optimizing radiation treatment planning for tumors using imrt

Optimizing Radiation Treatment Planning for Tumors Using IMRT

Laura D. GoadrichIndustrial Engineering & Department of Computer

Sciences at University of Wisconsin-Madison

April 19, 2004

Overview Radiotherapy motivation

Conformal radiotherapy IMRT

Mechanical constraints MIP method

Input/output Langer, et. al. Approach Monoshape constraints

Implementation results References

Motivation 1.2 million new cases of cancer each year in

U.S. (times 10 globally)

Half undergo radiation therapy

Some are treated with implants, but most with external beams obtained using radiotherapy treatments.

Radiotherapy Motivation Used to fight many types of cancer in almost every part

of the body Approximately 40% of patients with cancer needs

radiation therapy sometime during the course of their disease

Over half of those patients who receive radiotherapy are treated with an aim to cure the patient to treat malignancies to shrink the tumor or to provide temporary relief of symptoms

In the use of radiation, organ and function preservation are important aims (minimize risk to organs at risk (OAR)).

Planning Radiotherapy- CAT scan

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are needed to see this picture.

Conduct scans of the section of the body containing the tumor

Allows physicians to see the OAR and surrounding bodily structures

Planning Radiotherapy- tumor volume contouring



Isolating the tumor from the surrounding OAR is vital to ensure the patient receives minimal damage from the radiotherapy

Identifying the dimensions of the tumor is vital to creating the intensity maps (identifying where to focus the radiation)

Planning Radiotherapy- beam angles and creating intensity maps



Multiple angles are used to create a full treatment plan to treat one tumor.

Through a sequence of leaf movements, intensity maps are obtained



Option 1: Conformal Radiotherapy The beam of radiation used in treatment is a 10

cm square.

Utilizes a uniform beam of radiation ensures the target is adequately covered however does nothing to avoid critical structures

except usage of some blocks



Option 2: IMRT

Intensity Modulated Radiotherapy (IMRT) provides a shaped array of 3mm beamlets using a Multi-Leaf Collimator (MLC), which is a specialized, computer-controlled device with many tungsten fingers, or leaves, inside the linear accelerator.

Allows a finer shaped distribution of the dose to avoid unsustainable damage to the surrounding structures (OARs)

Implemented via a Multi-Leaf Collimator (MLC) creating a time-varying opening (leaves can be vertical or horizontal).



Classical vs. IMRT



IMRT machine


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IMRT: Planning- intensity map There is an intensity map

for each angle 0 means no radiation 100 means maximum

dosage of radiation

Multiple beam angles spread a healthy dose

A collection of shape matrices are created to satisfy each intensity map.

0 0 80 100 100 80 40 00 80 100 80 60 100 100 400 80 60 60 60 80 40 400 100 60 60 60 60 100 6060 60 80 80 80 80 80 020 40 20 20 40 80 20 00 100 60 80 100 100 100 00 40 80 100 80 80 0 00 0 60 100 40 0 0 0

Angle 55Þ

Intensity map to shape matrices

0 40 60 60 40 0 040 60 40 40 20 40 040 40 40 40 40 40 4040 40 40 40 40 40 4040 40 40 20 40 40 020 40 20 40 40 60 00 60 40 40 40 0 0

0 1 1 1 1 0 00 1 1 1 1 1 01 1 1 1 1 1 11 1 0 0 0 0 00 1 1 1 1 1 00 0 0 0 0 1 00 0 0 0 0 0 0

0 1 1 1 0 0 01 1 0 0 0 0 01 1 0 0 0 0 01 0 0 0 0 0 01 0 0 0 0 0 01 1 1 1 1 1 00 1 0 0 0 0 0

0 0 0 0 0 0 00 0 0 0 0 1 00 0 0 1 1 1 10 0 1 1 1 1 11 1 1 0 0 0 00 1 0 0 0 0 00 1 1 1 1 0 0

0 0 1 1 1 0 01 1 1 1 0 0 00 0 1 0 0 0 00 1 1 1 1 1 10 0 0 0 1 1 00 0 0 1 1 1 00 1 1 1 1 0 0

Original Intensity Matrix

Shape Matrix 1 Shape Matrix 2 Shape Matrix 3 Shape Matrix 4

Program Input/Output Input:

An mxn intensity matrix A=(ai,j) comprised of nonnegative integers

Output: T aperture shape matrices dt

ij such that zK of the matrices are used where K < T

Non-negative integers t (t=I..T) giving corresponding beam-on times for the apertures

Apertures obey the delivery constraints of the MLC and the weight-shape pairs satisfying

K is the total number of required shape matrices

kzk Ak1

K

Mechanical Constraints After receiving the intensity maps, machine specific shape

matrices must be created for treatment There are numerous types of IMRT machines currently in

clinical use, with slightly different physical constraints that determine the leaf positions (hence the shape matrices) possible for the device

Each machine has varying setup times which can dominate the radiation delivery time (beam-on time)

To limit patient discomfort and subtle movement from initial placing: limit the time the patient is on the table

Goals: Minimize beam-on time Minimize number of different shapes

Approach: Langer, et. al. Mixed integer program (MIP) with Branch and Bound by

Langer, et. al. (AMPL solver) MIP: linear program with all linear constraints using binary

variables Langer suggests a two-phase method where

First minimized beam-on time T is the upper bound on the number of required shape matrices

Second minimize the number of segments (subject to a minimum beam-on time constraint)

gt = 1 if an element switches from covered to uncovered (vice versa) = 0 otherwise

min z t Zt1

T

min gt Gt1

Z

In Practice While Langer, et. al. reports that solving both

minimizations takes a reasonable amount of time, he does not report numbers and we have found that the time demands are impractical for real application.

To obtain a balance between the need for a small number of shape matrices and a low beam-on time we have found that

numShapeMatricies*7 + beam-on time Initializing T close to the optimal number of matrices

+ 1 required reduces the solution space and solution time

Constraint: Leaves cannot overlap from right and left To satisfy the requirement that leaves of a row

cannot override each other implies that one beam element cannot be covered by the left and right leaf at the same time

pijt lij

t 1 dijt

pijt , lij

t ,dijt {0,1}

ptij= 1 if beam element in

row i, column j is covered by the right leaf when the tth monitor unit is delivered = 0 otherwiselt

ij is similar for the right leafdt

ij contains the final tth monitor unit

Constraint: Full leaves and intensity matrix requirements Every element between the leaf and the side

of the collimator to which the leaf is connected is also covered (no holes in leaves).

pijt pij1

t

lij1t lij

t0 1 0 1 0 0

NON-CONTIGUOUS

shape matrix:

leaf setting:0 1 1 1 0 0

CONTIGUOUS

shape matrix:

leaf setting:

Constraint: No leaf collisions

Due to mechanical requirements, leaves can move in only one direction (i.e. the right leaf to the right). On one row, the right and left leaves cannot overlap

0 0 0 1 0 00 1 0 0 0 0

0 0 0 1 0 00 0 1 0 0 0

COLLISION

NO COLLISION

shape matrix:

leaf setting:

shape matrix:

leaf setting:

li1, jt pij

t 1

li 1, jt pij

t 1

Constraint: Shape matrices reqs The total number of shape matrices expended it tallied

z= 1 when at least one beam element reamins exposed

when the tth monitor unit in

the sequence is delivered

= 0 otherwise

I is the number of rows

J is the number of columns

dijt

j1

J

i1

I

z t I J

z {0,1}

Must satisfy the intensity matrix for each monitor unit.

I is the intensity assigned to

beam element ij

dijt

t1

T

Aij

Constraint: Monoshape The IMRT delivery is required to contain only one shape matrix per monitor

unit, a monoshape First determine which rows in each monitor unit are open to deliver radiation

delivery it dijt delivery it

j1

Ncols

delivery {0,1}

deliveryit=1 if the ith row is being

used a time t

= 0 otherwise

Determine if the preceding row in the monitor unit delivers radiation

deliveryi 1,t deliveryit dropit

drop {0,1}

dropit=1 if the preceding row (i-1)

in a shape is non-zero

and the current row (i) is 0

= 0 otherwise

Constraint: Monoshape Determine when the monoshape ends

deliveryit delivery i 1,t jumpit

jump {0,1}

jumpit=1 if the preceding row (i-1)

in a shape is zero and the

current row (i) is nonzero

= 0 otherwise

There can be only one row where the monoshape begins and one row to end

jumpit 1i2

Nrows

deliveryi1,t 1 dropIt

I 2

Nrows

dropit 1i2

Nrows

Complexity of problem To account for all of the constraints there is a

large number of variables and constraints.type level Lowest Num Vars Avg Num Vars Largest Num Vars

prostate 5 1500 1765 2070prostate 10 2682 3168 3690

head&neck 5 2090 2238 2350head&neck 10 3465 3969 4212head&neck 100 24200 28372 32780pancreas 5 3480 3958 4164pancreas 10 5688 6841 8725

type level Lowest Num Consts Avg Num Consts Largest Num Constsprostate 5 2178 2707 3267prostate 10 3889 4838 5841

head&neck 5 3257 3519 3695head&neck 10 5511 6231 6606head&neck 100 56555 64800 72012pancreas 5 5518 6432 6687pancreas 10 9112 10961 13839

Comparison of results Corvus version 4.0

Angle Corvus BC30 Corvus BC3035 41 9 41 DNR80 22 5 32 18

135 40 8 42 DNR225 31 7 33 18280 23 6 25 12325 35 10 33 DNR


135 321 240 402 DNR225 375 180 415 180280 224 120 224 150325 430 200 391 DNR

Intensity Level 5 Intensity Level 10

Intensity Level 5Number of segments

Intensity Level 10

Number of Beam-on Time

Comparison of results Corvus version 5.0


135 6 4 17 15225 8 5 20 DNR280 7 4 19 12325 6 4 24 15

Angle Corvus BC30 Corvus BC3035 80 DNR80 100 140

135 80 150225 100 DNR280 80 120325 80 150

Number of Beam-on Time Intensity Level 5 Intensity Level 10

Number of segments Intensity Level 5 Intensity Level 10

Referenced Papers N. Boland, H. W. Hamacher, and F. Lenzen. “Minimizing beam-on time in

cancer radiation treatment using multileaf collimators.” Neworks, 2002. Mark Langer, Van Thai, and Lech Papiez, “Improved leaf sequencing

reduces segments or monitor units needed to deliver IMRT using multileaf collimators,” Medical Physics, 28(12), 2001.

Ping Xia, Lynn J. Verhey, “Multileaf collimator leaf sequencing algorithm for intensity modulated beams with multiple static segments,” Med. Phys. 25 (8), 1998.

T.R. Bortfield, D.L. Kahler, T.J Waldron and A.L.Boyer, X-ray field compensation with multileaf collimators. Int. J. Radiat. Oncol. Biol. 28 (1994), pp. 723-730.

Bortfield, Thomas, et. al. “Current IMRT optimization algorithms: principles, potential and limitations” Presentation 2000.

Dink, Delal, S.Orcun, M. P. Langer, J. F. Pekny, G. V. Reklaitis, R. L. Rardin, “Importance of sensitivity analysis in intensity modulated radiation therapy (IMRT)” 2003.

optimizing radiation treatment planning for tumors using imrt

Documents

leaf setting

radiotherapy imrt

radiotherapy treatments

radiotherapy motivationused

leaf collimator mlc

radiation treatment

planning intensity mapthere

intensity mapsmultiple