CS 326 A: Motion Planning Radiosurgical Planning

Radiosurgery Tumor = bad Brain = good Critical structures = good and sensitive Minimally invasive procedure that uses an intense, focused beam of radiation as an ablative surgical instrument to destroy tumors

The Radiosurgery Problem Dose from multiple beams is additive

Treatment Planning for Radiosurgery Determine a set of beam configurations that will destroy a tumor by cross- firing at it Constraints: –Desired dose distribution –Physical properties of the radiation beam –Constraints of the device delivering the radiation –Duration/fractionation of treatment Critical Tumor

Conventional Radiosurgical Systems Isocenter-based treatments Stereotactic frame required Luxton et al., 1993 Winston and Lutz, 1988 LINAC System Gamma Knife

Isocenter-Based Treatments All beams converge at the isocenter The resulting region of high dose is spherical Nonspherically shaped tumors are approximated by multiple spheres –“Hot Spots” where the spheres overlap –“Cold Spots” where coverage is poor –Over-irradiation of healthy tissue

Stereotactic Frame for Localization Painful Fractionation of treatments is difficult Treatment of extracranial tumors is impossible

Optimization Approach to Planning Treatment planning variables: –Isocenter locations –Treatment arcs –Collimator diameter –Beam weights User specifies most planning variables User defines constraints on dose to points and optimization function Optimization technique determines beam weights [Bahr, 1968; Langer et al. 1987; Webb, 1992; Carol et al., 1992; Xing et al., 1998, …]

Motion-Planning Approach Configuration space of the beam is a unit sphere Construct free space by projecting critical structures onto the sphere Search for longest arcs in free space Critical Structure Construction of free space [Schweikard, Adler, and Latombe, 1992, 1993]

Conformal Dose Distributions

The CyberKnife linear accelerator robotic gantry X-Ray cameras

Treatment Planning Becomes More Difficult Much larger solution space –Beam configuration space has greater dimensionality –Number of beams can be much larger –More complex interactions between beams Path planning –Avoid collisions –Do not obstruct X-ray cameras  Automatic planning required (CARABEAMER)

Inputs to CARABEAMER (1) Regions of Interest: Surgeon delineates the regions of interest CARABEAMER generates 3D regions

Inputs to CARABEAMER (2) Dose Constraints: (3) Maximum number of beams Critical Tumor Dose to tumor Falloff of dose around tumor Falloff of dose in critical structure Dose to critical structure

Basic Problem Solved by CARABEAMER Given: –Spatial arrangement of regions of interest –Dose constraints for each region: a  D  b –Maximum number of beams allowed: N (~ ) Find: –N beam configurations (or less) that generate dose distribution that meets the constraints.

Position and orientation of the radiation beam Amount of radiation or beam weight Collimator diameter Beam Configuration x y z   (x, y)   Find 6N parameters that satisfy the constraints

CARABEAMER’s Approach 1.Initial Sampling: Generate many (> N) beams at random, with each beam having a reasonable probability of being part of the solution. 2.Weighting: Use linear programming to test whether the beams can produce a dose distribution that satisfies the input constraints. 3.Iterative Re-Sampling: Eliminate beams with small weights and re-sample more beams around promising beams. 4.Iterative Beam Reduction: Progressively reduce the number of beams in the solution.

Initial Beam Sampling Generate even distribution of target points on the surface of the tumor Define beams at random orientations through these points

Evenly Spacing Target Points on Tumor Turk [1992] Normally distribute points on tumor surface Use potential field to better distribute points

Deterministic Beam Selection is Less Robust

Curvature Bias Place more target points in regions of high curvature

Dose Distribution Before Beam Weighting 50% Isodose Surface 80% Isodose Surface

CARABEAMER’s Approach 1.Initial Sampling: Generate many (> N) beams at random, with each beam having a reasonable probability of being part of the solution. 2.Weighting: Use linear programming to test whether the beams can produce a dose distribution that satisfies the input constraints. 3.Iterative Re-Sampling: Eliminate beams with small weights and re-sample more beams around promising beams. 4.Iterative Beam Reduction: Progressively reduce the number of beams in the solution.

Beam Weighting Assign constraints to each cell of the arrangement: –Tumor constraints –Critical constraints Construct geometric arrangement of regions formed by the beams and the tissue structures T C B1 B2 B3 B4

Linear Programming Problem 2000  Tumor   B2 + B4   B4   B3 + B4   B3   B1 + B3 + B4   B1 + B4   B1 + B2 + B4   B1   B1 + B2   Critical   B2  500 T C B1 B2 B3 B4 T

Elimination of Redundant Constraints 2000 < Tumor < < B2 + B4 < < B4 < < B3 + B4 < < B3 < < B1 + B3 + B4 < < B1 + B4 < < B1 + B2 + B4 < < B1 < < B1 + B2 < < Tumor < < B < B3 B1 + B3 + B4 < 2200 B1 + B2 + B4 < < B < B2 + B < B4 B2 + B4 < 2200 B1 + B2 + B4 < 2200

Results of Beam Weighting Before WeightingAfter Weighting 50% Isodose Curves 80% Isodose Curves

CARABEAMER’s Approach 1.Initial Sampling: Generate many (> N) beams at random, with each beam having a reasonable probability of being part of the solution. 2.Weighting: Use linear programming to test whether the beams can produce a dose distribution that satisfies the input constraints. 3.Iterative Re-Sampling: Eliminate beams with small weights and re-sample more beams around promising beams. 4.Iterative Beam Reduction: Progressively reduce the number of beams in the solution.

Iterative Re-Sampling The initial set of beam may not contain a solution. Find the best possible solution Keep beams that are useful Remove beams that are not useful Re-sample

A linear program is typically specified as: Minimize: c 1 x 1 + c 2 x c n x n Subject to: l 1  a 1,1 x 1 +a 1,2 x a 1,n x n  u 1 l 2  a 2,1 x 1 +a 2,2 x a 2, n x n  u 2 l m  a m,1 x 1 +a m,2 x a m, n x n  u m Reformulating the LP Problem …......

Using slack variables, we can rewrite this: Minimize: c 1 x 1 + c 2 x c n x n Subject to: a 1,1 x 1 + a 1,2 x a 1,n x n + s 1 =0, -u 1  s 1  -l 1 a 2,1 x 1 + a 2,2 x a 2,n x n + s 2 =0,-u 2  s 2  -l 2 a m,1 x 1 + a m,2 x a m,n x n + s m = 0,-u m  s m  -l m......

New slacks  1, …,  m : Minimize: Minimize: |  1 | + |  2 | |  m | Subject to: a 1,1 x 1 + a 1,2 x a 1,n x n + s 1 +  1 = 0,-u 1  s 1  -l 1 a 2,1 x 1 + a 2,2 x a 2,n x n +s 2 +  2 =0,-u 2  s 2  -l 2 a m,1 x 1 + a m,2 x a m,n x n + s m +  m = 0,-u m  s m  -l m … to Solve for the Best Possible Solution The idea is to minimize the sum of the infeasibilities

Re-Sampling Step Repeat until the constraints are met: 1.Run linear program to find closest possible solution 2.If some slack variables  1, …,  m  0 Eliminate beams with low weights Replace them with new beams: –Randomly generate beams in neighborhood of highly weighted beams –Randomly generate beams according to initial algorithm

CARABEAMER’s Approach 1.Initial Sampling: Generate many (> N) beams at random, with each beam having a reasonable probability of being part of the solution. 2.Weighting: Use linear programming to test whether the beams can produce a dose distribution that satisfies the input constraints. 3.Iterative Re-Sampling: Eliminate beams with small weights and re-sample more beams around promising beams. 4.Iterative Beam Reduction: Progressively reduce the number of beams in the solution.

Re-Sampling to Reduce Total # of Beams Repeat until dose constraints are met with specified number N of beams: 1.If too many beams in the solution: Eliminate beams with low weights Generate smaller number of beams 2.If no solution: Add more beams

Plan Review Calculate resulting dose distribution Radiation oncologist reviews If satisfactory, treatment can be delivered If not... –Add new constraints –Adjust existing constraints

Treatment Planning: Extensions Simple path planning and collision avoidance Automatic collimator selection Better dosimetry model Critical Tumor

Evaluation on Sample Case Linac plan 80% Isodose surface CARABEAMER ’s plan 80% Isodose surface

Another Sample Case 50% Isodose Surface 80% Isodose Surface LINAC plan CARABEAMER’s plan

Evaluation on Synthetic Data X 2000  D T  2400, D C   D T  2200, D C   D T  2100, D C  500 XX 10 random seeds n = 500 n = 250 n = 100 Beam Iteratio n Constraint Iteration X

Dosimetry Results 80% Isodose Curve90% Isodose Curve80% Isodose Curve90% Isodose Curve 80% Isodose Curve90% Isodose Curve80% Isodose Curve90% Isodose Curve Case #1Case #2 Case #3Case #4

Average Run Times n = 500 n = 250 n = n = 500 n = 250 n = :20:20:35:32:29:43:01:34:01:28:02:21:41:40:51:50:59:01:02:01:41:01:31:02:38:03:30:03:32:04:28:05:50:05:50:08:53:48:54:40:491:57:25:05:23:05:33:07:19:08:37:08:42:10:43:27:39:24:431:02:27:04:36:04:11:05:03:23:51:24:44:33:023:26:333:22:157:44:57:06:45:07:19:07:06:13:05:12:16:21:061:03:061:07:125:06:293:06:123:09:193:35:2825:38:3627:55:1853:58:561:40:551:44:181:41:196:33:027:11:01176:25:0244:11:0484:21:27 Case 1 Beam Constr Case 2 Beam Constr Case 3 Beam Constr Case 4 Beam Constr

Evaluation on Prostate Case 50% Isodose Curve70% Isodose Curve

Contact Stanford Report Contact Stanford Report News Service News Service / Press Releases Press Releases Stanford Report, July 25, 2001 Patients gather to praise minimally invasive technique used in treating tumors By MICHELLE BRANDT When Jeanie Schmidt, a critical care nurse from Foster City, lost hearing in her left ear and experienced numbing in her face, she prayed that her first instincts were off. “I said to the doctor, `I think I have an acoustic neuroma (a brain tumor), but I'm hoping I'm wrong. Tell me it's wax, tell me it's anything,'” Schmidt recalled. It wasn't wax, however, and Schmidt – who wound up in the Stanford Hospital emergency room when her symptoms worsened – was quickly forced to make a decision regarding treatment for her tumor. On July 13, Schmidt found herself back at Stanford – but this time with a group of patients who were treated with the same minimally invasive treatment that Schmidt ultimately chose: the CyberKnife. She was one of 40 former patients who met with Stanford faculty and staff to discuss their experiences with the CyberKnife – a radiosurgery system designed at Stanford by John Adler Jr., MD, in 1994 for performing neurosurgeries without incisions. “I wanted the chance to thank everyone again and to share experiences with other patients,” said Schmidt, who had the procedure on June 20 and will have an MRI in six months to determine its effectiveness. “I feel really lucky that I came along when this technology was around.” The CyberKnife is the newest member of the radiosurgery family. Like its ancestor, the 33-year-old Gamma Knife, the CyberKnife uses 3-D computer targeting to deliver a single, large dose of radiation to the tumor in an outpatient setting. But unlike the Gamma Knife – which requires patients to wear an external frame to keep their head completely immobile during the procedure – the CyberKnife can make real-time adjustments to body movements so that patients aren't required to wear the bulky, uncomfortable head gear. Since January 1999, more than 335 patients have been treated at Stanford with the CyberKnife The procedure provides patients an alternative to both difficult, risky surgery and conventional radiation therapy, in which small doses of radiation are delivered each day to a large area. The procedure is used to treat a variety of conditions – including several that can't be treated by any other procedure – but is most commonly used for metastases (the most common type of brain tumor in adults), meningomas (tumors that develop from the membranes that cover the brain), and acoustic neuromas. Since January 1999, more than 335 patients have been treated at Stanford with the CyberKnife. Cyberknife Systems

Motion Planning Where Are We? Where Do We Go From Here?

Where Are We?  Two main families of methods: - Probabilistic sampling (PRM)  Widely applicable, easy to implement, but remaining shortcomings - Criticality-based decomposition  Low-dimensional spaces, harder to implement  Diverse problems have been studied: - Basic path planning - Dynamic, kinodynamic, stability, visibility constraints - Uncertainty (no much success)  Some applications: - GE: Disassembly planning for the maintenance of aircraft engines - Delmia: Graphic environment for robot programming - Accuray: Radiosurgical planning - Softimage: Animation of digital actors - Kineo: Transportation of Airbus 800 fuselage

Where Do We Go From Here?  More complex constraints, e.g., aesthetics

Where Do We Go From Here?  More complex constraints, e.g., aesthetics  Dealing with deformable objects

Where Do We Go From Here?  More complex constraints, e.g., aesthetics  Dealing with deformable objects  Thousands of DoFs and more …

Where Do We Go From Here?  More complex constraints, e.g., aesthetics  Dealing with deformable objects  Thousands of DoFs and more …  Better understanding of underlying theoretical problems: - Mathematical structure/geometry of configuration, state, motion, … spaces - Impact of constraints (e.g., kinodynamics, aesthetics) on connectivity - Combination of criticality-based and sampling methods

Most existing motion planning techniques have been motivated by robotics applications. Robotics will remain important, but future progress in motion planning will be increasingly motivated by non-robotics applications, e.g., navigation in virtual worlds, digital actors, surgical planning, logistics, etc….