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Data Mining to Aid Beam Angle Selection for IMRT

Stuart Price-University of MarylandBruce Golden- University of Maryland

Edward Wasil- American UniversityHoward Zhang- University of Maryland School of Medicine

POMSDenver, Colorado

May 2013

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Outline

1. Introduction to IMRT2. Data Set3. Model Refinement4. Sorting the Solution Space5. Conclusions

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Motivation

• In 2012, an estimated 1.6 million Americans were diagnosed with some form of cancer

• Approximately 60% of all U.S. patients with cancer are treated with radiation therapy, most of them with external beam radiation therapy

• Intensity Modulated Radiation Therapy (IMRT) is the most common form of external beam radiation therapy

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IMRT Planning Problem

1. Identify the tumor and organs at risk (OAR)• The objective function is defined in this step

2. Select a set of beam angles to be used for treatment plan

• Automated set selection not currently integrated into commercial software

3. Calculate the intensity profiles for each angle• Currently automated by commercially available

software, but can take up to 30 minutes

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Objective

• Develop a model, using previously evaluated beam angle sets, to screen potential sets for those likely to produce good plans, before the computationally expensive step of optimization

• This tool could speed the search of good beam angle sets by reducing the amount of time spent optimizing bad plans

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• IMRT uses a gantry arm to allow radiation to be delivered from multiple angles

• A multi-leaf collimator is adjusted for each beam angle to shape the radiation

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• IMRT can adjust the amount of radiation received at each pixel offering far greater control than previous treatments such as 3D conformal mapping radiation therapy (3DCRT)

• The multi-leaf collimator is dynamically adjusted controlling the intensity to each pixel

• Images from Webb 2003 ©2003 by The British Institute of Radiology

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IMRT Planning Problem

1. Identify the tumor and organs at risk (OAR)2. Select a set of beam angles to be used for treatment

plan• Beam view method (Myrianthopoulos 1992)• Simulated annealing (Pugachev 2001)• Integer programming (D’Souza 2004) • Genetic algorithm (Li 2004)• Heuristic approach (Saher 2010)

3. Calculate the intensity profiles for each angle• Gradient techniques (Bortfeld et al. 1990)• Maximal entropy and maximal likelihood optimization (Llacer 1997)• Simulated annealing (Rosen et al. 1995)• Genetic algorithm (Ezzel 1996)

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Step 1: Identify Tumor and OAR

parotids

target

cord

• A number of sensitive structures including the parotids (salivary glands), spinal cord, and lymph nodes

• Different tissues have different tolerance to radiation

• The tumor and immediate adjacent tissue form the planning treatment volume (PTV) for which target radiation levels are set

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Penalty Score

• βi penalty weight

• di desired dose level, in Greys (Gy)

• Ai actual dose level• OAR set of organs at risk• PTV set of tissue in planned treatment volume

PTVi

iiiPTVOARi

iii AddAS )0,max()0,max(

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Penalty Score

Constraint Desired level

Weight

Less than 66% of the left parotid receiving 26 Gy 3

Less than 33% of the left parotid receiving 32 Gy 3

Less than 66% of the right parotid receiving 26 Gy 3

Less than 33% of the right parotid receiving 32 Gy 3

Less than 90% of the oral mucosa receiving 30 Gy 8

Less than 30% of the oral mucosa receiving 40 Gy 8

Maximum spinal cord dose 45 Gy 15

Maximum brain stem dose 54 Gy 15

More than 95% of the low-risk PTV receiving 54 Gy 6

Less than 5% of the low-risk PTV receiving 59.4 Gy 6

More than 95% of the high-risk PTV receiving 59.4 Gy 6

Less than 5% of the high-risk PTV receiving 70 Gy 6

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Step 2: Selecting Beam Angles

• There are diminishing returns for using more beam angles; our plans were constructed using 7 beam angles

• Plans were constructed such that beam angles were spaced at least 30 degrees apart

• Since some radiation passes through the tumor, beam angles were not placed between 170 and 190 degrees of another angle

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Step 3: Calculation of Intensity Profiles

• Each beam angle has about 200 pixels (also called beamlets or bixels) each of which can receive a different amount of radiation

• Beam intensities are optimized by P3 IMRT which uses the CT scan to help ensure precise calculations

• Current software and computers take several minutes to calculate and simulate all beam intensities

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Feasible Beam Angle Sets

Without Sorting

• All plans are evaluated• Low probability of

finding one of the best plans quickly

• Expected performance of partial evaluation of the list can be calculated based on the set of all possible orderings

Order Evaluated

1 2 3 …

ActualRank

43 27 18 …

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Feasible Beam Angle Sets

• Evaluate plans in order based on potential

• Expected performance of partial evaluation of the list can be calculated based on performance in cross validation

With Sorting

Sort

Order Evaluated

1 2 3 …

ActualRank

43 27 18 …

Order Evaluated

1 2 3 …

ActualRank

3 1 5 …

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Data Set

• Approximately 2700 sample treatment plans for 10 patients

• All patients had locally advanced head and neck cancer• Each plan has 7 angles from 72 possible angles at 5

degree intervals starting from 0 which is vertical from the floor

• 11 plans with 7 equally spaced angles are run for each of the 10 patients

• Remainder of plans were randomly chosen from valid angle sets

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5-Fold Cross-Validation

• Approximately 2700 plans were randomly assigned to 5 sets of approximately 540 plans

• Models were trained on 4 of the sets while tested on the remaining set

• Plans are ordered on their predicted penalty score. Ordered lists with an average of 54 plans, are constructed for each of the 10 patients

• A total of 50 sorted lists are used to evaluate the performance of each model (5 lists for each of the 10 patients)

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Models

• Linear Regression- Interpretable model with no preset model parameters

• K-Nearest Neighbor-An instance-based learning algorithm that uses the distance to and value of the nearest K neighbors to determine the predicted value

• Neural Network- Requires the use of many model parameters including topology, activation function, and learning algorithm

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Plans searched from machine sorted list

Average rank of best plan found (out of 54)

Probability of finding best plan

Probability of finding a top 3 plan

Probability of finding a top 5 plan

Bottom 10th percentile of best plan found

Baseline

Random 3 13.8 5.6 16.0 25.7 30

Random 6 7.9 11.1 30.3 45.9 18

Random 9 5.5 16.7 42.8 61.4 13

Random 12 4.2 22.2 53.7 73.1 10

Random 15 3.4 27.8 63.2 81.8 8

Linear Regression

Top 3 7.4 14 34 46 17Top 6 3.8 22 56 80 8Top 9 3.2 26 62 86 6Top 12 2.5 38 74 94 4Top 15 2.0 50 88 98 4

Neural Network

Top 3 7.1 16 40 52 15Top 6 3.7 32 64 84 10Top 9 2.9 38 74 90 5Top 12 2.4 50 78 94 5Top 15 2.0 56 86 98 4

K-Nearest Neighbor

Top 3 3.0 34 76 92 5Top 6 2.2 54 86 94 4Top 9 2.0 62 90 94 3Top 12 1.9 68 92 94 3Top 15 1.6 70 96 98 2

Average Rank of Best Plan Found

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0 3 6 9 12 15 180.0

2.0

4.0

6.0

8.0

10.0

12.0

14.0

16.0

Unsorted ListLinear RegressionNeural NetworkK-Nearest Neighbor

Number of Plans Evaluated(out of 54)

Ave

rage

Ran

k of

Bes

t Pla

n Fo

und

Probability of Finding Best Plan in List

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0 3 6 9 12 15 180

10

20

30

40

50

60

70

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Unsorted ListLinear RegressionNeural NetworkK-Nearest Neighbor

Number of Plans Evaluated(out of 54)

Prob

abili

ty o

f Fin

ding

Bes

t Pla

n

Probability of Finding a Top 3 Plan

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0 3 6 9 12 15 180

10

20

30

40

50

60

70

80

90

100

Unsorted ListLinear RegressionNeural NetworkK-Nearest Neighbor

Number of Plans Evaluated(out of 54)

Prob

abili

ty o

f Fin

ding

a T

op 3

Pla

n

Percent Difference of Penalty Score from Score of Best Plan in List

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0 3 6 9 12 15 180

5

10

15

20

25

30

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Unsorted ListLinear RegressionNeural NetworkK-Nearest Neighbor

Number of Plans Evaluated(out of 54)

% D

iffer

ence

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Conclusions

• Sorting greatly increases the chances that evaluating a subset of potential plans will find the best plan

• Neural network and linear regression models can quickly sort the entire space of angle sets for those likely to produce plans with low penalty scores

• K-nearest neighbor can incorporate each newly evaluated plan, without the need for training, to improve the models predictive value for choosing the next angle set to evaluate