A novel algorithm for the calculation of physical and biological irradiation quantities in scanned ion beam therapy: the beamlet superposition approach

TLDR: A new approach for ion irradiation outcomes computations, the beamlet superposition (BS) model, which satisfies these requirements and applies and extends the concepts of previous fluence-weighted pencil-beam algorithms to quantities of radiobiological interest other than dose.

Abstract: The calculation algorithm of a modern treatment planning system for ion-beam radiotherapy should ideally be able to deal with different ion species (e.g. protons and carbon ions), to provide relative biological effectiveness (RBE) evaluations and to describe different beam lines. In this work we propose a new approach for ion irradiation outcomes computations, the beamlet superposition (BS) model, which satisfies these requirements. This model applies and extends the concepts of previous fluence-weighted pencil-beam algorithms to quantities of radiobiological interest other than dose, i.e. RBE- and LET-related quantities. It describes an ion beam through a beam-line specific, weighted superposition of universal beamlets. The universal physical and radiobiological irradiation effect of the beamlets on a representative set of water-like tissues is evaluated once, coupling the per-track information derived from FLUKA Monte Carlo simulations with the radiobiological effectiveness provided by the microdosimetric kinetic model and the local effect model. Thanks to an extension of the superposition concept, the beamlet irradiation action superposition is applicable for the evaluation of dose, RBE and LET distributions. The weight function for the beamlets superposition is derived from the beam phase space density at the patient entrance. A general beam model commissioning procedure is proposed, which has successfully been tested on the CNAO beam line. The BS model provides the evaluation of different irradiation quantities for different ions, the adaptability permitted by weight functions and the evaluation speed of analitical approaches. Benchmarking plans in simple geometries and clinical plans are shown to demonstrate the model capabilities.

Figures

Figure 1. Workflow for a TPS exploiting the BS model.

Figure 7. Comparison between PlanKIT- and FLUKA-generated dose distributions corresponding to the irradiation of a skull-base chordoma with two opposing carbonion fields.

Figure 8. Transverse view of RBE-weighted dose, RBE and dose-averaged LET distributions, obtained planning with PlanKIT the irradiation of a head & neck tumour with two opposing proton or carbon-ion fields. The black line encloses the PTV, while the magenta line delineates the brain stem.

Table 1. Configurations considered for the measurement of the cubic SOBPs in the RW3 phantom.

Figure 4. Comparison of measured and PlanKIT-computed transverse dose distributions at six different depths along the deepest irradiated proton SOBP (265–315 mm range). The drawn isodose lines correspond to the 0.6, 0.9, 1.2, 1.5 and 1.8 Gy dose levels.

Figure 5. Comparison of FLUKA and PlanKIT dose-to-water distributions for carbonion beams hitting a lateral heterogeneity. (a) Isodose lines in the central plane of the 250 MeV u−1 beam. (b) Integrated depth-dose profiles for 150, 250 and 350 MeV u−1 beams.

Full text

Physics in Medicine & Biology
PAPER
A novel algorithm for the calculation of physical
and biological irradiation quantities in scanned ion
beam therapy: the beamlet superposition
approach
To cite this article: G Russo et al 2016 Phys. Med. Biol. 61 183
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183
Physics in Medicine & Biology
A novel algorithm for the calculation
of physical and biological irradiation
quantities in scanned ion beam therapy:
the beamlet superposition approach
GRusso
1
, AAttili
1
, GBattistoni
2
, DBertrand
5
, FBourhaleb
6
,
FCappucci
2
, MCiocca
7
, AMairani
7
, FMMilian
1
,
8
,
SMolinelli
7
, MCMorone
3
, SMuraro
2
, TOrts
5
, VPatera
4
,
PSala
2
, ESchmitt
1
, GVivaldo
1
and FMarchetto
1
1
Istituto Nazionale di Fisica Nucleare (INFN), Torino, Italy
2
Istituto Nazionale di Fisica Nucleare (INFN), Milano, Italy
3
Istituto Nazionale di Fisica Nucleare (INFN) and Università ‘Tor Vergata’, Roma,
Italy
4
Istituto Nazionale di Fisica Nucleare (INFN) Laboratori Nazionali di Frascati and
Università ‘La Sapienza’, Roma, Italy
5
Ion Beam Applications (IBA), Louvain-la-Neuve, Belgium
6
Internet—Simulation Evaluation Envision (I-SEE), Torino, Italy
7
Centro Nazionale di Adroterapia Oncologica (CNAO), Pavia, Italy
8
Universidade Estadual de Santa Cruz, Ilheus, Brazil
E-mail: russo@to.infn.it
Received 22 September 2014, revised 3 November 2015
Accepted for publication 10 November 2015
Published 2 December 2015
Abstract
The calculation algorithm of a modern treatment planning system for ion-
beam radiotherapy should ideally be able to deal with different ion species
(e.g. protons and carbon ions), to provide relative biological effectiveness
(RBE) evaluations and to describe different beam lines. In this work we
propose a new approach for ion irradiation outcomes computations, the
beamlet superposition (BS) model, which satises these requirements.
This model applies and extends the concepts of previous uence-weighted
pencil-beam algorithms to quantities of radiobiological interest other than
dose, i.e. RBE- and LET-related quantities. It describes an ion beam through
a beam-line specic, weighted superposition of universal beamlets. The
universal physical and radiobiological irradiation effect of the beamlets on
a representative set of water-like tissues is evaluated once, coupling the per-
track information derived from FLUKA Monte Carlo simulations with the
radiobiological effectiveness provided by the microdosimetric kinetic model
G Russo et al
Physical and biological ion-beam irradiation quantities computed via the BS model
Printed in the UK
183
PMB
© 2016 Institute of Physics and Engineering in Medicine
2016
61
Phys. Med. Biol.
PMB
0031-9155
10.1088/0031-9155/61/1/183
Paper
1
183
214
Physics in Medicine & Biology
Institute of Physics and Engineering in Medicine
IOP
0031-9155/16/010183+32$33.00 © 2016 Institute of Physics and Engineering in Medicine Printed in the UK
Phys. Med. Biol. 61 (2016) 183–214 doi:10.1088/0031-9155/61/1/183

184
and the local effect model. Thanks to an extension of the superposition
concept, the beamlet irradiation action superposition is applicable for the
evaluation of dose, RBE and LET distributions. The weight function for
the beamlets superposition is derived from the beam phase space density
at the patient entrance. A general beam model commissioning procedure is
proposed, which has successfully been tested on the CNAO beam line.
The BS model provides the evaluation of different irradiation quantities
for different ions, the adaptability permitted by weight functions and the
evaluation speed of analitical approaches. Benchmarking plans in simple
geometries and clinical plans are shown to demonstrate the model capabilities.
Keywords: beam model, ion therapy, treatment planning, relative biological
effectiveness, microdosimetric kinetic model, local effect model, Monte
Carlo
(Some guresmay appear in colour only in the online journal)
1. Introduction
The number of clinical facilities that employ ion therapy to treat cancer is increasing world-
wide. Most of these centres feature proton irradiation, since, compared to heavier ions,
protons are simpler to handle, and more compact and cheaper accelerators are available on the
market. A few centres make use of carbon ions, which are believed to constitute a better option
for the treatment of radio-resistant tumours thanks to their favourable increase of the relative
biological effectiveness (RBE) in the Bragg peak region. Recently, the use of ions other than
proton and carbon ions has been proposed (Kempe et al 2007) and some preliminary assess-
ment of the application of helium and oxygen ion beams has been performed (Fuchs et al
2012, Kurz et al 2012).
The use of ions different from protons entails the use of more complex irradiation-outcome
computation algorithms in treatment planning systems (TPS). The reason for this is two-fold:
rst, the calculation algorithm must account for nuclear fragmentation, which produces a
progressive build-up of secondary ions with the depth of penetration in the tissue and hence
causes an unwanted dose deposition beyond and aside the Bragg peak; second, it is neces-
sary to evaluate the RBE scaling, which is a patient-specic, spatially-variable and non-linear
function of the dose, applying some kind of radiobiological modelling on top of the estimate
of the local particle spectra. The RBE actually presents a small level of variability for pro-
tons as well (e.g. Gerweck and Kozin 1999, Britten et al 2013, despite the clinical adoption
of a constant 1.1 as recommended by the International Commission on Radiation Units and
Measurements (ICRU Report 78 2007). The impact of neglecting these RBE variations dur-
ing treatment planning is under evaluation by several institutions (Tilly et al 2005, Frese et al
2011, Carabe et al 2012, Dasu and Toma-Dasu 2013).
RBE values are usually characterised by big uncertainties (10% or more) and the employ-
ment of different radiobiological models by the different centres hinders the comparability
of clinical outcomes (Gueulette and Wambersie 2007, Uzawa et al 2009, Steinsträter et al
2012). For these reasons, it has been proposed that the treatment planning be evaluated solely
on the base of physical quantities, using the unrestricted linear energy transfer (the LET
∞
dened in the ICRU Report 85a (2011), in this article simply referred to as LET) as a sur-
rogate of the RBE to weight the variations of cell-inactivation efciency. This approach is
G Russo et al
Phys. Med. Biol. 61 (2016) 183

185
particularly well-suited to protons, for which a strong correlation between RBE and LET has
been observed (Britten et al 2013).
As a consequence of the above, there is growing interest in the ion-therapy community
for TPS’s capable of dealing with different ion species and of providing a local estimate
of the radiobiological effectiveness. Nevertheless, few of the computation algorithms cur-
rently employed for clinical use are providing these capabilities. Most of them are in fact
tailored to efciently compute dose distributions after proton irradiation, being analytical or
optimised Monte Carlo algorithms that cannot be readily applied to other ions. The most
notable exception is TRiP98, a research tool developed and used for planning carbon-ion
treatments within the framework of the GSI pilot project in Germany (Krämer et al 2000).
This tool has constituted the basis for the implementation of the Syngo
®
RT Planning software
(Siemens Healthcare, Erlangen, Germany), the only commercial TPS to date that incorporates
the computation of the RBE for carbon-ion spot scanning. However, the irradiation-outcome
computation algorithms of both TRiP98 and Syngo
®
are not conceived to be easily adapted to
different beam lines. For instance, Syngo
®
requires that the user provides the description of
the fragmentation in water by the pencil beams as a part of the commissioning process. The
users then have to carry out extensive, centre-specic Monte Carlo simulations in order to
provide the TPS with the necessary data.
At INFN we have envisioned an original modelling approach, the beamlet superposition
(BS) model, which permits to simulate the irradiation with different ions, to evaluate sev-
eral physical and radiobiological quantities and to simplify the commissioning procedure.
This model has been implemented in a new TPS computing kernel called PlanKIT (planning
Kernel for ion therapy), developed in cooperation with IBA. This paper describes the BS
model and its application into a treatment planning workow for spot-scanning (section 2),
and provides a demonstration of its capabilities (section 3).
2. Methods
2.1. Principles of the BS model
The BS model allows computing the three-dimensional effect of an ion eld incident on a
water-like material. Its present use within the PlanKIT code is to estimate the outcome of a
therapeutic ion irradiation delivered through the spot-scanning technique, but the methodol-
ogy is rather general and could be easily applied to model other problematics related to the
interaction of radiation with matter.
The BS model may be considered an extension of previous works on uence-weighted,
elemental-pencil-beam kernels (Schaffner et al 1999, Soukup et al 2005, Kanematsu et al
2009, Fuchs et al 2012). An ion beam—throughout this paper the word ‘beam’ is used as a syn-
onym of ‘spot’–is completely characterised by the phase space distribution of its ions, that is,
by the set of positions and momenta owned by its ions at a specic moment in time or while
traversing specic surfaces. Every ion beam can be thought of as composed of sub-units, here
called beamlets, that are obtained splitting the beam phase space in smaller phase spaces.
If the beam is traversing a material, and if the outcome of the interaction of the individual
beamlets with the material is known, then the total beam irradiation outcome can be computed
summing the separate beamlets action, as long as the considered action is linearly superpos-
able. This problem can be simplied if another point of view is considered. The idea is to start
evaluating the average result of the interaction of a very small beamlet with a representative
homogeneous material, i.e. water. Then the average action of whatever extended beam on this
material could be approximated with a superposition of opportunely positioned and weighted
G Russo et al
Phys. Med. Biol. 61 (2016) 183

186
replicas of the action of that beamlet. The smaller the adopted beamlet, the better the beam
reproduction.
Various physical and radiobiological quantities can be used to describe the local action of
an ion beam impinging on a biological tissue (throughout this work, the term local is used to
refer to a spatial resolution corresponding to a computed-tomography voxel, that is millimetre
scale). The most notable examples currently are:
– The absorbed dose, or simply dose, which is the mean energy imparted to an irradiated
volume divided by the mass of that volume (ICRU Report 85a 2011).
– The dose-averaged LET, which is the LET averaged by weighting each LET value by the
absorbed dose delivered with a LET between LET and LET + dLET (ICRU Report 16
1970).
– The relative biological effectiveness (RBE), which is the ratio of absorbed dose of a
reference beam of photons to the absorbed dose of any other radiation, notably high LET
radiations, to produce the same biological effect (ICRU Report 30 1979).
– The RBE-weighted dose, which is the absorbed dose multiplied by the corresponding
RBE (ICRU Report 85a 2011).
Since it is possible to express the quantities listed above in terms of linearly-superposable
quantities (as shown in section2.2.2), the BS model allows managing them all in parallel in
a comprehensive treatment planning workow. Throughout the paper, the expression beam
irradiation quantities is used for convenience to refer collectively to the spatial distributions
of this set of quantities (or their linearly-superposable precursors) that result from a specic
beam-tissue interaction.
A schematic view of the BS model workow is provided in gure1. Complementing the
knowledge about the beamlet irradiation quantities in water with beam-line-specic, irradia-
tion-specic and target-specic information, through the BS model it is possible to derive the
beam irradiation quantities in the target. The starting point is the evaluation of the irradiation
quantities of a restricted set of small beamlets in water (section 2.2). Since this constitutes a
fundamental and universal information, completely decoupled from the specicities of beam
lines and targets, it can be evaluated once and stored in look-up tables(LUTs) for later repeti-
tive use. At the TPS commissioning stage, the beam optics is extracted from the experimental
data that characterise the considered beam line (section 2.3.3). The beam optics describes how
the beam phase space density evolves while the beam is propagating in the treatment room;
the related mathematical formulation is reported in sections 2.3.1 and 2.3.2. Knowing the
beam optics and the incoming direction of the beam in the target reference system, it is pos-
sible to compute the beam phase space density at the target entrance. This phase space density
provides the notion of which beamlets to superimpose, how positioned and weighted, in order
to reconstruct the beam irradiation quantities. The procedure to perform the roto-translation
and weighted superposition of the beamlet irradiation quantities is presented in sections2.4.1
and 2.4.3. The method to approximate the beam phase space density at the target entrance as
a discrete sum of beamlet phase space densities is reported in the appendix. It is important
to underline that the same beamlets weights are exploited to determine several physical and
radiobiological quantities in parallel, not just the dose; this was not considered in the afore-
mentioned superposition models, which were restricted to dose computations. If the target is
not water or is not homogeneous (e.g. a patient), then the beamlets cross different morpholo-
gies and produce different results. Therefore, a mapping that associates coordinates in the con-
sidered medium to water-equivalent coordinates must be applied to approximately account for
the distortion of the beamlet irradiation quantities due to the traversed material (section 2.4.2),
as is commonly done in ion therapy (e.g. Schaffner et al 1999, Krämer et al 2000, Soukup
G Russo et al
Phys. Med. Biol. 61 (2016) 183

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Q1. What are the contributions mentioned in the paper "A novel algorithm for the calculation of physical and biological irradiation quantities in scanned ion beam therapy: the beamlet superposition approach" ?

The calculation algorithm of a modern treatment planning system for ionbeam radiotherapy should ideally be able to deal with different ion species ( e. g. protons and carbon ions ), to provide relative biological effectiveness ( RBE ) evaluations and to describe different beam lines. In this work the authors propose a new approach for ion irradiation outcomes computations, the beamlet superposition ( BS ) model, which satisfies these requirements. The universal physical and radiobiological irradiation effect of the beamlets on a representative set of water-like tissues is evaluated once, coupling the pertrack information derived from FLUKA Monte Carlo simulations with the radiobiological effectiveness provided by the microdosimetric kinetic model G Russo et al Physical and biological ion-beam irradiation quantities computed via the BS model Printed in the UK 183 PMB © 2016 Institute of Physics and Engineering in Medicine 2016 61 Phys.