Dose-Volume Based Ranking of Incident Beams and its Utility in Facilitating IMRT

Beam Placement

Jenny Hai, PhD.

Department of Radiation OncologyStanford University School of Medicine

Purpose

Beam orientation optimization in IMRT is computationally

intensive and various single beam ranking techniques

have been proposed to reduce the search space. Up to this

point, none of the existing ranking techniques considers

the clinically important dose-volume effects of the

involved structures, which may lead to clinically

irrelevant angular ranking. The purpose of this work is to

develop a clinically sensible angular ranking model with

incorporation of dose-volume effects and to show its

utility for IMRT beam placement.

1

Difficulty

The general consideration in constructing an angular ranking function is that a beamlet/beam is more preferable if it can deliver a higher dose to the target without exceeding the tolerance of the sensitive structures located on the path of the beamlet/beam. In the previously proposed dose-based approach, the beamlets are treated independently and, to compute the maximally deliverable dose to the target volume, the intensity of each beamlet is pushed to its maximum intensity without considering the values of other beamlets. When volumetric structures are involved, a complication arises from the fact that there are numerous dose distributions corresponding to the same dose-volume tolerance. In this situation, the beamlets are no longer independent and an optimization algorithm is required to find the intensity profile that delivers the maximum target dose while satisfying the volumetric constraint(s).

2

Method

In this study, the behavior of a volumetric organ was modeled by using the equivalent uniform dose (EUD). A constrained sequential quadratic programming algorithm (CFSQP) was used to find the beam profile that delivers the maximum dose to the target volume without violating the EUD constraint(s). To access the utility of the proposed technique, we planned a head and neck and thoracic case with and without the guidance of the angular ranking information. The qualities of the two types of IMRT plans were compared quantitatively.

3

Ranking function

The figure of merit of a beam direction is generally measured by how much dose

can be delivered to the target and is calculated using the a priori dosimetric and

geometric information of the given patient. A beam direction is divided into a

grid of beamlets. After a forward dose calculation using the maximum beam

intensity profile, the score of the given beam direction (indexed by i) is obtained

according to

dose delivered to the voxel by the beam from the direction indexed by i

number of voxels in the target

target prescription

4

Constraints

For each OAR we define the optimization constraint such that

the EUD value derived for the given dose distribution

during the optimization process should not exceed a user-

defined limit:

5

Optimization algorithm

Variables to be optimized included the intensities of the

beamlets passing through the PTV.We use CFSQP, having

the advantage of being capable of dealing with nonlinear

inequality constraints. The calculation starts with an initial

intensity profile, in which each beamlet is assigned with a

small but random value, and then iteratively maximize the

angular ranking function while satisfying the constraints.

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Comparison previous scores

Dependence of EUD score on the a parameter is presented in figure 3a. As a increases, the angular score curve approaches to the curve (denoted by the open circles) computed using the method proposed by Pugachev This calculation provides a useful check of the new algorithm. It is interesting to note that the change in the peak positions of the angular function can be as large as 20o when the sensitive structures are changed from serial (corresponding to a high a value) to parallel (corresponding to a low a value). The change in amplitude is also striking (from ~0.2 to ~0.7 at 80º and 280º).

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Clinical utility

We compare conventional, equispaced, plans with

“optimized” plan having beams directions selected at

peaks of the score function. After beam selection for both

types of plans, beamlets are optimized using a published

multi-objective approach. The DVHs for both cases show

improvements in all objectives.

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CFSQP convergence

Convergence behavior of the CFSQP algorithm is demonstrated by plotting the angular score as a function of iteration step (figure 2a) for the 225o direction. The EUDs of the sensitive structures at each iteration step are shown in figure 2b. With the chosen initial beamlet intensities (small but random values), the angular score is progressively increased while constraints are progressively saturated, limited by the tolerances of the sensitive structures. Constraints of the sensitive structures that are not on the path of the beam

remain to be constant through the iterative calculation.

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10 20 30 40 50 60

0

20

40

60

80

100

Conventional Optimized

DVH Comparison

Brainstem

Parotid

Cord

PTVV

olum

e (%

)

Dose (Gy) Head case: DVHs of the optimized and conventional plans

10 20 30 40 50 60

0

20

40

60

80

100

Conventional Optimized

DVH Comparison

R Kidney

L Kidney

Liver

Cord

PTV

Vol

um

e (%

)

Dose (Gy)Thoracic case: DVHs of the optimized and conventional plans

Head case: Angular score obtained with published EUD model parameters superimposed on the patient’s geometry. Angles selected for IMRT planning are shown by arrows.

Thoracic case: Angular score obtained with published EUD model parameters superimposed on the patient’s geometry. Angles selected for IMRT planning are shown by arrows.

0 25 50 75 100 125 150 1750.0

0.2

0.4

0.6PTV

Score convergence

An

gu

lar

ran

kin

g f

un

ctio

n

IterationFIGURE 2a Convergence behavior of the CFSQP algorithm for the 255º beam direction. Presented are evolutions of the angular ranking function

0 25 50 75 100 125 150 175

0

20

40

Constraints convergence

R Kidney

Liver

L Kidney

Cord

EU

Dto

lera

nce

- E

UD

IterationFIGURE 2b Convergence behavior of the CFSQP algorithm for the 255º beam direction.Presented are the sensitive structure constraints. Only the right kidney and the liver influence algorithm’s convergence since other structures are not on the path of the beam.

0 60 120 180 240 300 3600.0

0.2

0.4

0.6

0.8

1.0

1.2

Scores

a= 8 a=9 a=3 a=1 Selected anglesA

ngu

lar

ran

kin

g fu

nct

ion

Beam Angle (degree)

Head case: Angular ranking function of coplanar beam for a series of EUD a parameter values. The selected five beam directions for IMRT planning are labeled by arrows. The curve depicted by the open circles represents the result obtained using the approach described by Pugachev.

0 60 120 180 240 300 360

0.2

0.4

0.6

0.8

1.0

a= 8 a=9 a=3 a=1 Selected angles

ScoresA

ngul

ar r

anki

ng fu

nctio

n

Beam Angle (degree)Thoracic case: Angular ranking function of coplanar beam for a series of EUD a parameter values. The selected five beam directions for IMRT planning are labeled by arrows. The curve depicted by the open circles represents the result obtained using the approach described by Pugachev.

Conclusion

The EUD-based function is a general approach for angular

ranking and allows us to identify the potentially good and

bad angles for clinically complicated cases. The ranging

can be used either as a guidance to facilitate the manual

beam placement or as prior information to speed up the

computer search for the optimal beam configuration.

Given its simplicity and robustness, the proposed

technique should have positive clinical impact in

facilitating the IMRT planning process

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