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

TL;DR: 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.

Summary

1. Introduction

• The number of clinical facilities that employ ion therapy to treat cancer is increasing worldwide.
• The use of ions different from protons entails the use of more complex irradiation-outcome computation algorithms in treatment planning systems (TPS).
• RBE values are usually characterised by big uncertainties (10% or more) and the employment 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).
• 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.
• This paper describes the BS model and its application into a treatment planning workflow for spot-scanning (section 2), and provides a demonstration of its capabilities (section 3).

2.1. Principles of the BS model

• The BS model allows computing the three-dimensional effect of an ion field incident on a water-like material.
• The RBE-weighted dose, which is the absorbed dose multiplied by the corresponding RBE (ICRU Report 85a 2011).
• The starting point is the evaluation of the irradiation quantities of a restricted set of small beamlets in water (section 2.2).
• 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 aforementioned superposition models, which were restricted to dose computations.

2.2. Modelling universal beamlet irradiation quantities

• There are several strategies that can be used to describe the interactions of beamlets with matter.
• 2.1. Monte Carlo simulations of infinitesimal beamlets.
• In some others an explanation in terms of cell survival is not possible (e.g. nausea, fatigue, somnolence, acute edema, resulting from radiation-induced inflammatory cytokines), and even if the LQ parametrisation is still employed to describe the global dose-effect relationship, its use at the local level as outlined in the present model might not be appropriate.

2.3. Modelling the beam optics of a specific beam line

• The specificities of a beam line are manifested in its beam optics, that is the evolution of the beam phase space around the isocenter, in the absence of a target.
• The longitudinal phase space density is the combination of the energy spread coming from the acceleration and energy-selection systems with the energy spread due to the presence of material on the beam path.
• In fact, the Bragg peak produced in a water phantom by a beam that has traversed a passive element corresponding to a thickness ∆z of water-equivalent material can simply be obtained by removing the first ∆z at the phantom entrance from the Bragg peak that the same beam produces without previous interactions.
• Depending on the amount of available information on the beam line design, each parameter may be fixed or subjected to vary within a more or less restricted range.
• Ideally, the derived beam-line description should be physically meaningful and close to the real set-up in order to be trusted when extrapolating to configurations lacking of experimental characterisation.

2.4. Evaluating the beam irradiation quantities

• The computed beam phase space density at the patient’s entrance is used as weight for the superposition of the beamlet irradiation actions.
• The WEPL approach allows creating a correspondence between the path length of a particle in a heterogeneous material and its equivalent path length in water.
• – WEPLs are attributed to each position along the beam axis, integrating (28). –.
• In the BS model, these considerations apply as well to the other computed quantities, so the track-averaged-LET-to-water and dose-averaged-LET-to-water are computed, instead of their ‘to-medium’ counterparts.

3. Results and discussion

• The dose computation capabilities of PlanKIT were benchmarked against experimental data and FLUKA and Syngo® simulations, in order to evaluate the correctness of the implementation and provide some confidence in the BS model usage (sections 3.2–3.6).
• Five irradiation configurations were considered: single spots, square monoenergetic fields and cubic spreadout Bragg peaks in homogeneous materials, single beams in a simple heterogeneous geometry and a clinical case.
• In addition, in section 3.6.3 some computations are presented to show the kind of analysis the BS model allows.
• In section 3.1 the operations performed to commission the BS model on the employed beam line are reported.

3.1. Commissioning the BS model for the CNAO facility

• The BS model has so far been successfully commissioned to the CNAO and WPE (Westdeutsches Protonentherapiezentrum Essen) beam lines.
• For the sake of brevity, here just the results relative to the horizontal beam line located in the treatment room 3 of CNAO are shown.
• The longitudinal transfer functions were realised in terms of the WET distribution w(z) of section 2.3.1 and were independent of beam energy, as it is expected from physical considerations.
• The extrapolated proton and carbonion beam phase space densities at the vacuum exit window showed the anticipated decrease of spot size and divergence with increasing beam energy.
• As for the radiobiological modelling, the same tissue response made available by Syngo® and used for clinical carbon-ion treatment planning at CNAO and HIT was implemented in the PlanKIT LUTs.

3.2. Evaluation of single beams in a homogeneous phantom

• Proton and carbon-ion beam spot profiles were measured after the traversal of different thicknesses of water-equivalent material, in order to check the enlargement of beam size with depth.
• With the help of IBA-Dosimetry, tests were performed at CNAO to check its reliability with carbon-ion beams, obtaining performances comparable to the ones showed with protons.
• This validation is out of the scope of this paper; related measurements will be referred to in the product data sheet.
• For protons, the difference between the spot sigmas measured and simulated by PlanKIT was lower than 5% and 0.3 mm in all conditions but at the end of the range with the highest beam energies, where overestimates up to 10% and 0.7 mm were observed.
• At low energies the agreement was better than 3%.

3.3. Check of the low-dose contributions

• A water phantom (model 41023, PTW-Freiburg) was placed on the treatment table with its entrance face positioned at the isocenter.
• Three consecutive measurements were performed for each point and the mean value and standard deviation were computed.
• Measuring the dose in the centre of square monoenergetic fields made of evenly spaced spots of equal intensity provides a way to check whether the modelling of the low-dose envelope for a single spot is sufficiently accurate (Sawakuchi et al 2010, Grevillot et al 2011).
• Concerning the irradiation with proton fields, the percentage difference between the field size factors measured and evaluated by PlanKIT was lower than 1% for the 78% of the points, lower than 2% for 96% of the points, and lower than 3% for all the points.

3.4. Evaluation of cubic SOBPs in a homogeneous phantom

• Cubic SOBPs of different sizes and in-depth positions (listed in table 1) were irradiated in RW3 with both proton and carbon ions, with homogeneous RBE-weighted doses of 2 and 3 Gy (RBE), respectively.
• Since the Lynx® output was given in arbitrary units, the integral intensity of each image was normalised to the PlanKIT integral dose at the same depth.
• A closer look revealed that the minor ripple was ascribable to a too large computed spot size at high depths.
• In contrast, for the two shallower proton SOBPs, and in general for all depths in the phantom smaller than 23 cm, more than 98% of the surface was passing the 3%–3 mm 3D γ-index criteria.
• One cannot exclude the eventuality of a concurrent problem in the dose computation algorithm.the authors.

3.5. Evaluation of single beams in a heterogeneous phantom

• The authors also tested the BS model performances in the presence of important material heterogeneity.
• Monoenergetic beams were directed towards a heterogeneous phantom consisting of four adjacent homogeneous blocks made of different materials.
• This is likely arising from small differences between the conversion from Hounsfield numbers to WEPL implemented in PlanKIT and the one from Hounsfield numbers to material properties set in Fluka.
• In any case, this discrepancy was found to be of limited relevance when simulating clinical conditions (as shown in section 3.6.2).
• All in all, PlanKIT reproduced fairly well the beam perturbation caused by the presence of the material discontinuity, with results comparable to those reported in similar studies (Soukup et al 2005, Grevillot et al 2012).

3.6. Evaluation of a treatment plan

• The actual clinical treatment was planned at CNAO with the Syngo® software, using two laterally-opposed carbon-ion beams.
• As it is done routinely, the radiosensitivity of brain tissue was attributed to the whole head, using the LEM I with parameters specified in Krämer and Scholz (2000).
• It did not prevent the RBE-weighted dose distribution to pass the 3%–3 mm γ-index criteria in more than 98% of the PTV and in more than 99% of the patient volume having a dose greater than 1% of the maximum.
• Differences between the physical dose distributions produced by PlanKIT and FLUKA were visible both in the entrance path of the fields and in the PTV.
• In order to illustrate the possibilities offered by the BS model, a side-by-side evaluation of RBE and dose-averaged LET distributions following proton and carbon-ion irradiation is presented in figure 8 for the same treatment set-up considered in section 3.6.2.

4. Conclusions

• An algorithm for the computation of the physical and biological irradiation action of ion beams, the BS model, has been proposed and successfully implemented.
• Since the beamlet irradiation quantities in water are derived from Monte Carlo simulations, the obtained three-dimensional description is more detailed and more flexible compared to the usual analytical approaches: it allows expressing the outcome of the irradiation of different ion species in terms of different quantities, within the same framework.
• The BS model also extends the treatment of beam optics.
• The comparisons with experimental data and with FLUKA and Syngo® simulations provide high confidence in the model usage, albeit they cannot be considered sufficient to fully validate it for clinical applications.
• Besides, the radiobiological modelling must be subjected to further checks, benchmarking the use of LEM in the BS model either against TRiP98 or against in vitro experimental data, along the lines of what done by Krämer et al (2003).

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.

Figure 2. Mean dose per primary ion ⟨ ⟩ ( )D z r,0 , dose-averaged LET ⟨ ⟩ ( )z rLET ,D and radiobiological ( )α z r, parameter distributions for a quasi-infinitesimal beamlet of 270 MeV u−1 carbon ions impinging on a water phantom. For the evaluation of the α distribution, the MKM parameters reported in Kase et al (2008) for human salivary gland (HSG) cells were used.

Figure 3. Sample view of the BS model tuning based on the CNAO commissioning data. Upper part: extraction of the ripple-filter w(z) distribution and of the energy spread σE produced by the carbon-ion accelerator through the fit of experimental carbon-ions depth-dose curves in water, in presence and absence of the two ripple filters. Lower part: derivation of the virtual protons source produced by the protons accelerator at the vacuum exit window from the fit of protons spot-size evolution in air.

Figure 6. Comparison between PlanKIT- and Syngo®-generated dose distributions corresponding to the irradiation of a skull-base chordoma with two opposing carbonion fields.

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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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.