7/29/2017 Making Better IMRT Plans Using a New Direct ...amos3.aapm.org/abstracts/pdf/127-35488-418554-127653-1658800543.pdf · Making Better IMRT Plans Using a New Direct Aperture

7/29/2017

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Making Better IMRT Plans Using a New Direct Aperture Optimization Approach

Dan Nguyen, Ph.D.

Division of Medical Physics and Engineering

Department of Radiation Oncology

UT Southwestern

AAPM Annual Meeting

Aim of Radiotherapy Research

• Overall goal of radiotherapy research is to find practical and efficient ways to maximize radiation dose to the tumor while minimizing dose to normal tissues and organs.

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Planning Target Volume(PTV)

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Organ at Risk (OAR)

Intensity Modulated Radiation Therapy

• Intensity Modulated Radiation Therapy (IMRT) is a widely accepted and effective technique to radiotherapy.

• Inverse planning approach

• Planner defines prescription dose to the PTV and structure importance

• Fluence map optimization finds beamlet intensities that best satisfies planner criteria

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OAR

OAR

OARPTV

Fluence mapFluence map optimization

(FMO)

Problem of conventional IMRT

• Conventional FMO does not take into account hardware delivery constraints

• Once the fluences are optimized, they must be converted into an approximation deliverable by multileaf collimators (MLC).

• MLC Segmentation

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Mulitleaf Collimator (MLC)OptimizedFluence Map

MLC DeliverableFluence Map

Image courtesy of Varian Medical Systems, Inc. All rights reserved

Stratification MLC

Sequencing

Deliver!

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MLC Segmentation

• Aim of segmentation is to limit the number of deliverable apertures that the MLCs can form.

• Why? Delivering large number of small fields leads to complications with small field dosimetry error buildup and low output (longer treatment time).

• This segmentation step, particularly the stratification process, degrades the fluence map and the resulting dose distribution.

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Stratification MLC

Sequencing

Stratification MLC

Sequencing

Direct Aperture Optimization

• Direct Aperture Optimization (DAO) attempts to solve the problem by reformulating the optimization to account for machine constraints.

• Creates fluence maps that are directly deliverable.

• Removes need for MLC segmentation step.

• Commercial DAO uses a simulated annealing algorithm

• Stochastic algorithm

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Simulated annealing DAO

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The routine randomly selects either to change the intensity or a leaf position for modification.

A random number based on a Gaussian determines the size and direction of the change. The standard deviation of the Gaussian is

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1 /

Changes that lower the cost objective are always accepted. Otherwise, the change is accepted with a probability

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1 /

Shepard DM, Earl MA, Li XA, Naqvi S, Yu C. Direct aperture optimization: A turnkey solution for step-and-shoot IMRT. Medical Physics. 2002;29:1007-18

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Simulated Annealing DAO for VMAT

• From the seminal paper by Otto1, VMAT creates an arc by progressively sampling new beams (figure below), and using simulated annealing DAO to

• Solve for exactly one deliverable aperture for each beam

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1Otto, Karl. "Volumetric modulated arc therapy: IMRT in a single gantry arc." Medical physics 35.1 (2008): 310-317.

[1]

Simulated annealing DAO

• Changes 1 MLC leaf or aperture intensity at a time

• Worked well for VMAT because of progressive sampling of beams

• Added beams would adopt an aperture shape and intensity value from their neighbor

• In general has difficulty scaling to large problems with lots of variables to optimize

• DAO for static beam IMRT

• Multiple apertures per beam

• No progessive sampling

• Stochastic algorithm.

• Probabilistic nature of algorithm cannot guarantee reproducibility of results.

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Rethinking DAO Problem

• Need to come up with a way to find a fluence map that can be MLC sequenced without any modification to the fluence map.

• We want to optimize a fluence map that has

• Piecewise-constant regions.

• Limited number of discrete intensity levels

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Can be delivered by MLCs without further modification

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Rethinking DAO Problem

• Other goals

• Fast to solve

• Piecewise-constant regions can take any shape (no library of aperture to choose from)

• Large regions

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Image Segmentation

• In the domain of mathematics imaging and vision, effective image segmentation formulations and algorithms have been developed.

• Piecewise-constant Mumford-Shah formulation solved with Primal Dual Hybrid Gradient Algorithm1.

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1Chambolle A, Pock T. A First-Order Primal-Dual Algorithm for Convex Problems with Applications to Imaging. Journal of Mathematical Imaging and Vision. 2011;40:120-45.

[1]

Image Segmentation

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Regions can be arbitrarily shaped, and does not require a finite sized library of shapes for optimizer to search from


[1]

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Multiphase piecewise-constant Mumford-Shah function

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Mumford-Shah

• The original Mumford-Shah functional

• Proposed by Mumford and Shah in 19891

• Segments an image into piecewise smooth sub-regions

• Piecewise constant version proposed in 20012

• Also known as Chan-Vese model

• Used level-set functions to solve for piecewise constant regions

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1Mumford, David, and Jayant Shah. "Optimal approximations by piecewise smooth functions and associated variational problems." Communications on pure and applied mathematics 42.5 (1989): 577-685.2Chan, Tony F., and Luminita A. Vese. "Active contours without edges."Image processing, IEEE transactions on 10.2 (2001): 266-277.

Mumford-Shah

• Chan et al. proposed a convex relaxation method in 20061.

• Used a labeling array instead of level set functions.

• Easy scaling for any number of segments.

• Allowed for the problem to be efficiently evaluated with a proximal algorithm called primal dual hybrid gradient (PDHG)2 = fast.

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1Chan, Tony F., Selim Esedoglu, and Mila Nikolova. "Algorithms for finding global minimizers of image segmentation and denoising models." SIAM journal on applied mathematics 66.5 (2006): 1632-1648.2Chambolle A, Pock T. A First-Order Primal-Dual Algorithm for Convex Problems with Applications to Imaging. Journal of Mathematical Imaging and Vision. 2011;40:120-45.

[2]

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Mumford-Shah

• Multiphase Piecewise-Constant Formulation

• x is the original image

• u defines the shape of the segments

• c assigns a value to each segment

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, 12

u 0,

1


[1]

[1]

Mumford-Shah





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, 12

u 0,

1


[1]

[1]

Mumford-Shah





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, 12

u 0,

1


[1]

[1]

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Mumford-Shah Summary

• The multiphase piecewise constant Mumford-Shah function

• Can use a labeling array for segmentation

• Can be solved quickly with PDHG algorithm

• Solves for pairwise disjoint segments

• Solves all segments simultaneously

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The FMO formulation

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FMO formulation

• A common convex FMO formulation incorporates both a dose fidelity term and a total variation (TV) regularization term

• x is the fluence map

• A is the dose calculation matrix

• d is the prescription dose

• W weights the structures of interest

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FMO formulation

• TV regularization helps piecewise smooth the fluence maps

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Without TV regularization With TV regularization

DAO: Combining FMO with Mumford-Shah function

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Unifying FMO and image segmentation into a single formulation

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FMO with anisotropic TV Multiphase piecewise constant Mumford Shah1

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1Chambolle, Antonin, and Thomas Pock. "A first-order primal-dual algorithm for convex problems with applications to imaging." Journal of Mathematical Imaging and Vision 40.1 (2011): 120-145.

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, 12


12


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FMO with anisotropic TV

0, 0, 1 ,

Multiphase piecewise constant Mumford Shah1


, 12

12

, , 12

12

0, 0, 1 ,

, , 12

12

12


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, 12



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0, 0, 1 ,

, , 12

12

12


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, 12



Deterministic Direct Aperture Optimization

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0,

u 0, 1 , ,

, , 12

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0,

u 0, 1 , ,

, , 12

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Because of the third term, this formulation is not convex.

However, if we update one variable (x,c, or u) while holding the other 2 constant, we obtain a convex module.

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This can be locally solved by updating the variables in a alternating block fashion.

Module 1: Solve for x, while holding c and u constantModule 2: Solve for c, while holding x and u constantModule 3: Solve for u, while holding x and c constant

0,

u 0, 1 , ,

, , 12

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All 3 modules can be efficiently solved with PDHG

0,

u 0, 1 , ,

, , 12

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Evaluation

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Evaluation

• 3 planning cases were tested

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Patient

Number of allowed

segments per beam

( )

Prescription dose

(Gy)PTV volume (cc)

Glioblastoma Multiforme

(GBM)10 30 57.77

Lung (LNG) 10 50 47.84

Head & Neck (H&N) 20

54 197.54

59.4 432.56

69.96 254.98

Evaluation

• Shell and skin structures added around PTV•

• Dose was calculated for each patient for 1162 beams

• Convolution/Superposition (CVSP)

• Dose array resolution: 0.25 cm x 0.25 cm x 0.25 cm

• Beamlet resolution: 0.5 cm x 0.5 cm

• 20 beam angles were selected for each patient

• Column generation algorithm

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Evaluation

• 20 beam plans created using the DAO with Mumford-Shah (DAOMS) and the simulated annealing DAO (DAOSA) methods.

• DAOMS: is initialized to 0

• DAOSA: is initialized to have conformal beams around PTV

• Computer

• Intel Core i7-3960X CPU

• 6 physical cores overclocked to 4.00 GHz

• GeForce GTX 690 GPU

• 32 GB RAM

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Results

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Size of problem

Length of Number of non-zeros in dose

array

GBM 2,175 37,411,365

LNG 2,011 27,910,230

H&N 18,934 243,728,264

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Convergence

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0 200 400 600 800 1000 1200 1400 1600 1800 200010

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109

1010

Iteration

Obj

ectiv

e va

lue

GBM: Convergence plot for DAOMS

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

x 105

107

108

109

1010

GBM: Convergence plot for DAOSA

Iteration

Obj

ectiv

e va

lue

Modules 1&2

Module 3

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Total solve time

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0

5000

10000

15000

20000

25000

30000

35000

40000

GBM LNG H&N

time

(s)

Solve time

DAO_MS DAO_SA

DAOMS is 9.5 to 40 times faster

Lower is better

GBM: Dose Wash

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GBM: DVH

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0 5 10 15 20 25 30 350

0.1

0.2

0.3

0.4

0.5

0.6

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0.8

0.9

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Fra

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olum

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GBM: DAOMS

(solid) vs DAOSA

(dotted)

Dose (Gy)

PTVBrainBrainstemChiasmSpinalCordR Opt NrvL Opt NrvR EyeL EyeR LensL LensR CochleaL Cochlea

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LNG: Dose Wash

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LNG: DVH

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0 5 10 15 20 25 30 35 40 45 50 55 600

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

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Fra

ctio

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olum

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LNG: DAOMS

(solid) vs DAOSA

(dotted)

Dose (Gy)

PTVSpinalCordTracheaProximalBronchusHeartEsophagusLung

H&N: Dose Wash

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H&N: DVH part 1

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0 10 20 30 40 50 60 70 800

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

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Fra

ctio

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vol

ume

H&N part 1: DAOMS

(solid) vs DAOSA

(dotted)

Dose (Gy)

PTV6996PTV5940PTV5400BrainstemChiasm

H&N: DVH part 2

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0 10 20 30 40 50 60 70 800

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

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Fra

ctio

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vol

ume

H&N part 2: DAOMS

(solid) vs DAOSA

(dotted)

Dose (Gy)

CordR Opt NrvL Opt NrvR CochleaL CochleaL Parotid

H&N: DVH part 3

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0 10 20 30 40 50 60 70 800

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

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olu

me

H&N part 3: DAOMS

(solid) vs DAOSA

(dotted)

Dose (Gy)

MandibleLipsOral CavityLarynxPharynxEsophagus

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Statistics

• On average, DAOMS reduced Dmax and Dmean by (% of prescription dose):

• (GBM) 0.01% and 0.001%

• (LNG) 3.67% and 1.08%

• (H&N) 10.91% and 10.81%

• The average dose coverage, D98 and D99, was increased by 1.66% and 2.21% of the prescription dose.

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Aperture Comparison

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Segment evaluation

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02468

101214161820

GBM LNG H&N

Num

ber

of s

egm

ents

Average number of segments per beam

DAO_MS DAO_SAMaximum allowed number of apertures Lower is better

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Segment Evaluation

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0

10

20

30

40

50

60

GBM LNG H&N

Num

ber

of b

eam

lets

Mean number of beamlets in a segment

DAO_MS DAO_SAHigher is better

Discussion

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Discussion

• DAOMS results in perfectly piecewise constant fluence maps that are equivalent to apertures without additional stratification.

• In terms of computation speed, DAOMS is far superior

• 9.5 to 40 fold increase in speed to converge

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Discussion

• For simpler cases (GBM and H&N), DAOMS and DAOSA are very comparable in dosimetry.

• Similar OAR sparing (DAOMS does slightly better)

• DAOSA still competitive in PTV coverage and homogeneity.

• For complicated cases (H&N), DAOMS is clearly superior in all aspects

• DAOSA has difficulty reaching a pareto optimum

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Limitation of DAOMS

• A major limitation of DAOMS is that the piecewise constant segmentation only solves for pairwise disjoint regions

• This property causes DAOMS to have:

• More apertures on average (to increase complexity)

• Smaller apertures (each aperture competes for space)

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DAOSA: overlappingDAOMS: Pairwise disjoint

Conclusion

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Conclusion

• Novel DAO formulated by combining FMO with a multiphase piecewise constant Mumford-Shah segmentation.

• Can generate any shaped MLC segment on the fly.

• Dosimetrically competitive to commercial simulated annealing method for simple cases, and superior for complex cases.

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Thank you!

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Documents

7/29/2017 Making Better IMRT Plans Using a New Direct ...amos3.aapm.org/abstracts/pdf/127-35488-418554-127653-1658800543.pdf · Making Better IMRT Plans Using a New Direct Aperture