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Experimental determination of the correction factors for the beam quality in the SOBP of a C-12 beam using water calorimetry


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

In order to reduce this uncertainty, kQ factors were experimentally determined using water calorimetry in collaboration with the Heidelberg Ion‑Beam Therapy Center (HIT).

As applied at the HIT, radiation therapy with high‑energy ions offers a number of advantages over conventional photon therapy. For example, it has a higher biological effectiveness compared to photons, the beams penetrate deeper into tissue, and their spatial distribution is more precise due to their inverse depth dose curve and lower scattering [1]. However, this method does demand that the applied dose be determined with great accuracy. The quantity required for this purpose is the absorbed dose to water, which is determined in practice by means of calibrated 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 beam quality, kQ. Due to the lack of experimental data, kQ in carbon fields has been determined numerically, yielding a total uncertainty of 2.8 % according to TRS‑398 [2] and 2.2 % as per DIN 6801‑1 [3]. For photons, the total uncertainty amounts to just 0.6 % [4].

As part of a previous project implemented by PTB and HIT, researchers applying water calorimetry were able to experimentally determine kQ factors for different ionization chambers for the flat entrance channel of a monoenergetic carbon beam. The result of this experimental determination was a total uncertainty of 0.8 % for kQ [5].

In another project, which has now been successfully completed, kQ factors were determined for the spread‑out Bragg peak (SOBP). This was achieved by modulating the depth of the SOBP passively by means of a so‑called 2D range modulator (2DRM) [6]. Researchers were thus able to significantly reduce the irradiation time in comparison with an active scanning procedure as used in clinical practice and hence to determine heat conduction effects for water calorimetry with a low uncertainty. This ultimately resulted in a lower overall uncertainty of the experimentally determined kQ factors.

The radiation field generated with the 2DRM was characterized in detail by means of repeated measurements of the three‑dimensional dose distribution and in terms of homogeneity and reproducibility [7]. Based on this, various correction factors for both calorimetric and ionometric measurements were determined.

In determining the kQ factors, the dose absorbed in water was initially determined under the given irradiation modalities using the PTB water calorimeter. Afterwards, measurements with the ionization chambers PTW TM30013 and IBA FC65G were carried out in the water phantom of the calorimeter under the same irradiation conditions. The measurement set‑up of the calorimeter with the 2DRM positioned in front of it is shown in Figure 2. A total of 282 measurements were carried out within the scope of four measurement campaigns using the water calorimeter, and 70 measurements each were performed with the two ionization chambers mentioned above. An exact description of the measurement process as well as detailed results were published in [8].

Water calorimeter measurement set-up

Figure 1: Measurement set‑up of the water calorimeter (right) in front of the beam nozzle (left) with the 2DRM in the isocenter (middle).

It was ultimately possible to determine the kQ factors for both ionization chambers with a standard measurement uncertainty of 0.7 %. In comparison with the uncertainty of the factors indicated in the TRS‑398 report [2], this is a reduction by a factor of four.

The final kQ factors were compared with the values from TRS‑398 [2] and DIN 6801‑1 [3] as well as with the values determined for the entrance channel [5]. A graphic representation is shown in Figure 2.

This shows that the kQ values determined experimentally for the SOBP match the values indicated in DIN 6801‑1 within the measurement uncertainty, but are 1.3 % to 2.3 % below the values indicated in TRS‑398. These deviations might indicate that the assumptions made for the theoretical calculation of the kQ values for the SOBP in TRS‑398 are insufficient.

correction factors for the beam quality, 2 diagrams

Figure 2: Experimentally determined kQ factors for the entrance channel [5] and the SOBP [8] in comparison with the values indicated in references [2] and [3] for PTW TM30013 (left) and IBA FC65G (right). Graphic taken from [8].

In comparison with the kQ values determined experimentally in the entrance channel, the kQ factors determined in the SOBP are approximately 1.1 % to 1.9 % smaller. However, both experiments differ in terms of the applied entrance energy of the particles and especially in terms of the applied irradiation plan (raster scanning). The differences between the entrance channel and the SOBP could be further investigated by conducting further measurements in the entrance channel while applying the same energy (but without using the 2DRM) and the same irradiation plan as for the SOBP.


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

[2]    IAEA TRS‑398, V.12 (2006)

[3]    DIN‑Normenausschuss Radiologie (NAR), DIN 6801‑1 (2016)

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

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

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

[7]    K. Holm et al, Phys. Med. Biol. 65 (2020) 215003, doi.org/10.1088/1361-6560/aba6d5

[8]    K. Holm et al, Phys. Med. Biol. 66 (2021) 145012, doi.org/10.1088/1361-6560/ac0d0d


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

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