Study of the time and space distribution of β+emitters from
80 MeV/u carbon ion beam irradiation on PMMA.
C. Agodif, F. Bellinia,b, G.A.P. Cirronef, F. Collamatia,b, G. Cuttonef, E. De Luciac,
M. De Napolif, A. Di Domenicoa,b, R. Faccinia,b, F. Ferronia,b, S. Fiorea, P. Gauzzia,b,
E. Iaroccic,d, M. Marafinie, I. Matteig,c, A. Paolonic, V. Paterac,d, L. Piersantic,d,
F. Romanoe,f, A. Sartic,d, A. Sciubbac,d, C. Voenaa,b
aDipartimento di Fisica, Sapienza Universit` a di Roma, Roma, Italy
bINFN Sezione di Roma, Roma, Italy
cLaboratori Nazionali di Frascati dell’INFN, Frascati, Italy
dDipartimento di Scienze di Base e Applicate per l’Ingegneria, Sapienza Universit` a di Roma, Roma,
eMuseo Storico della Fisica e Centro Studi e Ricerche “E. Fermi”, Roma, Italy
fLaboratori Nazionali del Sud dell’INFN, Catania, ItalygDipartimento di Fisica, Roma Tre
Universit` a di Roma, Roma, Italy
Proton and carbon ion therapy is an emerging technique used for the treatment of
solid cancers. The monitoring of the dose delivered during such treatments and the
on-line knowledge of the Bragg peak position is still a matter of research. A possible
technique exploits the collinear 511 keV photons produced by positrons annihilation from
β+emitters created by the beam. This paper reports rate measurements of the 511 keV
photons emitted after the interactions of a 80 MeV/u fully stripped carbon ion beam at
the Laboratori Nazionali del Sud (LNS) of INFN, with a Poly-methyl methacrylate target.
The time evolution of the β+rate was parametrized and the dominance of11C emitters
over the other species (13N,15O,14O) was observed, measuring the fraction of carbon
ions activating β+emitters A0= (10.3±0.7)·10−3. The average depth in the PMMA of
the positron annihilation from β+emitters was also measured, Dβ+ = 5.3 ± 1.1 mm, to
be compared to the expected Bragg peak depth DBragg= 11.0 ± 0.5 mm obtained from
Keywords: Dosimetry; Bragg peak; NaI(Tl)
The use of proton and carbon ion beams has become more and more widespread as
an effective therapy for the treatment of solid cancers (hadrontherapy). These beams
have maximum energy density released at the Bragg peak (Fig. 1 Top) at the end of
their range, as opposed to X-rays or γ-rays, which are absorbed by the body with an
exponential decrease in the delivered dose with increasing tissue depth .
Due to their very favorable profile of released dose in tissue, the hadron beams can
be very effective in destroying the tumor and sparing the adjacent healthy tissue in
Preprint submitted to ElsevierFebruary 9, 2012
arXiv:1202.1676v1 [physics.med-ph] 8 Feb 2012
Figure 1: (a) Dose distributions as functions of water-equivalent depth estimated with the
GEANT MC for 279.2 MeV
togram) and bone (dotted histogram). Experimental data for depth dose distributions in PMMA
are shown by points. (b) Distributions of positron-emitting nuclei produced in these materials
as a function of water-equivalent depth .
12C nuclei in water (solid-line histogram), PMMA (dashed his-
comparison to the standard X-ray based treatment . On the other hand, the space
higher spatial selectivity of hadrontherapy asks for a dedicated approach to the delivered
The uncertainty on the position of the dose release in hadrontherapy treatment can
be due to different factors, i.g. quality and calibration of the Computed Tomography
(CT) images, possible morphologic changes occurring between CT and treatment, patient
mis-positioning and organ motion during the treatment itself. All these effects give an
overall uncertainty of the order of few millimeters, that can be larger than the dimension
of the dose release spot at the Bragg peak.
Several methods have been developed to determine the Bragg peak position by ex-
ploiting the secondary particle production induced by the hadron beam, and among these
one of the most promising is the PET-like technique: the collinear 511 keV photons pro-
duced by positrons annihilation from β+emitters created by the beam are measured.
The relationship between the β+emitters densities and the dose release has been stud-
ied with Montecarlo (MC) simulations, as shown in Fig. 1 . The measurement of the
rates of such emitters can also provide precise monitoring of the dose, which is in turn
essential for a good quality control of the treatment. This technique has been adopted
since long time with measurements after the irradiation [3, 4] and only recently on-beam
measurements are being developed .
To this aim, measurements are needed to allow the MC tuning, which is critical for the
appropriate development of the technique. In particular, a determination of the isotopic
composition of the β+emitters and the corresponding rates has not been performed
for the carbon ion treatments. Furthermore, papers in literature mostly report time
integrated measurements and do not investigate the time structure of the emission in
presence of irradiation.
In this paper we present measurements of the properties of the β+emitters, produced
in a Poly-Methyl Methacrylate (PMMA) phantom during an irradiation with carbon ions,
by observing the two 511 keV photons produced in the positron annihilation (γ−PET).
In section 1, we describe the setup of the experiment performed at the INFN Laboratori
Nazionali del Sud (LNS) in Catania in the interaction of a 80 MeV/u fully stripped carbon
beam with a PMMA target (see  for a related experiment with the same setup). Data
analysis tools are detailed in Sec. 2.
With the collected data we investigated three aspects of the β+emission: the isotopic
composition of the emitters (Sec. 3.1), their corresponding rates, via a study of the time
dependence of the emissions during irradiation (Sec. 3.2), and the position of the β+
emitters with respect to the Bragg peak (Sec. 4).
1. Experimental setup
Figure 2: Schematic view of the experimental setup: the NaI detectors are placed 20 cm away
from the PMMA. The acquisition is triggered by the coincidence of the two crystals. On the
right the picture of the actual experimental setup is shown.
The experimental setup is shown in Fig. 2. A 4 × 4 × 4 cm3PMMA target is placed
on an 80 MeV/u fully stripped12C ion beam. The beam rate, ranging from hundred
of kHz to ∼ 2MHz, is monitored with a 1.1 mm thick scintillator on the beam line,
placed at 17 cm from the PMMA, and read-out by two photomultiplier tubes (PMTs)
(Hamamatsu 10583) put in coincidence (Start Counter).
A pair of cylindrical NaI(Tl) crystals (r = 2.5 cm and h = 5 cm) is placed at 45◦
(225◦) with respect to the beam line, at 20 cm from the PMMA. The scintillation light
of the two crystals is detected by two Scionix V 14−EI PMTs triggered in coincidence
within a time window of 80 ns. A 12-bit QDC (Caen V 792N) and a 19-bit TDC (Caen
V 1190B) provide the measurements of energy and arrival time. We use NaI crystals to
detect the γ−PET signals because of their high light yield and energy resolution in the
O(1 MeV) ranges.
In order to perform position-dependent measurements, the PMMA can be moved
along the beam axis with an accuracy of 0.5 mm.
2. Data selection
From the charge collected in the two NaI detectors we measure the energy of the two
γ, i = 1,2) from the positron annihilation. To calibrate the NaI detectors we
used22Na (511 keV),137Cs (662 keV) and60Co (1.17 MeV and 1.33 MeV) sources. A
good linearity is obtained up to 1.5 MeV. The relative energy resolution at 511 keV is
σE/E = 2.7%; we define the signal window 0.48 < Ei< 0.53 MeV.
Fig. 3 shows the correlation between the E1
both detectors after requiring the other one to be in the signal window. A β+decay is
identified by the presence of two back-to-back photons with an energy compatible with
E = 511 keV. Thus the events with both energy depositions in the signal window provide
a background free measurement of the number of β+emitters.
γand the energy spectrum of
00.10.20.3 0.4 0.5 0.6 0.7 0.8
Entries Entries 371675 371675
Mean x 0.378Mean x 0.378
Mean y 0.387Mean y 0.387
RMS x 0.1699 RMS x 0.1699
RMS y 0.1713RMS y 0.1713
NaI 1 Energy Vs. NaI 2 Energy
Entries Entries 182505 182505
Mean Mean 0.3849 0.3849
RMS RMS 0.1553 0.1553
/ ndf / ndf
480.5 / 2 480.5 / 2
Constant Constant 2.348e+02 2.348e+02
Mean Mean 0.0000 0.0000
Sigma Sigma 0.00003 0.00003
0 0.1 0.2 0.30.4 0.5
NaI 1 qdc Delta T Cut
Figure 3: Left: correlation between the calibrated energy depositions in the two NaI detectors.
Right: calibrated energy spectrum in both NaI detectors after requiring one of the two to be in
the signal region (mean = 0.507 ± 0.012).
To evaluate the detection efficiency (?det) we simulated the experimental setup with
GATE , a simulation tool dedicated to medical imaging, radiontherapy and hadron-
therapy based on the GEANT4 MC code [8, 9].
In order to measure the position of the peak of the β+decay spatial distribution it
is important to evaluate the dependence of ?deton the position of the two photon vertex
with respect to the NaI detectors. To this aim we define x as the distance along the
beam line between the two photon vertex in the PMMA and the interception between
the beam line and the line connecting the two detectors (see Fig. 4).
Figure 4: Definition of the x and the D variables (see text).
The resulting functional dependence ?det(x) is shown in Fig. 5 and was parametrized
with a single gaussian.
In order to measure the γ−PET rate, the number of carbon ions NCmust be evalu-
ated. In a given time interval, NCis computed by counting the number of signals given
by the Start Counter (NSC) within randomly-triggered time-windows of Tw = 2 µs.
From the number of time windows considered (Nw) and the total acquisition time (Ttot),
the number of carbon ions NCis estimated to be:
The Start Counter efficiency ?SC= (96 ± 1)% has been estimated by exploiting the
two-sided PMT readout with negligible dark counts.
The number of impinging carbon ions has to be corrected for the dead-time ineffi-
ciency, ?DT has been estimated from the total acquisition time (Tdead) as:
?DT= 1 −Tdead
-40-30-20-100 1020 3040
Eff. in Simulazione MC
Figure 5: Detection efficiency as a function of the PMMA position on the beam line (χ2= 74/24,
xmean = −.046 ± 0.13 and σ = 13.45 ± 0.09). See text for details.
The measured values of ?DT range from 70% at an average carbon ion rate of 0.6 MHz
up to 47% at 2 MHz. This efficiency correction was then applied to data as described
3. Measurements of the time evolution of the β+emission
The rate of β+decays and the isotopic composition of the emitters was measured
as a function of time both during irradiation and in the intervals in between. The time
dependence of the emission during the irradiation results from two main contributions: (i)
the creation of new emitters induced by the passage of the carbon ions in the PMMA, and
(ii) the decay of the previously created ones. When the irradiation time is comparable
to the decay time of the emitters, the relation between the emitter and dose rates is
non-trivial. This is the case studied in this paper.
3.1. Isotopic composition of emitters
The isotopes that can be produced during the carbon ion irradiation of the PMMA
are11C,13N,15O and14O with half-lives of 29 min, 15 min, 2 min and 100 s respectively.
The wide spread of lifetimes allows to discriminate among isotopes. When the beam is
turned off (t=0), the time evolution of the β+decay rate (R(t)), is:
R(t) = R(0)
assuming Ns different species of isotopes with fractions fi and lifetimes τi. The
measured γ−PET, expected to be proportional to R(t)), in a run with no-beam as a
function of time is shown in Fig. 6.
Since there is an unavoidable unknown delay between the beam-stop and the start
of the run, there is an arbitrariness of the order of one minute on the measurement of t
Entries Entries 16 16
Mean 7.286 Mean 7.286
RMS 4.581RMS 4.581
02468 101214 16
NumGammaPET DeadTime Corrected
Figure 6: Distribution of the number of detected γ−PET as a function of time in a run with
no-beam; the fit with an exponential function is shown (τ = 33 ± 3 min, χ2/ndof = 15.3/13).
in Eq. 3. This effect compromises the sensitivity to the fast decaying isotopes (15O and
14O) and does not allow the combination of different runs. We have therefore decided to
analyze only the no-beam run with the largest statistics (shown in Fig. 6). The available
data does not allow us to perform a fit with a double exponential function accounting for
both11C and13N populations and therefore we can only test the hypothesis that one
isotope dominates. The fit with a single exponential function results in a lifetime τ =
33 ± 3 min (χ2/ndof = 15.3/13), thus indicating that the11C component is dominant.
3.2. Time evolution of the emission rate during irradiation
As stated in the introduction of section 3, the time evolution of the β+emitters
becomes non trivial when irradiation lasts for a time interval comparable with the lifetime
of the emitters. We therefore elaborated a model to describe the simultaneous occurrence
of new activations and decays of the β+emitters and used it to fit to the time evolution
of the measured rates, testing its goodness and extracting its parameters.
Defining the number of β+emitters for each of Nsspecies as Ns
τslifetime, we can write:
dec(s = 1,...,Ns), with
The first term on the right side of the Eq. 4 represents the activation induced by
the impinging carbon ions, with Araw
representing the fraction of carbon ions activating
β+emitters. The second term takes into account the decay of the activated nuclei with
decay times τs. Each species has an independent time evolution, so the measured γ−PET
evolution in the detector (Nγ) takes into account all species contributions:
Eq. 4 requires the knowledge of NC(t). As it can be seen for two different runs shown
in Figs. 7 (Left) and 9 (Left), NC(t) behavior cannot be always described with a function
that allows Eqs. 4 to be solved. We therefore developed two different methods: (i) an
analytical one to be used when NC(t) can be described by an analytical function, and (ii)
a numerical one that can always be applied, but requires the assumption of one dominant
isotope among the emitters.
Entries 35718 Entries 35718
Mean 30.95Mean 30.95
RMS 19.62 RMS 19.62
0 102030405060 70
NC x 106
Number of Carbon;armageddon/out/Explorer_Carbon1MHz_190311_Coll_LysoLT_200mm_out
Entries Entries 70 70
Mean Mean 37.64 37.64
RMS RMS 18.79 18.79
/ ndf / ndf
59.36 / 67 59.36 / 67
p4 p4 3.464e-08 3.464e-08
p5 p5 2.66 2.66
p6 p6 0.543 0.543
NumGammaPET DeadTime Corrected
Figure 7: Measured Nc (Left) and Nγ (Right) as a function of time. The fit of the measured Nγ
distribution using Eq. 7 (red line) gives the species ratio11C over13N (see Eq. 8).
3.2.1. Analytical method
The Fig. 7 (Left) shows the measured NC(t) fit by an exponential function (NC(t) =
νbeamexp(−t/τbeam)). In this case, the solution of Eqs. 4 and 5 is:
In Sec. 3.1 the lifetime measurement obtained from the fit of Fig. 6 indicates that the
11C component dominates. By using Eq. 6 we can now measure the relative contribution
to Nγ from11C and13N species, AC and AN. Assuming t0 as the time for which
dec(t0) = 0, Eq. 6 can be written as follow:
dec(t0) = NN
τbeam − e−
Fitting the time distribution of Nγwith Fig. 7 (Right), we obtain:
= 16.6 ± 2.7. (8)
The dominance of11C over13N is therefore confirmed.
3.2.2. Numerical method
In general the carbon ion rate cannot be parametrized with a simple function allowing
an analytical solution of Eq. 4. Therefore, a numerical method valid in the hypothesis of
one dominant isotope only has been developed. Defining the integral of the number of
carbon ions (Ni
can estimate, by approximating the derivative with the differential increment, the Araw
parameter in each single bin:
C) and of the detected γ−PET (Ni
γ) in the time bin i with BWwidth, we
where the raw suffix indicates that the measurement has not been corrected for the
detector efficiency. As an example, the numerical method has been applied to the NC
and Nγmeasurements shown in Fig. 7. The measured Araw
reported in Fig. 8. By minimizing the χ2, defined taking into account correlations and
assuming that the measured parameter is independent of the time bin, we obtain a mean
= (4.7 ± 1.0)·10−6, with χ2/DOF = 37/69.
parameters using Eq. 9 are
Entries Entries 69 69
Mean 34.81Mean 34.81
RMS 20.89 RMS 20.89
Time Bin [1min]
0 1020 3040506070
A x 10
Figure 8: Arawparameter time evolution and fit to a constant.
Conversely, we can exploit the same equations (9), assuming a measurement of Araw
from a calibration run, to estimate the number of incident carbon ions (Nγ
γ(Eq. 9) are measured for a specific data sample:
C), once the
We have tested this procedure on a long run (see Fig. 9 for the measured Nγ and
NC) with slightly unstable beam conditions. The Araw
parameter was estimated on the
shorter run from which Fig. 8 was taken, after adjusting for the detector efficiency as
detailed in the next section.
Number of Carbon;nuoviDic/EnergiCutOut/notte_out
Entries 427357 Entries 427357
Mean Mean 232.3 232.3
Entries 469 Entries 469
Mean 224.4Mean 224.4
RMS 141.9RMS 141.9
NumGammaPET DeadTime Corrected;nuoviDic/EnergiCutOut/notte_out
Figure 9: Measured Nc (Left) and Nγ (Right) as a function of time.
Fig. 10 shows the cumulative distribution of the number of ions estimated by the
measurements of γ − PET, Nγ
carbon ions measured with the Start Counter NSC
is visible, also at times comparable with the lifetimes of the decaying isotopes.
Cumulative PET-Estimated Carbon Number;nuoviDic/EnergiCutOut/notte_out
C, blue points, compared to the cumulative number of
C, magenta points. A good agreement
0 50100 150200250300350400450
NC?,NCSC x 109
NC?,NCSC x 109
Figure 10: Cumulative distribution of the number of carbon ion measured with the Start Counter,
(magenta points), compared to the number of ions estimated by the measurements of
γ − PET, Nγ
C(blue points). The plot on the right is a zoom in the first 50 min of acquisition.
4. Spatial dependence of the β+emission
The proposed numerical method to estimate NCrelies on the knowledge of the Araw
parameter (see Eq. 10). The Araw
parameter measurement described so far was corrected
only for the dead-time efficiency. To obtain the final A parameter we must correct for
the detector efficiency (?det). The latter depends on the position of the β+emitters along
the beam line with respect to the line connecting the two NaI detectors, as discussed in
Sec. 2. In order to study the spatial distribution of the emitters the Araw
measured for several positions of the PMMA, i.e. for several values of D as defined in
Eq. 4. It can be written as:
with dAec/dx(x|D) the density of emitters as a function of the depth x in the PMMA
(as defined in Fig. 4). The dependence on D takes into account the distribution shown
in Fig. 1 and the relative position of the PMMA and the NaI detectors.
literature  reports widths of the β+ emitter peak distribution smaller than ?(x) (Fig. 1),
we approximate dAec(x|D)/dx ∼ δ(x−(D −Dβ+)) where Dβ+ is the position of the β+
emitters within the PMMA. Finally we obtain:
m (D) =?det(x)dAec
m (D) = A0·?det(D − Dβ+)(12)
with A0the constant component of the A parameter, D the distance along the beam line
between the line connecting the NaI crystals and the beam entrance face of the PMMA
(see Fig. 4) and Dβ+ the mean position of the emitters in the same reference system.
A(D) ? 10-6
Figure 11: The measured Araw
as described in the text.
m (D) parameter as a function of the position of the PMMA, fitted
Fig. 11 shows the dependence of the measured A parameter from D: the width of
the distribution is consistent with the one of the efficiency in Fig. 5 thus confirming the
hypothesis used to obtain Eq. 12.
From the fit of the spectrum in Fig. 11 with the function in Eq. 12 we obtain:
=(10.3 ± 0.7)·10−3
(5.3 ± 1.1) mm.
The dose deposition in the PMMA has been simulated with FLUKA . The result
is shown in Fig. 12 as a function of the depth from the beam entrance face of the PMMA
with the beam entering form the left side of the plot. In our configuration the Bragg
peak is at 11.0 ± 0.5 mm from the beam entrance face (light yellow band) of the target.
The simulation is confirmed by the picture of the PMMA after the data taking , shown
in Fig. 12 (Inset): the dose distribution is visible by the deterioration (light yellow band)
of the PMMA.
246810 1214 161820
56 CAPITOLO 5. MISURE DI DOSE E POSIZIONE DEL PI
Figura 5.4. Foto del blocchetto di PMMA al termine dell’irraggiamento durant
mento di Catania. Si nota una zona gialla, indicativa di dove è stata rilasciat
la linea verticale rappresenta quindi la posizione del picco di Bragg. La seco
verticale che si nota, meno marcata e a profondità maggiore, è dovuta all’ulti
acquisizione, non trattata in questo lavoro di tesi, che è stata eseguita con il
alta intensità (∼ 10 MHz) avendo rimosso lo Start Counter.
|Dβ+− DBragg| = (5.7 ± 1.2) mm.
Fig. 3.8, ad esempio, la distanza fra i due picchi è di circa 10 mm per ioni
da 279.2 MeV/u, ed è ragionevole attendersi che questa distanza aumenti al
dell’energia della particella incidente.
We proposed, and validated with data, a model to describe the activated nuclei β+
decay during the irradiation. We demonstrated the possibility to estimate the number
of impinging carbon ions from the number of observed γ−PET.
We measured the ratio between the number of activated11C and13N to be AC/AN=
16.6 ± 2.7 and a number of (10.3 ± 0.7)·10−3generated11C ions, per impinging carbon
ion undergoing β+decay.
5.2Estrapolazione del numero di Carboni arri
partire dal numero di γ-PET
Una volta dimostrato che l’equazione che regola l’emissione di γ-PET
del PMMA colpito da ioni Carbonio è la 4.1, e che a dominare è l’attiva
11C (sezione 4.2.1), è possibile utilizzare la conoscenza della legge di deca
per invertire l’eq. 4.14 in modo da ricavare per ogni bin, a partire solam
parametro A e dal numero di γ-PET, il numero di Carboni giunti sul bers
È infatti possibile scrivere:
E(%) FLUKA simulation
Figure 12: Dose deposition in the PMMA simulated with FLUKA as a function of the depth
from the beam entrance face of the PMMA.
Using the measured value of Dβ+(Eq. 14) with the simulated Bragg peak position
DBragg, we obtain the distance ξ between the β+ emitters and the Bragg peaks: ξ =
We presented a study of the rate of γ−PET produced in the interaction of 80 MeV/u
fully stripped carbon ions with a PMMA phantom, using a pair of NaI crystal detectors.
Finally we measured the mean position of the β+emission to be Dβ+= (5.3±1.1) mm
from the beam entrance PMMA face, to be compared to the simulated Bragg peak
position DBragg= (11.0 ± 0.5) mm.
This information can be used as a benchmark for the β+emitters Montecarlo simu-
lation of hadrontherapy.
We would like to thank Carmelo Piscitelli for the realization of the mechanical sup-
port. The staff of the INFN-LNS (Catania, Italy) test beam is gratefully acknowledged
for their kind cooperation and helpfulness.
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