Modeling & Planning Deniz Güven Needle Insertion

Outline Problem Definition Model Definition Path Planning Work Done – Needle Model Implementation – Path Planning Implementation Future Work & Contributions References Page 2/21

Problem Definition Needle insertion,one of the most widespread surgical techniques Critical aspect for many medical diagnoses, treatments Errors in needle targeting may reduce the effectiveness of diagnosis or treatment Targeting is challenging due to – lack of maneuverability in tissue, – limited vision – obstructions between the needle's entry point and the target Page 3/21

Problem Definition (cont'd) Kinematic models of needle steering are presented These models allow one to use many path planning techniques developed by the robotics community Judiciously chosen paths allows needles to – reach targets more accurately – reach small targets in locations that are inaccessible via straight trajectories Page 4/21

Model Definition The model is for a needle developed by Webster et al [1] with a rigid, homogeneous tissue Needle is a bevel-tip, flexible needle which bends while inserted into the tissue Fig.1. Bevel tip Page 5/21

Model Definition (cont'd) Bending is due to the asymmetric cutting forces arouse by bevel-tip asymmetry Fig.2a. Symmetric-tip needle cuts tissue in the direction that the tip is moving * Fig.2b. Bevel-tip needle cuts tissue at an angle * *Fig.2 is from [2] Page 6/21

Model Definition (cont'd) Bevel-tip needle is driven by two velocity inputs – insertion speed, – rotation speed actuated from the base of the needle Rotational input at the base causes needle to turn about its shaft Needle follows a circular arc with radius r = 1/k Fig.3.Bevel tip needle model* Page 7/21

Model Definition (cont'd) Fig.4. Single bend. Needle insertion is 23.5cm * Page 8/21

Model Definition (cont'd) Fig.5. Double bend, 8.3cm insertion– 180° spin – 16.7 cm insertion * * Fig.3, Fig.4 and Fig.5 are from [1] Page 9/21

Path Planning Rapidly-exploring Random Tree (RRT), an exploration algorithm to quickly search a workspace for possible paths Works efficiently with differential constraints and global constraints(obstacle boundaries and velocity bounds) Main Idea: – Initialize root of the tree with initial configuration – Incrementally grow the tree towards the unsearched area of the workspace by random sampling Page 10/21

Work Done: Model Implementation Rotation and insertion of the needle are not simultaneous Modeling is done in 2D Only two bevel rotations: – Bevel-right : 0 º – Bevel-left : 180 º Curvature k= with 95 % confidence interval of ± Page 11/21

Work Done: Model Implementation (cont'd) Fig.6. Single bend, bevel-right. Circular path is shown in blue dashes Page 12/21

Work Done: Model Implementation (cont'd) Fig.7. Double bend, Rotation changes from bevel-right to bevel left Page 13/21

Work Done: RRT Implementation Configuration: – bevel-rotation – tip angle – tip position Input: – Initial configuration of the needle – Target zone – Total number of trials to grow the tree Output: – Needle path with control parameters or null Page 14/21

Work Done: RRT Implementation (cont'd) Main Idea: – Root the tree at initial configuration – Grow the tree into free workspace until target is reached or total number of trials are reached Sampling: – Random samples from free space: 85% – Target zone and center: 10% and 5% Page 15/21

Work Done: RRT Implementation (cont'd) Demo 1 Page 16/21

Work Done: RRT Implementation (cont'd) Fig.7. Initial configuration (bevel-right,-30,(0,0) ) 9-bend path with bevel- rotations shown with red arrows Page 17/21

Work Done: RRT Implementation (cont'd) Demo 2 Page 18/21

Work Done: RRT Implementation (cont'd) Fig.8. Initial configuration (bevel-right,-30,(0,0) ) 5-bend path with bevel- rotations shown with red arrows Page 19/21

Future Work & Contributions Improvements for avoiding null outputs from RRT Periodic motion of the tissue Dynamic model for needle and tissue Homogeneous, soft tissue Page 20/21

References [1] R. J. Webster III, N. J. Cowan, G. Chirikjian, and A. M. Okamura. Nonholonomic modeling of needle steering. In Proceedings of 9 th International Symposium on Experimental Robotics, [2] Ron Alterovitz and Allison M. Okamura Ken Goldberg. Planning for steer-able bevel-tip needle insertion through 2d soft tissue with obstacles. In in Proc. IEEE Int. Conf. on Robotics and Automation, Page 21/21

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