Managing uncertainty using robust optimization

Timothy ChanUniversity of Toronto

BIRS radiation therapy workshopMarch 12, 2011

Overview

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• Uncertainty in radiation therapy

• Methods to manage uncertainty– Robust optimization

• Areas for further research

“Top 10 Health Technology Hazards for 2011” by ERCI Institute

1. Radiation overdose and other dose errors during radiation therapy*

2. Alarm hazards

3. Cross-contamination from flexible endoscopes

4. The high radiation dose of CT scans

5. Data loss, system incompatibilities, and other health IT complications

6. Luer misconnections

7. Oversedation during use of PCA infusion pumps

8. Needlesticks and other sharps injuries

9. Surgical fires

10. Defibrillator failures in emergency resuscitation attempts

* Not on the 2010 Top 10

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New York Times articles

• Series of NYT articles in January 2010– “Radiation offers new cures, and ways to do harm,” Jan. 23, 2010

– “Case studies: when medical radiation goes awry,” Jan. 26, 2010

– “As technology surges, radiation safeguards lag,” Jan. 26, 2010

• Most issues cited were human errors, but they do mention software/programming flaws, missing part of the target

• Implicit discussions of setup errors, dose calculation errors, imaging error

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AIMMS robust optimization solver

• From a March 2009 press release by AIMMS:

• “…agreement to develop Robust Optimization support for AIMMS.”

• “Potential areas of application for Robust Optimization are…”– Medicine (e.g., Intensive Modulated Radiation Therapy)

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Types of uncertainty

• Imaging

• Contouring

• Dose calculation

• Set-up

• Motion– Organ position

– Breathing motion

• Delivery

• Modality-specific uncertainties– Range uncertainty in proton therapy

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• Margins– Batman’s utility belt

– Microscopic growth (CTV)

– Intrafraction motion (ITV)

– Set-up errors (PTV)

• Image-guidance– Acquire new images online/offline

– Adjust patient positioning

– Create new treatment plan

PTV

ITV

Methods to address uncertainty

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CTV

GTV

Robust optimization

• Somewhere in between using a fixed margin and acquiring new data constantly

• Robust optimization approach:– Create a model of the uncertain effect (e.g., breathing motion)

– Incorporate knowledge of uncertainty into the optimization process (as opposed to measuring sensitivity to uncertainty post-optimization)

– Robust treatments should be de-sensitized to uncertainty• E.g., resulting dose distributions may be more homogeneous

• For discussion purposes, will review selected contributions in IMRT and IMPT– Won’t be able to do justice to everybody, especially many

contributions from medical physics community

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Chu, Zinchenko, Henderson, Sharpe (2005)

• Application area/site: Prostate• Uncertainty: Setup (interfraction position errors in general)• Optimization problem: Minimize overdose/underdose penalties

subject to approximate DV-constraints and an ellipsoidal model of data uncertainty (SOCP formulation)

• Result: Robust

treatment delivered

comparable CTV

coverage with reduced

healthy tissue dose

over multiple

simulated scenarios9

Olafsson and Wright (2006)

• Application area/site: Nasopharynx

• Uncertainty: Dose calculation and interfraction position errors

• Optimization problem: Minimize overdose/underdose penalties subject to tumor dose bounds and an ellipsoidal model of data uncertainty (SOCP formulation)– Due to structure, solvable as a sequence of linear programs

• Result: Better tumor coverage vs. nominal (non-robust) plan; lower healthy tissue dose vs. margin plan

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Nohadani et al. (2009)

• Application area/site: Lung

• Uncertainty: Dose calculation (pencil beam vs. MC)

• Optimization problem: Minimizing expectation of quadratic penalties – probabilistic approach

• Result: Robust solution using fast, inaccurate pencil beam dose calculations has comparable dosimetric characteristics as one from Monte Carlo dose calculations

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Chan, Bortfeld, Tsitsiklis (2006); Bortfeld et al. (2008)

• Application area/site: Lung

• Uncertainty: Irregular breathing motion (intrafraction)

• Optimization problem: Minimize dose delivered subject to tumor coverage and polyhedral model of data uncertainty (LP)

• Result: Better tumor

coverage vs. nominal

(non-robust) plan;

lower healthy tissue

dose vs. margin plan

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Nominal

MarginRobust

Unkelbach, Chan, Bortfeld (2007); Unkelbach et al. (2009)

• Application area/site: Paraspinal• Uncertainty: Range and setup errors• Optimization problem: Minimize expected quadratic penalties;

minimize absolute worst case penalties• Result: Robust plans cover target reliably over multiple uncertain

scenarios

Nominal (overshoot) Robust (overshoot)13

Fredriksson, Forsgren, Hardemark (2011)

• Application area/site: Lung, paraspinal, prostate

• Uncertainty: Range and setup errors

• Optimization problem: Minimax stochastic program with quadratic penalties and range of possible values for probabilities (convex QP)

• Result: Balanced trade-off in tumor coverage and healthy tissue sparing between nominal (non-robust) and margin approaches

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New horizons for robust planning?

• Other cancer sites/modalities

• Improved clinical acceptance– Get robust planning into commercial TPS

– More experimental research to measure delivery of robust treatments (e.g., Vrancic 2009)

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New horizons for robust planning?

• Better models of uncertainty– Improved or more frequent imaging may allow us to create better,

more dynamic models of uncertainty• Cervical cancer: significant shrinkage possible in short time frame

• Adaptation– Adaptive radiation therapy largely remains separate from robust

methods

– Combine multi-stage robust methods with adaptive RT (e.g., AARC with infrequent uncertainty set updates)

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Overview of adaptive robust optimization in lung

• RO method uses uncertainty set of breathing motion PDFs to create treatments de-sensitized to irregular breathing motion

• “Static” robust optimization method used one uncertainty set throughout the fractionated treatment

• With newly acquired PDFs, uncertainty set can be updated and treatment can be re-optimized

• Updating algorithms– Exponential smoothing

– Running average

– Dirichlet distribution-based

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Treatment planning timeline

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Treatment planning Treatment delivery

Day 1 Day 2

Acquire images

Optimize treatment

Deliver treatment

Deliver treatment

Create uncertainty set

Acquire PDF data

Acquire PDF data

Update uncertainty set

Re-optimize Update uncertainty set

Re-optimize

Tra

diti

onal

Rob

ust

Ada

ptiv

e

Static robust vs. Adaptive robust

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Comparing adaptive approaches

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Conclusions

• Much activity in robust RT methods over last ~five years

• Future directions– Clinical-clinical

• Get in TPS

• Clinical trials

– Clinical-methodological• Applications to other sites

• Proton therapy

• Arc therapy

– Methodological• Better models of uncertainty

• Adaptive-robust

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Pflugfelder, Wilkens, Oelfke (2008)

• Application area/site: Paraspinal

• Uncertainty: Range and setup errors

• Optimization problem: Quadratic penalty functions – probabilistic approach

• Robust optimization problem: Quadratic penalty functions

• Result:

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Sequence of PDFs

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