Monte Carlo-based parametrization of the lateral dose spread for clinical treatment planning of scanned proton and carbon ion beams

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Abstract

Ion beam therapy using state-of-the-art pencil-beam scanning offers unprecedented tumour-dose conformality with superior sparing of healthy tissue and critical organs compared to conventional radiation modalities for external treatment of deep-seated tumours. For inverse plan optimization, the commonly employed analytical treatment-planning systems (TPSs) have to meet reasonable compromises in the accuracy of the pencil-beam modelling to ensure good performances in clinically tolerable execution times. In particular, the complex lateral spreading of ion beams in air and in the traversed tissue is typically approximated with ideal Gaussian-shaped distributions, enabling straightforward superimposition of several scattering contributions. This work presents the double Gaussian parametrization of scanned proton and carbon ion beams in water that has been introduced in an upgraded version of the worldwide first commercial ion TPS for clinical use at the Heidelberg Ion Beam Therapy Center (HIT). First, the Monte Carlo results obtained from a detailed implementation of the HIT beamline have been validated against available experimental data. Then, for generating the TPS lateral parametrization, radial beam broadening has been calculated in a water target placed at a representative position after scattering in the beamline elements and air for 20 initial beam energies for each ion species. The simulated profiles were finally fitted with an idealized double Gaussian distribution that did not perfectly describe the nature of the data, thus requiring a careful choice of the fitting conditions. The obtained parametrization is in clinical use not only at the HIT center, but also at the Centro Nazionale di Adroterapia Oncologica. © 2013 The Author 2013. Published by Oxford University Press on behalf of The Japan Radiation Research Society and Japanese Society for Therapeutic Radiology and Oncology.

Figures

  • Fig. 1. Example of measured lateral distributions [6] with corresponding MC simulations (normalized to the data) for proton (top, 157.53 MeV/u) and carbon ion (bottom, 299.94 MeV/u) beams in water, sampled at a depth of ~1.5 cm in the entrance channel (left, a and c) and of ~16.5 cm shortly before the Bragg peak (right, b and d). The double Gauss fit of the experimental data is also shown in comparison to the single Gauss approximation.
  • Fig. 2. Example of laterally integrated depth–dose distributions obtained with the simplified description of the HIT beamline for initial basic data generation (‘DB approximation’) [3] in comparison with the distributions obtained with the upgraded geometry used in this work (‘Explicit beamline’) for an intermediate proton beam energy of 142.66 MeV/u (left) and the lowest carbon ion energy of 88.83 MeV/u (right), which is sensitive to the Bragg-peak modulation from the tungsten wires in the beamline. The introduced shift accounts for the range degradation in the elements of the beamline and in air, which is not modelled in the DB approximation.
  • Fig. 3. Separation in depth of the integral doses of the narrow (n · (1 – w)) and broad (n · w) components of the double Gauss parametrization of measured data [6] in comparison with the simulated laterally integrated dose contributions from the lessscattering (all but protons and alpha particles) and more-scattering (protons and alpha particles) primary and secondary ions produced by an energetic 430.10 MeV/u carbon ion beam in water.
  • Fig. 4. Example of simulated lateral profiles for basic data generation, with corresponding double Gauss fit for the proton lowest beam energy (48.12 MeV/u, top) and carbon ion highest beam energy (430.10 MeV/u, bottom) sampled at 20% (left, a and c) and 100% (right, b and d) of the Bragg peak position. The different representation reflects the different fitting of r ·D(E,zeq,r) for protons (a and b) and D(E,zeq,r) for carbon ions (c and d), with related choice of semi- or double-logarithmic scale for improved display. Remaining limitations of the double Gaussian approximation are clearly visible, though mostly affecting the low-dose halo at a large distance from the central core of the pencil-beam. The green dashed line marks the level below which the data are no longer considered for the fit (cf. text).
  • Fig. 5. Typical trends in depth of the lateral basic data (i.e. fitted σ1 and σ2 and weight parameter w of the double Gauss) for protons (top) and carbon ions (bottom) at the lowest (left) and highest (right) available beam energy.
  • Fig. 6. Comparison of the HIT basic data input in both the HIT and CNAO TPS, with respect to the parameters deduced using the same fitting procedure described in this work, however applied to FLUKA MC simulations of lateral beam broadening in water using a detailed modelling of the CNAO beamline for proton beams [11]. Two similar energies of approximately 60 MeV/u (left) and 221 MeV/u (right) were considered. While the sigma parameters match fairly well, some discrepancies are observed in the weight factor w directly related to the broad Gaussian component, especially for low-energy proton beams. This is likely ascribed to less large-angle scattering material in the CNAO beamline.

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APA

Parodi, K., Mairani, A., & Sommerer, F. (2013). Monte Carlo-based parametrization of the lateral dose spread for clinical treatment planning of scanned proton and carbon ion beams. Journal of Radiation Research, 54(SUPPL.1). https://doi.org/10.1093/jrr/rrt051

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