Journal of NUCLEAR SCIENCE and TECHNOLOGY, 28[7], pp. 627~441

Organ

Doses for

as a Function

Environmental

of

Body

Gamma

Kimiaki

627

(July 1991).

Weight

Rays

SAITO

Department of Environmental Safety Research, Tokai Research Establishment, Japan Nina PETOUSSI,

Gesellschaft

fur

Atomic Energy

Research

Institute*

Maria ZANKL Richard VEIT, Peter and Gunter DREXLER Institut fur Strahlenschutz, Strahlen and Umweltforschung

JACOB

mbH Miinchen**

Received August 2, 1990 Revised February 14, 1991 The organ doses for r rays from typical environmental sources were determined with Monte Carlo calculations using anthropomorphic phantoms having different body sizes. It has been suggested that body weight is the predominant factor influencing organ doses for environmental rgrays,regardless of sex and age. A weight function expressing organ doses for environmental ays was introduced. This function fitted well with the organ doses calculated g r using the different phantoms. The function coefficients were determined mathematically with the least squares method. On the assumption that this function was applicable to organ doses for human bodies with diverse characteristics, the variances in organ doses due to race, sex, age and difference in body weight of adults were investigated. The variations of organ doses due to race and sex were not significant. Differences in body weight were found to alter organ doses by a maximum of 10% for g rays over 100 keV, and 20% for low-energy g rays. The doses for organs located deep inside a body, such as ovaries, differed between a newborn baby and an adult by a maximum factor of 2 to 3. For g rays over 100 keV, the variation was within a factor of 2 for all organs. The organ doses for adolescents more than 12 years agreed within 15% with those of the average adult. KEYWORDS: organ doses, effective dose equivalent, gamma rays, phantoms, Monte Carlo method, transport race, sex dependence, adults, age dependence There

I.

INTRODUCTION

Organ doses, being unmeasurable characteristics, need to be estimated from measurable properties using models. The most common mathematical model used for this purpose is the MIRD phantom(1)~(3)constructed from the reference man data shown in ICRP Publication 23m. Using this reference phantom, organ doses for various exposure conditions, mainly for radiation protection purposes, have been calculated. However, under real circumstances the size of a human body varies due to several factors.

body weight, environment, calculation, energy range,

are many

races

in the world,

and within

a race body sizes vary greatly. Furthermore, humans range widely in age, from infants to extremely old people. Considering these conditions, the differences in organ doses resulting from body size variations should be elucidated to estimate the effects of radiation on various populations. Some studies have examined the variation of organ doses with body size. O'Brien deterimined effective dose equivalents for a 3.4 * Tokai -mura ** Ingolstddter

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FEDERAL

, Ibaraki-ken, LandstraBe REPUBLIC

319-11. , D-8042 Neuherberg, OF GERMANY. 1

628

J. Nucl.

kg human body using a simplified manner(5). Cristy developed several phantoms of different sizes based on the MIRD phantom for the calculation of internal exposure(6). In project DS86, intended to reassess the A-bomb dosimetry in Hiroshima and Nagasaki, organ doses were calculated for some specific cases, also using modified MIRD type phantoms representing different ages(7). So far, however, there have been few studies that thoroughly investigated the effect of body size on organ doses for environmental g rays. We have previously calculated organ doses resulting from environmental g rays(8)(9) for male and female adults, a child 7 years old and a baby 8 weeks old using the anthropomorphic phantoms developed at GSF(8)(10)(11). It is desirable to easily obtain organ doses for other ages. Further, researchers have seldom investigated organ doses for persons heavier than the reference man. The purpose of this paper is to : (1) Develop a method to infer the organ doses of a human body having an arbitrary weight ; (2) Investigate the difference of organ doses due to the following factors : race, sex, age and difference in body weight of adults. The mathematical adult phantoms ADAM and EVA developed at GSF were modified to have arbitrary body sizes while keeping constant weight proportions of organs. Using the modified phantoms of ADAM and EVA, the organ doses for persons weighing 21.7 kg were calculated and compared with the organ doses for the phantom CHILD having the same weight. CHILD and BABY are realistic phantoms constructed from the data of X-ray computer tomography (CT). Moreover, organ doses were calculated for persons weighing 100 kg to obtain data for heavy persons. In addition, a weight function was introduced to express organ doses, and the organ doses calculated were fitted to the function mathematically using the least squares method. Further, the variation of organ doses was investigated by changing body weight as a parameter.

II.

See. Technol.,

CALCULATION OF ORGAN DOSES

Using the anthropomorphic phantoms ADAM, EVA(3), CHILD and BABY(10)(11)developed at GSF, we have previously calculated organ doses for g rays from the following typical environmental sources taking into account the r ray fields precisely(8)(9): (a) semi-finite volume source in the air ; (b) finite plane source in the ground ; and (c) semiinfinite volume source in the ground. Sources (a) and (b) are analogues of artificial radionuclides from nuclear facilities or nuclear tests ; 19 monoenergies of 15 keV to 10 MeV were considered. Source (c) models natural sources in the ground ; thus the main natural radionuclides of the 238Useries, the 232Th series and 40K were considered . Source (b) simulates deposited radioactivity and was assumed to lie at a depth of 0.5 g/cm2 to include the effect of ground surface roughness and initial migration into the soil. Since the sources considered here extend infinitely in the horizontal direction and each phantom is assumed to stand vertically on the ground, ays enter each phantom symmetrically gr around its body axis. To calculate organ doses, the following three-step procedure was applied. First, the ray transport in the environment was calgculated without considering a phantom using the Monte Carlo code YURI(12). Next, the secondary source that emits r rays according to the environmental g-ray fields from the transport calculation was constructed. Finally, the organ doses were calculated using the ADAM, EVA, CHILD and BABY codes for the g rays emitted from the secondary source. The validity of this procedure was discussed in the previous report(8). The body characteristics of these phantoms are shown in Table 1. Environmental conditions the same as those assumed in the previous report(8) were applied in this study. The detailed data of the calculation conditions are described in the report. The air kerma at 1 m height per unit source intensity could be affected by environmental conditions. For example, in the case of a

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Table

1

Body

characteristics

plane source in the ground, the air kerma apparently changes according to the source depth assumed. Nevertheless, the relation of air kerma at 1 m height to organ doses was found to be rather insensitive to the environmental conditions. This occurs because the relative shapes of energy spectra and angular distributions of g rays do not change significantly with varying environmental conditions(8). ADAM and EVA are mathematical phantoms based on ICRP reference man data which represents Caucasian adults. The shapes of bodies, organs and tissues are expressed with combinations of mathematical equations. CHILD and BABY are more realistic phantoms constructed from X-ray CT data from a child 7 years old and a baby 8 weeks old, respectively. Since the bodies are modeled by small cubic units called voxels, these phantoms ex-

of the

phantoms.

Table 2 lists the organ weights for CHILD and the reduced ADAM and EVA. The reduced EVA correlates well with the reduced ADAM in terms of organ mass and also of body proportion. On the other hand, some differences are evident between CHILD and the reduced EVA and ADAM. In terms of body proportion, CHILD has a much bigger head than the reduced EVA or ADAM. The reduced EVA and ADAM have nearly the same heights as CHILD (all about 115 cm), but the body thicknesses (13.4 and 13.5 cm, respectively) are smaller than that of CHILD (17.6 cm). This is because the horizontal cross section of an adult's body is more elliptical than that of a child's body, which is more circular.

press the fine structures of human bodies. In Japan, Yamaguchi is developing similar phantoms based on the data of nuclear magnetic resonant CP(13). In this study, ADAM and EVA were modified to expand and reduce the bodies while keeping the proportion of organ weight to body weight constant. This resulted in preserving constant body proportions. The body is not expanded or reduced in the true sense. Instead, the photon reaction cross sections of every organ are multiplied by a scaling factor. This produces the same effect on the calculations as the physical expansion or reduction of the body. To check if doses calculated by the modified ADAM and EVA were reasonable, the weights of ADAM and EVA were reduced to 21.7 kg which is the weight of CHILD. The ratio of organ weight to body weight also varies with age and sex. — 35 —

Table

2

Organ weights of CHILD reduced EVA and ADAM

and the

J. Nucl. Sci. Technol.,

630

The mass of several organs has a difference of more than a factor of 2 between CHILD and the reduced ADAM or EVA. For example, red marrow, lungs, kidneys, spleen and thymus as listed in Table 2. Moreover, the shapes and positions of organs are different between CHILD and the reduced EVA or ADAM. CHILD has organs that are precise copies of real organs. The organs of ADAM and EVA have simplified shapes and in some cases are not good approximations of real organs. Thus, the reduced EVA and ADAM have physical differences from CHILD. As mentioned before, to determine if doses calculated by the modified ADAM and EVA are reasonable, organ doses for environmental ays were calculated using g rthe reduced ADAM and EVA, each with a weight of 21.4 kg. The calculation was performed under the same environmental conditions as the previous calculation(8) using the same secondary sources. Only five source energies, 0.05, 0.1, 0.5, 1 and 3 MeV, were selected for sources (a) and (b). These energies were considered adequate to examine the variation of organ doses with body size. For source (c), the 238U series, the 232Th series and 40K identical to the previous report were examined. The calculated doses for 22 principal organs, shown in Tables 3~5, were compared between CHILD and the modified ADAM and EVA. In figures and tables in this paper, HE stands for effective dose equivalent. The ADAM and EVA programs calculate skeleton doses for a mixture of hard bone and red marrow. The CHILD and BABY programs calculate skeleton doses only for hard bone. Therefore, skeleton doses from ADAM and EVA were multiplied by correction factors that consider the difference of mass energy absorption coefficients between hard bone and combined hard bone and red marrow. This is not a rigorous treatment, therefore skeleton doses from ADAM and EVA may include systematic errors. Since the red marrow doses from ADAM and EVA are already corrected for this problem and related problems in the calculation programs(14), the regular ADAM and EVA output values were used.

The effective dose equivalent for CHILD was calculated using the weighting factors for the ICRP reference man(15). The weighting factors for children should be different from those for adults(16), however, we do not now have appropriate weighting factors for children. Therefore, the same weighting factors were used for all ages. A comparison was made for every case considered in this paper ; that is, five different source energies for sources (a) and (b), and the three nuclide series for source (c). The doses for CHILD were compared separately with those for the reduced ADAM, and with those for the reduced EVA. Therefore, there were 26 different comparisons for each organ common to ADAM and EVA. For each sexual organ, like ovaries, there were 13 comparisons. Some statistics of the discrepacies found in these comparisons are shown in Fig. 1.

Fig.

1

Statistics of discrepancies observed in comparisons of organ doses between CHILD and the reduced ADAM and EVA

The doses for small organs such as ovaries, thyroid, adrenals and thymus tend to show large discrepancies because of large standard deviations

— 36 —

in

the

Monte

Carlo

calculations.

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Vol. 28, No. 7 (July 1991)

This is shown in Fig. 1(a). Generally, the agreement is better for larger organs as seen from the comparison for a medium-sized organ, the stomach, in Fig. 1(b). This results mainly from the improved standard deviations. As Fig. 1(c) indicates, 80% of the total comparisons for the main organs show discrepancies of less than 10%. Most of the effective dose equivalents and whole body doses agree within 5% as shown in Fig. 1(d). Several cases exist with larger discrepancies, in some cases up to 35%, as seen in Fig. 1(c). Skeleton doses showed large systematic differences, because the dose calculation models are different between CHILD and the reduced ADAM and EVA as described previously. Skeleton doses contributed a dominant number of the large discrepancies in the total statistics. The doses for lungs show considerable discrepancies at low energy. These are also considered to be due to systematic causes. In this case, the discrepancies are not simply due to the differences of the calculation models but due to essential differences of the body structures. The lungs of CHILD are smaller than those of the reduced ADAM or EVA, thus are located relatively deep inside the thorax, while the lungs of ADAM or EVA are close to the surface of the thorax. Low-energy g rays are attenuated considerably before reaching the lungs for CHILD. This results in the lower doses compared with those for the reduced ADAM or EVA. Therefore, lung doses for low-energy ays contribute to the large discrepancies gr of the comparisons as well. The remaining large discrepancies are considered mainly due to large standard deviations in the Monte Carlo calculations for small organs. Generally speaking, at low energies the doses show less agreement. It is reasoned that for low-energy g rays the shielding effect of a body is sensitive to the difference of body structure owing to the high interaction probability. In fact, only 50~60% of the doses agree within 10% for 0.05 MeV r rays, while, about 80% of the doses agree for g rays of more than 0.1 MeV. Even for 0.05 MeV 7 rays, more than 80~90% of doses agree within 20%.

With respect to source distribution, the doses for the plane source in the ground (source (b)) show the least discrepancies. The quantities of doses agreeing within 10% are 74, 86 and 80% for sources (a)~(c), respectively. In source (b), since g rays come mostly from horizontal directions(8), the shielding effect of the body is the smallest of the three cases when the source energy is the same. Therefore, the fluctuations of doses are also minimum. The doses for main organs for CHILD and the reduced ADAM and EVA show good agreement. Consequently, it was found organ doses for a human weighing 21.7 kg, can be approximated by the doses calculated by the reduced ADAM and EVA. The physical characteristics of adult bodies are considered to be similar to ADAM and EVA. Adult bodies generally do not exhibit the differences observed between CHILD and the reduced ADAM and EVA. Thus, it is expected that organ doses for an adult having arbitrary weight over 21.7 kg are calculated properly with the modified ADAM and EVA. Organ doses for persons weighing 100 kg were calculated using expanded ADAM and EVA for the identical three source conditions. The aim of this calculation was to obtain organ doses for heavy persons and 100 kg is considered the maximum weight for calculation since few humans weigh more than 100 kg. The weight fraction of fat to total body weight tends to increase as the body gets larger. The fraction of fat for the Caucasian reference man corresponding to ADAM is 19.7%(17), while the fraction for a fairly plump man is 30%. Accordingly, the amount of fat for the plump man weighing 100 kg is larger than that for the expanded ADAM by about 10 kg. This corresponds to a fat layer about 1 cm thick provided the 10 kg of fat is distributed on the trunk surface uniformly. Unless g energy is extremely low, a 1 cm fat layer is viewed not to attenuate the doses much as inferred from the decrease of air dose by 1 cm water layer(18). Therefore, the doses from the expanded ADAM are expected to represent reasonably the organ doses

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J. Nucl.

for plump persons, though it is desirable that the effect of the fraction of fat be investigated further at a later opportunity. The organ doses for the expanded and reduced ADAM agreed well with those for the expanded and reduced EVA respectively, though the detailed data are not included here. The three phantoms having different body structure but the same weight show similar organ doses as a whole. This fact indicates that the body weight is the main factor to determine organ doses for environmental g rays. When g rays enter bodies from one direction, the differences of physical characteristics such as the positions and shapes of organs, even if the body weights are the same, could affect the organ doses significantly. For example, when photons enter the body from the anterior direction, the lung doses show differences between ADAM and EVA because of the shielding effect of the female breasts(19). On the other hand, when g rays enter the body from many directions, effect of partial differences in physical structures are diminished. From these observations, we conclude that body weight is the dominant factor in determining the organ doses for environmental ays, though further investigations gr using different phantoms are necessary to prove this thoroughly. III.

ORGAN DOSES AS A FUNCTION OF BODY WEIGHT

In Chap. II it was suggested that organ doses are determined mainly by the body weight. Expressing organ doses as a function of body weight would be useful. We introduced the following equation to express organ dose D : D= a exp(bw1/3),

(1)

where w is the body weight, and a and b are coefficients determined by organ and irradiation conditions. Equation ( 1 ) was deduced from the following considerations. In the case of external exposure, organ doses are thought to be strongly related to the degree incident photons are shielded prior to reaching the organ. Therefore, the organ doses would be

Sci. Technol.,

approximated by an exponential function of the path length, or the average path length when r rays penetrate the human body from more than two directions. The body dimensions, related to this average path length, are proportional to the cube root of the body weight provided the physical proportions are the same. Since, roughly speaking, physical proportions of human bodies are similar, organ doses would be expressed by an exponential function of the cube root of body weight. Equation ( 1 ) is transformed as follows : 1n D=1na+bw1/3.

(2)

Figures 2(a)~(h) and 3(a)~(d) show the logarithms of principal organ doses per air kerma at a 1 m height for a plane source in the ground and for a volume source in the ground, respectively, with the cube root of the body weight as the x-axis coordinate. Organ doses from the previous report(8) and calculated results in this study are shown together in these figures. Accordingly, for one case, three different organ doses from CHILD and the reduced ADAM and EVE were plotted for a body weight of 21.7 kg. Two different doses from the expanded ADAM and EVA were plotted for a weight of 100 kg. When more than two data points at the same weight were too close to be shown separately, some were omitted in these figures. For 4.2, 59.2 and 70.5 kg only one organ dose exists from BABY, EVA and ADAM, respectively. Effective dose equiva lents were plotted at the mean weights of a man and a woman. The organ doses give essentially straight lines in the weight ranges of 4.2~100 kg in these figures. Therefore, the organ doses are considered to be approximated by Eq. (1 ). Further, the fact that the organ doses change systematically with body weight implies that the conclusion made in Chap. II is valid. The coefficients of the equation were determined by the least squares method for each case. The coefficients to calculate the principal organ doses are shown in Tables 3~5 for the all cases considered here. The lines in Figs. 2 and 3 were plotted using these

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Vol. 28, No. 7 (July 1991)

Fig. 2(a)—~(h)

Fig. 3 (a)~ (d)

633

Dependency of organ doses on total body weight infinite plane source in ground (source (b))

Dependency of organ doses on total body weight for natural sources in ground (source (c))

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for

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J. Nucl. Table 5

Sci. Technol.,

Coefficients of the function calculating organ doses for semi-infinite volume source in ground (source (c))

coefficients. The organ doses derived from Eq. ( 1 ) and the fitted coefficients were compared with the original data. For each source, more than 90% of the organ doses coincided within a 10% discrepancy with the original doses. Though it is impossible to give a complete explanation of the fitted lines, the following quantitative features were recognized. In sources (a) and (b), the slopes of the lines are larger for 0.05 MeV than for the other energies. Also, the slopes do not show large differences for energies greater than 0.1 MeV. Slopes are large for deep-internal organs such as ovaries and red marrow. Slopes are rather small for organs situated near the body surface such as the breast and skin. However, the absolute values of organ doses can not be explained simply by the shielding effect due to the location of the organ because of an overlapping build-up effect. It should be noted that the slopes are similar even for the different source distributions when the initial g-ray energy is the same, though the absolute values are different. Therefore, coefficient b in Eqs. ( 1 ) and ( 2 )

is expected to be applied to the other source distributions : it is possible to estimate roughly the variation of organ doses with body weight for other source distributions unless the source distribution is extremely biased. In the case of natural sources, generally the slopes of the lines are small. The absolute values and the slopes are quite similar for the principal three sources, though the doses per air kerma for 238Uare slightly smaller than those for the other sources. VARIATION IV.OF ORGAN DOSES In this chapter, the degree of variation of organ doses with respect to race, sex, age and difference in weight of adults will be examined on the basis of the functions introduced in the previous chapter. Though there are specific factors other than body weight that affect organ doses in some cases, a general discussion based on the function of weight will provide useful information about the extent of variation of organ doses. 1. Race The doses for the principal organs were compared between the ICRP reference adults

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HVol. 28, No. 7 (July 1991)

and a Japanese male adult of average weight and a Japanese female adult of average weight. As the ICRP reference adult is based on Caucasian physical data, this comparison was intended to examine the difference of organ doses between different races. The weight of the ICRP reference adult is 70.0 kg for the male and 58.0 kg for the female. The average weight of a Japanese man and woman is 61.5 and 52.0 kg respectively according to the National Nutrition Survey in Japan(20). These values agree with the data shown by Tanaka who has investigated the physical characteristics of Japanese to construct the Japanese reference manc(17). Organ doses were derived from the function using these weight data. Almost all doses for the ICRP reference man and woman agree within 5% with those for the average Japanese man and woman, respectively. For 50 keV g rays from sources (a) and (b), about 30% of the organ doses show differences exceeding 5%, but not exceeding 10%. Since the weight of other major races in the world is not considered to be much different from those of Caucasians and Japanese, the differences of organ doses with respect to races are not considered to be large. 2. Sex The doses for main organs were compared between the ICRP reference man and woman, also between the Japanese man and woman each having average weight. The doses for organs common to males and females were compared, and the doses for organs particular to either sex, such as testes and ovaries, were excluded. For source (c), all comparisons show agreement within 5%. For the other sources, every organ dose agrees within 10% between male and female. For energy ranges greater than 0.1 MeV, 90% of the organ doses agree within 5%. In addition to the organ doses calculated from Eq. ( 1 ), the original organ doses from ADAM and EVA showed a similar degree of differences(8)(9). Consequently, the difference in organ doses due to sex is concluded to be quite small. 3. Difference in Body Weight of Adults Body sizes vary greatly even among adults.

In this section, differences in organ doses due to differences in body weight will be examined. Here, the body weights were assumed to be subject to normal distribution, and the average weight and standard deviations of weight of Japanese adults were calculated from the data shown in the National Nutrition Survey in Japan(20). The calculated average weight is 61.5 and 52.0 kg for male and female respectively, and the standard deviations 9.2 and 7.9 kg. These values agree with the data of Tanaka(17). Figures 4 and 5 show the variations of some representative organ doses for a plane source in the ground as a function of body weight in the range up to two-sigma deviation. The organ doses for volume source in air show nearly the same degree of difference. Within a two-sigma deviation of the normal distribution, 95% of the samples are contained, therefore, most of the adult population is included. The organ doses were normalized to the doses for persons of average weight. Four types of organs for each sex were selected to examine the tendency of dose differences : (1) an organ greatly affected by the body weight because it is located deep inside the body ; (2) an organ little affected because it is on the surface of the body ; (3) an organ moderately affected ; and (4) the whole body. Any risk-weighted average dose like effective dose equivalent is expected to be included between the minimum and maximum sloped lines in Figs. 4 and 5. Within a one-sigma standard deviation, the variations of organ doses were found to be quite small. Over 100 keV in sources (a) and (b), the organ doses vary only within 5%, and even at 50 keV the variation is within 10%. The variations become larger in the range of two-sigma, however, are within 10% with sources over 100 keV and within 20% at 50 keV. In the case of the natural source in the ground (source (c)), the organ doses vary within 10% in the range of two-sigma, which again is not large. From these data, it is concluded that the variation of organ doses with differences in body weight is within 10% in general. When

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Fig. 4

Variations of male organ doses due to differences in body weight for infinite plane source in ground (source (b))

Fig. 5

the initial g-ray energy is extremely low the variation may reach 20%. The variation could be larger in the energy region under 50 keV. However, the exposure to low-energy ays is not significant in the natural gr environment, since the emitted g rays decrease drastically before they reach the body because of the high probability of reactions with environmental materials. 4. Age The change of organ doses due to a person's age will be examined in this section. The average body weights of Japanese of different ages were obtained from the National Nutrition Survey in Japan(20). Since the average body weights do not show significant differ-

Variations of female organ doses due to differences in body weight for infinite plane source in ground (source (b))

ences between of 12 years, represent the

male and female up to an age the mean value was used to body weight for each age. The

organ doses for ages 0, 1, 3, 6, 9, 12 years were calculated using the representative body weights of 4.2, 10.6, 14.8, 21.2, 29.6 and 42.9 kg, respectively. The organ doses for each age were normalized to the doses for the average adult, which were calculated using the mean weight between a male and a female, except for the organs particular to each sex such as ovaries, breasts and testes. The variations of normalized doses with energy for some important organs are shown in Fig. 6 for a plane source in the ground

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1991)

Fig. 6

Variations of organ doses due to age for infinite plane source in ground (source (b))

(source (b)). In addition, the maximum, minimum and arithmetic mean values of the normalized doses for important 22 organs are shown in Table 6 for a plane source in the ground (source (b)), and in Table 7 for a Table 6

natural source in the ground (source (c)). The normalized organ doses for a volume source in the air (source (a)) are similar to those for a plane source in the ground (source (b)). Generally speaking, in sources (a) and (b),

Change of organ doses due to age for infinite plane source in ground (source (b))

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cents over 12 years old are very close to those for adults ; (2) the organ doses change greatly between a newborn and a 1-year-old child ; and (3) between the age of 1 and 12 years the normalized organ doses for children change approximately in inverse proportion to age. The normalized organ doses for natural sources (source (c)) are similar to those for 1 MeV g rays from the other sources. This was expected since at 1 m height the air kerma weighted average energies of g rays from the U series, the 232Th series and 40K are 238 all nearly 1 MeV.

Change of organ doses due to age for natural source in ground

(source

Sci. Technol.,

(c))

V. the differences of organ doses increase greatly as the energy decreases under 100 keV. However, for organs located near the body surface like the skin the differences are not large even under 100 keV. Also, for ages over 12 years, the differences do not change so much even under 100 keV. Since the body size of a 12-year-old child and an adult do not differ greatly, the difference in the shielding effect is small even for low-energy g rays having a high probability of interaction. The normalized doses vary little in the 100 keV to 3 MeV energy range. The dose difference due to age depends greatly on organs. For organs located near the body surface such as skin or the breasts, the difference is quite small. For example, the skin dose for a newborn baby coincides within 15% of that for an adult at all energies. On the other hand, for organs located well inside the body the difference is large. In the low-energy region, the doses differ between a newborn baby and an adult by a factor of 2 to 3 at maximum. In the energy range over 100 keV the maximum difference is about 70%. These also were observed in the previous work(8)(9). The normalized organ doses show a similar tendency for lungs, whole body and effective dose equivalent. It must be noted, however, that the absolute values are much different among these three doses. With respect to age, the following points were elucidated : (1) organ doses for adoles—46—

CONCLUSION

Organ doses for persons having five different weights were calculated using anthropomorphic phantoms. It was suggested that body weight is the main factor with respect to organ doses for g rays entering symmetrically around the body axis. The formula expressing organ doses as a function of body weight was introduced, and the coefficients were determined using the organ doses calculated for the three typical environmental sources. Then, on the assumption that this formula holds for any human being, the variation of organ doses was investigated changing body weight as a parameter. Differences in organ doses due to race and sex were found not to be significant. When doses for the average Caucasian and Japanese are considered, the difference is usually within 5%, and never exceeds 10% even for low-energy g rays. Usually, differences in body weights of adults up to two-sigma standard deviation cause variations of organ doses within 10%. However, the variations could reach 20% in the low-energy region. Differences in organ doses due to age greatly depend on the specific organ. The differences are large for deep-internal organs such as ovaries and intestines. The maximum difference found in this study was a factor of 2 to 3 which was observed between an adult and a newborn baby for 50 keV g rays. Over 100 keV the difference is within a factor of 2. For organs located near the body surface

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such as the skin, the difference is less than 15%. Organ doses for adolescents over 12 years old agree with those for adults within 15%. Many different human beings live in the world. So the concept of expressing organ doses as a function of body weight needs to be verified by more evidence. In some specific cases, for example lung doses for low-energy ays, some other factors besides body g r weight should be considered to obtain accurate organ doses. However, a generic view is essential to systematically understand these phenomena, so the relationship expressing organ doses and the variation of organ doses derived from the relationship function in this paper are expected to provide useful information for dose evaluations in the environment. REREFERENCES (1) SNYDER,W. S., FORD, M. R., WARNER,G. G., FISHER,H. L. : J. Nucl. Med. 10, Suppl. No. 3 (1969). (2) KOBLINGER, L.: Hungarian Acad. Sci. Central Res. Inst. Phys. Rep. KFKI-71-12, (1971). (3) KRAMER, R., ZANKL, M., WILLIAMS, G., DREXLER,G. : GSF-Bericht S-885, (1986). (4) ICRP Publ. 23, (1975). (5) O'BRIEN, K. : Radiat. Prot. Dosim., 3, 3~11 (1982). (6) CRISTY, M., ECKERMAN,K. F.: ORNL/TM-

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