Triple ionization chamber method for clinical dose monitoringwith a Be-covered Li BNCT field
Thanh Tat Nguyen, Tsuyoshi Kajimoto, Kenichi Tanaka, Chien Cong Nguyen,a)and Satoru Endoa),b)
Quantum Energy Applications, Graduate School of Engineering, Hiroshima University, 1-4-1 Kagamiyama,
Higashi-Hiroshima, Hiroshima 739-8527, Japan(Received 9 December 2015; revised 6 September 2016; accepted for publication
10 September 2016; published 20 October 2016)

Purpose: Fast neutron, gamma-ray, and boron doses have different relative biological effectiveness(RBE). In boron neutron capture therapy (BNCT), the clinical dose is the total of these dosecomponents multiplied by their RBE. Clinical dose monitoring is necessary for quality assurance of
the irradiation profile; therefore, the fast neutron, gamma-ray, and boron doses should be separately
monitored. To estimate these doses separately, and to monitor the boron dose without monitoring
the thermal neutron fluence, the authors propose a triple ionization chamber method using graphitewalled carbon dioxide gas (C–CO2), tissue-equivalent plastic-walled tissue-equivalent gas (TE-TE),and boron-loaded tissue-equivalent plastic-walled tissue-equivalent gas [TE(B)-TE] chambers. To
use this method for dose monitoring for a neutron and gamma-ray field moderated by D2O froma Be-covered Li target (Be-covered Li BNCT field), the relative sensitivities of these ionizationchambers are required. The relative sensitivities of the TE-TE, C–CO2, and TE(B)-TE chambers
to fast neutron, gamma-ray, and boron doses are calculated with the particle and heavy-ion transport
code system (PHITS).
Methods: The relative sensitivity of the TE(B)-TE chamber is calculated with the same method as
for the TE-TE and C–CO2 chambers in the paired chamber method. In the Be-covered Li BNCT
field, the relative sensitivities of the ionization chambers to fast neutron, gamma-ray, and boron
doses are calculated from the kerma ratios, mass attenuation coefficient tissue-to-wall ratios, andW -values. The Be-covered Li BNCT field consists of neutrons and gamma-rays which are emitted
from a Be-covered Li target, and this resultant field is simulated by using PHITS with the crosssection library of ENDF-VII. The kerma ratios and mass attenuation coefficient tissue-to-wall ratios
are determined from the energy spectra of neutrons and gamma-rays in the Be-covered Li BNCT
field. The W -value is calculated from recoil charged particle spectra by the collision of neutrons
and gamma-rays with the wall and gas materials of the ionization chambers in the gas cavities
of TE-TE, C–CO2, and TE(B)-TE chambers (10B concentrations of 10, 50, and 100 ppm in the
TE-wall).
Results: The calculated relative sensitivity of the C–CO2 chamber to the fast neutron dose in the
Be-covered Li BNCT field is 0.029, and those of the TE-TE and TE(B)-TE chambers are both equal
to 0.965. The relative sensitivities of the C–CO2, TE-TE, and TE(B)-TE chambers to the gamma-ray
dose in the Be-covered Li BNCT field are all 1 within the 1% calculation uncertainty. The relative
sensitivities of TE(B)-TE to boron dose with concentrations of 10, 50, and 100 ppm 10B are calculated
to be 0.865 times the ratio of the in-tumor to in-chamber wall boron concentration.
Conclusions: The fast neutron, gamma-ray, and boron doses of a tumor in-air can be separately
monitored by the triple ionization chamber method in the Be-covered Li BNCT field. The results showthat these doses can be easily converted to the clinical dose with the depth correction factor in the
body and the RBE. C 2016 Author(s). All article content, except where otherwise noted, is licensed
under a Creative Commons Attribution 3.0 Unported License. [http://dx.doi.org/10.1118/1.4963222]
Key words: accelerator-based boron neutron capture therapy, triple ionization chamber method,
neutron boron dose
1. INTRODUCTION
Fast neutron, gamma-ray, and boron doses have different
relative biological effectiveness (RBE) of 3.2, 1, and 3.8,
respectively.1 In boron neutron capture therapy (BNCT), the6049

Med. Phys. 43 (11), November 2016

clinical dose is the total of these dose components multipliedby their RBE. Clinical dose monitoring is necessary for
quality assurance of the irradiation profile; therefore, the fastneutron, gamma-ray, and boron doses should be separately
monitored.

0094-2405/2016/43(11)/6049/9© Author(s) 2016

6049

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Nguyen et al.: Clinical dose monitoring for BNCTIn most BNCT facilities, the gamma-ray dose is monitored
by using a thermoluminescence dosimeter.2–4 The boron doseis monitored by the gold activation method with foils or
wires, and the fast neutron dose is monitored by measuring
the neutron fluence with a fission chamber. Rogus et al.
used tissue-equivalent plastic-walled tissue-equivalent gas(TE-TE) and graphite-walled carbon dioxide gas (C–CO2)
chambers and the gold foil activation method to separate
fast neutron, gamma-ray, and boron doses at the MITRII research reactor.5 However, the gold activation method
takes 15 min to determine the thermal neutron fluence.6
Recently, several simple methods have been proposed for
dose monitoring. Ishikawa et al. proposed paired scintillator
detectors with an optical fiber (SOF) system. The paired
SOF consisted of boron-free and boron-loaded scintillator
detectors to acquire the thermal neutron fluence quickly.7 In
addition, Becker et al. proposed a triple ionization chamber
method with the TE-TE and magnesium-walled argon gas(Mg–Ar) chambers of the paired chamber method, and a
Mg–Ar chamber coated with 10B on the inside surface ofthe chamber wall [Mg(B)–Ar].8 The Mg(B)–Ar chamber withthe 10B-coated Mg wall had a good response to the thermal
neutrons. The boron dose was monitored by multiplying
the kerma factor by the thermal neutron fluence which
was determined by the Mg(B)–Ar chamber. Moreover, Fujii
et al. investigated the optimization of the chamber wall
thickness in a multionization-chamber system to improve
the separation of thermal neutrons, epithermal neutrons,
fast neutrons, and gamma-rays in BNCT.9 They added aboron-loaded polyethylene-walled N2 gas chamber and asilicon nitride-walled N2 gas chamber to the paired chamber
method in order to monitor the thermal and epithermal
neutron fluences, respectively. In these methods, the boron
dose was obtained from the measured thermal neutron
fluence by multiplying by the kerma factor. Thus, a simple
method is needed to estimate the boron dose without
relying heavily on the determination of the thermal neutron
fluence.
We propose a triple ionization chamber method to monitor
the three dose components separately. This method uses theC–CO2 and TE-TE chambers of the paired chamber method
and a boron-loaded tissue-equivalent plastic-walled tissueequivalent gas [TE(B)-TE] chamber. The TE(B)-TE chamber
has the same constituents as the TE-TE chamber, except forsmall amount of 10B which is contained in TE wall. The
paired chamber method with the TE-TE chamber and theC–CO2 chamber have been used to determine the fast neutron
dose and the gamma-ray dose.10 The TE(B)-TE chamber isused to obtain the boron dose. The triple ionization chamber
method with the TE-TE, C–CO2, and TE(B)-TE chambers
is an extension of the paired chamber method. To use ourmethod for dose monitoring in a neutron and gamma-ray
field moderated by D2O from a Be-covered Li target (Becovered Li BNCT field), the relative sensitivities of threeionization chambers to fast neutron, gamma-ray, and boron
doses are calculated with the particle and heavy-ion transport
code system (PHITS)11 with the cross section library of
ENDF-VII.12
Medical Physics, Vol. 43, No. 11, November 20166050

2. MATERIALS AND METHODS
2.A. Formulae for relative sensitivities of the triple
ionization chamber method

The readings (unit: Gy) from the three chambers [TE-TE,
RT ; C–CO2, RU ; and TE(B)-TE, RB] are expressed using therelative sensitivities of the ionization chambers of k, h, and α
for the fast neutron, gamma-ray, and boron doses, respectively,
as10
RT = kT D N + hT DG ,RU = kU D N + hU DG ,RB = kT D N + hT DG + α B D B,

(1)
(2)
(3)

where D N , DG , and D B are the fast neutron, gamma-ray,and boron doses (unit: Gy), respectively. Subscripts T, U,
and B indicate the TE-TE, C–CO2, and TE(B)-TE chambers,
respectively. Equations (1) and (2) are used for the pairedchamber method.10 The TE-TE and C–CO2 chambers containno 10B; therefore, they have no response to the boron dose
which is originated in the 10B(n,α)7Li reaction. The triple
ionization chamber method is based on the paired chamber
method with an added TE(B)-TE chamber with a small amountof 10B in the wall. The reading as stated in Eq. (3) includes
the fast neutron, gamma-ray doses of TE-TE chamber, and theboron dose. The relative sensitivity of the TE(B)-TE chamber
to boron dose is α B, and those to fast neutron and gamma-ray
doses are the same as kT and hT of the TE-TE chamber.
With Eq. (3) the boron dose can be monitored separately
by using the relative sensitivities of each chamber instead ofmultiplying the kerma factor by the thermal neutron fluence
for this technique.
The relative sensitivities of the ionization chambers to thefast neutron and gamma-ray doses depend on the radiation
field and are defined according to ICRU 26.10 Zeeman et al.
expressed these quantities of the ionization chambers withthe following parameters: the W -value ratio of the W -valueof the gamma-ray field from 60Co to that of the radiation
field of interest, WC /W (definition of W value is describedin Subsection 2.B.3 below); the wall-to-gas mass stopping
power ratio, Smg; the mass-energy absorption coefficientstissue-to-wall ratio, (µen/ρ)t /(µen/ρ)m , where S, µen, and ρ aremass stopping power, mass-energy absorption coefficient, anddensity of material,
respectively; and the kerma tissue-to-gasratio, K t /Kg , as in Eqs. (4) and (5).13 The relative sensitivityof the TE(B)-TE chamber to boron dose is similarly definedby Eq. (6),
 ((µen/ρ)t /(µen/ρ)m )C
WC

Smg C
,
WN
K t /Kg NWC Smg C ((µen/ρ)t /(µen/ρ)m )C,
hT ,U =WG Smg G ((µen/ρ)t /(µen/ρ)m )G
WC Smg C ((µen/ρ)t /(µen/ρ)m )CαB =.
(K t /K m ) B
W B Smg B
kT ,U =

(4)
(5)
(6)

Here, subscripts t, m, g, C, N, G, and B denote tissue,
wall material, gas, reference gamma-ray dose (e.g., 60Co
gamma-rays), fast neutron, gamma-ray, and boron doses,

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Nguyen et al.: Clinical dose monitoring for BNCT

6051

T I. W -values, mass attenuation coefficient tissue-to-wall ratios, andwall-to-gas mass stopping power ratios of the TE-TE and C–CO2 chambersin the 60Co gamma-ray field.
SymbolWC((µ en/ρ)t /(µ en/ρ) m )C(Smg)C

Ionization chamber

Value

Reference

TE-TE
C–CO2
TE-TE
C–CO2
TE-TE
C–CO2

29.3 eV
33.0 eV
1.001
1.126
1.000
1.009

14
17
14
16
14
15
F. 1. Input geometry for the PHITS calculations.



respectively. W N , W B, Smg B, and WG are calculated basedon the recoil particle energy spectrain the gas cavity of ioni
zation chambers, and K t /Kg N and ((µen/ρ)t /(µen/ρ)m )G are
calculated from the neutronand gamma-ray energy spectra.
The parameters of WC , Smg C , and ((µen/ρ)t /(µen/ρ)m )C forthe 60Co gamma-ray field are taken from the literature and arelisted in Table I.14–17 The calculation method for the W -value,
kerma ratio, mass energy absorption coefficient tissue-to-wallratio, and wall-to-gas mass stopping power ratio is describedin Subsection 2.B.
In order to use the triple ionization chamber methodfor dose monitoring, we are planning for the three-monitor
chamber to be set at the surface of the treatment position. The
dose components are monitored as the tumor kerma in-air. For
boron dose monitoring, when the 10B concentration in tissue
is assumed to be that in the tumor, ρt , the 10B concentration in
the chamber wall is ρc , the ratio of kerma in tissue to kerma
in the TE(B)-TE chamber wall from α particles and Li ionsproduced: (K t /K m ) B corresponds to ρt /ρc . Therefore, α B in
Eq. (6) can be expressed by α ′B asαB =α ′B =

ρc ′
α ,
ρt B

(7)


Wc Smg C
 ((µen/ρ)t /(µen/ρ)m )C ,W B Smg B(8)

Be layer (20 µm thick). The Be-covered Li target is attached
on a Cu backing plate (0.8 cm thick, 14 cm in diameter),target assembly (SUS304 stainless steel, 1.4 cm thick), andcirculating cooling water (2.2 cm effective thickness). In thiscalculation, the incident proton beam from the accelerator isassumed with the current, section diameter, and energy to
be 1 mA, 10 cm, and 2.86 MeV, respectively. Due to theexistence of Be layer on the surface of Li target, the protonenergy is reduced to 2.5 MeV at the surface of the Li layer.
To save calculation time, the calculation of the neutron energy
spectrum at the collimator exit is divided into two steps. First,
the proton-induced neutron energy spectrum from the target
is tallied at the downstream surface of the Li target. Second,
generated neutrons from the downstream surface of the target
are transported through the Cu backing plate, cooling water,target assembly, D2O moderator (20 cm thickness and 20 cm indiameter), and a collimator (polyethylene + 50 wt. % natural
LiF, 12 cm inside diameter, and a 10 cm outside diameter).
This neutron energy spectrum is tallied at the collimator exit.
The simulation geometry is shown in Fig. 1, and the neutronenergy spectrum is shown in Fig. 2.
Gamma-rays are produced by the 7Li(p,p′γ) reaction(prompt gamma-rays: PG) and by interaction between neutron
and materials around the target, such as Cu, H2O, SUS304

where reduced relative sensitivity α ′B is not dependent on
the 10B concentration in the wall of the TE(B)-TE chamber.
The parameters for calculating the TE(B)-TE chamber are
assumed to be the same as those of the TE-TE chamberbecause of the negligible 10B content of 10, 50, or 100 ppm.
To estimate the tumor dose in the body, a correction factor
dependent on the depth from the surface is needed. This
correction factor is discussed in Sec. 4.
2.B. Relative sensitivity calculations
2.B.1. Calculation of neutron and gamma-ray
energy spectra

Neutrons that are produced by the 7Li(p,n) reaction froma Be-covered Li target are considered as the neutron source
for this study. The cross section of the 7Li(p,n)7Be reaction in
the proton reaction sublibrary of ENDF-VII (Ref. 12) is used
to estimate the source term by PHITS. The target consists of
a Li layer (100 µm thick, 12 cm in diameter) covered with a
Medical Physics, Vol. 43, No. 11, November 2016

F. 2. Neutron and gamma-ray spectra at the collimator exit.

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Nguyen et al.: Clinical dose monitoring for BNCT

(secondary gamma-rays: SG). However, owing to the lackof cross section data for 7Li(p,p′γ) reaction in the crosssection library ENDF-VII, the prompt gamma-rays with anenergy of 478 keV from the (p,p′γ) reaction are produced
from an isotropic point source at the center of the Li target
according to Lee’s method,18 and they are transported throughthe cooling system, moderator, and collimator. The othergamma-ray production such as the 7Li(p,γ) reaction, gammaray from the first excited state through the 7Li(p,n)7Be∗
reaction, and decay gamma-rays from the resultant 7Be by
the 7Li(p,n)7Be reaction, are negligibly small (less than
2% of the total of PG and SG at the collimator exit).
The total gamma-ray spectra are shown at the exit of thecollimator in Fig. 2. These spectra are used for further chamber
simulations.
2.B.2. Recoil particle spectra in ionization chamber
gas cavities

The recoil particle spectra produced in the gas cavity ofeach chamber in the Be-covered Li BNCT field are calculatedwith neutron and gamma-ray spectra from Fig. 2 by PHITS.
These spectra are used for calculating the W -values. The input
geometries of the TE-TE, C–CO2, and TE(B)-TE chambers
are assumed to be spherical (IC-17, Farwest Technology Co.
Ltd.). The C–CO2 ionization chamber has graphite walls(543 mg cm−2), an internal volume of 2.5 cm3, and is filledwith CO2 gas. The TE-TE chamber has a TE wall (A-150 wall)(569 mg cm−2), an internal volume of 1 cm3, and is filled withmethane-based TE gas. The TE(B)-TE has the same geometry
as the TE-TE chamber except for a small amount of 10B (10,50, or 100 ppm) in the TE wall.
The element compositions of TE-TE, C–CO2, and TE(B)TE chambers19 are summarized in Table II. Each ionizationchamber is set at the collimator exit in this calculation, as
shown in Fig. 1.
2.B.3. W -value calculation

The W -value is the ratio of the total deposited energy to thetotal number of electron-ion pairs in the gas cavity produced

6052
T II. Compositions of TE-TE, C–CO2, and TE(B)-TE chambers.
Composition (%)
Element

TE
wall

TE(B) wall

Methane-based
TE gas

H
C
N
O
F
Ca
B

10.1
77.7
3.5
5.2
1.7
1.8
—

10.1
77.7
3.5
5.2
1.7
1.8
10, 50, 100 ppm 10B

10.2
45.6
3.5
40.7
—
—
—

C
wall CO2 gas
—
100
—
—
—
—
—

—
27.3
—
72.7
—
—
—

by incident neutron or gamma-ray in the ionization chamber.
For fast neutrons, the energy deposition and ion pairs arefrom H, C, O, and N ions, similar to α particles and Li
ions produced by the 10B(n,α)7Li reaction. For gamma-rays,
the energy deposition and ion pairs originate from electrons
emitted from the walls and gas by ionization and electronposition pair production processes. In this calculation, theW -values for fast neutrons (W N ), gamma-rays (WG ), and thesum of α particles and Li ions (W B) is calculated from theinitial differential energy spectrum, n j (Ei ), for recoil charged
particles of type j, in the gas cavity of ionization chambers.
The average energies per ion pair of W N , WG , and W B are
obtained asn j (Ei )Ei ∆Ei
j i
,
(9)
W = 
n j (Ei )Ei ∆Ei /W j (Ei )j iwhere W j (Ei ) is the jth recoil particle W -value at the ith
energy group, Ei . Summation over j is carried out by H, C, N,
and O ions for fast neutrons, electrons for gamma-rays, andα particles and Li ions induced by the 10B(n,α)7Li reaction,
which is related to the boron dose. W j (Ei ) ( j = H, α, C, N, O)
in TE gas are taken from the values reported by Goodman and
Coyne.20 WLi(E) of Li ion in TE gas is calculated using thescaling law from Wα (E) of α particles with the corresponding
reduced energy ε = E/M z 4/3, where M is the particle massand z is the nuclear charge.17 W j (Ei ) for j = H, α, Li, C, N,

F. 3. (a) Average energy per ion pair of α particles, and H, Li, C, N, and O ions in TE gas (Ref. 20). (b) Fitted curve of the average energy per ion pair of α
particles and C and O ions in CO2 gas (Ref. 21). (c) Fitted curve of the average energy per ion pair of electrons in TE and CO2 gases (Refs. 17 and 21).
Medical Physics, Vol. 43, No. 11, November 2016

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Nguyen et al.: Clinical dose monitoring for BNCT

6053

T III. Fitting parameters of Eqs. (10) and (11).

α particles and C and O ions in CO2 gas
Electrons in TE gas
Electrons in CO2 gas

a

b

c

d

12.22
995.241396.3

0.94
7.25
9.5

0.35
3.47
3.49

27.04
29.32
31.89

gas according to the Bethe-Bloch formula23 with the meanenergy for α particles and Li ions. The α particle and Li ion
energy spectra in TE wall and TE gas are calculated from theneutron fluence of the outputs in the second calculation stepby PHITS.

3. RESULTS
O in TE gas are shown in Fig. 3(a). Several experimental
values for W j (Ei ) ( j = α, C, O) in CO2 gas are available atenergies of 24.5 × 103 to 5.11 × 103 keV for α particles, and24.5–370 keV for C and O ions.21 Therefore, for W j (Ei ) in
CO2 gas for α particles, C and O ions are obtained by a scaling
function of W (ε) with the reduced energy fitted using Eq. (10)[Fig. 3(b)]. We (Ei ) of electrons in TE and CO2 gas are obtainedby fitting with Eq. (11) based on previous data17,21 [Fig. 3(c)].
The results of the fitted parameters are listed in Table III. The
error of the fitted values and experimental values is less than
1% for electrons in TE/CO2 gas and less than 3% for recoil
particles in CO2 gas,a
+ d,(0.434 ln(ε − b))ca
+ d.
We (E) =(ln(E − b))c

W (ε) =

(10)
(11)

2.B.4. Kerma ratio and mass-energy absorption
coefficient tissue-to-wall ratio calculation


The kerma ratio of tissue-to-TE/CO2 gas, K t /Kg N for
neutrons and the tissue-to-wall ratio of mass-energy absorption coefficients in tissue and the C/TE wall for gamma-rays
are calculated as
K f , t (Ei )Φn (Ei )

i
(12)
,
K t /Kg N = 
K f ,g (Ei )Φn (Ei )i) ( µ enρ (Ei ) t Ei ΦG (Ei )i)((µen/ρ)t /(µen/ρ)m )G =  ( µ
(13)
,
en
Ei ΦG (Ei )ρ (Ei )imwhere subscripts t and g denote tissue and gas, respectively; K f , t (Ei ) and K f ,g (Ei ) are kerma factors in tissue
and TE/CO2 gas at energy Ei from the literature data,19
respectively; the mass-energy absorption coefficients for eachelement are taken from the data reported by Hubbell and
Seltzer;22 and Φn (Ei ) and ΦG (Ei ) are the neutron fluenceand gamma-ray fluence at energy Ei , respectively. These
neutron and gamma-ray fluences are obtained at the collimatorexit.

2.B.5. Wall-to-gas mass stopping power
ratio calculation


The wall-to-gas mass stopping power ratio, Smg B for
the Be–Li BNCT field is estimated from the mass stopping
power of α particles and Li ions in the TE wall and TE
Medical Physics, Vol. 43, No. 11, November 2016

3.A. W -value calculation from the recoil particle
spectra in gas cavities

The recoil particle spectra induced by neutrons in thegas cavities of TE-TE, TE(B)-TE, and C–CO2 chambers areshown in Figs. 4(a)–4(c). The electron spectra due to gammarays are shown in Fig. 4(d). Figure 4(a) shows the spectra of H,
C, N, and O ions in the TE gas of TE-TE chamber. Figure 4(b)shows the identical spectra of H, C, N, and O ions with thosein Fig. 4(a), and the energy spectra of α particles and Li
ions for a 10B concentration of 100 ppm originating from the10
B(n,α)7Li reaction in the boron-loaded TE-plastic [TE(B)plastic] wall. The shape of energy spectra of α particles and Li
ions does not change with the 10B concentration even in casesof 10 and 50 ppm [not shown in Fig. 4(b)] because α particle
and Li ion yields are proportional to the 10B concentration.
Therefore, at higher 10B concentrations in the TE(B)-TE
chamber wall, the fraction of energy deposition and ion-pairs
produced by α particles and Li ions increase. Figure 4(c)shows the spectra of C and O ions, which are products ofneutron elastic scattering with C and O in the C–CO2 chamber.
A small amount of α particles is produced by the 17O(n,α)
reaction, with a fluence of three orders of magnitude lower
than C and O ions; therefore, its contribution to the W N -valueof the C–CO2 chamber is negligible. Figure 4(d) shows theenergy spectra of electrons in the TE gas of the TE-TE/TE(B)TE chambers and CO2 gas of the C–CO2 chamber. Because
the electrons from gamma-rays produced by the 10B(n,αγ)
reaction are negligibly small (less than 0.1% compared tothe electrons due to PG and SG), the energy spectra ofelectrons in the TE(B)-TE chamber do not change with the10
B concentration and are the same as that of the TE-TE
chamber.
W N and WG for TE-TE, C–CO2, and TE(B)-TE chambers,
and W B for TE(B)-TE chamber are calculated, and the results
are summarized in Table IV. The W N and WG for TE-TE
chamber have the same values as those for TE(B)-TE chamber.
The W B of the TE(B)-TE chamber is not dependent on 10B
concentration.
3.B. Kerma ratio, mass-energy absorption coefficienttissue-to-wall ratio, and wall-to-gas mass stopping
power ratio

The calculated results of the kerma ratios of the TETE, C–CO2, and TE(B)-TE chambers, and the mass-energy
absorption coefficient tissue-to-wall ratios are listed inTable IV. The wall-to-gas mass stopping power ratio is
calculated by using the energy spectra of α particles andLi ions in Fig. 4(b).

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F. 4. (a) Recoil particle spectra in the TE gas in the TE-TE chamber. (b) Recoil particle spectra in the TE gas of the TE(B)-TE chamber at a 10B concentrationof 100 ppm. (c) Recoil particle spectra in the CO2 gas of the C–CO2 chamber. (d) Electron spectra in the gas cavity of the TE-TE, C–CO2, and TE(B)-TE
chambers.

3.C. Relative sensitivities of ionization chambers

The relative sensitivities of the ionization chambers for the
Be-covered Li BNCT field are listed in Table V. The relative
sensitivities of the TE-TE and TE(B)-TE chambers to the fastT IV. Calculated results of the W -values, kerma ratios, mass attenuation
coefficient tissue-to-wall ratios, and wall-to-gas mass stopping power ratio
for the TE-TE, C–CO2, and TE(B)-TE chambers.
SymbolWN
WG
WB(K t /K g ) N((µ en/ρ)t /(µ en/ρ) m )G(Smg) B

Ionization chamber

Value

TE-TE, TE(B)-TE
C–CO2
TE-TE, TE(B)-TE
C–CO2
TE(B)-TE
TE-TE, TE(B)-TE
C–CO2
C–CO2
TE(B)-TE

30.82 eV62.02 eV29.3 eV
33.0 eV33.8 eV
0.986
20.3
1.108
1.002

Medical Physics, Vol. 43, No. 11, November 2016

neutron dose (kT and k B) are the same; that of C–CO2 chamberto the fast neutron dose, kU is approximately 33 times smaller
than the kT and k B due to lack of hydrogen in chamber;and those of TE-TE, C–CO2, and TE(B)-TE (hT and hU ) to
the gamma-ray dose are 1 with the calculation uncertainty of1%.
T V. Relative sensitivities of the ionization chambers to the Be-covered
Li BNCT field.
Relative sensitivity
Chamber

Subscription

k

h

α′B

C–CO2
TE-TE

U
T

0.029
0.965

1.000
0.999

TE(B)-TE

B

0.965

0.999

—
—
0.865a0.864b
0.866ca

10 ppm 10B.
50 ppm 10B.
c
100 ppm 10B.

b

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Nguyen et al.: Clinical dose monitoring for BNCT6055

The reduced relative sensitivity of the TE(B)-TE chamberto the boron dose, α ′B is independent of the 10B concentrationin the chamber wall, as in Eq. (8). The calculated results of
α ′B show the same value of 0.865 within the uncertainty of
5%.
The relative sensitivity of the TE(B)-TE chamber to boron
dose, α B, is calculated as in Eq. (7). α B depends on the ratioof the in-tumor (ρt ) to TE(B)-TE chamber in-wall (ρc ) 10B
concentrations, and it is expressed as 0.865(ρc /ρt ).
The uncertainties of the relative sensitivities to fastneutron and boron doses are estimated to be less than 5%
for the fast neutron and boron doses and less than 1%
for the gamma-ray dose with the PHITS statistical error
calculation, and errors of other quantities in Refs. 20 and
24–26.

4. DISCUSSION
From the neutron and gamma-ray energy spectra in Fig. 2,
the mean neutron energy weighted with the kerma factor is
calculated to be 0.2 MeV and the mean gamma-ray energy
weighted by the mass attenuation coefficient of gamma-rays
is calculated to be 1.36 MeV. The relative sensitivities of
TE-TE, C–CO2, and TE(B)-TE chambers to gamma-ray, hT
and hU , are equal to unity within the calculation uncertainty.
The calculated results of hT and hU are consistent with therecommended value of ICRU 26.10 The relative sensitivitiesof the TE-TE chamber (kT ) and C–CO2 chamber (kU ) to
the fast neutron dose in the Be-covered Li BNCT field areplotted against the mean neutron energy [Figs. 5(a) and 5(b)]comparing with those for monoenergetic neutrons. The differences of kT in the Be-covered Li BNCT field and the resultsof Jansen et al. and Endo et al. for monoenergetic neutrons
are 4.8% and 2.4%, respectively.27,28 These differences are
consistent with our calculation uncertainties. The kU valueof our calculation has around 28% of difference from thecalculation by Endo et al.30 This difference seems large,
however, propagated uncertainties of neutron and gammaray absorbed doses are not large as they are estimated to
be around 5% and 1%, respectively. Therefore, the obtained
relative sensitivities can be used for dose monitoring with
sufficient uncertainty.
Based on the calculation results and Eqs. (1)–(3), the fastneutron, gamma-ray, and boron doses in the Be-covered Li
BNCT field are expressed separately as
D N = 1.1(RT − RU ),DG = RU − 0.03RT ,ρt
D B = 1.16 (RB − RT ).
ρcdepth correction factor and the RBE. The RBE of these dosecomponents can be taken from the IAEA-TECDOC 1223.1
The total clinical dose, DC (Gy-Eq), in the tumor is calculatedas
DC = 3.2η N · D N + η G · DG + 3.8η B · D B,

(17)

where subscripts N, G, and B indicate fast neutron,
gamma-ray, and boron doses, respectively, and η k (k = N,G, and B) is the depth correction factor for each dosecomponent.
The η k is calculated by the ratio of the dose at each depth
to that on the surface of the phantom. This ratio shows that adose changes according to the spectrum distortion of neutrons

(14)
(15)
(16)

Monitored doses D N , DG , and D B are the tumor
doses in-air. This shows that the boron dose can bemonitored as D B in-air without considering the thermal
neutron fluence if the 10B concentration in the tumor is
known.
The tumor dose of the fast neutron, gamma-ray, and boron
doses in the body should be corrected by the corresponding
Medical Physics, Vol. 43, No. 11, November 2016

F. 5. (a) Calculated k T of the BNCT neutron field plotted against the mean
neutron energy (closed triangles). Previous data for monoenergetic neutrons
are shown for Refs. 27–29. (b) Calculated kU of the BNCT neutron fieldplotted against the mean neutron energy (closed triangles). Previous data formonoenergetic neutrons are shown for Refs. 29–31.

F. 6. Depth correction factor of fast neutron, gamma-ray, and boron doses.

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Nguyen et al.: Clinical dose monitoring for BNCT

and gamma-rays in the body. Tanaka et al.32 calculated thedepth dose curves in a light water phantom for fast neutron,
gamma-ray, and boron doses for D2O moderated 7Li(p,n)7Be
neutrons with 2.5 MeV incident protons. η of the fast neutron,
gamma-ray, and boron doses can be estimated from the depth
dose curves (Fig. 6). In this research, these depth correction
factors can be used to estimate the tumor doses in the body.
The total clinical dose, DC (Gy-Eq), can be quickly calculatedwith Eq. (17). Thus, these doses can be converted easily to theclinical dose with the depth correction factor in the body andthe RBE.

5. CONCLUSION
We proposed a triple ionization chamber method to monitor
fast neutron, gamma-ray, and boron doses for BNCT. For the
triple ionization chamber method, the relative sensitivitiesof the TE-TE, C–CO2, and TE(B)-TE chambers in theneutron and gamma-ray field moderated by D2O from a
Be-covered Li target were calculated. The fast neutrondose, gamma-ray dose, and boron dose of a tumor inair were estimated by this method. The tumor dose in-air
was converted to a clinical dose by correcting with thedepth correction factor in the body and RBE. The results
indicate that the clinical dose can be monitored by the triple
ionization chamber method. The differences of kT at meanenergy in the Be-covered Li BNCT field to monoenergetic
neutrons are consistent with previous calculations within
the calculation uncertainties. The kU is quite different fromprevious calculations, however, the uncertainties of neutronand gamma-ray absorbed doses are estimated to be around
5% and 1%, respectively.
ACKNOWLEDGMENT
The authors are grateful to Asia Jinzai Program andPhoenix Leader Education Program of Hiroshima University
for their financial support and good advice on writing ascientific paper.

CONFLICT OF INTEREST DISCLOSURE
The authors have no COI to report.

a)Present address: Engineering Department, Industrial Equipment Division,

Sumitomo Heavy Industries, Ltd.
b)Author to whom correspondence should be addressed. Electronic mail:endos@hiroshima-u.ac.jp
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