Radiation Protection Dosimetry Advance Access published April 5, 2015 Radiation Protection Dosimetry (2015), pp. 1–4
doi:10.1093/rpd/ncv141
NANODOSIMETRIC TRACK STRUCTURE IN HOMOGENEOUS EXTENDED BEAMS V. Conte*, D. Moro, P. Colautti and B. Grosswendt LNL-INFN, viale dell’Universita` 2, Legnaro I-35020, Italy *Corresponding author: [email protected]
INTRODUCTION In view of the importance of particle track structure to understand and to monitor the initiation of irradiation damage to the relevant sub-structures of living cells like the DNA and higher-order genomic structures, the properties of the tracks of ionising radiation of specified radiation quality must be measured. Such measurements are feasible today by counting the number of ionisations produced inside a small gas volume by ionising particles directly crossing it, or passing nearby at a well-defined distance. The most appropriate measuring device, available at present for this purpose, is the so called track-nanodosimeter, installed at the TANDEM-ALPI accelerator complex of LNL(1). This track-nanodosimeter measures the frequency of ionisation cluster-sizes caused by primary particles of specified radiation quality (charge state and velocity) within a cylindrical target volume V while penetrating through it or passing nearby at specified impact parameter r. The target volume is filled with gaseous propane at a density of r ¼ 5.47 mg cm23; its size is defined by a non-homogeneous efficiency map with a diameter and height of about 3.7 mm which corresponds to a mass per area of about 2 mg cm22. Hence, at a density of 1 g cm23 the target volume is comparable in size to a segment of the chromatin fibre, 20 nm in diameter and height. The impact parameter r is changed in the experiment by moving the target volume perpendicularly to the centre line of a circular pencil beam of primary particles (beam radius rbeam ¼ 0.4 mm). The formation of ionisation clustering in the ‘nanometre’ sized volume is studied at LNL experimentally and by Monte Carlo simulation, for light ions of different charge state and velocity(2). In view of a potential application of the data for purposes of radio-biology or treatment planning in
hadron therapy, it is the aim of the present work to apply the experimental data, measured with pencil beams at different impact parameters r, also to derive ionisation-cluster-size distributions which can be expected in homogeneous extended radiation fields of radius Rfield with Rfield rbeam. This application is based on a numerical integration of the measured cluster-size frequencies over the impact parameter, around the centre line of the primary particle beam. DETERMINATION OF IONISATIONCLUSTER-SIZE DISTRIBUTIONS As just described, the track-nanodosimeter measures the number of ionisations n caused in a target volume V with a diameter (Dr)V of about 2 mg cm22 in mass per area by the passage of a particle at defined impact parameter r. The impact parameter is changed in the experiments in steps of 0.25 mm from r ¼ 0 mm up to a maximum value of r ¼ 8 mm, or (rr) ¼ 4.4 mg cm22 if the impact parameter is given in mass per area. At each impact parameter, 5` 106 tracks are collected to get a satisfactory statistics. Results are presented in the form of the probability pn(r) that exactly n ionisations are produced inside the volume V, by a particle of specified radiation quality passing at impact parameter r from the V centre. A dedicated Monte Carlo model has been expressly developed to supplement the measurements with simulations. For a detailed description of this model, which includes the response function of the detector, see the authors’ previous publications (2 – 4). To determine the ionisation-cluster-size probabilities Pn(Rfield) in the centre of an extended field of radius Rfield . rbeam from the experimental data measured with a pencil beam at different impact
# The Author 2015. Published by Oxford University Press. All rights reserved. For Permissions, please email: [email protected]
Downloaded from http://rpd.oxfordjournals.org/ at Fudan University on May 14, 2015
Physical aspects of particle track structure are important in determining the induction of clustered damage in relevant subcellular structures like the DNA and higher-order genomic structures. The direct measurement of track-structure properties of ionising radiation is feasible today by counting the number of ionisations produced inside a small gas volume. In particular, the so-called track-nanodosimeter, installed at the TANDEM-ALPI accelerator complex of LNL, measures ionisation cluster-size distributions in a simulated subcellular structure of dimensions 20 nm, corresponding approximately to the diameter of the chromatin fibre. The target volume is irradiated by pencil beams of primary particles passing at specified impact parameter. To directly relate these measured track-structure data to radiobiological measurements performed in broad homogeneous particle beams, these data can be integrated over the impact parameter. This procedure was successfully applied to 240 MeV carbon ions and compared with Monte Carlo simulations for extended fields.
V. CONTE ET AL.
parameters r, the integration procedure of Equation (1) was applied
Pn ðRfield Þ ¼
2 R2field
Rð field
dr r pn ðrÞ:
ð1Þ
0
RESULTS AND DISCUSSIONS Cluster-size formation by needle beams To give an impression of the present results, Figure 1 shows a significant selection of ionisation cluster-size distributions pn(r) due to 240 MeV 12C-ions at different impact parameters 0 mm r 8 mm directly measured with the track-nanodosimeter for needle beams, 0.4 mm in diameter, and simulated by dedicated Monte Carlo code.
Figure 1. Ionisation cluster distributions pn(r) for 240 MeV 12 C-ions at different impact parameters r (see the insert); (symbols): experiment, (lines): simulation.
Cluster-size formation by extended particle beams As discussed above, the integration of the probability density pn(r) over the impact parameter allows the simulation of a radiation field of radius Rfield . rbeam. In the case of an extended homogeneous parallel particle beam crossing the target at its centre, the integration of the data plotted in Figures 1 and 2 leads to a distribution of probabilities Pn(Rfield) which are shown in Figure 3 as a function of the ratio Rfield/RV, where RV is the radius of the target volume. At first glance it can be recognized in the figure that the experimentally based distributions and those from the Monte Carlo simulation are in a very satisfactory agreement. The shape of the curves shown in Figure 3 is similar to that of the curves presented in Figure 2 but
Figure 2. Probability pn(r) of measuring an ionisation cluster of size n from 240 MeV 12C-ions passing at impact parameter r, as a function of r; (symbols): experiment, (lines): simulation.
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Downloaded from http://rpd.oxfordjournals.org/ at Fudan University on May 14, 2015
The integration procedure of Equation (1) based on the measured cluster-size distributions pn(r) simulates the irradiation of a target volume with an efficiency map of spherical symmetry with a homogeneous parallel circular beam of radius Rfield crossing the volume at its centre. To determine Pn(Rfield) by Monte Carlo simulation, the rotational symmetry around the axis of the primary particle beam which is assumed in the integration procedure, and the rotational symmetry of the efficiency map had to be taken into account (for more details of the efficiency map, see the work of De Nardo et al.(1)). Because of this, the integration procedure applied to the experimental data was directly simulated by a rotation of the target volume relative to the position of each single primary particle of the extended beam. This rotation of the target volume ensured that the particle track sees always the same efficiency map as in the measurements.
In Figure 2 the data of Figure 1 are represented in a different way, by plotting the probability pn(r) of measuring a cluster of n ionisations, as a function of the impact parameter r, for cluster sizes n ¼ 0, 1, 2, 7 and 10. At first glance it can be observed in the figure that the probability of cluster n ¼ 0 is always increasing with increasing impact parameter, while the probability pn(r) for cluster sizes 0 , n , 7 is increasing up to r 2 mm which approximately corresponds to the volume border, and then it decreases if the impact parameter further increases. In contrast, pn(r) for cluster sizes n 7 decreases monotonously with increasing r. To understand this behaviour, one should consider that the pathlength of the primary trajectories inside the target volume decreases from its maximum value, corresponding to the volume diameter, to zero if the needle beam shifts from the volume centre at r ¼ 0 to the volume border at r ¼ 2 mm.
NANODOSIMETRIC TRACK STRUCTURE IN HOMOGENEOUS EXTENDED BEAMS
Figure 4. Cluster-size distributions Pn(Rfield) for a homogeneous parallel irradiation field of 240 MeV 12Cions, with the field radius Rfield as a parameter; (symbols): experiment, (lines): simulation.
smoothed by the integration over the beam area. For a 240 MeV 12C ion beam with a radius Rfield smaller than the radius RV of the target volume (RV ¼ 1.85 mm), the probability of cluster size zero is small and the probability P2(Rfield), for instance, is greater than P1(Rfield). If the field radius extends the volume radius RV, the situation is reversed: the cluster-size probability is highest for cluster size n ¼ 0, and it is lower for greater cluster sizes. In addition, Pn(Rfield) for sizes n 1 decreases with increasing field radius, showing a slope of this decrease which is almost the same for all cluster sizes. The data plotted in Figure 3 are presented in Figure 4 in the usual way of ionisation-cluster-size probabilities Pn(Rfield) as a function of n, for five different values of the field radius Rfield as a parameter.
Figure 5. Contribution Fn (in)(R) to cluster size probability Pn(Rfield) due to the inner part of radius R of a homogeneous circular 240 MeV-12C-ion beam of radius Rfield ¼ 8 mm; (symbols): experiment, (lines): simulation.
For Rfield ¼ 0.5 mm all particles of the primary particle beam cross the target volume close to its centre, and consequently the distribution is peaked at about cluster size n ¼ 7, similarly to the cluster-size distribution for the pencil beam used in the measurements (see Figure 1). If the cross section of the irradiation field is approximately the same as that of the target volume, the distribution has still a peaked shape, due to the large contribution of particles crossing the volume close to its centre, but the position of the maximum of the distribution shifts to a cluster size n as small as 2. If the beam further enlarges, the distribution changes its shape, showing a greater probability at cluster size n ¼ 0 and a decreasing probability with increasing cluster size. In addition, if Rfield/Rv . 2, the shape of the distributions for n 1 is quite similar and only P0(Rfield) is markedly increasing with Rfield. If one now considers a homogeneous parallel radiation field of radius Rfield, the cluster-size distribution Pn(Rfield), shown in Figure 4, can be split into two contributions: one from the inner part of the beam (due to particles passing at impact parameter r R) and another one from the outer cylindrical shell (R r Rfield). Taking into account that, in a particle beam of radius Rfield, (R/Rfield)2 is the probability that a particle is included within a beam cross section of radius R, the inner contribution F(in) n (R), due to particles included in the inner part of radius R is then equal to the product (R/Rfield)2` Pn(R). To give an impression of such data, Figure 5 presents the contributions Fn (in)(R) in the case Rfield ¼ 8 mm, as a function of the ratio R/Rv. As it is obvious from the figure, the contribution to cluster size n ¼ 0 is continuously increasing, whereas the contribution to larger cluster sizes is almost constant for R/RV . 1.5. Ions passing at impact parameters r . 1.5 RV mainly contribute with zero events.
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Figure 3. Probability Pn(Rfield) of measuring a cluster of size n, as a function of the ratio Rfield/RV, for a homogeneous parallel beam of 240 MeV 12C-ions; (symbols): experiment, (lines): simulation.
V. CONTE ET AL.
In order to complete the discussion of cluster-size distributions in extended beams, Figure 7 shows the ionisation-cluster-size probability Pn(Rfield, d) in the case of an irradiation with a homogeneous parallel circular beam of radius Rfield ¼ 8 mm, for different target distances d, representing the position of the target volume with respect to the central line of the irradiating beam. At first glance it is clear from the figure that the distributions are almost the same as long as the target is inside the area covered by the primary particle beam, and that the measured characteristics of the track structure change only if the target is positioned close to the border of the beam or outside of it.
Figure 7. Cluster-size distribution Pn(Rfield, d) due to 240 MeV 12C-ions at different target distances d (see the inset) in the case of a homogeneous parallel circular irradiation field of radius Rfield ¼ 8 mm; (symbols): experiment at d ¼ 0, (lines): simulation.
To continue with the discussion of the results, Figure 6 shows the contributions Fn (in)(R) already presented in Figure 5 for Rfield ¼ 8 mm, but plotted as a function of cluster size n, with the inner radius R as a parameter. As can be easily seen in Figure 6, the contributions become almost identical for about R 3 mm, or R/RV ¼ 1.5, and enlarging the beam radius causes almost exclusively an addition of zero events, whereas the probabilities F(in) n (R) for cluster sizes n 1 remain almost the same. Hence, it can be concluded that, for 240 MeV carbon ions in a homogeneous extended field of radius Rfield . 1.5 RV, the only relevant contribution to the cluster-size formation in the target volume V is due to ions passing the volume with impact parameter r , 1.5 RV.
CONCLUSIONS The track-nanodosimeter installed at LNL-INFN allows the direct measurement of track structure characteristics at defined impact parameter from a widely homogeneous pencil particle beam of radius rbeam. If one assumes that the beam radii Rfield of interest in radio-biology or radiation therapy are much larger than the beam radius which can be applied experimentally, the idea of the integration of experimental data is of general interest. The procedure allows the determination of the relative frequency Pn(Rfield) of cluster-size n due to ionising particles of specified radiation quality measured or simulated for a given target distance in the case of an irradiation with a homogeneous parallel circular beam of radius Rfield and a target volume having an efficiency map of spherical symmetry.
FUNDING This work is supported by the 5th Scientific Commission of the Istituto Nazionale di Fisica Nucleare (INFN) of Italy. REFERENCES 1. De Nardo, L., Alkaa, A., Khamphan, C., Conte, V., Colautti, P., Se´gur, P. and Tornielli, G. A detector for track-nanodosimetry. Nucl. Instrum. Methods. Phys. Res. A. 484, 312–326 (2002). 2. Conte, V., Colautti, P., Grosswendt, B., Moro, D. and De Nardo, L. Track structure of light ions: experiments and simulations. New J. Phys. 14, 093010 (2012). 3. De Nardo, L., Colautti, P., Conte, V., Baek, W. Y., Grosswendt, B. and Tornielli, G. Ionization-cluster distributions of a-particles in nanometric volumes of propane: measurement and calculation. Radiat. Environ. Biophys. 41, 235– 256 (2002). 4. Grosswendt, B., Conte, V. and Colautti, P. An upgraded track structure model: experimental validation. Radiat. Prot. Dosim. 161, 464–468 (2014).
Page 4 of 4
Downloaded from http://rpd.oxfordjournals.org/ at Fudan University on May 14, 2015
Figure 6. Contribution Fn (in)(R) to cluster size probability Pn(Rfield) due to the inner parts of radii R of a homogeneous circular 240 MeV-12C-ion beam of radius Rfield ¼ 8 mm, plotted as a function of cluster size n; (symbols): experiment, (lines): simulation.
doi:10.1093/rpd/ncv141
NANODOSIMETRIC TRACK STRUCTURE IN HOMOGENEOUS EXTENDED BEAMS V. Conte*, D. Moro, P. Colautti and B. Grosswendt LNL-INFN, viale dell’Universita` 2, Legnaro I-35020, Italy *Corresponding author: [email protected]
INTRODUCTION In view of the importance of particle track structure to understand and to monitor the initiation of irradiation damage to the relevant sub-structures of living cells like the DNA and higher-order genomic structures, the properties of the tracks of ionising radiation of specified radiation quality must be measured. Such measurements are feasible today by counting the number of ionisations produced inside a small gas volume by ionising particles directly crossing it, or passing nearby at a well-defined distance. The most appropriate measuring device, available at present for this purpose, is the so called track-nanodosimeter, installed at the TANDEM-ALPI accelerator complex of LNL(1). This track-nanodosimeter measures the frequency of ionisation cluster-sizes caused by primary particles of specified radiation quality (charge state and velocity) within a cylindrical target volume V while penetrating through it or passing nearby at specified impact parameter r. The target volume is filled with gaseous propane at a density of r ¼ 5.47 mg cm23; its size is defined by a non-homogeneous efficiency map with a diameter and height of about 3.7 mm which corresponds to a mass per area of about 2 mg cm22. Hence, at a density of 1 g cm23 the target volume is comparable in size to a segment of the chromatin fibre, 20 nm in diameter and height. The impact parameter r is changed in the experiment by moving the target volume perpendicularly to the centre line of a circular pencil beam of primary particles (beam radius rbeam ¼ 0.4 mm). The formation of ionisation clustering in the ‘nanometre’ sized volume is studied at LNL experimentally and by Monte Carlo simulation, for light ions of different charge state and velocity(2). In view of a potential application of the data for purposes of radio-biology or treatment planning in
hadron therapy, it is the aim of the present work to apply the experimental data, measured with pencil beams at different impact parameters r, also to derive ionisation-cluster-size distributions which can be expected in homogeneous extended radiation fields of radius Rfield with Rfield rbeam. This application is based on a numerical integration of the measured cluster-size frequencies over the impact parameter, around the centre line of the primary particle beam. DETERMINATION OF IONISATIONCLUSTER-SIZE DISTRIBUTIONS As just described, the track-nanodosimeter measures the number of ionisations n caused in a target volume V with a diameter (Dr)V of about 2 mg cm22 in mass per area by the passage of a particle at defined impact parameter r. The impact parameter is changed in the experiments in steps of 0.25 mm from r ¼ 0 mm up to a maximum value of r ¼ 8 mm, or (rr) ¼ 4.4 mg cm22 if the impact parameter is given in mass per area. At each impact parameter, 5` 106 tracks are collected to get a satisfactory statistics. Results are presented in the form of the probability pn(r) that exactly n ionisations are produced inside the volume V, by a particle of specified radiation quality passing at impact parameter r from the V centre. A dedicated Monte Carlo model has been expressly developed to supplement the measurements with simulations. For a detailed description of this model, which includes the response function of the detector, see the authors’ previous publications (2 – 4). To determine the ionisation-cluster-size probabilities Pn(Rfield) in the centre of an extended field of radius Rfield . rbeam from the experimental data measured with a pencil beam at different impact
# The Author 2015. Published by Oxford University Press. All rights reserved. For Permissions, please email: [email protected]
Downloaded from http://rpd.oxfordjournals.org/ at Fudan University on May 14, 2015
Physical aspects of particle track structure are important in determining the induction of clustered damage in relevant subcellular structures like the DNA and higher-order genomic structures. The direct measurement of track-structure properties of ionising radiation is feasible today by counting the number of ionisations produced inside a small gas volume. In particular, the so-called track-nanodosimeter, installed at the TANDEM-ALPI accelerator complex of LNL, measures ionisation cluster-size distributions in a simulated subcellular structure of dimensions 20 nm, corresponding approximately to the diameter of the chromatin fibre. The target volume is irradiated by pencil beams of primary particles passing at specified impact parameter. To directly relate these measured track-structure data to radiobiological measurements performed in broad homogeneous particle beams, these data can be integrated over the impact parameter. This procedure was successfully applied to 240 MeV carbon ions and compared with Monte Carlo simulations for extended fields.
V. CONTE ET AL.
parameters r, the integration procedure of Equation (1) was applied
Pn ðRfield Þ ¼
2 R2field
Rð field
dr r pn ðrÞ:
ð1Þ
0
RESULTS AND DISCUSSIONS Cluster-size formation by needle beams To give an impression of the present results, Figure 1 shows a significant selection of ionisation cluster-size distributions pn(r) due to 240 MeV 12C-ions at different impact parameters 0 mm r 8 mm directly measured with the track-nanodosimeter for needle beams, 0.4 mm in diameter, and simulated by dedicated Monte Carlo code.
Figure 1. Ionisation cluster distributions pn(r) for 240 MeV 12 C-ions at different impact parameters r (see the insert); (symbols): experiment, (lines): simulation.
Cluster-size formation by extended particle beams As discussed above, the integration of the probability density pn(r) over the impact parameter allows the simulation of a radiation field of radius Rfield . rbeam. In the case of an extended homogeneous parallel particle beam crossing the target at its centre, the integration of the data plotted in Figures 1 and 2 leads to a distribution of probabilities Pn(Rfield) which are shown in Figure 3 as a function of the ratio Rfield/RV, where RV is the radius of the target volume. At first glance it can be recognized in the figure that the experimentally based distributions and those from the Monte Carlo simulation are in a very satisfactory agreement. The shape of the curves shown in Figure 3 is similar to that of the curves presented in Figure 2 but
Figure 2. Probability pn(r) of measuring an ionisation cluster of size n from 240 MeV 12C-ions passing at impact parameter r, as a function of r; (symbols): experiment, (lines): simulation.
Page 2 of 4
Downloaded from http://rpd.oxfordjournals.org/ at Fudan University on May 14, 2015
The integration procedure of Equation (1) based on the measured cluster-size distributions pn(r) simulates the irradiation of a target volume with an efficiency map of spherical symmetry with a homogeneous parallel circular beam of radius Rfield crossing the volume at its centre. To determine Pn(Rfield) by Monte Carlo simulation, the rotational symmetry around the axis of the primary particle beam which is assumed in the integration procedure, and the rotational symmetry of the efficiency map had to be taken into account (for more details of the efficiency map, see the work of De Nardo et al.(1)). Because of this, the integration procedure applied to the experimental data was directly simulated by a rotation of the target volume relative to the position of each single primary particle of the extended beam. This rotation of the target volume ensured that the particle track sees always the same efficiency map as in the measurements.
In Figure 2 the data of Figure 1 are represented in a different way, by plotting the probability pn(r) of measuring a cluster of n ionisations, as a function of the impact parameter r, for cluster sizes n ¼ 0, 1, 2, 7 and 10. At first glance it can be observed in the figure that the probability of cluster n ¼ 0 is always increasing with increasing impact parameter, while the probability pn(r) for cluster sizes 0 , n , 7 is increasing up to r 2 mm which approximately corresponds to the volume border, and then it decreases if the impact parameter further increases. In contrast, pn(r) for cluster sizes n 7 decreases monotonously with increasing r. To understand this behaviour, one should consider that the pathlength of the primary trajectories inside the target volume decreases from its maximum value, corresponding to the volume diameter, to zero if the needle beam shifts from the volume centre at r ¼ 0 to the volume border at r ¼ 2 mm.
NANODOSIMETRIC TRACK STRUCTURE IN HOMOGENEOUS EXTENDED BEAMS
Figure 4. Cluster-size distributions Pn(Rfield) for a homogeneous parallel irradiation field of 240 MeV 12Cions, with the field radius Rfield as a parameter; (symbols): experiment, (lines): simulation.
smoothed by the integration over the beam area. For a 240 MeV 12C ion beam with a radius Rfield smaller than the radius RV of the target volume (RV ¼ 1.85 mm), the probability of cluster size zero is small and the probability P2(Rfield), for instance, is greater than P1(Rfield). If the field radius extends the volume radius RV, the situation is reversed: the cluster-size probability is highest for cluster size n ¼ 0, and it is lower for greater cluster sizes. In addition, Pn(Rfield) for sizes n 1 decreases with increasing field radius, showing a slope of this decrease which is almost the same for all cluster sizes. The data plotted in Figure 3 are presented in Figure 4 in the usual way of ionisation-cluster-size probabilities Pn(Rfield) as a function of n, for five different values of the field radius Rfield as a parameter.
Figure 5. Contribution Fn (in)(R) to cluster size probability Pn(Rfield) due to the inner part of radius R of a homogeneous circular 240 MeV-12C-ion beam of radius Rfield ¼ 8 mm; (symbols): experiment, (lines): simulation.
For Rfield ¼ 0.5 mm all particles of the primary particle beam cross the target volume close to its centre, and consequently the distribution is peaked at about cluster size n ¼ 7, similarly to the cluster-size distribution for the pencil beam used in the measurements (see Figure 1). If the cross section of the irradiation field is approximately the same as that of the target volume, the distribution has still a peaked shape, due to the large contribution of particles crossing the volume close to its centre, but the position of the maximum of the distribution shifts to a cluster size n as small as 2. If the beam further enlarges, the distribution changes its shape, showing a greater probability at cluster size n ¼ 0 and a decreasing probability with increasing cluster size. In addition, if Rfield/Rv . 2, the shape of the distributions for n 1 is quite similar and only P0(Rfield) is markedly increasing with Rfield. If one now considers a homogeneous parallel radiation field of radius Rfield, the cluster-size distribution Pn(Rfield), shown in Figure 4, can be split into two contributions: one from the inner part of the beam (due to particles passing at impact parameter r R) and another one from the outer cylindrical shell (R r Rfield). Taking into account that, in a particle beam of radius Rfield, (R/Rfield)2 is the probability that a particle is included within a beam cross section of radius R, the inner contribution F(in) n (R), due to particles included in the inner part of radius R is then equal to the product (R/Rfield)2` Pn(R). To give an impression of such data, Figure 5 presents the contributions Fn (in)(R) in the case Rfield ¼ 8 mm, as a function of the ratio R/Rv. As it is obvious from the figure, the contribution to cluster size n ¼ 0 is continuously increasing, whereas the contribution to larger cluster sizes is almost constant for R/RV . 1.5. Ions passing at impact parameters r . 1.5 RV mainly contribute with zero events.
Page 3 of 4
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Figure 3. Probability Pn(Rfield) of measuring a cluster of size n, as a function of the ratio Rfield/RV, for a homogeneous parallel beam of 240 MeV 12C-ions; (symbols): experiment, (lines): simulation.
V. CONTE ET AL.
In order to complete the discussion of cluster-size distributions in extended beams, Figure 7 shows the ionisation-cluster-size probability Pn(Rfield, d) in the case of an irradiation with a homogeneous parallel circular beam of radius Rfield ¼ 8 mm, for different target distances d, representing the position of the target volume with respect to the central line of the irradiating beam. At first glance it is clear from the figure that the distributions are almost the same as long as the target is inside the area covered by the primary particle beam, and that the measured characteristics of the track structure change only if the target is positioned close to the border of the beam or outside of it.
Figure 7. Cluster-size distribution Pn(Rfield, d) due to 240 MeV 12C-ions at different target distances d (see the inset) in the case of a homogeneous parallel circular irradiation field of radius Rfield ¼ 8 mm; (symbols): experiment at d ¼ 0, (lines): simulation.
To continue with the discussion of the results, Figure 6 shows the contributions Fn (in)(R) already presented in Figure 5 for Rfield ¼ 8 mm, but plotted as a function of cluster size n, with the inner radius R as a parameter. As can be easily seen in Figure 6, the contributions become almost identical for about R 3 mm, or R/RV ¼ 1.5, and enlarging the beam radius causes almost exclusively an addition of zero events, whereas the probabilities F(in) n (R) for cluster sizes n 1 remain almost the same. Hence, it can be concluded that, for 240 MeV carbon ions in a homogeneous extended field of radius Rfield . 1.5 RV, the only relevant contribution to the cluster-size formation in the target volume V is due to ions passing the volume with impact parameter r , 1.5 RV.
CONCLUSIONS The track-nanodosimeter installed at LNL-INFN allows the direct measurement of track structure characteristics at defined impact parameter from a widely homogeneous pencil particle beam of radius rbeam. If one assumes that the beam radii Rfield of interest in radio-biology or radiation therapy are much larger than the beam radius which can be applied experimentally, the idea of the integration of experimental data is of general interest. The procedure allows the determination of the relative frequency Pn(Rfield) of cluster-size n due to ionising particles of specified radiation quality measured or simulated for a given target distance in the case of an irradiation with a homogeneous parallel circular beam of radius Rfield and a target volume having an efficiency map of spherical symmetry.
FUNDING This work is supported by the 5th Scientific Commission of the Istituto Nazionale di Fisica Nucleare (INFN) of Italy. REFERENCES 1. De Nardo, L., Alkaa, A., Khamphan, C., Conte, V., Colautti, P., Se´gur, P. and Tornielli, G. A detector for track-nanodosimetry. Nucl. Instrum. Methods. Phys. Res. A. 484, 312–326 (2002). 2. Conte, V., Colautti, P., Grosswendt, B., Moro, D. and De Nardo, L. Track structure of light ions: experiments and simulations. New J. Phys. 14, 093010 (2012). 3. De Nardo, L., Colautti, P., Conte, V., Baek, W. Y., Grosswendt, B. and Tornielli, G. Ionization-cluster distributions of a-particles in nanometric volumes of propane: measurement and calculation. Radiat. Environ. Biophys. 41, 235– 256 (2002). 4. Grosswendt, B., Conte, V. and Colautti, P. An upgraded track structure model: experimental validation. Radiat. Prot. Dosim. 161, 464–468 (2014).
Page 4 of 4
Downloaded from http://rpd.oxfordjournals.org/ at Fudan University on May 14, 2015
Figure 6. Contribution Fn (in)(R) to cluster size probability Pn(Rfield) due to the inner parts of radii R of a homogeneous circular 240 MeV-12C-ion beam of radius Rfield ¼ 8 mm, plotted as a function of cluster size n; (symbols): experiment, (lines): simulation.
