Planning Curvature and Torsion Constrained Ribbons for Intracavitary Brachytherapy Sachin Patil, Jia Pan, Pieter Abbeel, Ken Goldberg UC Berkeley EECS

Cancer Sites

Brachytherapy Internal radiation therapy – Radioactive source travels in catheters to tumor vicinity Intracavitary Brachytherapy

Limitations of current treatment options: Lack of proximity to tumor  Insufficient radiation to tumor volume Undesirable radiation exposure to healthy tissue Patient discomfort, no personalization

Tumor Coverage Standard approachNew approach Multiple dose locations desired proximal to tumor

3D Printing Stratasys uPrint SE Plus 3D Systems ProJET HD D Printed Implant [Garg et al. 2013]

Customized 3D Printed Implants [Garg et al. 2013]

Channel Constraints Curvature constraints: Finite dimensions of radioactive seed Limited flexibility of catheters Extraction of support material

Independent Channels Infeasible for larger number of dose locations Mutually collision free Constraints on local/cumulative curvature

Ribbons

Improved arrangement  Improved coverage How do we create these implants?

Ribbon Kinematic Model Consider ribbon cross-section: Orient ribbon cross-section along binormal of Frenet-Serret frame [Frenet 1847; Serret 1851]

Ribbon Kinematic Model Frenet-Serret equations: Some manipulation yields:

Ribbon Kinematic Model This gives the following model:Planning parameters: : speed : curvature : torsion

Why Frenet-Serret Frame? Different curvatures, lengths: Difficult to plan for Same curvatures, lengths: Easier to plan for

Problem Specification Input: Implant volume conforming to patient anatomy from CT/MR scans Dose dwell segment poses Parameters of catheter and radioactive source  channel width, curvature and torsion limits

Problem Specification Objective: Compute ribbons such that: Curvature and torsion constrained Optimal – minimize energy Mutually collision-free

Related Work Planning rigid body motions in SE(3) without obstacles: Zefran et al. 1998; Belta et al. 2004; Goemans et al. 2005; Biggs et al. 2008; Cripps et al. 2012; etc. Planning using physically-based models of curves/ribbons: Moll et al. 2006; Bretl et al. 2014; etc. Planning for bevel-tip steerable needles: Alterovitz et al. 2006,2007; Hauser et al. 2009; Xu et al. 2009; Duindam et al. 2010; Van den Berg et al. 2010; Patil et al. 2012; etc.

Planning Challenges Nonholonomic systemCollision avoidance

Planning Approach Two steps: Sequential: Rapidly-exploring random trees (RRT) in SE(3) state space Simultaneous: Local optimization using sequential quadratic programming (SQP)

RRT Planner a b Sample random point in R 3 Find nearest tree node that contains sample within reachable set Connect Add new node and edge to tree Repeat till goal found or maximum iterations exceeded Collision detection a entry dose dwell segment For each dose dwell segment: [Patil et al. 2012; Garg et al. 2013]

RRT Limitations Non-smooth ribbons; unnecessary twists No notion of optimality

(Simultaneous) Local Optimization Optimization variables: Minimize energy (rotational strain) : subject to Entry / initial pose constraint Kinematic constraints Bounds on curvature/torsion Collision constraints [Schulman et al. 2013]

Optimization on SE(3) SE(3) is not a vector space: Locally parameterize SE(3) through its tangent space se(3)

Optimization on SE(3) 1)Seed trajectory: 2) Solve: where and 3)Compute new trajectory: [Saccon et al. 2013]

RRT + Local Optimization Two steps: Sequential: Rapidly-exploring random trees (RRT) in SE(3) state space Simultaneous: Local optimization using sequential quadratic programming (SQP)

RRT + Local Optimization

Intracavitary Brachytherapy Scenario RRT: Collision-free ribbons; unnecessary twists RRT + Local optimization: final solution

Intracavitary Brachytherapy Scenario 46% improvement in coverage (metric as defined by Garg et al. 2013) Limited to 18 channelsCan include up to 36 channels

Performance [single 3.5 Ghz Intel i7 processor]

Address global optimality of solutions [Bento et al. NIPS 2013s] Automatic computation of dose dwell segments Clinical studies (UC San Francisco Medical Center) Future Work

Ribbons – Planning Applications

Source available at: Thank You Contact:

Narrow Passage Scenario No probabilistic completeness guarantees

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