Rigid Needles, Steerable Needles, and Optimal Beam Algorithms

1. Rigid Needles, Steerable Needles, and Optimal Beam Algorithms Ovidiu Daescu Bio-Medical Computing Laboratory Department of Computer Science University of Texas at Dallas (Joint work with Yam Ki Cheung and Anastasia Kurdia)

2. Needles (who likes them?) φ • Rigid needle: cannot bend • Steerable needle: can bend • State of needle described by tip position, orientation, and bevel direction

3. Steerable needles φ The state of the needle is described by tip position, tip orientation, bevel direction Composed of a highly flexible material, with a bevel tip Offers greater mobility compared to rigid needles for minimally invasive medical procedures. Needle traces out a curve path inside the tissue. Rotating the base, the needle can be steered to avoid vital organs.

5. Rigid Needle: Optimal Directions

6. Optimal Directions

7. Optimal Direction in Radiation Therapy

8. Weighted subdivisions

9. Weighted Distance Metric s p a b t ||ab||=|ab|wi ||p||=∑|p∩Ri|wi

10. Cases • Optimal directions in weighted regions • Optimal link in weighted regions • k-link minimum cost paths • Steerable needle paths • Most results in 2D, some extend to 3D

11. Optimal Direction L L T T The line L “probes” R The line L “penetrates” R

12. Optimal Link S L T An optimal link problem between a source S and a target T.

13. Optimal Direction/Link -width   L L T T The line L “probes” R The line L “penetrates” R

14. Optimal Direction – Strip Cover L T

15. Optimal Direction – Cone Cover T

16. K-Link Minimum Cost Path A 9-link path. A 4-link path.

17. The LinkSolver Software

18. Property 2D: Optimal link goes through a vertex T

19. Property 2D: Optimal link goes through a vertex  T

20. 1D Problems • In ray space • Much faster to solve than 2D optimization problems v T

21. A subproblem at v • 1D optimization • The objective function is “not nice” • Can approximate optimal solution • do this for all subproblems at v • prune-and-search: fast in practice • Can model it as a 2D linear objective function problem • use SOLF algorithm v T

22. Extend to 3D • Optimal ray • Goes through vertex • Goes through two edges  2D optimization problems! v

23. How to handle 3D ? • Get many 2D slices • Automatically • As suggested by expert

24. Steerable Needle: Overview Minimally invasive surgical techniques have been highly successful in improving patient care, reducing risk of infection, and decreasing recovery times and treatment costs. A thin flexible needle, inserted into the human body and steered them from outside. Can reach targets inaccessible to traditional stiff needles One of the ways to reduce invasiveness of radiotherapy, biopsy collection, other procedures.

25. Treatment plan • The position of the needle depends on • Original insertion angle • Ability of the needle to bend • The number of rotations performed and angle of each rotation • Bending of the needle depends on physical properties of the needle and the environment • A treatment plan would consist of initial insertion point and orientation and a sequence of rotations

26. Problems with steerable needles • Rotation at the base does not directly correspond to the rotation at the needle tip • More rotations result in larger deviation of the actual position of the needle tip from the predicted position • The tissue experiences deformation Implications: • A desired treatment plan should minimize the number of rotation to minimize the error • It should also avoid or minimize damage to vital organs

27. Algorithmic goals Design algorithms to compute optimal treatment plans Create computer simulations and visualization of the interaction between the needle and the human tissue to aid the surgeons in planning the procedures.

28. Preliminary work Can characterize the number of rotations and compute treatment plan in absence of obstacles in 2D and 3D Given a target, the minimum number of rotations required to reach the target can be found fast

29. Work in progress Compute the optimal path in the presence of polygonal obstacles

30. Current (competing) projects • Laboratory for Computational Sensing and Robotics at Johns Hopkins University • “Steering Flexible Needles in Soft Tissue“ • Funding: NSF • Focus on probabilistic methods of computing trajectory.

31. Current (competing) projects Medical Robotics Technology Center at Carnegie Mellon University “Needle Steering for Brain Surgery” Funding: The Pittsburgh Foundation, NSF Searching for optimal physical properties of the needle Showed that constantly spinning the needle during insertion makes the needle move in straight line

32. Current projects • Laboratory for Biomedical Computing at UTD and UTSW research groups? • Preliminary work started with Lech Papiez’s group • Funding: ? • Focus on deterministic methods.

33. Main Goal: Handle 3D • Want real time solutions • Use multiple 2D slices (hundreds) • Independent problems in each slice • Solve in parallel on a cluster of computers • Business model: outsource computation • Data at UTSW • Computing cluster at UTD • Transfer anonimous data (random ID)