Journal ArticleDOI

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

, T. Orts2
07 Jan 2016-Physics in Medicine and Biology (IOP Publishing)-Vol. 61, Iss: 1, pp 183-214

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.

AbstractThe 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.

Topics: Ion beam (51%), Superposition principle (51%)

### 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).

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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
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
InternetSimulation Evaluation Envision (I-SEE), Torino, Italy
7
Centro Nazionale di Adroterapia Oncologica (CNAO), Pavia, Italy
8
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
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

25 citations

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