Managing uncertainty using
robust optimization
Timothy Chan
University of Toronto
BIRS radiation therapy workshop
March 12, 2011
Overview
• Uncertainty in radiation therapy
• Methods to manage uncertainty
– Robust optimization
• Areas for further research
2
“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
Methods to address uncertainty
• Margins
–
–
–
–
Batman’s utility belt
Microscopic growth (CTV)
Intrafraction motion (ITV)
Set-up errors (PTV)
PTV
ITV
CTV
GTV
• Image-guidance
– Acquire new images online/offline
– Adjust patient positioning
– Create new treatment plan
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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
Nominal
coverage vs. nominal
(non-robust) plan;
lower healthy tissue
dose vs. margin plan
Robust
Margin
12
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
Treatment planning
Treatment delivery
Adaptive
Robust
Traditional
Day 1
Acquire
images
Optimize
treatment
Create
uncertainty set
Deliver
treatment
Day 2
Deliver
treatment
Acquire
PDF data
Update
Re-optimize
uncertainty
set
Acquire
PDF data
Update
Re-optimize
uncertainty
set
18
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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