovitz, R., Goldberg, K., Okamura, A.: Planning for steerable bevel-tip needle insertion through 2d soft tissue with obstacles. In: IEEE International Conference on Robotics and Automation, pp. 1640–1645 (2005)Google Scholar
  4. 4.
    Bereg, S., Kirkpatrick, D.: Curvature-bounded traversals of narrow corridors. In: 21st Symposium on Computational Geometry (SoCG), pp. 278–287 (2005)Google Scholar
  5. 5.
    Cook IV, A.F., Wenk, C.: Link distance and shortest path problems in the plane. In: Goldberg, A.V., Zhou, Y. (eds.) AAIM 2009. LNCS, vol. 5564, pp. 140–151. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  6. 6.
    Dror, M., Efrat, A., Lubiw, A., Mitchell, J.S.B.: Touring a sequence of polygons. In: 35th ACM Symposium on Theory of Computing (STOC), pp. 473–482 (2003)Google Scholar
  7. 7.
    Dubins, L.E.: On curves of minimal length with a constraint on average curvature, and with prescribed initial and terminal positions and tangents. American Journal of Mathematics 79(3), 497–516 (1957)zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Duindam, V., Xu, J., Alterovitz, R., Sastry, S., Goldberg, K.: 3d motion planning algorithms for steerable needles using inverse kinematics. In: Eighth International Workshop on Algorithmic Foundations of Robotics, WAFR (2008)Google Scholar
  9. 9.
    Maheshwari, A., Sack, J.-R., Djidjev, H.N.: Link distance problems. In: Handbook of Computational Geometry (1999)Google Scholar
  10. 10.
    Mitchell, J.S.B., Rote, G., Woeginger, G.J.: Minimum-link paths among obstacles in the plane. In: 6th Symposium on Computational Geometry (SoCG), pp. 63–72 (1990)Google Scholar
  11. 11.
    Xu, J., Duindam, V., Alterovitz, R., Goldberg, K.: Motion planning for steerable needles in 3d environments with obstacles using rapidly-exploring random trees and backchaining. In: IEEE Conference on Automation Science and Engineering, CASE (2008)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  1. 1.Department of Computer ScienceUniversity of Texas at DallasRichardsonUSA
  2. 2.Department of Computer ScienceUniversity of Texas at San AntonioSan AntonioUSA

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