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Determination of the absorbed dose to water in the SOBP of a C-12 beam


Reference dosimetry performed with calibrated ionization chambers in carbon beams has a significantly higher measurement uncertainty than that in high‑energy photon fields. This is mainly attributable to the relatively high uncertainty of the correction factor for the radiation quality kQ, which must be theoretically calculated in carbon beams because no experimental data are available.

kQ factors can be determined experimentally with a small measurement uncertainty using water calorimetry. Such measurements are now being performed in the spread‑out Bragg peak (SOBP) of a carbon beam.

Radiation therapy with high‑energy ions, as applied at the Heidelberg Ion Beam Therapy Center (HIT), offers a number of advantages compared with conventional photon beam therapy [1]. Ions have higher biological effectiveness compared to photons; they also penetrate deeper into tissue and their spatial distribution is more accurate due to their inverse depth dose curve and lower scattering. Combined with the intensity‑modulated raster scan technique applied at HIT, it is thus possible to deposit the dose with high precision in the target volume while the surrounding tissue is protected. In addition to being deposited in a spatially precise way, the applied dose must be accurately determined. The quantity required for this purpose is the absorbed dose to water, which is determined in practice by means of calibration ionization chambers.

The standard measurement uncertainty of dosimetry based on ionization chambers is currently still much higher when using carbon beams than when using high‑energy photons. This is mainly due to the high uncertainty of the correction factor for the radiation quality kQ,Q0 (short: kQ). This correction factor is used to correct the difference in the response of the ionization chamber between the reference beam quality Q0, by means of which the chamber has been calibrated (usually 60Co), and the beam quality at hand Q (in the present case: 12C).

Due to the lack of experimental data, kQ for carbon beams has been determined numerically, which involves a total uncertainty of 2.8 % [2]. For photons, the total uncertainty merely amounts to 0.6 % [3].

Within the scope of a previous project realized by PTB and HIT, it had already been possible to determine experimental kQ factors for different ionization chambers for the flat input channel of a monoenergetic carbon beam. The corresponding measurements were carried out using water calorimetry at the QS beamline at HIT. The total uncertainty yielded for kQ was 0.8 % [4].

This project is now being continued with the determination of kQ factors for the spread‑out Bragg peak (SOBP). By comparing the kQ factors determined for the input channel and for the SOBP, a possible dependency on the linear energy transfer (LET) of the radiation may be detected.

Heat conduction effects must be given special consideration when using water calorimeters in the SOBP. Active scanning of the SOBP (i.e., by varying the particle energy for different maximum ranges) as performed in routine hospital procedures takes approx. 8 min. at a field size and a dose that are sufficient for using calorimetry (in this case: 6 × 6 × 6 cm3 and 1.5 Gy). However, over such a time period, the induced heat distribution would considerably dissolve, which would lead to a high correction factor for this effect, and thus high uncertainty. This would, in turn, result in an increased total uncertainty of the determined value of kQ.

To prevent this effect, the irradiation duration must be drastically reduced. This can be achieved by modulating the depth of the SOBP passively by means of a so‑called 2D range modulator (2DRM) developed at the Helmholtzzentrum für Schwerionenforschung (GSI Darmstadt) [5] (see Fig. 1). The 2DRM consists of many pyramidal pins that vary the energy of the incident beam depending on the position on the pins, thus causing the beam's depth to fan out. In this way, it suffices to irradiate with a monoenergetic field, and the irradiation duration is reduced to approx. 90 s. The 2DRM is manufactured additively and adjusted exactly to the desired dose distribution.

Fig. 1: Schematic drawing of the 2DRM.

The irradiation plan used for the calorimetric measurements was optimized regarding homogeneity, and the field yielded in combination with the 2DRM was exhaustively characterized [6]. For this purpose, the dose distribution was measured in 3D by means of an ionization chamber array whose depth inside a water phantom can be adjusted with a remote control. The corresponding setup was manufactured at PTB and is depicted in Fig. 2.

Fig. 2:   Front view of the ionization chamber array in the water phantom setup with a watertight PMMA casing around the array and a linear drive to modify the depth with a remote control.

The field homogeneity was determined as the standard deviation of the measured dose values inside a spherical volume with a radius of 20 mm around the center of distribution (which will later be the point of measurement of the calorimeter). This standard deviation was smaller than 1.1 % for all repeated measurements. The time stability of the field was determined from the mean standard deviation of the repeated measurements from each other. This deviation amounted to 0.26 %. The dose distribution is shown in Fig. 3.

These values allowed us to conclude that the dose distribution is suitable for the following measurements for determining kQ factors by means of water calorimetric measurements.

Fig. 3:   Dose distribution of the irradiation field for the calorimetric measurements. Left: Depth dose profile (the red dots were measured with the ionization chamber array in the water phantom, the blue dots with the PTW peak finder). Right: Lateral distribution at the measurement point (center of the SOBP) across the x- (y = 0) and the y‑axis (x = 0), measured with the ionization chamber array.

To date, a total of 223 measurements have been carried out within the scope of three measurement campaigns using a water calorimeter, and 70 measurements were carried out using ionization chambers for the PTW TM30013 and IBA FC65G chambers.

The kQ factors determined based on the preliminary assessment of the measurements suggest a difference from previous results obtained in the input channel. A new measurement campaign is planned to investigate this deviation. The preliminary uncertainty budget shows a total uncertainty of the kQ factors of less than 1 % for both of the chambers used.



[1]       M. Durante and J. Loeffler, Nat. Rev. Clin. Oncol. 7 (2010) 37–43

[2]       IAEA TRS-398, V.12 (2006)

[3]       P. Andreo et al, Phys. Med. Biol. 65 (2020) 095011

[4]       J.-M. Osinga-Blättermann et al, Phys. Med. Biol. 62 (2017) 2033–2054

[5]       Y.Simeonov et al, Phys. Med. Biol. 62 (2017) 7075-7096

[6]       Holm et al, Phys. Med. Biol. (2020), DOI: 10.1088/1361-6560/aba6d5



Opens local program for sending emailA. Krauss, Department 6.2, Working Group 6.23

Opens local program for sending emailK. Holm, Department 6.2, Working Group 6.23