Managing uncertainty using robust optimization

1. Managing uncertainty using robust optimization Timothy Chan University of Toronto BIRS radiation therapy workshop March 12, 2011

2. Overview • Uncertainty in radiation therapy • Methods to manage uncertainty • Robust optimization • Areas for further research

3. “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

4. 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

5. 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)

6. Types of uncertainty • Imaging • Contouring • Dose calculation • Set-up • Motion • Organ position • Breathing motion • Delivery • Modality-specific uncertainties • Range uncertainty in proton therapy

7. Methods to address uncertainty PTV • 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 ITV CTV GTV

8. 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

9. 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 scenarios

10. 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

11. 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

12. 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 Nominal Robust Margin

13. 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)

14. 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

15. 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)

16. 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)

17. 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

18. Treatment planning timeline Treatment planning Treatment delivery Day 1 Day 2 Acquire images Optimize treatment Deliver treatment Deliver treatment Traditional Robust Create uncertainty set Acquire PDF data Acquire PDF data Update uncertainty set Re-optimize Update uncertainty set Re-optimize Adaptive

19. Static robust vs. Adaptive robust

20. Comparing adaptive approaches

21. 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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23. 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:

24. Sequence of PDFs