WWW. S he VR 21 . b1 e i . 1 : : . - : - 1 .. . t . +. - A 1 TN -3 SI SAS 1 1. UNCLASSIFIED ORNL + V ! - - - * 4 17 - A- 1 ? . WW # . 802 PS: 11 IL 11 1 . N . 2/ Matt.42.. .......:qu o ** ***an mo ang pangarm. V o m er plads. Woww.the we Paper to be included in proceedini!" sind Symposium on Protection Against Widiationis in Space, Gatlinburc, !.: 27: October 12-14, 1951 - ORNG-P-.802 CONF-230-2a CALCULATED TISSUE CUBRET-TO-DOSE CONVERSION FACTORS FOR NUCLEONS OF ENERGY BELOW 400 MeV** W. E. Kinney Oak Ridge National Laboratory DIE- DEC 301964 WASTER C. D. Zerby Union Carbide Research Institute Tarrytown, New York I. Introduction To assess the hazard to personnel encountering high-energy radiation in space or near accelerators, it is necessary to have a means of estimating the biological effects of these radiations. A useful and simple way of obtaining such an estimate is to multiply the current of a given type of incident particle by the appropriate current-to-dose conversion factor to obtain a measure of the dose received. Of course the physiological effects of radiation can be determined only by experiment, but in the past these effects have been correlated with the dose in the case of low-energy radiation. Hence it is expected that the same situation will prevail at high enersy alti:ough the correlation may be more com- plicated. To facilitate possible correlations, a series of Monte Carlo calcula- CA tions were carried out to determine many details about the energy deposition in tissue as a function of depth. From these data rad (1 rad = 100 ergs/g) and rem **- (roentgen equivalent man) doses were calculated and current-to-dose conversion factors for the surface and 5-cm-deptin doses and for the average whole-body and peak doses were extracted for hazard evaluation. Both incident neutrons and protons from 60- to 400-MeV incident energy were considered. W Since the method of converting energy deposition to rem dose will be sub- ject to change as additional data become available, the energy deposited by the *Research sponsored by the National Aeronautics and Space Administration (NASA Order R-104) under Union Carbide Corporation's contract with the V.S. Atomic Energy Commission. > W. i -2- protons as they passed through various energy ranges at the various depths was calculated separately. In this way any pocferred set of quality factors (QF) can be applied in the future with r:lative case. In addition to the proton energy deposition data, information about energy deposition by heavy recoils and heavy charged particles was computed, and was reported separately for the same reason. A detailed breakdown of the energy deposition data 1s given elsewhere? - - - for the depths and conditions corresponding to those for which the current-to- dose conversion l'actors were calculated. Previous calculations by Neary and Mulvey of the tissue dose from high- energy radiations estimated maximum permissible fluxes of nucleons in the 40- to 1000-MeV energy range on the basis of rather qualitative considerations. Gibson periormed calculations on energy deposition in tissue involving very conservative assumptions regard:ing the deposition processes. Turner et al.4 recently performed more detailed Monte Carlo calculations of the tissue dose due to protons up to .. 4 , 400 MeV; the present calculation is an independent extension of this study. Detailed experiments of the tissue dose from high-energy radiation are very scarce. The experiment of Shalnows is an isolated example of the measurement of the dose from high-energy neutrons. His data include the dose as a function of 27 depth in tissue-like material from approximately 140-MeV neutrons stripped from 280-MeV deuterons on Cu and from a broad spectrum from charge-exchange reactions of 480-MeV protons on Be. The methods employed in the calculation will first be described and will then be followed by a comparison of these results with experiment and previous calculations. The current-to-dose data will then be presented and " discussed. * . i II. Methods The interaction of a high-energy nucleon with matter initiates a complex avalanch of lower energy secondary particles which proceeds through the medium, increasing in population and decreasing in total energy as energy is deposited in the medium. In general, a nonelastic interaction with a nucleus produces, first of all, several secondary nucleons which are due to direct interactions of the incident particle with the nuclear constituents and which have energies ranging from a few MeV up to a large fraction of the incident particle energy. There is left a highly excited, recoiling nucleus which ride itself of most of 1.ts excese energy hy evaporating nucleons and heavy particles of relatively low energy of the order of a few MeV. Any energy left after evaporation presumably goes into the production of electromagnetic radiation. A series of Monte Carlo program for the IBM-7090 computer has been written to study the transport of nucleons of energies up to 400 MeV through quite arbitrary geometrical configurations. The intranuclear cascade is treated by a subroutine version of Bertini's code? which is itself a Monte Carlo nucleon transport calculation on an intranuclear scale and gives the velocities and types of particles resulting from direct interaction processes. The evaporation portion of the cascade is handled by Dresner's subroutine, 8 which is essentially the same as Dostrovsky's calculation. Protons below 50 MeV were allowed to proceed to the end of their range with no nuclear interaction, while neutrons below this energy were transported by an existing neutron transport code. 10 dose in tissue due to nucleons of energy less than 400 MeV, with the hope of arriving at some practical, usable current-to-dose conversion factors of molto - - - - sufficient generality of application, a 30-cm-thick infinite slab of tissue was chosen for study. The tissue was assumed to have a composition of CalifoO57N with a density of 1 g/cm®, absumptions which result in the nuclear densities given in Table 1. The average Ionization potentials which were used in the stop- ping power formula for the computation of the range are also listed in Table 1. Table 1. Composition and Mean Excitation Potentials for Tissue Element Nucleon Density [(nuclei/cms) x 10 Mean Excitation Potential (ev) 17.5 99.0 6.265 x 102 2.55075 x 102 9.3975 x 1003 1.3425 x 103 74.44 86.0 In the application of the current-to-dose conversion factors it is to be expected that widely varying angular distributions of nucleons incident upon the body will be encountered. In order to provide current-to-dose conversion factors which could be used to estimate upper and lower bounds on the doses for practical cases of interest, the nucleons were made to impinge on the tissue slab both normally in a broad beam and isotropically, with the expectation that these two extremes of incident angular distribution would represent the bounding cases. One can, of course, construct an angular distribution which results in a dose greater than the isotropic dose as, for example, a 400-MeV proton beam incident at such an angle as to be entirely stopped in the 30-cm-thick slab and thus yield a higher average dose than the isotropic case. It is felt, however, that such distributions would be most unrealistic. Generally 10,000 monoenergetic source nucleons were introduced at each of the source energies of 400, 300, 200, 100, and 60 MeV and for each angular distribution. The 30-cm-thick slab was ha divided into 30 subslabe of 1 cm thickness, and a print-out was then made of the energy deposited in each subslab due to primary protons, secondary cascade protons, secondary evaporated protons, evaporated heavy (m888 > 1) particles, and recoil nuclei resulting from both high-energy nuclear Interactions and low-energy neutron elastin collj.sions. The residual nucleus excitation energy available for gamma-ray production was also recorded in each subslab. The dose as a function of depth was calculated in units of rads and rems. For the purpose of converting the rad to rem units, the energy deposition result- ing from protons as they passed through the energy ranges 0-1, 1-5, 5-10, 10-50, and > 50 MeV was recorded separately. Average QF values, for each interval, of 8, 3, 1.25, 1, and i, respectively, were calculated from the QF vs LET (linear energy transfer) curve shown in Fig. 1. The graphical data were derived from tabulated values in the National Bureau of Standards Handbook 59, 12 which agree very closely with the recommendations of the 1962 report of the RBE committee to the ICRP and ICRU. 13 The values of the energy of the proton shown in Fig. 1 . were correlated with the LET values by means of the stopping power formulas. . The constant value of 20 for the QF above an LET value of 1750 MeV/cm shown in Fig. 1 is not from Handbook 59 but constitutes a quite arbitrary as- sumption that a saturation effect takes place and can be represented by a constant QF at high LET values. It should be noted that under all circumstances the QF value of 20 is applied to the dose from the heavy evaporation particles and recoil nuclei in calculating the rem dose since their LET value is generally above 1750 MeV/cm. Because of the wcertainties connected with the QF vs LET curve Schaefer14 suggested that the dose data be recorded in energy intervals in a manner similar ... . to that described above so that any preferred set of QF's could be employed to calculate the rem dose with relative ease. III. Comparison with Other Work . . =. In an attempt to establish the degree of reliability of the calculations, the results were compared with those obtained by other investigators, with particular interest given to a comparison with two neutron dose experiments. Both experiments were performed with multienergetic neutrons and, rather than perform- ing two lengthy calculations with neutrons introduced in an energy spectrum into a model of the experimental configuration, the results of our selected mono- energetic neutron dose caículations in the assumed tissue were applied as nearly as possible. ainintatart van Shalnovs measured the dose as a function of depth in water and paraffin dummies due to neutrons which were incident in a broad beam and which resulted from the stripping reaction of 280-MeV deuterons on a thick copper target and natin m also from the charge exchange of 480-MeV protons on beryllium. Serber15 gives the energy spectrum of neutrons stripped from deuterons as Sakatsetasin N(E) DE = - wala En) + €afa DE, where - N(E) dE = the number of neutrons in the energy range de about E, E = neutron energy in MeV, E, = the kinetic energy of the deuteron in Mev, € = the binding energy of the deuteron = 2.18 Mev. menanaman magram . " #.. C This 18 a spectrum having a half width of 1.5 (E9€)* which, for 280-MeV deuterons, is equal to 37 Mev. The measured doses as a function of depth due to neutrons stripped from 280-MeV deuterons are compared in Fig. 2 with the calculated results for 100-MeV neutrons normally incident in a broad beam on an infinite slab of tissue. The results have not been normalized and agreement is seen to be excellent. . The neutron spectrum from the charge-exchange reaction of 480-MeV pro- tons on beryllium as measured by Dzhelepov et al. 16 is given in Fig. 3, where the extrapolation assumed for this work is indicated. The average neutron energy is roughly 380 MeV, with 30% of the neutrons lying between 350 and 480 MeV, 25% between 250 and 350 MeV, and 21% between 150 and 250 MeV. In an attempt to compare the calculated doses due to monoenergetic sources with the measured dose from the charge-exchange neutrons, the calculated doses for normal incidence were weighted rather crudely with the spectrum. The 400- MeV neutron calculated doses were weighted with the integral of the spectrum above 350 MeV. Similarly, the 300-MeV results were weighted with the integral from 250 to 350 MeV, the 200-MeV results with the integral from 150 to 250 MeV, and the 100-MeV doses with the integral below 150 MeV. The resultant weighted dose as a function of depth is compared with measured values for the charge- exchange neutrons in Fig. 4. Again there has been no normalization; however, although the order of magnitude of the calculated and measured doses agrees approximately, the shape of the dose vs depth curves is not in the excellent agreement seen in the comparison in Fig. 2. The experimental result in this case : shows a flat behavior of the dose as a function of depth, while the calculated curve rises with increasing depth. Crude calculations show that a large number of low-energy neutrons could account in large measure for the flat behavior of the experimental results. LAW " " . .. Neary and Mulveyê have estimated the permissible fluxes of Incident nucleons of energy in the range 40 to 1000 MeV which will produce a dose in a period of 40 hr equal to 0.3 rem, the value of maximum weekly dose recommended by the National Committee on Radiation Protection and Measurements. 17 They estimated the relative biological effectiveness of the nucleons and assumed that all the energy was deposited within a distance equal to the range in the case of protons and within a mean free path in the case of neutrons. They then computed an average dose over these distances to arrive at the permissible incident flux. Their results are compared in Fig. 5 with maximum fluxes based on the results of our calculations for both normally incident and isotropically incident nuclcons. We determined the fluxes by computing average whole-body doses over the 30-cm slab for all the neutron calculations and for the protons of incident energy greater than 220 MeV, the energy at which the range of protons in tissue is 30 ? cm. For protons below 220 MeV ke averaged the doses over the range of protons. The differences are greatest in the case of neutrons, where our results indicate that fluxes higher by a factor of 2 to 4 may be permitted. The differences are chiefly due to the assumption by Neary and Mulvey that there was complete absorp- tion of the neutron while we considered a 30-cm-thick slab. The mean free path for neutrons in the 100- to 400-MeV energy range is approximately 80 cm, and so 70% of the primary neutrons at normal incidence pass through the slab without suffering interaction and therefore without depositing energy; many of the secondary neutrons also escape. The permitted fluxes of neutrons incident isotropically are, of course, less than those permitted at normal incidence since the former neutrons travel, on the average, twice as far as the latter in the slab. The permitted proton fluxes resulting from our calculations are also higher than those of Neary and Mulvey. At low energies the permitted fluxes · " * " Y . X . . - 2 . -9- agree but at around 70 MeV they start to diverge, the divergence increasing up to 220 MeV, the energy at which normally incident protons can just get through the slab. This is due to the effective QF for the incident proton from our calculations being lower than that assumed by Neary and Mulvey. Our effective QF, which is equal to the ratio of total rem to totul rad dose, falls from 1.3 at 100 MeV to 1.1 at 200 MeV (see Fig. 14), while the values of Neary and Mulvey rise from 1.24 at 70 MeV to 1.6 at 190 MeV. Above 220 MeV our permitted flux of normally incident protons increases since the jrimarj.es are now able to escape, as indicated in Fig. 8. The curve of permitted flux for isotropically "cident protons, however, turns over above 220 MeV and falls since the higher ciergy protons produce more secondaries than do the lower energy ones, and while the average rad dose remains constant with increasing energy the rem dose increases am slightly, as shown in Fig. 9. Gibsons computed the energy removed from primary nuclear beams by tissue, making the very conservative assumption that all the energy of nucleons absorbed is available and deposited locally. Actually, a considerable portion of the energy 18 expended in overcoming the binding energy of the nucleons within the nucleus, and also much of it leaks out. The proton doses computed by Gibson are higher than ours by a factor of up to 2, while the neutron doses range from a factor of 3 higher at low energy to 4 higher than our average dose and 14 higher than our surface dose at 400 MeV. IV. Results As stated previously, Monte Carlo calculations were performed for both normally and isotropically incident protons and neutrons with energies of 60, 100, 200, 300, and 400 MeV. Ten thousand source particles were used for each case. The unsmoothed results from the case of normally incident 200-MeV : 1 -10- protons presented in Fig. 6 indicate typical results and the statistical in- certainties associated with the data. Additional details and the remainder of the cases are presented in another report." For the case of normal incidence the dose from primary protons presented in Fig. 6 approximates, as expected, the stopping power curve for ionization energy loss as a function of depth in tissue. It is only an approximation because some of the protons are removed from the beam by nonelastic events and so the energy deposition falls below the stopping power curve. At 200-MeV incident energy the increase in the stopping power with decreasing energy (and hence with depth) is sufficiently rapid to make up for the removal of particles by nonelastic events, thus causing the dose to increase initially as the depth increases. At about 400 MeV the two effects almost balance and the energy deposition from the primary beam decreases slightly with depth, only to increase again near the end of the range as the stopping power increases. Of course, for normally incident 400-MeV protons the rise at the end of the range is not experienced in our model of the body because their range is 84 cm. Ine ene- gy deposition by secondary protons indicated in Fig. 6 includes the contribution from cascade protons ejected in nonelastic events, nuclear evaporation protons, and protons from elastic scattering with hydrogen as a result of either neutron or proton interactions. Initially the dose from the secondary protons increases with depth as the number of secondary particles builds up from cascades initiated by the primary beam. Near the end of the range of the primary beam (26.5 cm), where the particle energies are low, the contribution from secondary protons decreases rapidly as a result of the decrease in the number of nonelastic events creating secondary particles. Beyond the -12- # range of the primary beam there is still a contribution from secondary protone ejected by neutrons that have migrated to that depth. The dose from the heavy particles shown in Fig. 6 includes the contri- bution from the recoil of the residual nuclei after a nonelastic event, nuclear recoils (other than protons) from elastic scattering of low energy neutrons, and nuclear evaporation particles (other than protons). The dose from these parti- cles 18 remarkably flat over most of the range of the primary beam, decreasing appreciably only near the end of the range, where contributions come only from neutron-initiated events. The dose from residual nuclei shown in Fig. 6 actually indicates the energy created in the form of photons by transitions to the ground states of the residual nuclei after nonelastic events. The contribu- tion to the dose from these radiations is usually so small for the cases con- sidered that we did not calculate the migration of the photons; in fact, reference to the data 18 omitted in the remainder of the figures. From the detailed depth-dose data of all the cases calculated, certain doses were extracted to establish current-to-dose conversion factors. The particular ones chosen were the average whole-body dose, the surface dose, the dose at a depth of 5 cm, which is the average depth of the blood-forming organs, and the peak dose. These data are presented in Figs. 7 through 14. The detailed results for normally incident protons are presented in Fig. 7 as an indication of the significance of the various contributions. Here the primary proton, secondary proton, and heavy particle rad and rem doses are presented separately. In Fig. 7 the reason for the primary proton dose having a discontinuity at 215 MeV is that above this energy the proton beam penetrates 30 cm of tissue and some of the energy is not deposited. The decrease in dose with increasing 12. 2.-- - - . 22 energy above 215 MeV is accounted for by the decrease in stopping power with . increasing energy in this energy range. Thus less energy 18 deposited in the 30 cm of tissue as the energy increases. It 18 Interesting to note that the rem dose of the primary or secondary protons in Fig. 7 18 not appreciably different from the corresponding rad dose. This is because most of the protons are created with energies well above 1 MeV and they therefore deposit the greatest fraction of their energy with a QF close to unity. The heavy-particle rem dose, on the other hand, 18 exactly a factor . 20 above the rad dose because the LET value of these particles 18 always above 1750 MeV/cm. This Interesting situation, which admittedly depends on the ad hoc but perhaps reasonable assumption that the QF 18 20 and constant at high LET val.ues, causes the heavy-particle contribu- tion to the total rem dose to be greater than the secondary proton dose for moet energies. For instance, at 100 MeV the secondary proton rem dose 18 approxi- mately 6% of the total dose, while the heavy-particle rem dose contributes At 400 MeV these percentages are each approximately 35%. Figure 8 presents the total average whole-body rad and rem results for both normally incident neutrons and protons. Also shown is the average whole: body rad dose that would be received if the proton beam were totally absorbed. In comparison with the latter curve, it is easy to see that below 215 MeV little error would be introduced if the whole-body rad dose were calculated on the basis that all the energy is totally absorbed. By dividing the rem dose by the rad dose, one obtains the average QF. In all cases presented this average QF is significantly greater for incident neutrons in comparison with incident protons. The difference can be attributed to the fact that in the case of incident protons the dose from the primary protons with its associated QF which is near wity makes the most significant contribution -13- to the total rad or rem dose. Thus the average QF would be expected to be close to wity. In the case of incident neutrons approximately 11% of the rad dose 18 contributed by the heavy particles, but its associated QF of 20 makes it the most significant contributer to the rem dose (the QF associated with the secondary proton dose 18 close to wity). An approximate calculation indicates that under these oircumstances the average QF should be close to y for the neutz on cases. Indeed, the average QF for normally incident protons ranges from 1.3 at 100 MeV to 1.4 at 400 MeV, while for normally incident neutrons It ranges from 4.2 at 100 MeV to 3.4 at 400 MeV. L * - The curves for the average whole-body dose for isotropically incident particles shown in Fig. 9 are quite similar to the corresponding ones from the normal ly incident cases, and little need be said about them. In Figs. 10 and 11, where the 5-cm-depth doses are reported, there is a definite cutoff at 80 MeV for incident protons. This is because protons in the range of approximately 80 MeV and below are less than 5 cm in tissue and cannot make a contribution at that depth. The curves for the surface doses shown in Figs. 12 and 13 are not markedly different from the corresponding 5-cm-depth dose curves. .- - - . Figures 14 and 15 present the maximum dose curves for normally incident and isotropically incident neutrons and protons. The depth at which these mexi- mums occur is presented in Table 2. The apparent discontinuity in the normally incident proton curve shown in Fig. 14 18 explained by the fact that below 215-MeV incident energy. the maximum occurs at the end of the range of the protons where the stopping power is very high. Above 215-MeV incident energy the range of protons 18 greater than 30 cm; so the maximum in the body occurs at some ..: -14- Table 2. Depth at Which Maximum Dose Occurs Depths (cm) for Source Energies of 400 MeV 300 MeV 200 MeV 100 MeV .60 MeV Source Normal protons 30 Normal noutrono 30 Isotropic protons 5 Isotropic neutrons 15-25 30 30 5 15-25 24-25 20-30 5 15 6-7 5-10 3 5-10 5 0 0 intermediate proton energy where the stopping power is much less than that at in the end of its range. The meximm doses for energies bo’low 215 MeV were obtained by averaging the dose over the last centimeter of its range. The current-to-rem dose conversion curves shown in Figs. 8 through 15 can be fit by an expression of the form logio D = A + BE + CE , where D 18 the dose in rem per nucleon per cm and E is the energy in MeV. Table 3 contains the values of the coefficients. Space does not permit the inclusion of the partial rad doses as a func- tion of depth so that arbitrary QF's may be applied in arriving at a rem dose. This detailed data may be found in ref. 1. V. Conclusion The most striking feature of this calculation is the significant contri- bution that the heavy particle recoils makes to the rem dose for case of incident neutrons or protons. In the case of incident protons the contribution is in general of the order of 10 to 20% but for incident neutrons it constitutes the 7 -15- E- Table 3. Coefficients of the Expansion for the Rem Dose Log D for Various Cases Average dose Normally Incident Protons -7.72 + 6.4 x 103€ - 1.1 x 10°3g2; 60 < E < 215, .-6.20. - 4.3 x 1035 + 5.5 x 10*852; 215 < E < 400, -6.27 - 4.6 x 10"Og + 6.4 x 10"@ge; 80 < E - 400, 5-cm-deep dose Surface dose -6.64 - 2.2 x 10°3E + 2.9 x 10°8E2; 60 < E < 400 Maximo dose -6.02 - 1.2 x 10°3E; 60 < E < 215 6.62 - 1.1 x 10°3E; 215 < E < 400 Average dose 5-cm-deep dose Surface dose Normally Incident Neutrons -7.43 +2.7 x 10°*E; 60 < E < 400 -7. 38; 60 < E < 400 -7.59 + 3.7 x 10°%E; 60 < E < 400 -7.35 + 3.8 x 10°*E; 60 < E < 400 Maximum dose Average dose Isotropically Incident Protons -7.79 + 7.9 x 10°3E - 1.7 x 10°5E; 60 < E < 215 -7.07 + 1.2 x 10°3E - 1.3 x 108E2; 215 < E < 400 -6.57 - 5.4 x 10°45; 80 < E < 400 -6.30 - 2.7 x 103E + 3.7 x 108E2; 60 < E < 400 -6.26 - 2.9 x 103E + 4.1 x 108E; 60 < E < 400 5-cm-deep dose Surface dose Maximum dose Isotropically Incident Neutrons Average dose 5-cm-deep dose' -7.26 + 5.6 x 10°4E; 60 < E < 400 -7.18 + 3.9 x 10°4E; 60 < E < 400 -7.26 + 4.5 x 10°4E; 60 < E < 400 -7.18 + 4.0 x 10Ⓡ4E; 60 + NEUTRONS, rem DOSE NEUTRONS, rad 10-8 100 500 200 300 400 INCIDENT ENERGY (Mev) 1 TO til ALL NY W 12. + . 117 h DATE FILMED 4/26 165 V ? * . . 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