Tomographic Anthropomorphic Models. Part IV: Organ Doses for Adults due to Idealized External Photon Exposures

Transcription

1 Tomographic Anthropomorphic Models Part IV: Organ Doses for Adults due to Idealized External Exposures M. Zankl, N. Petoussi-Henss, U. Fill, D. Regulla Institut für Strahlenschutz November 2002 GSF-Bericht 13/02

2 Contents Abstract Introduction The voxel phantoms Monte Carlo calculations Doses to bone and red bone marrow Results and Discussion Description of the data presented Comparison of conversion coefficients between voxel and mathematical models Comparison of conversion coefficients for voxel models Conclusions References Appendix A Conversion coefficients for anterior-posterior (AP) broad parallel beams 35 Appendix B Conversion coefficients for posterior-anterior (PA) broad parallel beams 63 Appendix C Conversion coefficients for left lateral (LLAT) broad parallel beams 91 Appendix D Conversion coefficients for right lateral (RLAT) broad parallel beams 119 Appendix E Conversion coefficients for rotational (ROT) broad parallel beams 147

3 1 Abstract The present report contains extensive tables and figures of conversion coefficients of organ and tissue equivalent dose, normalised to air kerma free in air for voxel anthropomorphic phantoms and for standard geometries of external photon radiation, estimated with Monte Carlo techniques. Four realistic adult voxel phantoms were used for the calculations, based on computed tomographic data of real people: three male phantoms, two of them being of average size, one representing a big man, and one female phantom of a tall and somewhat over weighted woman. The geometries considered were broad parallel beams, supposing to simulate standard occupational exposures. The directions of incidence are anterior-posterior, posterior-anterior, left lateral, right lateral and a full 360 rotation around the body's longitudinal axis. The organ dose conversion coefficients given in this catalogue were calculated using a Monte Carlo code simulating the photon transport in the voxel models. Conversion coefficients are given for the equivalent dose to 23 organs and tissues and for monoenergetic photons with energies between 10 kev and 10 MeV. The primary raw data from the Monte Carlo calculation are presented in tables and figures. For comparison purposes, in the figures fitted data of the conversion coefficients for the mathematical phantoms Adam and Eva (both consisting of organs with the so-called reference masses) are also shown. The variation of the conversion coefficients from voxel to mathematical model as well as from voxel to voxel model is extensively described. The positioning of some organs is compared for the voxel and mathematical models and some deficiencies of the latter ones are revealed. The impact of the size of the model as well as the individual variation on the conversion coefficients is also discussed.

4 2 1 Introduction Models of the human body are needed in order to estimate the radiation dose received by the different tissues or organs of the body resulting from an irradiation. This could be an irradiation of a patient due to medical purposes, for example a diagnostic x-ray examination, or an irradiation that a person receives at his working place, i.e. a radiation worker at a nuclear power station or at several other places where radiation sources are used, e.g. in radiology. Furthermore, irradiations to all of us (i.e. general public) occur due to the natural environment and often due to man-made contaminations. For all these cases the radiation doses absorbed in the organs of the human body have to be estimated in order to estimate the risk connected to these irradiations. The International Commission on Radiological Protection (ICRP) elaborates since more than 50 years a system for radiological protection, based on quantities, concepts and basic recommendations. The concept of radiation protection is based on the justification, optimisation and limitation of the radiation exposure. This concept resulted in a dose limitation system for occupational and man-made environmental radiation exposures to ensure that the radiation risk would not exceed legally established limits. The quantity to be limited in radiation protection of occupationally exposed persons is the effective dose, E, which is a combination of so-called equivalent doses of several organs and tissues of the body that are considered more radiosensitive and therefore critical. E = HT wt = T T where H T is the mean organ equivalent dose, the quantity assumed related to the stochastic radiation risk. It is derived from the mean organ absorbed dose, D T, i.e. the total amount of deposited in an organ (or tissue), T, per mass of the organ, by multiplying with a radiation weighting factor, w R reflecting the relative biological effectiveness of the incident radiation. The organs and tissues together with their respective tissue weighting factors w T can be found in ICRP Publication 60 (ICRP 1991) and are shown in Table 1. D T w R w T

5 3 Table 1: Tissue weighting factors, w T, for the evaluation of effective dose, E. Tissue or organ Tissue weighting factor, w T Gonads 0.20 Colon 0.12 Lungs 0.12 Red bone marrow 0.12 Stomach 0.12 Bladder 0.05 Breast 0.05 Liver 0.05 Oesophagus 0.05 Thyroid 0.05 Bone surface 0.01 Skin 0.01 Remainder * 0.05 * The organs constituting the remainder are the following: adrenals, brain, small intestine, kidneys, muscle, pancreas, spleen, thymus and uterus. The equivalent dose conversion coefficients for the remainder are evaluated as arithmetic mean values of the conversion coefficients for these nine organs. E is then the quantity to be limited in radiation protection of occupationally exposed persons. Following new and extended epidemiological data, the ICRP attributes risks for stochastic effects of R = Sv -1 to a population of both sexes and all ages, and R = Sv -1 to a working population (ICRP 1991), where the unit sievert refers to the effective dose E. This means, by multiplying a specific value of effective dose (in sieverts) by 7.3 or 5.6, the percentage probability of a resulting detriment could be evaluated. Therefore, it is evident the necessity to estimate the organ and tissue equivalent doses and the effective dose in order to be able to judge the risk of an irradiation. As neither organ equivalent doses nor effective dose are measurable, the so-called conversion coefficients relate organ doses to measurable dose quantities.

6 4 To estimate the equivalent doses in the body and consecutively the risk to a person or population, there are two approaches, an experimental and a theoretical one and both require representations of the human body, socalled phantoms or models. The experimental determination is very difficult whereas the mathematical modelling of an exposure has been proved to be extremely flexible and powerful. For this purpose, a series of models of the human body were designed in the past, together with computer codes simulating the radiation transport and deposition in the body. The phantoms, i.e. the models used for the representation of the human body in dose calculations, can range from simple geometric forms such as spheres, cylinders or slabs to complex representations of detailed anatomical features. Such complex models, used since 1966 for the estimation of organ doses are the so-called mathematical phantoms, which are models whose body organs and tissues are described by mathematical expressions representing planes or cylindrical, conical, elliptical or spherical surfaces. This model was named MIRD after the initials of the Medical Internal Radiation Dose Committee of the US Society of Nuclear Medicine where it was initially developed (Snyder et al 1969, 1979). From this, several paediatric models were derived to represent infants and children of various ages, for example those from Cristy (1980) and Cristy and Eckerman (1987 a-f). As an improvement to these hermaphrodite model, separate male and female adult mathematical models have been introduced by Kramer et al (1982) called Adam and Eva. More recently, four phantoms representing the adult female, non-pregnant and at 3 stages of pregnancy, were elaborated by Stabin et al (1999). All these models represent an average or standard individual as defined by ICRP s data on Reference Man (ICRP 1975). Obviously, these mathematical models, although they have a large number of organs and their respective masses are in accordance with the ICRP data on Reference Man, are rigid, stylised and unrealistic, concerning organ shape and location. The development of anatomically realistic mathematical models from medical imaging data started as an extension and improvement to these earlier phantoms. These models use computed (CT) or magnetic resonance (MR) tomographic data of real persons to provide three-dimensional representations of the human body and comprise a large number of volume elements (voxels) all of the same size but with differing composition according to the organ to which they belong.

7 5 Among other laboratories, GSF started the development of voxel models covering various ages (Zankl et al 1988, Veit et al 1989). Such models have been the subject of increasing interest and acceptance, and others have been developed elsewhere using CT or MR imaging. Dimbylow (1996) elaborated a male adult whole body voxel phantom from a set of serial MRI slices from one subject. More recently, a male adult voxel phantom has been constructed from high-resolution photographic images of the Visible (Spitzer and Whitlock, 1998, Xu et al 2000). Partial body models were also developed: Zubal et al (1994, 1996) developed a head-to-torso phantom as well as a head phantom with fine resolution whereas Caon et al (1999) constructed a trunk model of a 14-year-old female. For almost thirty years the mathematical MIRD-type phantoms, based on the anatomical data of the reference man as defined in ICRP Publication 23 (ICRP 1975) found wide acceptance and were used from several groups for numerous applications in the field of radiation protection to compute organ doses from external and internal exposures, environmental, medical and occupational., electron as well as neutron exposures were considered, together with Monte Carlo codes simulating the transport of radiation in the body. Conversion coefficients for external radiation from idealized geometries are compiled in a joint ICRP/ICRU Publication (ICRP 1996, ICRU 1998). Concerning photon external exposures, a large amount of data appearing at the above publications, stem from the GSF and were estimated using the MIRD type phantoms Adam and Eva (Zankl et al 1997). In view of the advantages of the new voxel models, discussed below, new sets of conversion coefficients using adult male and female voxel models were calculated and are presented here, for idealized geometries.

8 6 2 The voxel phantoms A recent overview of the GSF voxel phantoms has appeared in Petoussi- Henss et al (2002). Saito et al (2001) describe the voxel phantom of a Japanese male. A detailed presentation of Donna will appear soon (Fill et al in preparation). Four voxel phantoms were used for the present calculations: three of them were constructed at the GSF (Zankl and Wittman 2001, Petoussi-Henss et al 2002, Zankl et al 2002) and the fourth one was constructed at Yale University (Zubal et al 1994). Table 2 shows the voxel phantoms used, giving also the age, height and weight of the individual from whose data the phantoms were constructed. Figure 1a shows the male phantom Golem, shown for comparison purposes together with the mathematical model Adam (Figure 1b). The GSF voxel phantoms contain a large number of organs and tissues including all ICRP critical organs except bone surface. Table 3 shows the masses of some selected organs of these phantoms. In the same table, the masses of the ICRP 23 Reference Man are also shown. a b Figure 1: View of selected organs of the male phantom Golem and the male mathematical model Adam

9 7 Table 2: Voxel phantoms used for the present calculations Name Gender Age Type Weight (kg) DONNA female 40 years wholebody, with standardized GI tract Height (cm) Size of voxel (mm 3 ) Nr of organs GOLEM male 38 whole-body years Voxelman male? head to (65.2) 2 (170) mid-thigh VISHUM male 38 years from knees upwards (87.8) (125) Constructed at Yale University (Zubal et al 1994) 2 value in parenthesis indicates the weight/height of the phantom (partial body), whereas the value without the parenthesis indicates the weight/height of the patient. Voxelman was constructed at Yale University (Zubal et al 1994, 1996). This is the model of an adult male of height 178 cm and weight 70.2 kg who had been scanned from head to upper thigh using computed tomography (CT). The external dimensions are similar to the Reference Man data for male persons (ICRP 1975). A total number of 54 different organ and tissues was defined in this model, comprising those organs considered radiation-sensitive by ICRP (ICRP 1991), except thymus. Red bone marrow was segmented in the long bones, and "skin" comprises also the subcutaneous adipose tissue. The voxel dimensions given in the literature are not unequivocal. For the present work, a voxel height of 4 mm was assumed, resulting in an overall height of 94.4 cm from head to upper thigh, which seems reasonable compared to the reported total body height. From the description of the scan geometry (image diameter: 480 mm, original scan resolution: 512x512 pixels) and the reported data reduction to 128x128 pixels, a voxel side length of 3.75 mm in the image plane was reconstructed.

10 8 Golem (Zankl and Wittmann 2001) was segmented from the whole body CT data of a 38-year old male patient of 176 height and 68.9 kg weight, i.e., a person similar to the male Reference Man in his external dimensions. Donna (Fill et al in preparation) is the model of a 40-year old female patient of 176 cm height and about 80 kg weight; that means she is taller and heavier than the female Reference Man but most of her organ masses are in good agreement. Donna has a standardized GI tract which has been segmented from a high resolution CT data set of the intestinal region of another female patient and was then fitted into the pelvic region (Fill et al in preparation). The Visible was constructed at GSF from CT data from the Visible Project of the American National Library of Medicine. This project provides CT and MRI as well as high-resolution photographic image data of the donated body of an executed man from Texas, USA. The model comprises the body from head to knees and has a voxel resolution of 0.91x0.94x5 mm 3. To best fit with the photographic image data, the pixel side lengths were determined by comparing the front-to back and left-toright distances of the CT and the photographic data set in several images at corresponding height positions. For the photographic images, pixel dimensions of 0.33x0.33 mm 2 were assumed. The fact that the pixel dimensions thus reconstructed for the CT images differ slightly in width and depth indicates the probability of a moderate distortion of either the CT or the photographic data set. Another possible explanation might be that certain degradation processes may have started in the dead body between CT scanning and cryosectioning. This would mean that part of the differences in the image sequences are due to changes in the body itself, not to differences caused by the image modalities. Another voxel model of the same individual exists, called VIP-Man, segmented from the photographic images (Spitzer and Whitlock 1998, Xu et al 2000). For all GSF voxel models, the content of red bone marrow was estimated for each skeletal voxel separately from its original grey value and the location of the bone voxels. That means, following literature data (Cristy 1981, ICRP 1995), all bone marrow below mid of humeri and femurs was assumed inactive, i.e., yellow. At all other locations, the marrow was assumed as mixture of equal volumes of red and yellow bone marrow. This method is described in more detail in Zankl and Wittmann (2001) and results in a distribution of the red bone marrow among different bones that agrees reasonably well with literature data (Cristy 1981, ICRP 1995).

11 9 Table 3. Organ and tissue masses (g) of the voxel phantoms whose conversion coefficients are shown in this report. For comparison purposes, the masses of the ICRP Reference Man are also shown (ICRP 1975, ICRP 1995). Organ or tissue Golem Voxelman Visible Donna ICRP Reference Man ICRP Reference Female adipose tissue (26040.) adrenals bladder wall Bladder contents brain breast colon wall eye lens gall bladder wall heart kidneys liver lungs muscle (21160.) 1 (40970.) oesophagus ovaries pancreas red marrow skeleton (6448.) 1 (8841.) skin (18000.) 1 (1950.) small intestine cont spleen stomach wall stomach contents testes thymus thyroid uterus yellow marrow parentheses indicate that corresponding mass of the lower legs is missing 2 glandular tissue only 3 wall (muscle) only 4 not separated

12 10 The main differences of the voxel to MIRD-type phantoms are summarised in Table 4. The more significant advantage of the voxel phantoms towards the mathematical ones, is their realism concerning anatomy: the organ shape as well as the organ location is realistic, since computed tomographic images from a real person were employed for their construction. The distance between the organs is an important parameter, particularly for internal dosimetry where several organs are the so-called source organs and all the others are the targets. The realism of the organ shape is demonstrated in figure 2 where a CT slice of Golem is appearing, together with a cross-section of the MIRD-type phantom Adam. Table 4: Principal differences of voxel to MIRD-type phantoms Organ shape Mathematical reduced to a (over-) simplified form Tomographic / voxel as identified on the slice images; realistic Organ size rigid; representative Depending on individual; variable, for each dimension independently (influence of body mass on doses) Organ topology Often unrealistic realistic Skeleton homogeneous mixture of all skeletal components; variation of red bone marrow distribution among different bones and at various ages considered amount of bone marrow and hard bone assessed from the CT data, for each bone voxel separately, i.e. with high resolution

13 11 Figure 2. Comparison of an axial slice of the voxel phantom Golem (right) to the corresponding one of the mathematical phantom Adam (left). Organs shown: adrenals, liver, lungs, spleen, stomach wall, stomach contents. 3 Monte Carlo calculations The radiation transport in the human phantoms was calculated using a Monte Carlo code following individual photon histories (Veit et al 1989). For each single particle history, the parameters influencing its actual course were selected randomly from their probability distributions. The radiation processes considered inside the human body were photoelectric absorption, Compton scattering and pair production. The cross section data for the photon interaction processes for single elements were taken from a library of the ORNL (Roussin et al 1983). From these elemental data, cross section data for body tissues were evaluated according to chemical composition and density. The media considered for the present calculations were hard bone, red and yellow bone marrow, muscle tissue, skin, soft tissue, adipose tissue, lung tissue and air. The tissue compositions were those described in ICRU Report 44 (ICRU 1989) and are shown in table 5; the composition of "soft tissue" was averaged from those of brain, GI tract, heart, kidneys, liver, ovaries, pancreas, spleen, testes and thyroid. The transferred at a point of inelastic photon interaction was assumed to be deposited at that point; secondary electrons were not pursued further ("kerma approxima-

14 12 Table 5: Elemental compositions (percentage by mass) and densities of body tissues (from. ICRU Report 44 (1989) Tissue 1 H 6 C 7 N 8 O 11 Na 12 Mg 15 P 16 S 17 Cl 19 K 20 Ca 26 Fe ρ (g/cm 3 ) Hard (=cortical) bone Cartilage Skin Blood Muscle tissue Soft tissue a) Red bone marrow Breast (mammary gland) Yellow bone marrow Adipose tissue Lung tissue a) The composition for soft tissue was evaluated as an average of the compositions for brain, GI tract, heart, kidney, liver, ovary, pancreas, spleen, testis and thyroid

15 13 tion"). The main advantage of this technique is its high calculation speed, since the pursuit of secondary particles is rather time-consuming, especially in the high- domain, where the ranges of these particles are long. The kerma approximation is valid as long as there is approximate secondary particle equilibrium, which can be supposed for all points located well within the body, due to the moderate differences of the photon cross sections for the tissues in the human body and in view of the macroscopic approach considering mean organ and tissue doses. However, for superficial organs, such as skin and testes, the kerma approximation leads to overestimations of up to a factor of two at photon 10 MeV; for these organs, it is valid only below approximately 1 MeV (Saito et al 2001, Chao et al 2001). Nevertheless, since the conversion coefficients calculated with the kerma approximation are overestimations of the true values, they are still useful for radiation protection purposes where conservative estimates usually are acceptable. The irradiation conditions considered in this study were idealized beam geometries commonly assumed to represent occupational exposures, i.e., irradiation by broad parallel beams of monoenergetic photons. The directions of photon incidence were anterior-posterior (AP), posterior-anterior (PA), left lateral (LLAT), right lateral (RLAT) and a full 360 rotation of the photon beam around the longitudinal axis of the body (ROT). The field size comprised the total width and height of the body. The monodirectional geometries are considered to approximate radiation fields produced by single sources and particular body orientations, whereas the ROT geometry is an approximation of a person who moves randomly in the radiation field of a single source, or irradiation from a widely dispersed planar source. The photon energies considered were monochromatic and ranged from 10 kev to 10 MeV. The absorbed dose to an organ or volume was evaluated as the total amount of deposited in this organ or volume, divided by its mass. The radiation weighting factor is unity for photons of all energies (ICRP 1991), the equivalent dose is therefore numerically equal to the absorbed dose. As the amount of deposited depends on the number of photon histories simulated, a more meaningful dose quantity is evaluated by normalizing the resulting equivalent dose to a measurable quantity which is also proportional to the number of histories; therefore, the dose values in this study are not expressed as absolute values of equivalent dose but rather in the form of conversion coefficients by normalization to the quantity air kerma free-in-air.

16 14 For each irradiation, million photon histories were simulated. This led to relative statistical uncertainties (in terms of coefficients of variance) for the calculated organ dose conversion coefficients that were generally below approximately 2% for photon energies above 30 kev. For small organs, such as adrenals, breast (glandular tissue only), oesophagus, ovaries, testes, thymus, thyroid and uterus, the coefficients of variance sometimes amounted up to 7%, predominantly for geometries where the organ in question was oriented away from the radiation beam, and for eye lenses in PA geometry up to 37%. For photon energies below 30 kev the coefficients of variance were higher than for the higher energies and could amount up to 100%, if the deposition is due to one single event. In these cases, however, the organ doses are so small that they can be neglected. For large, extended organs, such as muscle, red bone marrow, skeleton and skin the coefficients of variance were below 0.3% for photon energies above 30 kev, and up to 4% below 30 kev. 3.1 Doses to bone and red bone marrow Further approximations were made to derive the doses to bone surface and red bone marrow: Bone surface is a thin layer typically about 10 μm in thickness (ICRP 1975) of tissue covering the bones. Being far beyond voxel resolution, it cannot be directly modeled in voxel models (and has not been modeled in mathematical body models either). Below approximately 300 kev, the cross sections for bone are considerably higher than those for soft tissue. Consequently, the dose to bone surface is significantly enhanced by an increased production of secondary electrons in the bones, compared to the dose to soft tissues beyond the range of these secondary electrons, such as the soft tissue organs. This enhanced dose to the tissue closely adjacent to bones is, however, not as high as the mean dose to the bone (Drexler 1968); the latter is, consequently, a conservative estimate of the dose to the bone surface in this photon range. For higher photon energies, the cross sections of bone and soft tissues have a similar magnitude, and the doses are similar as well. Therefore, no attempt has been made to exactly determine the dose to bone surface; instead, the mean dose to the skeleton (including hard bone, red and yellow bone marrow) was taken as a conservative estimate of this dose.

17 15 As mentioned above, for each voxel in the skeleton, the relative contents of hard bone, red and yellow bone marrow were estimated from the original grey values and the location of the bone voxels. Following literature data (Cristy 1981, ICRP 1995), all bone marrow below mid of humeri and femurs was assumed inactive, i.e., yellow. At all other locations, the marrow was assumed as mixture of equal volumes of red and yellow bone marrow. Based on these volume ratios, the cross sections were combined from those for hard bone, red and yellow bone marrow for each bone voxel individually, and also the mass of each bone voxel was evaluated using the densities of the three compounds and their relative volume contribution. For calculating the dose to the red bone marrow, the following procedure, described by Zankl et al (2002), was adopted: since each bone voxel was considered as composed of various proportions of hard bone, red and yellow bone marrow, each amount of deposited in a bone voxel was also considered as distributed among these constituent tissues. In a first step, the amount was subdivided to the different tissues using the mass ratios of these tissues in the voxel. In a second step, the difference of the mass absorption coefficients of these tissues was accounted for: the mass absorption coefficient of a voxel under consideration was combined from the individual ones, and then the ratio of the mass absorption coefficients for red bone marrow and for the mixture was taken as a correction factor for the deposited in red bone marrow. Furthermore, the dose enhancement to red bone marrow due to an increased amount of secondary electrons released in the hard bone proportion of a voxel was considered by using correction factors suggested by Spiers (1969) that are based on measured chord length distributions in bone marrow cavities. In summary, the deposited in red bone marrow at the occasion of an individual photon interaction in a bone voxel, is evaluated as E rbm = E b r rbm μen ( E ρ ph μen ( E ρ ) rbm ph ) b S( E ph ), (1) where E rbm is the amount of deposited at the occasion of a photon interaction in the red bone marrow proportion of a voxel, E b is the amount of deposited in the entire bone voxel, r rbm is the mass proportion of red bone marrow in the respective bone voxel, E ph is the photon before the interaction, and S(E ph ) is the dose enhancement correction factor (Spiers 1969) at photon E ph ;

18 16 μen μen μen μen ( E) = rhb ( E) + rrbm ( E) + rybm ( E),(2) ρ b ρ hb ρ rbm ρ ybm where r hb, r rbm and r ybm are the mass proportions of hard bone, red and yellow bone marrow in the bone voxel under consideration, ( E) is the μen ρ mass absorption coefficient at photon E for medium i, (i {hb, rbm, ybm} indicating the medium hard bone, red bone marrow or yellow bone marrow, respectively), and i r r + r =1. (3) hb + rbm ybm E b is used for calculating the dose to the skeleton, E rbm for calculating the dose to red bone marrow. For Voxelman the application of the above method was not possible since the original grey values were not available to the authors of the present work, thus the correction factors S(E ph ) from Spiers (1969) have been applied to the deposited in the segmented red bone marrow regions. 4 Results and Discussion 4.1 Description of the data presented The organ doses were evaluated in the form of so-called "dose conversion coefficients", i.e., as mean organ equivalent doses normalized to a measurable quantity. The normalization quantity for the idealised geometries is the "air kerma free-in-air"; the conversion coefficients are given the unit Sv Gy -1. The organs for which conversion coefficients are given in this report are those defined as sensitive to ionising radiation by ICRP (1991). For comparison purposes, also a risk-weighted whole body equivalent dose quantity was evaluated, for each voxel model separately. This quantity was calculated as weighted average of the single organ equivalent dose conversion coefficients, along the ICRP definition of effective dose, E (ICRP

19 ). That means, each individual organ equivalent dose conversion coefficient was multiplied with the appropriate tissue weighting factor w T as given in ICRP Publication 60 (ICRP 1991), and these products were summed up. The dose to the remainder was evaluated as arithmetic mean of the single organ doses, and, following ICRP Publication 67 (ICRP 1993), the upper large intestine was not included among the remainder organs, thus reducing their number to nine. However, since each model is either male or female, not all gender-specific organs could be included in the evaluation of this model-specific dose quantity. For the male models, dose to breast was not included, and since the remainder comprises also the uterus the remainder dose was evaluated as the arithmetic mean of the doses for eight organs only. Consequently, the resulting dose quantity is, although similar to effective dose, in fact a different quantity. For the sake of clarity, it was, therefore, given the name H <model>. 4.2 Comparison of conversion coefficients between voxel and mathematical models The anatomical differences between voxel and MIRD-type phantoms, discussed in section 2, explain the deviation of the voxel conversion coefficients to those obtained with the mathematical phantoms. Since the mathematical models Adam and Eva represent male and female reference persons, their organ dose conversion coefficients would be expected to lie within the range of data spread out by the individual voxel models of this work, ideally close to those of Golem and Voxelman who have external dimensions similar to those of Reference Man. For many organs, the conversion coefficients for the mathematical models are indeed within the range of the individual voxel values, for example for brain and pancreas PA irradiations. For other organs and irradiation directions like thyroid AP, kidneys AP, lower large intestine PA, and pancreas RLAT, the conversion coefficients for Adam and Eva are more oriented towards the edges of the range of values for the other organs shown in the above figures, thus indicating that these organs are in a somewhat extreme location in the mathematical models. Although it is obvious that the number of voxel models available for this study is not sufficient to draw conclusions that would be statistically significant, we believe that their spread in body dimension is large enough to give at least an indication of the spread of individual organ equivalent dose conversion coefficients that may be expected for persons of different statures. It is ensured at least that the individual variability of organ doses cannot be smaller than that found in this work.

20 18 An extended overview of the comparison between the organ equivalent dose conversion coefficients for the mathematical and 7 voxel models is given in Zankl et al (2002). A detailed interpretation of these results and conclusions drawn about the appropriateness of the organ topology in the mathematical models are given in the following on the basis of the unidirectional geometries. (Since ROT geometry is an average of all angles of incidence, the differences are more moderate than those for the unidirectional geometries, and the reasons for the differences are the same.) For the photon energies up to ca. 30 kev, where the photons have only little ability to penetrate, the organ dose conversion coefficients depend strongly on even slight individual variations, and the differences may amount to hundreds of per cent. However, the conversion coefficients are very small in this range, and their statistical uncertainty is large compared to the values at higher photon energies. For photon energies above 1 MeV the penetration is relatively high, and individual differences are of minor consequence. Therefore, in the following the conclusions on the influences of individual anatomy on the calculated organ doses refer to the intermediate photon energies, between 60 and 200 kev, where many of the conversion coefficients have their highest values. The organs discussed appear in an alphabetical order and the conclusions were drawn not only on the basis of the 4 voxel phantoms whose conversion coefficients are presented in this report, but also on three additional ones (Zankl et al 2002, Fill et al in preparation). Adrenals: For the adrenals, the equivalent doses for the mathematical models are comparatively low for AP and high for PA photon incidence; that means these organs are at an extremely posterior location, compared with the organ topology found in the voxel models of this study. The doses calculated for the mathematical models are, however, inside the range of values for the voxel models; thus, though extremely posterior, the location of the adrenals does not seem to be outside the spread found among the persons included in this study. Bladder: For the bladder, the equivalent doses for Adam and Eva are high for all geometries except PA; that means they are on average extended more towards the front and both sides than in the voxel models. This is probably not a deficiency of the mathematical models: it can be rather assumed that the bladder occupies less than average space in the voxel models due to having been emptied shortly before acquisition of the CT scan.

21 19 Brain: The location of the brain in the mathematical models seems to agree well with that in the voxel models when concluded from a first glance of the conversion coefficient; it seems just less than average shielded against irradiation from AP. This is, however, due to a slight deficiency in the mathematical models: the brain is represented by the volume contained in the skull and the cerebellum has not been included. This part of the brain, however, is shielded against AP irradiation by the facial skeleton, thus reducing the AP conversion coefficients for the whole brain for the more realistic model geometries. Breast: The slight difference in the breast dose is probably due to a different representation of the tissue under consideration in both model types: whereas for Eva the mean dose to the entire breast has been calculated, for the voxel model Donna the dose to glandular tissue only has been considered. Colon: The colon seems at an "average" location in the mathematical models with respect to AP irradiation, and more than average shielded against RLAT irradiation, whereas the colon dose for the mathematical models overestimates the maximum dose for the voxel models by 4-10% for PA irradiation, and underestimates the minimum voxel model dose by 12-18% for LLAT irradiation. With respect to organ topology this means that the colon is located too far in the back and less extended to both sides (especially towards the left side) in the mathematical models. More details are given below for the lower and upper large intestines, which are the two parts of the colon. Eye lenses: The organ equivalent dose conversion coefficients for the eye lenses evaluated for the mathematical models are inside the spread of values calculated for the voxel models for all geometries involved in this study. Kidneys: The kidneys are more than average shielded against AP irradiation in Adam and Eva and moreover the maximum dose among the voxel models is overestimated by 16-26% for PA irradiation in the mathematical models. This means that the kidneys are clearly located more in the front in reality than in the mathematical models. Liver: The liver doses for mathematical and voxel models are in good agreement only in relation to RLAT irradiation; for AP and ROT, the con-

22 20 version coefficients for the mathematical models are high, for LLAT they are low, and for PA they overestimate by 6-13% the respective values for voxel models. The low values for LLAT, combined with average values for RLAT geometry, must be due to the highly eccentric elliptical cross section of the mathematical models (including both arms) that leads to a rather large lateral diameter. Furthermore, the high values for AP together with an overestimation for PA irradiation result from this peculiar shape that leads to small front-to-back diameters at the sides of the trunk (and, consequently, a tendency to too shallow locations for laterally positioned organs) compared to the realistic cross sections that tend to be more "rectangular". Lower large intestine: For the lower large intestine (i.e., descending and sigmoid colon including rectum), the conversion coefficients for Adam and Eva are high compared to those for the voxel models for AP and PA irradiation, and low for both lateral directions. Since a large part of this organ is also placed at one side of the body, this is again due to the small frontto-back diameter at the sides of the trunk together with the large lateral diameter. With respect to exact positioning it should be noted that the organs of the alimentary tract are highly variable also within an individual, so that an "erroneous" location of such an organ in the mathematical models could be concluded only on the basis of large deviations between mathematical and voxel models together with a low variability among the different voxel models, which is not the case. Lungs: For the lungs, the Adam and Eva conversion coefficients are high for all directions of photon incidence, and for PA they present an overestimation of 1-13%. This is due to the fact that the lungs extend to very superficial locations at their bottom in the mathematical models, whereas in reality are shielded by thicker layers of overlying tissues. Moreover, shielding by the ribs seems to be more effective in reality than in the mathematical models, especially for the PA geometry, and to some extent also for the lateral geometries. Muscles: The muscle dose conversion coefficients for Adam and Eva are high for all geometries, however without a true overestimation. Since in the mathematical models this tissue has not been explicitly modelled, the quality of the estimated dose depends strongly on the volume chosen to approximate the muscles. In the present study, for the mathematical models the entire amount of "tissue" not assigned to any other organ has been taken to represent muscle. As this volume is shielded from the incoming

23 21 radiation only by the skin, whereas in reality the muscles are shielded by subcutaneous adipose tissue, it is clear that the mean "tissue" dose results in a conservative estimate of the muscle dose. This should, however, not be considered as a deficiency of the mathematical models, since muscles were included among the tissues of interest long after the mathematical models had been designed, and due to the low weighting factor assigned to this tissue (as part of the remainder) no additional effort seemed necessary for a respective revision of the mathematical models. Oesophagus: Adam's and Eva's equivalent dose conversion coefficients for the oesophagus are low for AP and high for both lateral irradiation geometries; for PA they present an overestimation by 7-13%. This means that the oesophagus is at an extremely posterior location in these models; with respect to lateral irradiation, probably again the less effective shielding by the ribs is the reason for the comparably high doses for the mathematical models. Ovaries: On the basis of one voxel phantom only, no conclusion can be drawn for the location of the ovaries. However, a further study (Fill et al in preparation) including two more female voxel models indicated a possible exaggerated anterior location and a more lateral position of Eva's ovaries, compared to voxel models. Moreover, the ovaries seem not to be entirely symmetrical in the voxel models, probably as a consequence of the asymmetry of the intestines that occupy the larger part of the pelvic volume. Pancreas: The pancreas equivalent dose conversion coefficients for the mathematical models agree with those for the voxel models for LLAT, are low for RLAT, high for AP, and they present an overestimation of 7-24% for PA irradiation. The pancreas is an asymmetrical organ, and its lateral extension is greater in the mathematical models than observed in the voxel models. Since a larger proportion of this organ extends to a more lateral position in Adam and Eva, the reason for the conversion coefficients being high both for AP and PA irradiation is again due to the small front-to-back diameter at the sides of the trunk. With respect to its lateral position, its position to the right side agrees for all body models, whereas it extends further towards the left side in the mathematical ones. That this is, at a first glance, not properly reflected by the relation of the conversion coefficients for the lateral geometries, is again due to a bias resulting from the extremely large lateral diameter of the mathematical models leading to more shielding and, thus, to dose reduction for lateral radiations.

24 22 Red bone marrow and skeleton: The red bone marrow dose for the mathematical models is low for AP and high for both lateral geometries, whereas it overestimates the voxel values by 9-15% for PA geometry. On the other hand, the mean conversion coefficients for the whole skeleton are in good agreement for all geometries, thus indicating good agreement of the average shielding of the skeleton for mathematical and voxel models. Nevertheless, single bones appear to have more shallow locations in the mathematical models than in the voxel models. Spine and pelvis are also situated at an extremely posterior location in the mathematical models, whereas the ribs have a very superficial position with respect to lateral radiation. These bone groups, however, happen to contain the larger amounts of red bone marrow; consequently, the location of these bones influences the red bone marrow dose more than that of other bones. This leads to the observed differences in red bone marrow equivalent dose conversion coefficients for mathematical and voxel models. Skin: For skin dose, there is good agreement between the different body models, whereby the conversion coefficients for the mathematical models tend to be high for PA and both lateral geometries. Whereas the skin of the mathematical models is fully symmetrical with respect to AP and PA irradiation (with the exception of female breast only), the shapes of the voxel models are different: they are flatter at the posterior than at the anterior side, which is only partly due to their lying position and would be true also for standing persons. Therefore, the amount of skin at the front side is higher than that at the rear side of the body, and this leads to somewhat lower skin doses for PA irradiation than for AP. For lateral incidence, the whole amount of skin at the side of the body facing the radiation field is superficial due to the elliptical cross section for the mathematical models, whereas the more rectangular trunk cross sections of the voxel models result in self-shielding of the skin layers along the anterior and posterior body surfaces. Small intestine: The small intestine equivalent dose conversion coefficients for the mathematical models agree with those for the voxel models for AP and RLAT irradiation, are low for LLAT and overestimate the voxel values by 15-20% for PA irradiation. This means that the small intestine in Adam and Eva is highly shielded against radiation from the left side, again due to the large lateral diameter, and is more posteriorly located compared to the voxel models. The organs of the alimentary tract are, however, considered to have a large intra-individual variability, depending also strongly on the time after a meal and the composition of the latter.

25 23 Hence, the moderate discrepancies of the mathematical versus voxel model dose values (together with a relatively high inter-individual variability for PA and LLAT geometries among the voxel models) are not evidence enough to conclude an unrealistic position of the small intestine in the mathematical models. Spleen: The spleen dose conversion coefficients are generally high for the mathematical models, with the exception of RLAT irradiation, where they are low; for PA geometry, they present an overestimation of 2-7%. In the mathematical models the spleen is very shallowly located with respect to PA irradiation, and also its front-to-back extension is very small compared with the appearance in the voxel model. With respect to RLAT geometry, again the large lateral diameter of the mathematical models results in the high amount of tissue shielding the organ from radiation. Stomach: The stomach wall dose conversion coefficients for the mathematical models overestimate those for the voxel models by 11-16% for AP irradiation, are high for PA, low for RLAT and in the centre of the spread for LLAT irradiation. For the AP geometry, again an extremely shallow position of the organ is the reason for the overestimation and for PA the reduced front-to-back diameter leads to a reduced shielding and, consequently, relatively high doses. With respect to the lateral position, it seems at a reasonable depth below the left surface, but the distance to the right body surface is large, again due to the large lateral diameter of the trunk. For the RLAT geometry, the doses for the mathematical models present underestimations by 34-45%. Although the stomach location usually is considered to vary largely among different individuals and also in a single individual during the course of a day, the overestimation of the stomach AP doses for the mathematical models seems to be a systematic deviation, compared to the moderate variations between the voxel models, as can be judged from figure A.21. Testes: Adam's testes equivalent dose conversion coefficients overestimate those for the voxel models by 3-9% for AP irradiation, slightly underestimates them for LLAT irradiation and agrees with those for the voxel models for PA and RLAT irradiation. Although the Visible had only one testicle, there is no obvious reason for the lateral asymmetry found for Golem and Voxelman, except that none of the persons assumed an entirely symmetric position during the CT scan. The overestimation for AP irradiation is only small and probably due to the somewhat oversimplified representation of the male genitalia region in the mathematical model.

26 24 Thymus: The thymus doses for the mathematical models are high for most geometries, with the exception of PA irradiation where they are low. Thus, this organ seems a bit more superficially located in the mathematical models than in the voxel models, and at this shallow depth the lateral diameter of the mathematical models' trunk is small, leading thus to relatively high doses for lateral radiation incidence. Thyroid: Another interesting case is the thyroid: here the doses for the mathematical models are high for AP and low for PA irradiation, and for LLAT and RLAT incidence, they present overestimations by 44-58% and 40-49%, respectively. In relation to AP irradiation, the thyroid is situated at a shallow depth for all body models considered, for the mathematical models the depth is similar to the smallest depth found among the voxel models. The posterior part of the neck of the mathematical body models has not been designed too carefully and is, thus, rather stocky, corresponding to the stockier among the voxel models of this study, therefore resulting in comparatively low thyroid doses for PA irradiation. Furthermore, in the mathematical models the thyroid is located in the neck which is sharply separated from the trunk and has only a small lateral extension; in reality, however, the neck and trunk are not separated by a clear line, and the thyroid is located in the height of the shoulders where the lateral extension of the body is slowly decreasing with increasing height. Thus, the thyroid is much more shielded from lateral radiation incidence in a real body than in the mathematical models, which is the reason for the large overestimations observed for lateral photon incidence. Upper large intestine: For the upper large intestine (i.e., ascending and transverse colon), the equivalent dose conversion coefficients for the mathematical models present good estimates of the doses for voxel models for AP and RLAT irradiation, whereas they present overestimations by 15-27% for PA and underestimations by 26-37% for LLAT irradiation. The reasons are again the unrealistic front-to-back and lateral diameters of the trunk ellipses of the mathematical models, compared to the more rectangular cross sections of real bodies: as the upper large intestine is not centrally located but situated towards the right side of the body, a proper distance from the anterior body surface leads to a too shallow distance from the posterior surface, and a proper distance from the right side of the body means too large a distance from the left side. However, here again a large variability among the dose values among the voxel models can be seen,