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

Overview 2 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 3

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 4

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) 5

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

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 7 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 8

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 9

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 10

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 11

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 12 Nominal Margin Robust

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 14

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) 15

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) 16

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 17

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

Static robust vs. Adaptive robust 19

Comparing adaptive approaches 20

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 21

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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: 23

Sequence of PDFs 24