Medical considerations to guide mixed integer formulations of IMRT planning problems from MD to NP...
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Transcript of Medical considerations to guide mixed integer formulations of IMRT planning problems from MD to NP...
Medical considerations to guide mixed integer formulations of
IMRT planning problemsfrom MD to NP to CR
Mark Langer, MD
Radiation Oncology
Indiana University Medical Center
Formulations and fabulations
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Bahr, GK Radiol, 1968
Sonderman, Abrahamson, Op Res 1985; Lee
Langer, M, Int J Rad Onc 1990
Problem Scale• Beams – 9 to 36
– may need to choose “best” 9 of 36
• Beamlets per beam– 100 – 400
• Structures– 3-6
• Constraint tolerances– 3% at any point, or within 3mm if dose
gradient ≥ 30%/cm
• Optimization bound tolerance– 1 fraction size (about 2.5%)
Voxeldose calculated on a grid
.25mm X 0.25mm on a slice, slices 0.5 cm apart
10 cm wide
.25 cm
Dose distribution – matrix stored
Dose distribution - isodose plot
Dose distribution – dose volume histogram
10 cm
long1600 grid pts/slice X 20 = 32 000
4 -6 critical structures
Treatment volume
What kind of accuracy is expected?What is the Point to Take home?
• Dose at individual points– recommended agreement calculations vs measured:
– Low dose gradient (<30%/cm) region: 4% dose– High dose gradient region: 4mm
• Dyk, J. Van et al, for the Comm. Of Medical Physicists of the Ontario Cancer Institute and Foundation
• Int. J. Radiat. Oncol. Biol. Phys. 26:261-73(1993)
What kind of accuracy is expected?
• Dose at individual points• Measured vs. calculated doses
– “The phantoms will be designed to assess the accuracy of a delivered dose (+5%) near the center of the target”
Cumberlin, R. and Kaplan, R; NCI guidelines for IMRT as posted on ITC website (http://itc.wustl.edu; 05/17/04)
What kind of accuracy is expected?Radiation needs to be Fullfilling
Dose distribution across a volumeDose distribution against a standard– any discrepancy between the submitting institution's
DVHs and those computed by the ITC in excess of +5% (or 3 cc for small structures) in total volume or +5% (relative to the absolute structure volume) of the volume calculated to be at or above the appropriate TD 5/5 dose for the particular structure will need to be resolved prior to successfully completing the Dry Run Test
http://itc.wustl.edu/ 11/27/02 Image Guided Therapy Center
What kind of accuracy is required?Optimization must be better than good
• “In order to satisfy [the 1976 ICRU] recommendation [of 5%], each step in the radiotherapeutic process has to be performed at an accuracy better than 5%”
• Declich, F. et al, “dosimetric evaluation of a commercial 3-D treatment planning system using Report 55 by AAPM Task Group 23”Rad Onc 52: 69-77
What kind of accuracy is expected?When are outliers outliars?
• Target dose homogeneity
– “Dose Variation within the Planning Target volume…should be kept within +7% and -5% of the prescribed dose…otherwise, it is the responsibility of the radiation oncologist to decide whether this can be accepted or not ” ICRU report 50, section 2.4.1.
Homogeneity and the Maximum doseBrush off the Biggest
• For 2D, max target dose only counted for an area >2cm2 (ICRU Report 29)
• For 3D, max target dose only counted for a volume whose min. diameter is >15mm (ICRU 50)
• Outside the target, similarly sized volume called “hot spot” (ICRU 50)
Homogeneity and the minimum doseSmall is dutiful
• “In contrast to the situation with the maximum absorbed dose, no volume is limit is recommended when reporting minimum dose.” (ICRU 50, section 2.4.4.)
Normal tissue maximums
• Can apply minimum volume rule if maximum dose is not critical
• Otherwise, a smaller volume is applied• ICRU 50• Cord,e.g.
Structure Fraction held to Dose Limit
Limit on Total Dose
Limit on Dose per Fraction
Spinal Cord 100% 45 Gy+3% 2 Gy
Lung 66%-5% 20 Gy+3% 2 Gy
microscopic tumor
100% 45 Gy-3% 2 Gy
Normal Tissue LimitsNormal Tissue and Tumor Dose Limits
Homogeneity Limit
ObjectiveStructure Maximize
Tumor min dose
Bound on Improvement
2.5%
Structure Volume Homogeneity limit
(max – min dose)
Target 100% -5% ≤10%
Gaining Traction
• Sparsing of [aij ] matrix
• Sampling of point set {i}
• Sampling of beamlet set {j}– Geometric (e.g, by target\normal tissue
projections)– Random, iterative (fill in the holes)– Numerical – column generation
Sources of Discrepancy
c
0.25 cm
Report discrepancies
- isodose plot grid ≠ dose calculation grid - pixel grid finer than dose calculation grid - dvh sampling is
inferior - within voxel
variations, if >50%/cm →>5% in 1mm
2
2
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10
Optimization Failures
+ +
+
+
++
Types of Discrepancies
• Violations– In volume– in Dose– In homogeneity
• Shortfalls
Dose (in Gy)
% VolumeHeart Volume
100%
50%
60 Gy35 Gy(1) Absolute dose limit
4% vol error
4% e
rror
in d
ose
NEEDED: An Accounting for error in estimates of dose and volume when the dvh is constructed
Dose (in Gy)
% VolumeHeart Volume
100%
50%
60 Gy35 Gy(1) Absolute dose limit
Type I reported violation: A dvh through this point would be clearly be in violation; it lies within the hatched region, that is placed outside the range of uncertainty in volume (4%) and dose (4%)
4% vol error
4% e
rror
in d
ose
Dose (in Gy)
% Volume Heart Volume
100%
50%
60 Gy35 Gy(1) Absolute dose limit
4% vol error
4% e
rror
in d
ose
Type II violation : A point lies outside the 4% dose calc error, but it could lie within the 4% uncertainty in estimating the volume holding that point
Dose (in Gy)
% Volume Heart Volume
100%
50%
60 Gy35 Gy(1) Absolute dose limit
Type III violation :The dose volume histogram lies within the region of ±4% uncertainty in dose and volume. But >4% volume exceeds the dose limit by some amount, and there is an error of >4% in dose within some part of the volume. The maximum recorded dose is plotted, along with the range of error in volume holding that dose (0%-4%)
Maximum violations in lung dose-volume limit in no shortfall 3D trials
# sample points
trials #trials with lung violations
#trials with shortfalls
Volume violation
Dose violation
450 35 11 5 3% 4.9 Gy
600 35 11 6 4% 7.4 Gy
800 34* 8 8 2% 4.1 Gy
* one trial could not be solved
Langer, M.; et al, “The reliability of optimization under dose-volume limits”, Int. J. Radiat Oncol. Biol. Phys. 26:529-538; 1993
Sampling and time
Sampling points
Avg time 95th percentile
Maximum time
450 3.78 min 12.3 min. 36 min.
600 4.03 min 17.9 min 31 min
800 56 min 101 min 1315 min
Langer, M.; et al, “The reliability of optimization under dose-volume limits”, Int. J. Radiat Oncol. Biol. Phys. 26:529-538; 1993
Formulations and fabulations
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Sonderman, Abrahamson, Op Res 1985
Langer, M, Int J Rad Onc 1990
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Rardin, R.; Langer, M.P.; Preiciado-Walters, F.; Thai, V. Column Generation for IMRT Cancer Therapy Optimization with Implementable Segments. Euro/Informs Joint International Meeting, #2704, July 6-10, 2003, Istanbul. (meeting presentation)
Langer, M.; Thai, V. Delivery of Static Field IMRT is Improved by Avoiding Discretization of Intensity Levels. Int. J. Radiat. Oncol. Biol. Phys. 54(2):156; October 6-10, 2002, New Orleans, LA (meeting presentation).
Langer, M.; Thai, V.; Papiez, L. Improved Leaf Sequencing Reduces Segments or Monitor Units Needed to Deliver IMRT Using Multileaf Collimators. Med. Phys. 28(12): 2450-2458; 2001.
Preciado-Walters, F.; Langer, M.P.; Rardin, R.; Thai, V. Column generation for IMRT Cancer Therapy - Optimization with Implementable Segments.
Cord 45 Gy Target dose homogeneity .85Maximize minimum target dose
Target DVH (optimization sample points[182])
0
10
20
30
40
50
60
70
80
90
100
4500 5000 5500 6000 6500 7000 7500 8000 8500 9000
Dose (cGy)
Continuous LevelsDiscrete Levels
Intensity map
Continuous Levels relaxed homogeneity
Structure Clinical plan Criteria
IMRT constraint template (starting)
PTV PTV1=54 Gy
PTV2=70 Gy
Max dose 120% prescribed
PTV1
prescribed=54Gy
PTV2
prescribed=70Gy
PTV1 =51.3-56.7 Gy
PTV2 =66.5-73.5 Gy
Penalty =25
spinal cord
Max dose 40 Gy Max dose = 35 Gy
Penalty = 100
Brain stem
Max dose 45 Gy Max dose = 35 Gy
Penalty = 100
1.2 x (54)=64.8
1.2 x (70)=84
Hunt, MA et al, IJROBP 49:623-632; 2001
What is the effect of uncertainty in geometry?
Minimum Dose
79.279.6 79.8
McCormick, T.C.; Dink, D.; Orcun, S.; Pekny, J.; Rardin, R.; Baxter, L.; Langer, M. Projecting the Effect of Target Boundary Uncertainty on the Tumor Dose Prescription to Guide Contouring for Treatment Planning. Int. J. Radiat. Oncol.Biol. Phys. 57(2 suppl):S235 (2003) Amer. Soc. Therap. Radiol. Oncol. 45th Annual Meeting (meeting presentation).
Conclusions
• MDs can formulate the planning problems
• They are combinatorially complex
• We can identify levels of required accuracy
• Is there an advantage or disadvantage to incorporate delivery constraints?