Beam angle optimization in IMRT: are we really optimizing what matters?

• Author: Humberto Rocha,Joana Matos Dias,Maria do Carmo Lopes,Tiago Ventura,Brígida da Costa Ferreira
• DOI: http://doi.org/10.1111/itor.12587
• Published date: 01 May 2019
• Date: 01 May 2019

Intl. Trans. in Op. Res. 26 (2019) 908–928

DOI: 10.1111/itor.12587

INTERNATIONAL

TRANSACTIONS

IN OPERATIONAL

RESEARCH

Beam angle optimization in IMRT: are we really optimizing

what matters?

Humberto Rochaa,b , Joana Matos Diasa,b, Tiago Venturac,

Br´

ıgida da Costa Ferreirad,e and Maria do Carmo Lopesc,e

aFEUC and CeBER, Av. Dias da Silva 165, 3004-512 Coimbra, Portugal

bINESCC, Rua Silvio Lima, 3030-290 Coimbra, Portugal

cIPOC-FG, EPE, Av. Bissaya Barreto98, 3000-075 Coimbra, Portugal

dESS.PP, Rua ValentePerfeito 322, 4400-330 Vila Nova de Gaia, Portugal

eI3N.UA, Departamento de Fisica, Universidadede Aveiro, 3810-193 Aveiro,Portugal

E-mail: hrocha@mat.uc.pt [Rocha];joana@fe.uc.pt [Dias]; tiagoventura@ipocoimbra.min-saude.pt [Ventura];

bcf@ess.ipp.pt [Ferreira]; mclopes@ipocoimbra.min-saude.pt [Lopes]

Received 8 January 2018; received in revised form 16 July 2018; accepted 28 July 2018

Abstract

Intensity-modulated radiation therapy (IMRT) is a modern radiotherapy modality that uses a multileaf

collimator to enable the irradiation of the patient with nonuniform maps of radiation from a set of distinct

beam irradiation directions.The aim of IMRT is to eradicate all cancerous cells by irradiatingthe tumor with

a prescribed dose while simultaneously sparing, as much as possible, the neighboring tissues and organs.The

optimal choice of beam irradiation directions—beam angle optimization (BAO)—can play an important role

in IMRT treatment planning by improving organ sparing and tumor coverage, increasing the treatment plan

quality.Typically,the BAO search is guided by the optimal value of the fluence map optimization(FMO)—the

problem of obtaining the most appropriate radiation intensities for each beam direction. In this paper, a new

score to guide the BAOsearch is introduced and embedded in a parallel multistart derivative-freeoptimization

framework that is detailed for the extremely challenging continuous BAO problem. For the set of 10 clinical

nasopharyngeal tumor cases considered, treatment plans obtained for optimized beam directions clearly

outperform the benchmark treatment plans obtained considering equidistant beam directions typically used

in clinical practice. Furthermore,treatment plans obtained considering the proposed score clearly improvethe

quality of the plans resulting from the use of the optimal value of the FMO problemto guide the BAO search.

Keywords:intensity-modulated radiation therapy; beam angle optimization; parallel multistart; derivative-free optimiza-

tion

1. Introduction

Cancer is a continuously increasing health problem with respect to its mortality and incidence

features.Radiation therapy (RT) is used formore than half of the cancer patients, either with curative

C

2018 The Authors.

International Transactionsin Operational Research C

2018 International Federation ofOperational Research Societies

Published by John Wiley & Sons Ltd, 9600 Garsington Road, Oxford OX4 2DQ, UK and 350 Main St, Malden, MA02148,

USA.

H. Rocha et al. / Intl. Trans.in Op. Res. 26 (2019) 908–928 909

++=

Fig. 1. Illustration of a multileaf collimator (with nine pairs of leaves) with different aperturesand corresponding

radiation maps whose superimposition originates anintensity map with different beamlet intensities.

intent or simply to give important symptom relief. The aim of RT is to eradicate all cancerous cells

by irradiating the tumor with a prescribed dose while simultaneously sparing, as much as possible,

the neighboring tissues and organs. Intensity-modulated radiation therapy (IMRT) is a modern

type of RT that uses a multileaf collimator to transform the radiation beam into a discrete set of

small beamlets with different intensities (Fig. 1). This discretization of the radiation beam is used

for a more accurate control of the three-dimensional dose distribution. The problem of optimizing

the radiation intensities is usually known as fluence map optimization (FMO), and is usually a

large-scale programming problem that requires the computation of algorithms to achieve valuable

solutions.

In IMRT, radiation is usually generated by a linear particle accelerator mounted on a C-arm

gantry capable of rotating along a central axis. Selected radiation beams irradiate the tumor, from

different directions,depositing in an additive way the total radiation dose in the tumor while aiming

to spare the surrounding tissues and organs. In clinical practice, equispaced coplanar irradiation

directions are typically used, that is, beam angle directions evenly distributed on the plane of

rotation of the linear accelerator’s gantry. However, the choice of appropriate beam irradiation

directions—beam angle optimization (BAO)—canenhance treatment plan quality (Das and Marks,

1997). Furthermore, for particular tumor sites, as for intracranial tumors, the use of optimized

beam irradiation directions substantially improves treatment plan quality (Bangert et al., 2013).

The main reason for the clinical use of equispaced beam angle ensembles is inherent to the challenge

of solving the BAO problem, a nonconvex problem with many local minima on a vast search space

(Craft, 2007).

The problems of finding the optimal beam angle directions and the corresponding optimal radia-

tion maps can be addressed sequentially, considering geometric features or dosimetric surrogates as

quality measures of the beam angle ensembles to guide the BAO search (Llacer et al., 2009; Bangert

and Oelfke, 2010). Alternatively, BAO and FMO problems can be solved simultaneously and the

optimal FMO value is used as quality measure of the beam angle ensembles. The second approach

is predominant in the literature as it grants reliability and optimality as beam angle directions for

IMRT are often nonintuitive (Stein et al., 1997). Two different mathematical formulations for the

BAO problem have been used. A combinatorial BAO formulationcan be obtained by considering a

discrete subset of all possible angle directions in [0,360]. Many different algorithms have been used

to address the combinatorial BAO problem, including gradient search (Craft, 2007), neighborhood

search (Aleman et al., 2008), response surface approaches (Aleman et al., 2009), branch-and-prune

(Lim and Cao, 2012), hybrid approaches (Bertsimas et al., 2013), genetic algorithms (Dias et al.,

2014), or matheuristic approaches (Cabrera et al., 2018). Alternative combinatorial strategies have

C

2018 The Authors.

International Transactionsin Operational Research C

2018 International Federation of OperationalResearch Societies