Nuclear Model Calculations on the Production of Auger Emitter 165 Er for Targeted Radionuclide Therapy

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1 J. Mod. Phys., 2010, 1, doi: /jmp Publishd Onlin Octobr 2010 ( Nuclar Modl Calculations on th Production of Augr Emittr 165 Er for Targtd Radionuclid Thrapy Abstract Mahdi Sadghi 1, Milad Enfradi 2, Claudio Tnriro 3 1 Agricultural, Mdical and Industrial Rsarch School, Nuclar Scinc and Tchnology Rsarch Institut, Karaj, Iran 2 Faculty of Enginring, Rsarch and Scinc Campus, Islamic Azad Univrsity, Thran, Iran 3 Dpartmnt of Enrgy Scinc Sungkyunkwan Univrsity, Suwon, Kora msadghi@nrcam.org Rcivd Jun 6, 2010; rvisd July 16, 2010; accptd Jun 25, 2010 Augr lctron mitting radionuclids hav potntial for th thrapy of small-siz cancrs bcaus of thir high lvl of cytotoxicity, low-nrgy, high linar nrgy transfr, and short rang biologic ffctivnss. Augr mittr 165 Er (T 1/2 = 10.3 h, I EC = 100%) is a potnt nuclid for targtd radionuclid thrapy. 165 Er xcitation function via 165 Ho(p,n) 165 Er, 165 Ho(d,2n) 165 Er, 166 Er(p,2n) 165 Tm 165 Er, 166 Er(d,3n) 165 Tm 165 Er, nat Er(p,xn) 165 Tm 165 Er and 164 Er(d,n) 165 Tm 165 Er ractions wr calculatd by ALICE/91, ALICE/ASH (GDH Modl & Hybrid Modl) and TALYS-1.2 (Equilibrium & Pr-Equilibrium) cods and compard to xisting data. Rquisit for optimal thicknsss of targts wr obtaind by SRIM cod for ach raction. Kywords: 165 Er, Augr Elctron, Excitation Functions, TALYS-1.2, ALICE-ASH 1. Introduction Th doubl strand DNA hlix prsnts a diamtr of 2 nm. In a typical Augr radiation dcay, th highst nrgy dposition occurs in sphrs of 1-2 nm, as dscribd lswhr [1]. This mans that th calculatd local nrgy dposition of an Augr mittr incorporatd into DNA would hit both DNA strands with an nrgy of 1.6 MGy or highr. This radiation nrgy is thrfor largly sufficint to disrupt both DNA strands ovr distancs of svral nuclotids [2,3]. Augr lctron mitting radionuclids in cancr thrapy offr th opportunity to dlivr a high radiation dos to th tumor clls with high radiotoxicity whil minimizing toxicity to normal tissu [4]. Bsids th dirct ffct of Augr lctrons on DNA doubl strands, an indirct radiation ffct of Augr nrgy dposition will occur via production of radicals [5]. Th radicals diffus frly in th intracllular spac and can caus furthr DNA damag. Evn a bystandr ffct by diffusion of radicals through gap junctions has bn dscribd [6]. Only vry fw radionuclids xists that dcay xclusivly by EC-mod without any accompanying radiation, 165 Er is on of thm. Augr lctrons ar mittd by isotops that dcay by lctron captur (EC) or hav intrnal convrsion (IC) in thir dcay. In ach dcay of ths isotops, a cascad of vry low nrgy lctrons is mittd [7]. In this work, svral mthods for 165 Er production using ALICE/91, ALICE/ASH (GDH Modl & Hybrid Modl) and TALYS-1.2 (Equilibrium & Pr-Equilibrium) cods hav bn studid. Aim of th prsntd study is to compar th calculatd cross sctions for th production of 165 Er via diffrnt ractions with incidnt particl nrgy up to 50 MV as a part of systmatic studis on particl-inducd activations on mtal targts, thortical calculation of production yild, calculation of targt thicknss rquirmnt and suggstion for optimum raction to produc Erbium Thory 2.1. Calculation of Excitation Function Cross sctions for 165 Ho + p,d 166 Er + p,d 164 Er + d and nat Er + p ractions wr calculatd by using ALICE/91, ALICE/ASH (GDH Modl & Hybrid Modl) and TA- LYS-1.2 (Equilibrium & Pr-Equilibrium) cods [9-11]. Th cods wr usd simultanously to incras th accuracy of calculations. An optimum nrgy rang was dtrmind and mployd to avoid th formation of th radionuclid impuritis and dcras th xcitation functions of th inactiv impuritis as far as possibl. To fur-

2 218 M. SADEGHI ET AL. thr achiv th aim, fasibility of th 165 Er production via various nuclar ractions pr low/mdium nrgy acclrators was invstigatd. According to SRIM cod (Th Stopping and Rang of Ions in Mattr); th rquird thicknss of th targt was calculatd for ach raction ALICE/ASH Cod Th ALICE/ASH cod [12] is a modifid and advancd vrsion of th ALICE cod [9] and ALICE/LIVERMORE. Th gomtry dpndnt hybrid modl (GDH) as adoptd originally is usd for th dscription of th pr-quilibrium particl mission from nucli [13,14] Pr-Compound Dutron Emission Following closly th xhaustiv analysis of th cod ALICE/ASH by Brodrs and its collaborators [12] th main faturs of th dutron mission from th compound systms (as a clustr), rlativ to th Frmi Enrgy (E F ), from all th raction channls, ar summarizd as: 1) At nrgis blow th E F, th pick-up of nuclons, 2) At nrgis abov E F th possibl coalscnc of whr E is th xcitation nrgy, E F is th Frmi nrgy, g and g ar th singl particl lvl dnsitis for particls and hols, rspctivly, Θ(x) is th Havisid function, Θ = 0 for x < 0 and Θ = 1 for x > 0.Th singl particl lvl dnsitis for particls and hols ar calculatd by Bták and Dobš [16] g = A/14 (3) h p h k E k EF h k F k0 stats of two xcitd nuclons, 3) Th possibility of ractions that includs th Knock-out of a pr-formd dutron 4) Finally th inclusion of a fast or priphral dirct mchanism rsulting in dutron formation and scap. Taking into considration all th abov, th modifid cod calculats th dutron spctrum from th contribution of th individual diffrntial cross sctions of such procsss as PU,C KO D d d d d (1) dε dε dε dε d d d d Th uppr indx stands for Pick-Up, Coalscnc, Knock-out and Dirct raction rspctivly. Th cross sctions ar in somhow proportional to th rlativ numbr of stats availabl for such raction channl to occur. Exprssions for such cross sctions wr drivd by Brodrs t al. [13]. Using basic statmnts of th hybrid modl [15]. Th xciton lvl dnsity is calculatd by Bták and Dobš [23] taking into account th finit dpth of th nuclar potntial wll ω p,h,e g g C 1 E ke (2) p!h! n 1! n1 g A/E F (4) On should not that nuclar surfac ffcts [17-19] influnc th ffctiv valu of th Frmi nrgy E F usd for th calculation of pr-compound particl spctra. This point is discussd blow. Th xciton coalscnc pick-up modl proposd by Sato t al. [20] is usd for th calculation of th dσ P-U,C /dε d spctrum componnt [28]. ωp-k,h,u λdεd F (5) nn km2 PU,C dσ σ E ε Q g D dε ω p,h,e λ ε λ ε non 0 k,m d d d n d 0 d d d d whr F k,m is th dutron formation factor qual to th probability that th dutron is composd of k particls abov th Frmi lvl and m particls blow; ε d is th channl mission nrgy corrsponding to th dutron mission; λ d is th dutron mission rat; λ + d is th intranuclar transition rat for th absorption of th dutron in th nuclus; g d is th dnsity of singl particl stats for th dutron. Th dutron mission (λ d) and absorption (λ + d) rats ar calculatd. In analogy with α-particl mission th knock-out componnt of th pr-compound dutron mission spctrum is writtn as follows λdεd ko dσ g ω p-1,h,u σ E Φ E g Dn (6) dε gp ω p,h,e λ ε λ ε non 0 d 0 d d nn0 d d d d d whr th factor Φ d dscribs th initial numbr of xcitd dutron clustrs in th nuclus Φ d = 2F d (E 0 ) (7) whr F d is th probability of intraction of th incidnt particl with th pr-formd dutron rsulting in its xcitation in th nuclus; and th factor of two rflcts th normalization on th numbr of particls in th initial xciton stat n 0. Th gnral xprssion for F d is [21]

3 M. SADEGHI ET AL. 219 σxd E0 Fd Z A Z σ xp E 0 σ xn E 0 σ xd E 0 A A whr x rfrs to th initial proton or nutron, σ xd, σ xp and σ xn ar th cross-sctions of th lastic intraction of projctil with dutron, proton and nutron, rspctivly, corrctd for a Pauli principl, is th numbr of pr-formd dutrons in th nuclus, Z and A ar th numbr of protons and nuclons in th nuclus corrctd for a numbr of clustrd dutrons. Th dirct componnt of th dutron spctrum is [21] λdεd D * dσ ω U σ dε ω 1p,0h,E λ ε λ ε non d d d d d whr th final lvl dnsity ω*(u) is approximatd by ω(0p,1h,u).γ/g d with th γ valu qual to MV 1 for all nucli and xcitation nrgis. To improv th agrmnt of calculations and th masurd dutron spctra, it is usful to writ th dirct componnt of th spctrum in th following form g d λdεd D 2 dσ (E α 2 E F) =σ non α 1 xp 2 + g d dεd 2(α3E F) λdε d+λdεd (10) whr α 1, α 2 and α 3 ar paramtrs and E F is th ffctiv valu of th Frmi nrgy. Th valus of α i can b obtaind from analysis of xprimntal dutron spctra. Th global paramtrization of α i paramtrs is hardly possibl [12] TALYS-1.2 Cod TALYS-1.2 cod is optimizd for incidnt projctil nrgis, ranging from 1 kv up to 200 MV on targt nucli with mass numbrs btwn 12 and 339. It includs photon, nutron, proton, dutron, triton, 3 H, and α-particls as both projctils and jctils, and singl-particl as wll as multi-particl missions and fission. All xprimntal information on nuclar masss, dformation, and low-lying stats spctra is considrd, whnvr availabl [22] and if not, various local and global input modls hav bn incorporatd to rprsnt th nuclar structur proprtis, optical potntials, lvl dnsitis, γ-ray strngths, and fission proprtis. Th TALYS cod was dsignd to calculat total and partial cross sctions, rsidual and isomr production cross sctions, discrt and continuum γ-ray production cross sctions, nrgy spctra, angular distributions, doubl diffrntial spctra, as wll as rcoil cross sctions. Th pr-quilibrium particl mission is dscribd using th two-componnt Exciton modl. Th modl implmnts (8) (9) nw xprssions for intrnal transition rats and nw paramtrization of th avrag squard matrix lmnt for th rsidual intraction obtaind using th optical modl potntial [23,24]. Th phnomnological modl is usd for th dscription of th pr-quilibrium complx particl mission. Th quilibrium particl mission is dscribd using th Hausr-Fshbach formalism. 3. Rsults In th calculations of th hybrid and GDH modl, th cod ALICE/ASH was usd. This cod can b applid for th calculation of xcitation functions, nrgy and angular distribution of scondary particls in nuclar ractions inducd by nuclons and nucli with nrgy up to 300 MV. Th gnralizd suprfluid [25] has bn applid for nuclar lvl dnsity calculations in th ALICE/ASH cod. Th ALICE-91 and ALICE/ASH cods us th initial xciton numbr as n 0 = 3. But in ths modls th diffrnt alpha (α), dutron (d) and proton (p) xciton numbrs ar usd in th pr-quilibrium GDH modl calculations. In dtails, th othr cod modl paramtrs can b found in rfrnc [12]. In ALICE/ASH cod, th hybrid and gomtry dpndnt hybrid modl (GDH) for pr-compound missions and th Wisskopf-Ewing modl for compound ractions ar slctd. Although thr ar som discrpancis btwn th calculations and th xprimntal data, in gnrally, th nw valuatd hybrid and GDH th pr-quilibrium modl calculations (with ALICE/ASH) ar vry clos to th xprimntal data in Figurs 1, 2, and 6. In addition, th GDH and hybrid modl calculations ar clos to ach othr, gnrally. Indd, calculatd mission cross sctions with GDH and hybrid modl by using ALICE/ASH cod show th bst agrmnt with th xprimntal data for nat Er(p,xn) 165 Tm 165 Er raction in Figur 6. Morovr, ths cross sctions in harmony with th xprimntal data for 165 Ho(p,2n) 165 Er nucli xcpt for th (p,n) raction in which th xprimntal data hav followd abov thortical calculations in Figur 1. Th rason is that th nw dvlopd pr-quilibrium raction mchanism ALICE/ASH includs angular momntum convrsion. Not only it givs us mor information for nw nuclar raction rsarch, but also it lts us calculat cross sctions up to many hundrds MV nrgy lvl. In fact, whn taking th pairing nrgy and th mass shll corrction into considration, th xprimntal valus ar in bttr agrmnt with th thortical rsults [26]. In conclusion all figurs show that, although a fw calculatd data follow th xprimntal ons from abov or blow as paralll, gnrally all th compard data ar in agrmnt with ach othr.

4 220 M. SADEGHI ET AL. Figur 1. Excitation function of 165 Ho(p,n) 165 Er raction by: TALYS 1.2 cod comparison of calculatd xcitation functions of 165 Ho(p,n) 165 Er raction with th valus rportd in litratur. Figur 2. Excitation function of 165 Ho(d,2n) 165 Er raction by: TALYS 1.2 cod comparison of calculatd xcitation functions of 165 Ho(d,2n) 165 Er raction with th valus rportd in litratur. Figur 3. Excitation function of 166 Er(p,2n) 165 Tm 165 Er raction by: TALYS 1.2 cod cods. No xprimntal data ar rportd in litratur.

5 M. SADEGHI ET AL. 221 Figur 4. Excitation function of 166 Er(d,3n) 165 Tm 165 Er raction by: TALYS 1.2 cod othr cods. No xprimntal data ar rportd in litratur. Figur 5. Excitation function of 164 Er(d,n) 165 Tm 165 Er raction by: TALYS 1.2 cod and othr cods. No xprimntal data ar rportd in litratur. Figur 6. Excitation function of nat Er(p,xn) 165 Tm 165 Er raction by: TALYS 1.2 cod comparison of calculatd xcitation functions of nat Er(p,xn) 165 Tm 165 Er raction with th valus rportd in litratur.

6 222 M. SADEGHI ET AL Excitation Function of 165 Ho(p,n) 165 Er Raction Excitation functions of th proton-inducd raction on Holmium-165 wr dtrmind by ALICE/91, AL- ICE/ASH and TALYS-1.2 cods, and th xprimntal data that hav bn studid by Byr t al. (2004) [27] and Tárkányi t al. (2008) [28]. Th valuation of th rsults of th calculations showd that th bst rang of nrgy that favor th raction is from 12 to 7 MV. Carrir-fr 165 Er production can b obtaind using a proton an nrgy of lss than 9 MV. Thr is a rlativly good agrmnt btwn th xprimntal data by Tárkányi t al. and th prdiction of th xcitation function mad by ALICE/91 cod up to 11 MV. According to calculations from SRIM cod th rquird targt thicknss should b µm (S Figur 1) Excitation Function of 165 Ho(d,2n) 165 Er Raction According to rsults from th ALICE/91, ALICE/ASH and TALYS-1.2 cods, th optimum nrgy rang for th projctil particl (dutron) to produc 165 Er from 165 Ho targt in this cas is from 16 to 11 MV. Hybrid Modl prdicts that th maximum of th cross sction (a = A/18) is mb at an nrgy of 13 MV. Th sparation of isotop impuritis is not possibl by chmical mthods, so this raction is non carrir fr for 165 Er production (S Figur 2). This raction was invstigatd only by Tárkányi t al. (2008) [29]. ALICE/91 and ALICE/ASH cods agr wll with th masurd data from Tárkányi t al. up to 20 MV. Also, th rsults of TALYS-1.2 cod ar lss than xprimntal data, ALICE/91 and ALICE/ASH cods Excitation Function of 166 Er(p,2n) 165 Tm 165 Er Raction 165 Er can also b producd using th 166 Er(p,2n) 165 Tm raction which is unstabl, 165 Tm (T 1/2 = h), th bst rang of incidnt nrgy was stimatd for proton nrgis from 23 to 16 MV. Th maximum for th cross sction, as by th GDH modl (a = A/9) is prdictd to b mb at th nrgy of 21 MV. Also 166/164 Tm impuritis ar gnratd which cannot b sparatd by chmical mthods. Also this raction was lading to non-isotopic impuritis of stabl ( 166/164 Er). Thr hav not bn any xprimntal data for ths ractions in th litratur, thrfor only thortical calculations hav bn shown in Figur 3. Also, thr is a rlativly good agrmnt btwn th prdiction of th xcitation function mad by TALYS-1.2, ALICE/91 and ALICE/ASH cods. Th thortical thick targt will giv a yild of MBq/µA h. Rcommndd thicknss of th targt is 31.8 µm Excitation Function of 166 Er(d,3n) 165 Tm 165 Er Raction According to cods, optimal nrgy rang of th projctil particl (dutron) to produc 165 Tm from 166 Er targt is from 22 to 29 MV within this rang th maximum cross sction prdictd by Hybrid Modl (a = A/9) is mb at an nrgy of 25 MV. Also 166 Tm (T 1/2 = 7.7 h), 164 Tm (T 1/2 = 2 min) and 163 Tm (T 1/2 = 1.81 h) impuritis ar gnratd which cannot b sparatd by chmical mthods. Th non-isotopic impuritis of activ ( 166/165 Er) wr also producd in th raction. Thr hav not bn any xprimntal data for ths ractions in th litratur, thrfor only thortical calculations hav bn shown in Figur 4, so nuclar modl calculations can play an important rol in xcitation function of 166 Er(d,3n) 165 Tm 165 Er raction. Also, th rsults of TALYS-1.2 cod ar lss than ALICE/91 and AL- ICE/ASH cods. Th thortical thick targt givs a yild of 42.9 MBq/µAh. Rcommndd thicknss of th targt is 31.4 µm Excitation Function of 164 Er(d,n) 165 Tm 165 Er Raction According to ALICE/91, ALICE/ASH and TALYS-1.2 cods, th bst nrgy rang of th projctil particl (Dutron) to produc 165 Tm from 164 Er targt is found to b from 13 to 8 MV and maximum cross sction is prdictd by th Hybrid modl(a = A/18) to b mb at an nrgy of 10 MV. Also 164 Tm (T 1/2 = 2 min) and 163 Tm (T 1/2 = 1.81 h) impuritis ar gnratd and thy could not b sparatd by chmical mthods (S Figur 5). This raction was also producing Non-isotopic impuritis of high cross sction ( 164/163 Er). Th thortical thick targt yild is MBq/µA h. Rcommndd thicknss of th targt is 90 µm Excitation Function of nat Er(p,xn) 165 Tm 165 Er Raction Excitation functions of th proton-inducd raction on nat Er wr calculatd by ALICE/ASH and TALYS-1.2 cods. Th data from th calculations showd that in ordr to optimiz isotop production th bst rang of th nrgy is 29 to 20 MV. Th calculatd xcitation functions of nat Er(p,xn) 165 Tm 165 Er ractions ar compard with th xisting xprimntal valus in Figur 6. Th rsults of TALYS-1.2 and ALICE/ASH cods ar good

7 M. SADEGHI ET AL. 223 Tabl Er production yild via diffrnt nuclar ractions by SRIM and TALYS 1.2 cods. Raction Isotopic abundanc (%) Enrgy rang (MV) Targt thicknss (m) Thorical yild (MBq/Ah) 165 Ho(p,n) 165 Er Ho(d,2n) 165 Er Er(p,2n) 165 Tm 165 Er Er(d,3n) 165 Tm 165 Er Er(d,n) 165 Tm 165 Er nat Er(p,xn) 165 Tm 165 Er agrmnt with th masurd data from Tárkányi t al. (2009) [30]. Th sparation of isotop impuritis is not possibl by chmical mthods, so this raction is non carrir fr for 165 Tm production. According to SRIM cod th rquird targt thicknss should b µm Calculation of th Rquird Thicknss of Targt To obtain th optimum physical dimnsions of th targt such as th thicknss som stimations from th SRIM cod (Th Stopping and Rang of Ions in Mattr); wr prformd [31]. Th physical thicknss of th targt layr is chosn in such a way that, for a givn bam/targt angl gomtry (90 ), th incidnt bam on th targt ara will produc a compound nuclus with an xcitation nrgy with th calculatd optimum nrgy to favor th slctd vaporation channl. To minimiz th thicknss of th thin film targt, a gomtry of 6 is prfrrd; so th rquird thicknss of th layr will b smallr with a cofficint 0.1 (not: it is not clar what this phras mans, what is such cofficint). Th calculatd thicknsss for ths idal ractions ar shown in Tabl Calculation of Thortical Yild Enhanc of th projctil nrgy, th bam currnt and th tim of bombardmnt incras th production yild. Th production yild can b calculatd as blow, -1 NH E2 L -λt de Y= I1 σede E1 M dρx (11) whr Y is th product activity (in Bq) of th product, N L is th Avogadro numbr, H is th isotop abundanc of th targt nuclid, M is th mass numbr of th targt lmnt, σ(e) is th cross sction at nrgy E, I is th projctil currnt, de is th stopping powr, λ is d( x) th dcay constant of th product and t is th tim of irradiation [32]. Th production yilds of 165 Er via diffrnt ractions wr calculatd using th Simpson numrical intgral as of Equation (11) (Tabl 1). 4. Conclusions Rsult of th calculations and considrations prdictd that th high yild will b achivd by dutron bombardmnt of a natural rbium targt. Nvrthlss this procsss lad to form th radioisotop and isotop impuritis that hav high cross sction than 165 Er. 164 Er (d,n) 165 Tm 165 Er, 166 Er(d,3n) 165 Tm 165 Er and 165 Ho (d,2n) 165 Er ractions ar too much undsirabl than th prior raction, Bcaus of high impuritis go along with th product. Howvr, 165 Er production via 166 Er(p,2n) 165 Tm 165 Er raction lad to high cross sction for 165 Tm, but this raction can not b rsultd in no-carrir addd of 165 Er production. 165 Ho(p,n) 165 Er is suggstd as th bst mthod to produc 165 Er, gnrating minimum impuritis. Morovr, its non-carrir addd production fasibility using proton nrgy of lss 9 MV can b considrd as a brilliant advantag. Solvnt xtraction (by HDEHP (di-(2-thylhxyl) phosphoric acid); H 3 Cit (citric acid); HLact (lactic acid) and HGlyc (glycolic acid) and ion xchang chromatography ar th bst mthod which usd for sparation rbium radionuclids from Ho targts solution. 5. Rfrncs [1] A. I. Kassis, Cancr Thrapy with Augr Elctrons: Ar W Almost Thr? Journal of Nuclar Mdicin, Vol. 44, No. 9, 2003, pp [2] J. L. Humm, R. W. Howll and D. V. Rao, Dosimtry of Augr-Elctron-Emitting Radionuclids, Rport No. 3 of AAPM Nuclar Mdicin, Task Group No. 6, Mdical Physics, Vol. 21, No. 12, 1994, pp [3] R. W. Howll, V. R. Narra, K. S. Sastry and D. V. Rao,

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9 M. SADEGHI ET AL. 225 Comparison with Othr Production Routs, Applid Radiation and Isotop, Vol. 67, No. 2, 2009, pp [31] J. Ziglr, J. Birsack and U. Littmark, Th Stopping and Rang of Ions in Mattr, SRIM Cod, USA, [32] M. Sadghi, A. Zali and B. Zinali, 86 Y Production via 86 Sr(p,n) for PET Imaging at a Cyclotron, Applid Radiation and Isotop, Vol. 67, No. 7-8, 2009, pp