On the Eptihermal Neutron Energy Limit for Accelerator-Based Boron Neutron Capture Therapy (AB-BNCT): Study and Impact of New Energy Limits
OOn the Eptihermal Neutron Energy Limit for Accelerator-Based Boron NeutronCapture Therapy (AB-BNCT): Study and Impact of New Energy Limits
Marine Herv´e a, ∗ , Nadine Sauzet a , Daniel Santos a a Univ. Grenoble Alpes, CNRS, Grenoble INP, LPSC-IN2P3, 38000 Grenoble, France
Abstract
Background and purpose: Accelerator-Based Boron Neutron Capture Therapy is a radiotherapy based on compact acceleratorneutron sources requiring an epithermal neutron field for tumour irradiations. Neutrons of 10 keV are considered as the maximumoptimised energy to treat deep-seated tumours. We investigated, by means of Monte Carlo simulations, the epithermal range from10 eV to 10 keV in order to optimise the maximum epithermal neutron energy as a function of the tumour depth.Methods: A Snyder head phantom was simulated and mono-energetic neutrons with 4 di ff erent incident energies were used: 10eV, 100 eV, 1 keV and 10 keV. B capture rates and absorbed dose composition on every tissue were calculated to describe andcompare the e ff ects of lowering the maximum epithermal energy. The Therapeutic Gain (TG) was estimated considering the wholebrain volume.Results: For tumours seated at 4 cm depth, 10 eV, 100 eV and 1 keV neutrons provided respectively 54 %, 36 % and 18 %increase on the TG compared to 10 keV neutrons. Neutrons with energies between 10 eV and 1 keV provided higher TG than 10keV neutrons for tumours seated up to 6.4 cm depth inside the head. The size of the tumour does not change these results.Conclusions: Using lower epithermal energy neutrons for AB-BNCT tumour irradiation could improve treatment e ffi cacy,delivering more therapeutic dose while reducing the dose in healthy tissues. This could lead to new Beam Shape Assemblydesigns in order to optimise the BNCT irradiation. Keywords:
AB-BNCT, epithermal energy, biological dose
1. Introduction
Boron Neutron Capture Therapy (BNCT) is a binaryradiotherapy intended for the treatment of invasive andextended tumours with complex spatial distribution orradio-chemotherapyresistants. This radiotherapy con-sists in fixing B on cancer cells through targeting car-riers and then submitting the patient to an adapted epi-thermal energy (between 0.5 eV and 10 keV) neutronfield [1, 2]. Neutron capture by the stable isotope Bresults in the production of an alpha ( He) particle anda lithium ( Li) nucleus, as described in (1a) and (1b).Those nuclear particles have path lengths between 4.8and 8.9 µ m in tissues and a high linear energy transfer(from 160 to 200 keV / µ m) [3]. As the average cell dia-meter reaches 10 µ m for human tissues, neutron captureproducts only a ff ect the targeted cell by releasing mostof their energy inside the cell volume and sparing sur-rounding cells.As neutron capture reaction on B cross section in-creases exponentially at low neutron energies, thermal ∗ Corresponding author : [email protected] neutrons are required at the tumour level to optim-ise the number of neutron captures and thus the treat-ment e ffi cacy. Thermal neutron fields are consideredmainly for superficial cancer cases, such as superficialmelanomas[4]. Since neutrons are thermalised and ab-sorbed in tissues, incident neutrons with energies higherthan thermal energies are required for non-superficialtumours treatment. However, neutrons toxicity in tis-sues increases significantly over 10 keV [5], mainly dueto the increase of energy transferred by elastic scatteringon hydrogen nuclei. So the usual maximum neutron en-ergy considered is about 10 keV, allowing to reach deepseated tumours and to reduce secondary dose which rep-resents the dose deposited in healthy tissues [6].The first BNCT clinical treatments were performedexclusively using nuclear research reactors to produceneutron fields [7, 8, 9, 10]. In order to provide facilit-ies suitable for hospital environment, an active researchis made around compact accelerator neutron sources[11]. The use of low energy particle compact acceler-ators and targets adapted to cope with high power (15to 30 kW) for neutron production led to the develop-ment of Accelerator-Based BNCT (AB-BCNT) facilit- Preprint submitted to Physica Medica European Journal of Medical Physics 5th February 2021 a r X i v : . [ phy s i c s . m e d - ph ] F e b B + n −→ [ B ∗ ] He + Li Q = . MeV (1a) He + Li Q = . MeV + γ [0 . MeV ] (1b) ies [12]. In this context, an AB-BNCT facility projectwas launched at the Laboratory of Subatomic Physicsand Cosmology (LPSC) in France [13, 14]. The pur-pose is to use a compact accelerator coupled to a beryl-lium target using the Be(d(1 . B reaction asa neutron source [15]. In the frame of this project, oneimportant issue is to maximise the treatment e ffi cacy,optimising the neutron energy range used for irradiationto minimise the absorbed dose in healthy tissues dur-ing the treatment. This article presents the study madeon the e ff ects on treatment e ffi cacy of di ff erent neut-ron energy by Monte Carlo simulations. Its principleis based on the study of the decomposition of the dosein tumour and healthy tissues, resulting from di ff erentmono-energetic epithermal neutrons.First of all, the simulation setup used for this study isdescribed. The results obtained are then discussed andthe last part concludes on the optimised neutron ener-gies proposed at the output of the beam shape assembly(BSA). All the results presented here are made in theframe of a brain cancer study but might be extended toother body organs.
2. Material and Methods H, O, C and N represent more than 99% inweight of all atoms in human brain tissues [16]. The ab-sorbed dose in healthy tissues results mainly from neut-ron scattering reactions and neutron capture reactionson the nuclei constitutive of the brain. As thermalisationthrough tissues is done by neutron scattering, it contrib-utes to the secondary dose on healthy tissues. In BNCT,the total absorbed dose in tissues can be expressed asfollowing [17]: D T = D B + D n + D p + D γ (2)The biological dose uses Relative Biological E ff ect-iveness (RBE) factors to take into account the di ff erentbiological e ff ectiveness of each component, it can be ex-pressed as following [17]: D w = w c ∗ D B + w p ∗ D n + w n ∗ D p + w γ ∗ D γ (3) The biological dose will be expressed in Gy[RBE]units to distinguish it from the absorbed dose expressedin Gy. The method used to calculate the biological dosein BNCT is still an active field of research in the BNCTcommunity [18, 19]. As the aim of this study is to com-pare di ff erent neutron energies, average values of RBEfactors are used and summarised in Table 1. Thosevalues are obtained considering Boronophenylalanine(BPA) as boron carrier [20].tissue tumour brain skull skin w c w n w p w γ Table 1: RBE factors for BPA boron carrier
Each dose component of the total dose is associatedto a di ff erent nuclear reaction, detailed below: • B(n, α ) Li reaction to the called boron dose D B ,considering the ionisation energy released by thealpha particle and lithium nucleus, • H(n,n’) H reaction to the called neutron dose D n ,considering the ionisation energy released by thehydrogen resulting from the elastic neutron scat-tering, • N(n,p) C to the called proton dose D p , consid-ering the ionisation energy released by the protonand the carbon nucleus, • H(n, γ ) H reaction and the residual gamma from B capture reaction ( B(n, γ ) Li) to the calledgamma dose D γ , only considering the energy trans-ferred by the photon by pair production, Comptonand photoelectric scattering.The occurrence of each nuclear reaction depends onits associated cross section, a function of the neutron en-ergy. Three of them are neutron capture reactions withcross section following a 1 / v law when neutron energydecreases in the thermal range energy [21], v being theneutron velocity, as shown in Figure 1. Thus, thermal2eutron fields penetrate poorly into tissues and cannotreach deep seated tumours. Epithermal neutrons fields,which thermalise as they penetrate the tissue, ensure toobtain thermal neutrons at the tumour level to maximisecapture probability on B.Moreover, in the epithermal energy range, cross-section values for elastic neutron scattering reactionsvary from less than 1% for C and O to 7% for Hand up to a maximum of 19% for N, see Figure 1.Neutrons with energy between 1 eV and 10 keV havea quite similar probability to interact by elastic scat-tering process. As thermalisation is achieved throughelastic scattering on tissue nuclei, this process seemsalmost independent of the neutron energy in the epti-hermal range. Then, it could be assumed that the penet-rability of neutrons inside the brain does not stronglychange with their initial epithermal energy as it waspointed out in [22]. For elastic neutron scattering re-actions, the energy transferred to the nuclei is propor-tional to the neutron incident energy. So the second-ary dose induced by scattering reactions increases withhigher epithermal neutron energy. In this context, re-ducing the neutron energy from the present referenceenergy of 10 keV to lower epithermal energies will in-crease the absorbed dose in the tumour while reducingthe secondary dose resulting from elastic scattering re-actions on healthy tissues. This hypothesis is exploredhereafter by Monte Carlo simulations.
Simulations have been processed with the MonteCarlo code MCNP. The geometry includes a humanhead phantom with a brain tumour. The universe aroundthe phantom was set empty to reduce calculation timeand to ensure the initial value of the neutron energyreaching the phantom.The phantom considered here is a Snyder head modelphantom [23] with a spherical tumour as shown in Fig-ure 2 and tissues having the composition and densityrecommended by ICRU-46[16] (see Table 2).Surface equations for brain, skull and skin in theSnyder model used were respectively determined by thefollowing equations:( x + ( y + ( z − . = x . + ( y . + ( z . = x . + ( y . + ( z . = .
14 cm , consisting ofa 1 . ff erent depths in-side the brain. The tumour is centred in X and Y and istranslated on the Z axis of the geometry. Tumour depthis set between 4 cm and 8 cm, with 1 cm step, to coverfive non-superficial cancer cases, and having the samecomposition as the brain tissue. B concentrations are added to the ICRU-46 tissuescomposition, with 52.5 ppm in the tumour, 15 ppm inthe brain, 22.5 ppm in the scalp and 15 ppm in the skull[24]. The B concentration ratios for healthy tissuesand tumours compared to B concentration in bloodare listed in Table 3. The blood B concentration con-sidered is 15 ppm.tissue tumour brain skull skintissue to blood ratio 3.5 1 1 1.5
Table 3: Tissue to blood ratios of B concentration for healthy tissuesand tumour.
The neutron source was defined as a 21 cm diameterdisc, simulating a Beam Shape Assembly (BSA) outputof 10.5 cm radius and allowing to provide a complete ir-radiation of the head phantom. Neutrons are sent with amono-energetic energy and uniformly on the disc alongthe Z axis, as it can be seen in Figure 3. In order toexplore the whole epithermal range, simulations wereperformed at the following energies: 10 eV, 100 eV, 1keV and 10 keV.
Due to the energy range of interest (from thermal toepithermal neutrons), thermal treatment is implementedin the simulations. Free-gas treatment is used in thesimulation model above 4 eV, representing the energythreshold below which thermal scattering laws are im-plemented with the use of S( α , β ) functions [25]. Thesefunctions treat a specified material in the thermal regimeas a molecular compound, taking into account the ef-fects on cross sections of molecular structure and vibra-tion modes. Only some materials are tabulated [26]. Ashuman tissues are similar to light water in compositionand density, the tabulated data of light water were selec-ted.MCNP uses variance reduction techniques, includ-ing implicit capture and weight cut-o ff parameters. Theweight is a value allocated to a particle that is calcu-lated at each step of its track according to the prob-ability of the current event to happen. In general, the3 igure 1: a. (left)Elastic scattering cross section from ENDF data base for H, N, C and O ; b. (right) Neutron cross section from ENDF database for B(n, α ) Li, N(n,p) C and H(n, γ ) H Weight %tissue ρ (gr / cm ) H C N O Na Mg P S Cl K CaSkull 1.61 5 21.2 4 43.5 0.1 0.2 8.1 0.3 17.6Brain 1.04 10.7 14.5 2.2 71.2 0.2 0.4 0.2 0.3 0.3Skin 1.09 10 20.4 4.2 64.5 0.2 0.1 0.2 0.3 0.1 Table 2: Densities and compositions for brain, skull and skin tissues, ICRU-46Figure 2: Snyder head phantom model with tumour at 4 cm depth, ZXprojection Figure 3: Snyder head phantom model with a tumour at 4 cm depth,3D view showing the neutron source location and its emission direc-tion ff forthe simulation, leading to the use of so-called analogcapture, process during which reduction weight is notperformed and neutrons are killed if capture occurs.Moreover, light and heavy ion recoil physics modelshave been used. These parameters provided an out-put file with all interactions needed to determine energytransfer between neutrons and tissue nuclei.Two simulation sets were computed for each geo-metry to obtain dose components values: from tallieson the one hand to estimate capture rate for D B and D p calculation and to estimate the energy deposited byphotons for D γ calculation and from PTRAC analysis,on the other hand, for estimating energy transferred byelastic scattering to hydrogen nuclei for D n calculation.One estimated standard deviation is used to computethe observable uncertainties proper to each dose com-ponent. The relative uncertainties are maintained under1 % for every dose component estimation. The neutron capture reaction rate on B in tissues asa function of the energy was the first quantitative ob-servable studied, to show the impact on the boron dose D B D B . The secondary dose in healthy tissues wasexplored, to understand the correlation between neutrondose and proton dose variations when reducing the neut-ron energy. As the main objective is to compare treat-ment e ffi cacy of di ff erent mono-energies, the Thera-peutic Gain (TG) was calculated. It is defined as theratio between the total biological dose in the tumour andthe total biological dose in the brain.This paper is structured as follows : first, the dose in-duced by the boron capture in the tumour is presented;then, a complete study of dose components in healthytissues is described, considering a tumour at 4 cm depth in order to evaluate the impact of the neutron energy onhealthy tissues dose components; the influence of thetumour depth on the total biological dose in healthy tis-sues is discussed afterwards; the results of the total bio-logical dose in the tumour and in healthy tissues as afunction of the neutron energy are also presented; fi-nally, the study of the TG is shown.
3. Results
In the following sections, results will be presented us-ing a relative di ff erence to compare 1 keV, 100 eV and10 eV to 10 keV simulated data. It is expressed in per-centage and obtained with the following formula: δ = ( results ( E ) results (10 keV ) − ∗
100 (7)This allows to compare results from lower epithermalenergy to the results obtained at 10 keV and to quantifythe di ff erences between values in order to conclude onthe most useful energy. Study of the dose in the tumour: focus on theboron dose D B In this section, a focus is made on the boron dose D B in the tumour representing the therapeutic dose forBNCT treatments. To estimate the boron dose D B , theneutron capture reaction rate on B in the tumour nor-malized per unit mass of tissue and per neutron sourceis studied. Figure 4 shows the relative di ff erence in per-centage with respect to 10 keV values of 1 keV, 100 eVand 10 eV results. For a tumour seated at 4 cm depthin tissues, the number of captures on B in tumour in-creases by 78 % with 10 eV neutrons and by 23 % with1 keV neutrons, in comparison with capture rates ob-tained for 10 keV neutrons. For deeper tumours, at 6cm depth for example, the number of B captures is 11% and 13 % higher at 10 eV and 1 keV respectively,and 13 % higher at 100 eV than at 10 keV. Neutrons at10 eV energies induce less captures on B than 10 keVneutrons for tumours located at depth higher than 6.6cm into tissues. Neutrons at 100 eV and 1 keV induceless captures than 10 keV neutrons for tumours locatedat depth higher than 7 cm.
Secondary dose on healthy tissues: study with thetumour at 4 cm depth
In the following sections, observables on healthy tis-sues are studied with the tumour at 4 cm depth. Theaim is to compare doses components of healthy tissues5 igure 4: Relative di ff erence in percentage of neutron capture reaction rate on B in the tumour per mass unit, between the di ff erent epithermalenergies and 10 keV, as a function of tumour depth, with 52.5 ppm of B in the tumour. when reducing the neutron kinetic energy in the epi-thermal range. The influence of the tumour depth on thetotal biological doses of healthy tissues will be studiedin section 3.4. B in healthytissues : brain, skin and skull
In order to understand the e ff ects of reducing neutronepithermal energy on the boron dose D B in healthy tis-sues, neutron capture reaction rates on B were evalu-ated for healthy tissues with a tumour at 4 cm depth andnormalised per unit mass. Table 4 presents the obtainedresults.An important increase of B capture rates for theskull and the skin can be observed when considering100 eV or 10 eV energy irradiation, with up to 74 % and87 % increase respectively in comparison with 10 keVenergy neutrons. For the brain, the number of neutroncaptures on B rises by 17% at maximum when redu-cing the epithermal energy to 10 eV. Relative gaps withrespect to 10 keV values for the skin and the skull arehigher than relative gaps with respect to 10 keV valuesfor the brain. Moreover in absolute values, we observedthat neutron capture rates on B in the skull were al-ways lower than values obtained in the skin, values evenlower than in the brain, implying that the brain is thehealthy tissue with the highest boron dose D B . p in healthy tissues The absorbed proton dose D p was evaluated forhealthy tissues. The absorbed proton dose D p resultsfrom ionisation of protons produced by the N(n,p) Creaction. Table 5 shows the relative di ff erence in per-centage with respect to 10 keV values of results ob-tained for lower epithermal energies.It is interesting to note that the relative gap of the ab-sorbed proton dose D p in healthy tissues of energies in[10 eV; 100 eV; 1 keV] with respect to results obtainedat 10 keV is similar to the one obtained consideringthe B(n, α ) Li reaction rate normalized per unit mass.This can be explained by the fact that the N(n,p) Creaction used in the computation of the absorbed protondose D p and the B(n, α ) Li reaction have both analog-ous cross section variation in the epithermal range. Thestudy of the absolute values shows that the brain is thehealthy tissue receiving the highest value of dose from N(n,p) C reaction for all energies. n in healthy tissues The absorbed neutron dose D n results from protonionisation of protons produced by H(n,n’) H’ elasticscattering process. Figure 5 shows D n in the brain, theskull and the skin, evaluated for di ff erent epithermalneutron energies, still in the case of a head phantom witha spherical tumour of 3 cm radius located at 4 cm depth.These results show that reducing the initial neutronenergy by an order of magnitude enables a reduction of60eV 100eV 1keV 10keVg − (10 − ) % g − (10 − ) % g − (10 − ) % g − (10 − ) %brain 28.23 ± ± ± ± / skull 11.06 ± ± ± ± / skin 13.56 ± ± ± ± / Table 4: Absolute values and relative di ff erence in percentage with respect to 10 keV values of neutron capture reaction rates on B per mass uniton healthy tissues and per neutron source, for lower epithermal energies (for a tumour at 4 cm depth, with 15 ppm of B in brain and skull and22.5 ppm of B in skin). − ) % Gy(10 − ) % Gy(10 − ) % Gy(10 − ) %brain 8.44 ± ± ± ± / skull 6.01 ± ± ± ± / skin 5.16 ± ± ± ± / Table 5: Absolute values in Gy and relative di ff erence in percentage with respect to 10 keV values of the absorbed proton dose D p in healthytissues, for lower epithermal energies (for a tumour at 4 cm depth, with 15 ppm of B in brain and skull and 22.5 ppm of B in skin).Figure 5: Absorbed neutron dose D n in healthy tissues as a function of the neutron incident energy, expressed in Gy and per neutron, with 15 ppmof B in the brain and the skull and 22.5 ppm of B in the skin. D n , on every healthy tissue. Thevariation of the neutron dose D n in healthy tissues ishigher than the variation of the proton dose D p and theboron dose D B for the same energy range. In this case,the skin is the tissue associated to highest values of D n ,for all energies studied. p and theneutron dose D n in healthy tissues The sum of the proton dose D p and the neutron dose D n was studied to evaluate the dose contribution of pro-ton ionisation from capture reaction. Results presentedin Table 6 and the relative di ff erence in percentage withrespect to values obtained at 10 keV is also indicated.The same profile can be observed for all tissues: re-ducing the neutron epithermal energy from 10 keV tolower epithermal energies appears to reduce the totaldose produced by proton ionisation, as the relative gapis negative for all energies between 10 eV and 1 keV andfor every healthy tissues. The only exception is at 10 eV,where the sum of the absorbed proton dose D p and ab-sorbed neutron dose D n in the skull is 19 % higher thanat 10 keV. It can be noted that the lowest value of thesum of the proton dose and the neutron dose is reachedfor 1 keV energy neutrons. γ in healthy tissues The absorbed gamma dose D γ results mainly , in theframe of this study, from the radiative capture reaction H(n, γ ) H on hydrogen as no photon flux is implemen-ted in the source. Table 7 shows D n in the brain, theskull and the skin, evaluated for di ff erent epithermalneutron energies, still in the case of a head phantom witha spherical tumour of 3 cm radius located at 4 cm depth.The photon dose D γ in healthy tissues decreaseswhen the neutron energy increases. This variation issimilar to the variation of the neutron dose D n and theboron dose D B , as the cross sections associated to thereactions characterising those dose components equallyvary in the epithermal range. But the relative gap withrespect to 10 keV values is not the same for the photondose D γ and those two others dose components as the2.2 MeV photon produced by the radiative capture onhydrogen will not be entirely contained in the phantomand will escape the geometry, releasing only a fractionof its energy in tissues. Total biological dose in tissues
The previous section has presented the di ff erent com-ponents of the dose deposited in the healthy tissues and the B capture rate normalised per unit mass in the tu-mour. Hereafter, we focus on a global analysis, based onthe sum of all the components and using RBE factors toobtain the total biological dose.
The relative di ff erence between the total biologicaldose deposited in the tumour tissue at 10 keV and valuesobtained at lower epithermal energies is represented inFigure 6.Total biological dose in tumour results show the sametrend as the previous results obtained for B neutroncapture reaction rate in tumour: lower epithermal en-ergy deliver more dose inside the tumour for depth upto 6 . . D B is themajor component of the total biological dose in tumourdue to the B concentration in the tumour.
The total biological dose in healthy tissues was stud-ied in the case of a tumour at 4 cm depth. Table 8 rep-resents the total biological dose in healthy tissues.The total biological dose in healthy tissues increaseswhen the incident neutron energy is lowered. Exceptfor the skin, where the total biological dose decreaseswhen reducing the energy from 10 keV to 1 keV or 100eV. Our results on absolute values of the total biologicaldose in healthy tissues show that the brain received thehigher value of dose, for every energy studied.
Influence of the tumour position on healthy tissueobservables
The influence of the tumour depth was studied forevery dose component of healthy tissues (being theneutron dose D n , the proton dose D p , the boron dose D B and the gamma dose D γ ) and for the total biologicaldose in healthy tissues. Table 9 presents the relative gapin % of the total biological dose in healthy tissues for atumour at 4 cm depth and a tumour at 8 cm depth.The variation observed on the total biological dose inhealthy tissues is between 0 .
3% and 4 .
7% for all ener-gies and tumour depths studied. The impact of the tu-mour position in the phantom can be considered as neg-ligible, so the study made in section 3.2 can be extendedfor tumours up to 8 cm depth in tissues.
Figure of Merit to optimise the incident neutronenergy
The TG allows to evaluate the advantages and draw-backs of reducing neutron energies from 10 keV to80eV 100eV 1keV 10keVGy(10 − ) % Gy(10 − ) % Gy(10 − ) % Gy(10 − ) %brain 8.44 ± -4 ± -6 ± -11 ± / skull 6.01 ± ± -3 ± -17 ± / skin 5.17 ± -60 ± -67 ± -66 ± / Table 6: Absolute values in Gy per neutron source and relative di ff erence in percentage with respect to 10 keV values of the sum of the absorbedproton dose D p and absorbed neutron dose D n in healthy tissues for lower epithermal energies (for a tumour at 4 cm depth, with 15 ppm of B inbrain and skull and 22.5 ppm of B in skin). − ) % Gy(10 − ) % Gy(10 − ) % Gy(10 − ) %brain 8.71 ± ± ± ± / skull 5.67 ± ± ± ± / skin 4.06 ± ± ± ± / Table 7: Absorbed photon dose D γ in healthy tissues as a function of the neutron incident energy, expressed in Gy and per neutron, with 15 ppm of B in brain and skull and 22.5 ppm of B in skin.Figure 6: Relative di ff erence in percentage of the total dose in the tumour, between the di ff erent epithermal energies with respect to 10 keV, with52 . B in tumour − ) % Gy(10 − ) % Gy(10 − ) % Gy(10 − ) %brain 20.00 ± ± ± ± / skull 10.95 ± ± ± ± / skin 13.65 ± ± -0.4 ± -14 ± / Table 8: Absolute values in Gy[RBE] per neutron source and relative di ff erence in percentage with respect to 10 keV values of the total biologicaldose in healthy tissues for lower epithermal energies (for a tumour at 4 cm depth, with 15 ppm of B in brain and skull and 22.5 ppm of B inskin).
90 eV 100 eV 1 keV 10 keVbrain 4.7 % 4.1 % 3.4 % 2.7 %skull 0.5 % 0.5 % 0.4 % 0.3 %skin 0.6 % 0.5 % 0.5 % 0.3 %
Table 9: Relative gap in percentage of the total biological dose inhealthy tisses with a tumour at 8 cm depth compared to values ob-tained with a tumour at 4 cm, with 15 ppm of B in brain and skulland 22.5 ppm of B in skin. lower epithermal energies. It is defined as following: TG = D totaltumour D totalbrain (8)Where D totaltumour is the total biological dose in the tumourrepresenting the dose deposited by all the particles res-ulting from the neutrons interactions in the tumour andD totalbrain is the total biological dose in the brain.In order to obtain a relevant ratio to consider the im-pact of the neutron energy in the epithermal range, thetherapeutic ratio is evaluated considering the total bio-logical dose in the brain. For treatment evaluation, themaximum dose in the brain is considered for the thera-peutic ratio. As in the frame of our study we are con-sidering a total irradiation of the phantom, it is morerelevant to consider the whole brain volume [27].Thus, this figure of merit allows to evaluate the op-timisation of the epithermal energy. The relative di ff er-ence in percentage between values obtained for 1 keV,100 eV and 100 eV compared with respect to 10 keVvalues is shown in Figure 7.For tumours seated at 4 cm depth, 10 eV, 100 eV and1 keV neutrons provided respectively 54 %, 36 % and18 % increase on the TG compared to 10 keV neutrons.In the case of a 5 cm depth tumour, this increase is con-tained between 10 and 20 % for neutrons with energybetween 10 eV and 1 keV. The relative di ff erence inpercentage with respect to 10 keV of lower epithermalenergies studied is positive up to 5 . . Influence of the tumour size
In order to evaluate the influence of the tumour sizeon the figure of merit features, the same study was con-ducted with a tumour with a radius two times smallerthan previously. The tumour volume was 1.77 cm fora 0.75 cm radius sphere. Results of this study conductto similar observations for all observables including thefigure of merit proposed by this study, as pointed out in Figure 8 with the relative di ff erence in percentage com-pared to 10 keV results of the figure of merit for lowerepithermal energies.For a tumour with a volume of 1 .
77 cm , the figure ofmerit reaches higher values with lower epithermal en-ergy than 10 keV, for tumours seated up to 5 . .
4. Discussion
Results presented in 3.1 show that epithermal neut-rons with energies lower than 10 keV can reach deepseated tumours, up to 6 . B capture rate inside the tumour. The resultson B capture rate in tumours support the premise madeon epithermal neutron range that penetrability does notdepend strongly on their initial energy.Nevertheless, the skull and the skin are highly im-pacted by the reduction of the neutron energy. Capturereaction rate on N and on B nuclei increase by 70 to80 % when reducing from 10 keV to 10 eV the neutronkinetic energy. But the reduction of the neutron dose D n - dose induced by hydrogen scattering compensatefor the increase of the proton dose D p , leading to a di-minution of the total absorbed dose from proton ionisa-tion (see Table 6). Lowering the incident neutron en-ergy lowers the energy transferred to hydrogen nuclei :reducing the incident neutron energy reduces the doseresulting from elastic scattering of neutrons on the hy-drogen nuclei in tissues. The absorbed neutron dose D n declines faster than the increase of the absorbed protondose D p . Their sum is maximum for 10 keV neutronsand it reaches a minimum around 1 keV neutrons forevery healthy tissue, showing the positive impact of re-ducing the initial epithermal energy. If we focus on theabsolute value of the total biological dose in healthy tis-sues, the brain is the tissue with the highest dose valuefor each energy studied in the epithermal range. Theuse of the healthy tissue with the highest total biologicaldose in the definition of the TG validate the pertinenceof the figure of merit.As explained in 3.5, the TG is calculated using thetotal biological dose in the brain as this study does notconsider a realistic neutron field for a treatment but awide, mono-energetic and unidirectional neutron field.The TG calculated is higher for neutrons energies be-low 10 keV, for tumours located at depth up to 6 . . igure 7: Relative di ff erence in percentage of ratio between total biological dose in the tumour and total biological dose in the brain, between thedi ff erent epithermal energies and 10 keV, with 15 ppm of B in brain and skull and 22.5 ppm of B in skinFigure 8: Relative di ff erence in percentage of ratio between total absorbed dose in tumour and total absorbed dose in brain, with a 0 . B in brain and skull and 22.5 ppm of B in skin. . tumour, compared to 6 . tumour.The results presented are based on the computation ofthe biological dose. This dose is estimated using RBEfactors. Those factors are considered as fixed and areextracted from [20]. But as pointed out in [18], the useof fixes RBE factors may mislead the estimation of thebiological dose in tissues. A more precise model is de-scribed in this paper, using experimental data of survivalexperiments and based on first-order repair of sub-lethallesions and synergetic interactions between di ff erent ra-diations. This model is not implemented here because itapplies to specific clinical examples in the frame of real-istic treatment cases. As the aim of this study is to com-pare doses induces by di ff erent epithermal energy neut-ron, the standard estimation of the biological dose usingfixed RBE is considered as su ffi cient. The results ob-tained in this study can be compared to those obtained in[28], where RBE factors are examined as parameters in-fluencing the optimal neutron source energy estimation.Our results are in agreement with the results presentedin [28] : the use of neutron source in the range of 10 eVto few keV improves the capture reaction rate on Band the optimal neutron energy for tumours seated at 4cm from the skin is focused around 2 keV. Moreover,results presented in [29] indicate that neutrons with afew keV energy induce higher values of FoM, such asthe TG considering the maximum biological dose in thebrain. In the same study, the TG reaches a maximumaround 3 keV for 5 cm depth tumour and for a tumourat 8 cm depth the TG is 14 % higher for 10 keV neut-rons than for 1 keV neutrons (values extract from Figure4 of [29]). In comparison, we observe that the use of 1keV neutrons diminish the TG by 8 % compared to 10keV neutrons (see Figure 7) for 8 cm depth tumours.Those results can be considered as consistent as Bisce-glie work is based on a di ff erent simulation parameters,such as a higher tumour to blood ratio (4.3 instead of3.5 in this work) and lower RBE factors for protons (1.6for D n and D p components) and B reaction (2.3 for D B component).The results of the simulation could be confirmed byexperimental measurement of the B capture rate asa function of neutron kinetic energy. This measure-ment could be realised, in the near future, by the neut-ron spectrometer Mimac-FastN with a boron coatingon the cathode used as an active phantom [30]. Theprinciple of the active phantom is based on B cap-ture reaction products detection to estimate the capture rate on the tumour inside the phantom simulated by theboron coating. A layer of tissue equivalent material isplaced between the boron coating and a well character-ised mono-energetic neutron field, which energy can beset in the studied epithermal range.
5. Conclusion Di ff erent mono-energetic epithermal neutron fieldperformances were computed with MCNP and com-pared to the required optimized energy for AB-BNCTtreatment set at 10 keV. The study was conducted for atumour at di ff erent depths inside a head phantom.The Therapeutic Gain was defined as the ratiobetween the total biological dose in the tumour andthe total biological dose in the brain. Here the wholevolume of the brain is considered because the neutronfield is wide and irradiate directly the totality of thephantom. The main objective was to compare inducedTG of the di ff erent mono-energetic neutron fields stud-ied. The relative gap between the results obtained atan eptihermal energy and the results obtained at 10 keVallow to quantify the variation in TG . This lead to high-light the volume in the brain for which the use of epi-thermal energies lower than 10 keV would increase thetreatment e ffi cacy. This volume can be defined as thelayer between the surface and 6 . ff ects described at each energy will add up. Moreover,as our results were provided normalized per incidentneutron, the use of lower epithermal neutron energiesmight reduce the irradiation time needed to deliver therequired dose in tumours. This irradiation time is alsolinked to the maximum tolerable dose to normal brain.In other words, it can be assumed that the maximumexposure treatment time can be increased if higher val-ues of dose in tumours are needed as the reduction ofepithermal energies induces a reduction of the total ab-sorbed dose in the brain, in the case of tumours seatedup to 6 . . Acknowledgement
We thank Olivier Meplan (LPSC) for the helpprovided about Monte Carlo simulations and MichaelPetit ( Laboratoire de micro-irradiation, de M´etrologieet de Dosim´etrie des Neutrons (IRSN)) for the help onPTRAC implementation.
Declaration of Competing Interest
The authors declare no competing interests.
Appendix A. Kerma coe ffi cients Usually in dosimetry, kerma coe ffi cients (also calledkerma factors) are used to determine the dose inside adefined volume. Kerma is an acronym for kinetic energyreleased in matter . The kerma is defined as the energytransferred to charge particles per unit mass at a point ofinterest, including radiative-loss energy but excludingenergy passed from one charged particle to another [31]: K = d (cid:15) tr dm (A.1)Under Charged-Particle Equilibrium (CPE), the kermacalculated in a volume is equal to the absorbed dose inthe volume. For indirectly ionizing radiations from ex-ternal sources, CPE is verified in a volume if the follow-ing conditions are satisfied : the atomic composition ofthe medium is homogeneous; the density of the mediumis homogeneous; there exists a uniform field of indir-ectly ionising radiation (i.e. the rays must be only neg-ligibly attenuated by passage through the medium); noinhomogeneous electric or magnetic fields are present(chapter III section II.B [31]). CPE is not verified if thefield of indirectly ionising radiation is not uniform in thestudied volume.We are now considering neutrons as the indirectlyionising particles. In this case, kerma coe ffi cients can becalculated using experimental cross section data. Totalkerma coe ffi cients are defined as the sum of kerma coef-ficients from each significant reaction channel of thestudied element. The estimation of those coe ffi cientsrequires the details of angular and energy distributionof secondary particles emitted during the reaction. For example, the elastic recoil kerma coe ffi cients can be ex-pressed as : k el = N m M E n M (1 − f m ) σ el (A.2)where m is the mass of the neutron, M is the mass ofthe residual nucleus, M is the mass of the compoundnucleus, E n is the kinetic energy of the incident neut-ron, σ el is the elastic cross section and f m is the firstLegendre coe ffi cient of elastic angular distribution [32].This first Legendre coe ffi cient represents the cosine ofthe mean angle between the recoil and the direction ofthe incident neutron. Moreover, kerma coe ffi cients in-duced by capture can be expressed as : k capt = N A σ ( Q i + E n ) M (A.3)where σ is the capture cross section of the consideredreaction, Q i is the Q value of the reaction and E n is the kinetic energy of the incident neutron [23].Estimated total kerma coe ffi cients and elastic recoilcoe ffi cients for hydrogen are presented in FigureA.9. For neutron energy higher than few eV, elasticrecoil kerma coe ffi cients correspond to total kermacoe ffi cients. For epithermal and fast neutron, elasticscattering is the main process inducing dose deposit intissues when considering neutron interactions with hy-drogen. Estimated total kerma coe ffi cients and capturecoe ffi cients for nitrogen are presented in Figure A.10.Here, capture kerma coe ffi cients match total kermacoe ffi cients up to few keV. For neutrons in thermalrange and a part of epithermal range, dose depositionis mainly achieved trough capture, regarding neutroninteractions with nitrogen. The characterisation of theneutron dose D n by the elastic scattering on hydrogenand the characterisation of the proton dose D p with the(n,p) capture on nitrogen is in agreement with kermacoe ffi cients computation as detailed above.However, in the case of our study CPE is not verified,as the neutron field in the phantom is not homogeneous.Transient Charged Particle Equilibrium (TCPE) isconsidered easier to achieve than CPE and allows toestablish a relation of proportionality between dose andkerma. Although, longitudinal and lateral equilibriaconditions are required to achieve TCPE in the wholevolume of study, as explained in [33] for a photonirradiation case. The half-width of the radiation fieldmust exceed the maximum lateral motion of sourceparticle and the position of interest must be deeper thanthe maximum range of charged particles. Due to thegeometry of our problem, it cannot be assumed that in13 igure A.9: Total kerma coe ffi cients from [23] and calculated elastic recoil kerma coe ffi cients for hydrogen.Figure A.10: Total kerma coe ffi cients from [23] and calculated capture kerma coe ffi cients for nitrogen. ffi cients cannot beused to compute the total dose in tissues as CPE andTCPE are not achieved in the considered volumes ofour study. Dose computation using kerma coe ffi cientscan be done if smaller volumes are considered insidea wider one (with homogeneous composition anddensity and other CPE conditions are verified). Thepeak dose (defined as the dose inside a 1 cm volume[34]) is calculated using kerma coe ffi cients. The totaldose in a tissue can also be calculated using kermacoe ffi cients. 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