Dosimetry for ion-beam therapy using fluorescent nuclear track detectors and an automated reader. Heidelberg, Germany

Transcription

1 Dosimetry for ion-beam therapy using fluorescent nuclear track detectors and an automated reader Steffen Greilich 1,2,*, Jeannette Jansen 1,2, Grischa M. Klimpki 1,2, Jasper J.M. Kouwenberg 3, Alexander Neuholz 1,2, Tina Pfeiler 1,2, Shirin Rahmanian 1,2, Alexander Stadler 1,2, Leonie Ulrich 1,2 1 Division of Medical Physics in Radiation Oncology, German Cancer Research Center (DKFZ), D Heidelberg, Germany 2 Heidelberg Institute of Radiation Oncology (HIRO), National Center for Radiation Research in Oncology (NCRO), D Heidelberg, Germany 3 Radiation, Science & Technology, Delft University of Technology, Mekelweg 15, 2629 JB Delft, Netherlands Keywords Luminescence dosimetry; Aluminum oxide; Confocal microscopy; Radiation detection and imaging Abstract For the assessment of effects of clinical ion-beams, dosimetry has to be complemented by information on particle-energy distribution or related quantities. Fluorescence nuclear track detectors made from C,Mg-doped alumina single crystals allow for the quantification of ion track density and energy loss on a single-track basis. In this study, their feasibility and accuracy to quantify fluence, linear-energy-transfer (LET) distributions, and eventually dose for a spread-out carbon ion Bragg peak was investigated. We found that while for the primary ions track densities agreed within a percent range with the reference data generated by Monte-Carlo radiation transport, the number of low-let fragments in the beam was largely underestimated by approximately a factor three the effect was most pronounced for protons where the measured fluence deviates at least an order of magnitude. Nevertheless, due to the dose * Corresponding author: s.greilich@dkfz.de 1

2 major contribution of carbon ions, the determination of the individual detector sensitivity could be identified as the main source of uncertainty in LET (and dose) assessment. In addition, we conclude that using an automated, dedicated FNTD reader device despite its inferior optical properties improves outcome due to the considerably larger amount of data available as compared to a state-of-the-art multi-purpose confocal laser scanning microscope. Introduction Ion Beam Cancer Therapy (IBCT), i.e. radiotherapy with heavy charged particles, promises improved clinical outcome for many tumor types compared to conventional treatments using megavoltage X-ray or electron beams [1]. Consequently, both the number of centers and treatments has increased steeply during the last decade [2]. The defined range of ions and their inverse depth-dose profile enable further dose escalation in the tumor and better sparing of healthy tissue. In addition, especially ions heavier than protons show an enhanced relative biological efficiency (RBE) [3]. The latter is commonly included for IBCT prescription as a multiplication factor to the physical dose. The RBE is thereby in most cases estimated by radiobiological models such as the local effect model (LEM) [4] which in turn need the particle spectrum, i.e. the fluence dφ Z (E)/dE differential in kinetic energy E of projectiles with charge Z, or similar information such as microdosimetric spectra as input parameter. Clinical ion beams become inevitably multi-energetic multi-particle beams by energy loss straggling and inelastic nuclear scattering. Furthermore, the energy spectrum often collapsed to a single number specifier of radiation quality like the fluence- or dose-averaged linear energy transfer (flet, dlet) [5] impacts a number of other quantities relevant for dosimetry [6] such as the stopping power ratios [7], the W value [8], or the quenching of solid state detectors. Also planning tools for physical dose need data on the particle spectra or phase space, e.g. Monte-Carlo based transport simulations [9]. Powerful detectors to characterize phase space, particle or microdosimetric spectra, are mostly active, silicon-based, and rather complex [10, 11, 12]. Small, passive track detectors such as track etch detectors (TEDs) or fluorescent nuclear track detectors (FNTDs) do not match those devices in accuracy but allow for easier handling and additional applications. Fluence and energy loss of ion beams can be determined on a single track level [13, 14, 15]. Alumina-based FNTDs show a wider LET range and higher spatial resolution than TEDs, which makes them a promising candidate for a number of applications in 2

3 IBCT [16] with respect to dosimetry [17], radiobiology [18] and treatment verification, potentially even in vivo. Such single-track based dosimetry does not suffer from quenching. In this study, we report on the performance of alumina-based FNTDs for fluence, energy loss, and dose determination in a spread-out carbon ion Bragg peak (SOBP) using an automated reader device. 2. Material and Methods 2.1 Dosimetry for IBCT The gold standard for dosimetry in clinical ion beams are ionometric measurements using air-filled chambers, where current dose-to-water based protocols such as the IAEA TRS-398 [19] use a calibration coefficient N w,q0 to relate the charge produced in the air volume represented by the corrected electrometer reader M to the dose D w,q in a specific beam quality Q: D w,q = M N w,q0 k i k Q,Q0 Eq. 1 While k i represents a number of factors accounting for chamber related corrections, k Q,Q0 allows to transfer the calibration coefficient from the calibration beam quality Q 0 to the user quality Q. k Q,Q0, and k i change very little with beam quality: for example, the variation in k Q,Q0 for a standard Farmer chamber (PTW30001) is not more than 5 in proton beams with residual ranges between 0.5 and 30 g/cm². This makes air-filled ionization chambers a powerful tool for high-accuracy dosimetry in ion beams but at the same time indicates that they can provide only very limited information on beam quality. Most solid-state dosimeters such as films, TLDs, OSLDs, alanine, gels, etc., suffer significant sensitivity dependence on radiation quality in ion beams, especially signal quenching in high-let beams [6]. Secondary signals such as LET-dependent ratios between peaks in a glow curve or OSL emission bands, can be utilized for LET determination and response correction [20]. It seems, however, hardly feasible to establish a unique relation between these secondary signals and a radiation quality specifier such as LET, let alone the energy spectrum, for ions heavier than protons [21]. 3

4 Fluence-based assessment of absorbed dose D using single track detectors relies in contrast on the relation D = Φ S/ρ, Eq. 2 where Φ is the particle fluence and S/ρ the mass stopping power of the particles. For multi-energetic, multi-particle fields this relation has to be expanded to Z max E max D = dφ Z(E) de Z=1 E min S(E, Z) de ρ to take into account contributions from particles varying in charge Z and kinetic energy E due to the dependence of mass stopping-power from these parameters. To determine the dose based on Eq. 2, the fluence of particles as well as their respective stopping power have to be measured. Eq Fluorescence nuclear track detectors Alumina single crystals doped with carbon and magnesium (Al 2 O 3 :C,Mg) exhibit a high concentration of complex F 2+ 2 (2 Mg) color centers that undergo radiochromatic transformation into F + 2 (2 Mg) centers when exposed to ionizing radiation. The number of centers transformed depends on the local energy deposition. The F + 2 (2 Mg) centers show high quantum-yield intra-center fluorescence at 750 nm when excited around 620 nm with a short life-time of 75+/-5 ns. This allows for the use of confocal laser scanning microscopy to assess 3D energy deposition patterns with µm-resolution and reconstruction of single ion tracks and their energy loss [15]. All detectors used in this study were produced by the Crystal Growth Division of LANDAUER Inc. (Stillwater, Oklahoma, USA), cut along the optical c-axis into small rectangular plates ( mm 3 ), and polished on one of their large sides to optical quality. 2.3 Fluorescence read-out For previous studies of our group, FNTDs have been read out by a commercial laser scanning microscope (ZEISS LSM ConfoCor 3) with the configuration described in [16]. Using a high-na, oil-immersion objective and avalanche photodiodes (APDs) in photon-counting mode, superb image quality and good signal-to- 4

5 noise ratio could be achieved. Sample processing is, however, hampered by manual operation. Also, early saturation of the APDs limits the usable dynamic range. The LANDAUER FXR700RG CLSM - a research version of the commercial system [22] - is in contrast fully automated and dedicated to high-throughput processing. It features an air objective (100x/0.95NA), current-mode APDs and 2D galvoscanning. The reduction in resolution due to the lower NA is clearly seen in Fig. 1. The 640 nm laser diode was measured to provide 4 mw power at the sample (measured using an Ophir NOVA II powermeter). The laser power is significantly higher compared to the LSM710 (approx. 40 times), and the user has to be aware of potential signal bleaching, which we found however to be in the permille range when re-reading image stacks at the same position. The signal to noise ratio was found comparable for a 90 MeV/u 12 C sample, being approx. 17 for the FXR700RG and 25 for the LSM710 operated at full laser power. The confocal pinhole is fixed to 1 AU, and an APD in current mode is used to detect the fluorescence light. As a second channel (reflected light) a photo-diode (PD) is available. The FXR700RG can process up to 76 samples in a massive scan, i.e. reading multiple stacks across each detector (Fig. 2). For the samples irradiated in this study, 49 (7x7) frame of 100x100 µm² (504x504 pixel) were read-out per sample, with 41 slices in depth (0 100 µm in 2.5 µm steps). 2.4 Image processing All image processing was done using the FNTD extension package for the R language [23]. It provides a scriptable interface to the Java-based FNTD library which in turn uses the NIH-based IMAGEJ [24] and a number of its plugins as a class library. For this study, version of the FNTD package was used. It allowed to run the entire processing from raw image data to final results in a single script and is provided as open-source software under GPL3 license at The package can import the image output of both the FXR700RG (32-bit float text files) and the LSM710 (16-bit integer, Zeiss LSM format). Images were first background-subtracted using a histogram-based routine from the MOSAIC ToolSuite for IMAGEJ [25]. A modified version of the MOSAIC feature point extraction algorithm [26] was then employed to identify ion tracks. This tool is specifically tailored for identification ( tracking ) of ion beam footprints in fluorescence images ( trackspots ) and linking them correctly to reconstruct the ion tracks. Its success rate and throughput is significantly higher that of the original version and also makes it capable of successfully processing high-fluence images [27]. 5

6 The fluorescence intensity η of the trackspots was evaluated as the maximum I of pixel intensities I(x, y) within a six pixel radius, with local coordinates x and y with respect to the trackspot center found by the tracking tool [15]. Subsequently, the mean intensity η and the fluctuation of intensity σ η ( intensity-straggling, as the coefficient of variation sd(η)/η ) along each track were calculated. While intensity data from the LSM710 have to be corrected for variable laser-power and saturation effects [15], the output from FXR700RG could be used directly. Corrections for sensitivity fluctuation across the detector area, spherical aberration, field-of-view non-uniformity, and angular dependence of the fluorescence signal were applied as described by [28]. 2.5 LET calibration and assessment η can be related to the energy loss of a particle over one image slice. Due to energy loss straggling it varies considerably (up to approx. 40 % for fast protons). By averaging η along a track, the fluctuation is minimized and the mean intensity η can be used as an estimator of stopping power or L, respectively (neglecting delta electrons that leave the immediate vicinity of the track). To establish a relation between energy loss of a particle and fluorescence intensity η, a set of 66 FNTDs was read out on the FXR700RG. The set covers irradiations with protons, helium, carbon and oxygen ions covering an LET range in alumina from approx. 1 to 150 kev/µm. A superset of these samples was used in a previous study for calibration of the LSM710 [15]. For each detector, four stacks with 21 image slices (100x100 µm², 504x504 pixel) were acquired from the detector surface to 100 µm depth with 5 µm spacing (see Fig. 2 for a schematic illustration). The time per image was 10 s (pixel dwell time ca. 40 µs). While covering approximately twice the volume, the read-out of all samples took less than 24 hours in total compared to about three person weeks (24 h / 7 days a week) for the LSM710. Fig. 3 shows the LET-intensity relation. Similar to [15], a logarithmic function η = a log ( L,Al 2 O 3 b with a = and b = was found to describe the data better than a power law function. LET could then be evaluated from fluorescence intensity by + 1) Eq. 4 L,Al2 O 3 = b (10 η a 1) Eq. 5 6

7 The function however is purely empirical and the underlying mechanism is still unknown. Alas, parameters can interpreted: a is a scaling factor, accounting for the sensitivity of the optical system, the processing of light counts, but also for the sensitivity of the corresponding FNTD(s). log b represents the slope of the intensity-log LET-relation for large η and L values. While b was assumed to be the same for all FNTDs used in the SOBP measurements, a was expected to vary. To determine a for each FNTD, the fluence-weighted LET from transport simulation (see section 2.7) was matched for the high-let peak (first five depths) or the low-let peaks (other depths). The variation in sensitivity matched values found in previous studies (approx. 20 %, 1 s.d.). 2.6 Fluence and dose assessment The mean intensity η or L, respectively, was then used to divide particles into three groups: primary particles, low-let and high-let fragments (Fig. 3). The fluence of a single particle i assigned to a group j, Φ ij, was determined by dividing the measured particle s track lengths l i by the readout volume V (Fig. 2): Φ ij = l i V The fluence of a group or the total fluence was calculated by summing the respective particle fluences. Other examples of groups are particles of charge Z (if distinguishable) or particles within a defined LET interval. Eq. 3 can be used to obtain the dose of particle group j by Eq. 6 where N j is the total number of tracks in group j and Φ ij the fluence and (L,Al2 O 3 ) ij the LET of the individual track. The total dose is given by D = N j D j = Φ ij (L,Al2 O 3 ) Eq. 7 ij i=1 j D j. 2.7 Monte Carlo transport simulation 7

8 Reference data for the SOBP irradiations were created using the FLUKA code, version c.4 [29, 30]. The same settings were as in [21] were used. In brief, HADROTHE defaults and the DPMJET-III and RQMD libraries were employed, the Sternheimer parameters and ionization potential (76.8 ev) for water were adjusted, and scoring was done using the USRBIN (dose, LET) and USRTRACK (fluence, spectra) cards together with AUXSCORE and a customized MGDRAW routine. The beam was assumed to exit the accelerator mono-energetically, and the beam application system and ripple filter were represented by a simplified geometry. 3. Experiments and results 3.1 Irradiation FNTDs were irradiated at the Heidelberg Ion-Beam Therapy Center (HIT) in a spread-out Bragg peak ranging from approx. 10 to 15 cm depth in water and being composed of 18 pristine carbon Bragg peaks with energies between 219 and 280 MeV/u (Fig. 4, upper panel). FNTDs were placed at seven distinct positions in the entrance channel, SOBP and tail, using slabs of RW3 (PTW Freiburg) water equivalent plastic. Taking into account the water-equivalent thickness (WET) of the beam application system and the distance to the iso-center (0.3 mm [31]) and the thickness of the FNTDs that were facing with their non-polished side towards the beam (0.165 cm WET), the effective depths were approx. 0.75, 1.75, 8.75, 10.75, 12.75, and cm. The planned entrance fluence of approx / cm 2, corresponding to a flat biological dose of 2 GyRBE (for Chordoma cells) in the SOBP was scaled down by a factor of 10 (yielding / cm 2 entrance fluence) in order to stay well below the fluence limits of the FNTDs even in the presence of fragments. 3.2 LET, fluence, and dose results Fig. 5 shows the distributions of track mean intensity, converted into LET in water together with the reference data. As the peaks appear well separated, they can be attributed to the primary carbon ions (high LET) and lighter fragments (mainly protons and helium, which could also be identified using intensity straggling). The measured peak for the carbon primaries appears wider than for the reference, 8

9 which is most pronounced in the entrance channel. At the distal edge of the SOBP (14.75 cm), no carbon ions were recorded. At shallow depths (0.75 cm, 1.75 cm) considerable numbers of particle with lower but some also with higher LET than the primary ions were detected. Medium-LET (lithium, beryllium, or boron) peaks are visible at SOBP depths with optimized histogram scaling. Protons (lowest LET-peak) are largely underestimated at all positions and only significantly present at the two largest depths. The latter results in a considerable underestimation of fragment and total fluence (Fig. 4, middle panel), while the fluence of primary ions agrees much better with the reference data. This is also reflected in the measured fluence-weighted LET (Fig. 4, lower panel) where values for carbon ions show the same trend as the reference but fragment data are significantly overestimated due to the absence of low LET protons. Consequently, measured dose values are underestimating the reference. As lighter fragments contribute less to the total dose in the entrance part and the SOBP, the underestimation is mitigated. 4. Discussion The experiments yielded promising results for the assessment of fluence, LET and dose in a therapeutic carbon beam, but also revealed a number of challenges that have to be addressed in order to deliver more accurate outcomes. The broadening of the (primary) peak in the LET spectrum can be interpreted as a result of the line-width of the system (approx. 4 % in the respective intensity range, translating to ca. 10 % in LET) and the differences in carbon fluence / LET for the most distal position in the Bragg peak can be assumed to arise from small positioning errors. The most obvious issues, however, are the underestimation of proton fluence and the variation in detector sensitivity resulting in LET (and dose) uncertainties. Concerning the first, visual inspection of the raw image data and tracking results did not reveal a considerable number of trackspots that had not been identified or excluded from analysis. We are currently investigating three potential causes for the underestimation: (a) a lack of sensitivity of the FXR700RG reader as for example compared to the LSM700, (b) an outshining effect, i.e. dim trackspots becoming invisible in the presence of many bright, high-let tracks, and (c) the wider angular distribution of light fragments as tilted tracks become elongated and dimmer in microscopy images and potentially muting them undetectable. Preliminary data do not support the first two hypotheses. In high-quality scans using the LSM700, we did not see a strong increase in proton tracks, but rather many energy deposition events of similar magnitude that could however be identified as end-tracks of delta-electrons (cf. Fig. 1). 9

10 As for the sensitivity correction, the method of matching the LET, especially as done for the first five depths, adds a considerable amount of unwanted arbitrariness to the analysis and obviously explains much of the agreement in dose. A potential alternative could be the use of sensitivity-invariant quantities such as intensity-straggling as an internal calibration or the use of an external standard such as an additional test radiation or the blue/green fluorescence in FNTDs. Also, we had to cut some highintensity tracks which gave due to the logarithmic relation used for intensity and LET extreme, unphysical LET contributions, dominating the dose calculation. 5. Conclusion The results show that it is in possible to use FNTDs for dosimetry in ion-beams with a semi-automated workflow where the user interaction is limited to the identification of suitable parameters for trackspot identification and linking, and sensitivity calibration of the individual FNTDs. Despite the inferior optical specifications of the FXR700RG reader compared to the Zeiss LSM710, no obvious disadvantage for the presented application was seen. Rather, better dynamic range in light detection is crucial for carbon beams and high-throughput capability not only enables to achieve good track statistics and a reasonable number of samples per experiment but also enables more accurate corrections such as spherical aberration or field-of-view non-uniformity due to the large amount of data. To improve the outcome further, the reasons for underestimation of low-let particle fluence have to be found and if possible avoided, and a more robust method for individual detector calibration should be sought. Acknowledgements The authors would like to thank Mark Akselrod for his longstanding support of our project. We greatly benefitted from the most competent and uncomplicated help for the FXR reader by Jonathan Harrison and Vasiliy Fomenko (Landauer Inc.). Our studies would not have been possible with the help of many colleagues at the Heidelberg Ion Therapy Center (HIT), most prominently we gratefully acknowledge Andrea Mairani s help with the FLUKA code, and Stephan Brons being an invaluable support before, during, and after beam time shifts. 10

11 References [1] Marco Durante and Jay S. Loeffler. Charged particles in radiation oncology. Nature Reviews Clinical Oncology, 7(1):37 43, [2] Particle Therapy Co-operative Group PTCOG. Particle therapy facilities in operation Accessed: September, 19th. [3] W. T. Chu, B. A. Ludewigt, and T. R. Renner. Instrumentation for treatment of cancer using proton and light-ion beams. Review of Scientific Instruments, 64: , [4] Thomas Friedrich, Uwe Scholz, Thilo Elsässer, Marco Durante, and Michael Scholz. Calculation of the biological effects of ion beams based on the microscopic spatial damage distribution pattern. International Journal of Radiation Biology, 88(1-2): , [5] ICRU. Linear energy transfer. Technical Report 16, International Commission on Radiation Units and Measurements, [6] Christian P Karger, Oliver Jäkel, Hugo Palmans, and Tatsuaki Kanai. Dosimetry for ion beam radiotherapy. Physics in medicine and biology, 55(21):R193, [7] Oksana Geithner, P Andreo, N Sobolevsky, G Hartmann, and O Jäkel. Calculation of stopping power ratios for carbon ion dosimetry. Physics in medicine and biology, 51(9):2279, [8] Tatsuaki Kanai, Toshiyuki Kohno, Shinichi Minohara, Michio Sudou, Eiichi Takada, Fuminori Soga, Kiyomitsu Kawachi, and Akifumi Fukumura. Dosimetry and measured differential w values of air for heavy ions. Radiation research, 135(3): , [9] Thomas Tessonnier, Tiago Marcelos, Andrea Mairani, Stephan Brons, and Katia Parodi. Phase space generation for proton and carbon ion beams for external users applications at the heidelberg ion therapy center. Frontiers in Oncology, 5:297, [10] Emma Haettner, Hiroshi Iwase, Michael Krämer, Gerhard Kraft, and Dieter Schardt. Experimental study of nuclear fragmentation of 200 and 400 MeV/ u 12 C ions in water for applications in particle therapy. Physics in Medicine and Biology, 58(23):8265,

12 [11] J Jakubek, C Granja, B Hartmann, O Jaekel, M Martisikova, L Opalka, and S Pospisil. Selective detection of secondary particles and neutrons produced in ion beam therapy with 3d sensitive voxel detector. Journal of Instrumentation, 6(12):C12010, [12] Anatoly B Rosenfeld. Novel detectors for silicon based microdosimetry, their concepts and applications. Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, 809: , [13] I. Jadrnícková, F. Spurný, and A. G. Molokanov. Spectrometry of linear energy transfer and its use in high-energy particle beams. Physics of Particles and Nuclei Letters, 5(6): , [14] F. Spurný, I. Jadrnícková, V.P. Bamblevski, and A.G. Molokanov. Upgrading of LET track-etch spectrometer calibration: Calibration and uncertainty analysis. Radiation Measurements, 40(2-6): , Proceedings of the 22nd International Conference on Nuclear Tracks in Solids. [15] Grischa Klimpki, Henning Mescher, Mark S. Akselrod, Oliver Jäkel, and Steffen Greilich. Fluencebased dosimetry of proton and heavier ion beams using single track detectors. Physics in Medicine and Biology, 61(3): , [16] Steffen Greilich, Julia.-M. Osinga, Martin Niklas, Florian M. Lauer, Grischa Klimpki, Felix Bestvater, James A Bartz, Mark S Akselrod, and Oliver Jäkel. Fluorescent Nuclear Track Detectors as a Tool for Ion-Beam Therapy Research. Radiation Measurements, 56: , [17] Julia-Maria Osinga, Stephan Brons, James a Bartz, Mark S Akselrod, Oliver Jäkel, and Steffen Greilich. Absorbed Dose in Ion Beams: Comparison of Ionisation- and Fluence-Based Measurements. Radiation Protection Dosimetry, 161(1-4): , February [18] Martin Niklas, Amir Abdollahi, Mark S. Akselrod, Jürgen Debus, Oliver Jäkel, and Steffen Greilich. Subcellular spatial correlation of particle traversal and biological response in clinical ion beams. International Journal of Radiation Oncology*Biology*Physics, 87: , [19] IAEA. Absorbed dose determination in external beam radiotherapy. Technical Report 398, International Atomic Energy Agency, [20] Dal A Granville, Narayan Sahoo, and Gabriel O Sawakuchi. Calibration of the Al2O3:C optically stimulated luminescence (OSL) signal for linear energy transfer (LET) measurements in therapeutic proton beams. Physics in Medicine and Biology, 59(15):4295,

13 [21] Eduardo G Yukihara, Brandon A Doull, Md Ahmed, Stephan Brons, Thomas Tessonnier, Oliver Jäkel, and Steffen Greilich. Time-resolved optically stimulated luminescence of Al2O3:C for ion beam therapy dosimetry. Physics in Medicine and Biology, 60(17): , Featured Article. [22] Mark S. Akselrod, Vasiliy V. Fomenko, James A. Bartz, and T.L. Haslett. Automatic neutron dosimetry system based on fluorescent nuclear track detector technology. Radiation Protection Dosimetry, 161:86 91, [23] R Development Core Team. R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria, ISBN [24] C.A. Schneider, W.S. Rasband, and K.W. Eliceiri. NIH Image to Image J: 25 years of image analysis. Nature Methods, 9, [25] J. Cardinale. Histogram-based background subtractor for imagej. Technical report, ETH Zurich, [26] Ivo F. Sbalzarini and Petros Koumoutsakos. Feature point tracking and trajectory analysis for video imaging in cell biology. Journal of Structural Biology, 151(2): , [27] J. J. M. Kouwenberg, L. Ulrich, O. Jäckel, and S. Greilich. A 3d feature point tracking method for ion radiation. Physics in Medicine and Biology, 61(11): , [28] J. A. Bartz, S. Kodaira, M. Kurano, N. Yasuda, and M. S. Akselrod. High resolution charge spectroscopy of heavy ions with FNTD technology. Nuclear Instruments and Methods in Physics Research B, 335:24 30, September [29] Alfredo Ferrari, Paola R. Sala, Alberto Fasso, and Johannes Ranft. FLUKA: A multi-particle transport code (Program version 2005) [30] T.T. Böhlen, F. Cerutti, M.P.W. Chin, A. Fasso, A. Ferrari, P.G. Ortega, A. Mairani, P.R. Sala, G. Smirnov, and Vlachoudis. The {FLUKA} code: Developments and challenges for high energy and medical applications. Nuclear Data Sheets, 120(0): , [31] K Parodi, A Mairani, S Brons, BG Hasch, F Sommerer, J Naumann, O Jäkel, T Haberer, and J Debus. Monte carlo simulations to support start-up and treatment planning of scanned proton and carbon ion therapy at a synchrotron-based facility. Physics in medicine and biology, 57(12):3759,

14 14

15 Fig. 1: Fluorescence image of an FNTD located at the SOBP of a 12 C irradiated sample read-out both by the Zeiss LSM710 ConfoCor 3 (left) and the Landauer FXR700RG (right).the lower NA of the objective lens of the FXR700RG results in a lower spatial resolution (FWHM) of 0.36 µm (1.7 µm) lateral (axial) in contrast to 0.20 µm (0.8 µm) for the LSM710 in the configuration used. 15

16 Fig. 2: Cartoon of an FNTD readout. A single track crosses with a length l i the read out volume V of a stack with four slices in depth. In total six stacks are read in the FNTD arranged as three by two frames. 16

17 Fig. 3: LET as a function of fluorescence signal for the investigated data set read-out using the FXR700RG and the settings described. The solid black line shows the calibration curve, the dashed lines the 95 % its confidence interval. 17

18 dose to water / Gy fluence-weighted LET in water / (kev/um) fluence / (10e6 / cm2) Primaries Fragments Total depth / cm depth / cm depth / cm Fig. 4: Reference and measured data for dose, fluence, and fluence-weighted LET. The group fragments refers to low-let fragments while total reflects the additional contribution by high-let fragments. A fluence of cm -2 corresponds to 100 tracks measured per frame and 4900 tracks per sample, respectively. 18

19 Fig. 5: LET distribution for the seven measurement depths. Reference data from transport simulation are given in grey, measured data (histogram) in black. The scaling of the reference data on the abscissa is arbitrary, but kept constant, except for the first two panels (0.75 cm, 1.75 cm) were it was scaled by 7 to enhance visibility. The red vertical lines define the interval of LET values which were assigned to carbon ions. 19

20 Position / cm Component Fluence / 10 6 cm -2 flet / (kev/µm) Dose / mgy Low LET fragments (0.004) 4.5 (0.2) 0.54 (0.04) 0.75 Primaries 1.40 (0.02) 14.3 (0.3) 32.2 (0.7) High LET fragments (0.004) 48.8 (2.5) 1.7 (0.3) Total 1.50 (0.02) 14.4 (0.3) 34.4 (0.9) Low LET fragments 0.12 (0.01) 3.8 (0.1) 0.75 (0.04) 1.75 Primaries 1.32 (0.01) 14.8 (0.1) 31.3 (0.5) High LET fragments (0.002) 49.1 (2.3) 2.1 (0.2) Total 1.47 (0.01) 14.5 (0.2) 34.1 (0.7) Low LET fragments 0.48 (0.01) 3.3 (0.1) 2.55 (0.05) 7.75 Primaries 1.02 (0.01) 23.6 (0.2) 38.8 (0.7) High LET fragments (0.001) 99.7 (1.5) 0.42 (0.01) Total 1.51 (0.02) 17.3 (0.2) 41.8 (0.7) Low LET fragments 0.66 (0.01) 4.5 (0.1) 4.8 (0.1) Primaries 0.74 (0.01) 32.2 (0.3) 38.3 (0.7) Total 1.40 (0.02) 19.2 (0.2) 43.0 (0.7) Low LET fragments 0.56 (0.01) 4.1 (0.1) 3.7 (0.1) Primaries 0.51 (0.01) 44.0 (0.9) 35.9 (1.0) Total 1.07 (0.01) 23.0 (0.5) 39.6 (1.0) Low LET fragments 0.62 (0.01) 5.1 (0.2) 5.0 (0.2) Low LET fragments 0.49 (0.01) 3.1 (0.1) 2.4 (0.1) Tab. 1: Results for fluence, fluence-weighted LET, and dose, given for the tracks assigned to the group of primary particles, low- and high-let fragments, respectively. In brackets, the standard uncertainty is given as evaluated from the variance between the frames. For the two largest depths, only low-let fragments were assumed to be recorded. The actual existence of high-let fragments cannot be definitely concluded from the spectra and has to be discussed with respect to the deficiencies of the used logarithmic intensity-let-relation. 20