- Email: [email protected]
A new approach for the calculation of critical organ dose in nuclear medicine applications
ARTICLE IN PRESS
Applied Radiation and Isotopes 62 (2005) 405–410 www.elsevier.com/locate/apradiso
A new approach for the calculation of critical organ dose in nuclear medicine applications Dog˘an Yas-ara,, A. Beril Tug˘rulb a
TAEA, C - ekmece Nuclear Research and Training Center, Health Physics Division, P.O. Box 1, Atatu¨rk Airport, Istanbul 34149, Turkey b Istanbul Technical University, Institute for Energy, Nuclear Research Division, Ayazag˘a Kampu¨su¨ 80626, Maslak, Istanbul, Turkey Received 21 August 2003; received in revised form 10 June 2004; accepted 5 August 2004
Abstract The geometrical factor that is calculated to keep in mind the radiation source and detector position is rather frequently used in radiation measuring and calculating methods. In this study, using the geometrical factor is intended to suggest a new model to measure the absorbed dose in nuclear medicine applications. Therefore, the source and target organ’s geometries are accepted to be disc and parallel to each other. In this manner, a mathematical model for the geometry of these discs is proposed and a disc–disc geometry factor is calculated. Theoretical calculations have been carried out with the MIRD (medical internal absorbed dose) method, which is widely used to the absorbed dose calculations in nuclear medicine. Absorbed radiation dose is separately calculated for a target organ, which is the testis, with disc–disc geometry factor model and MIRD model. Both the results are compared and the results of disc–disc geometry factor model are shown to be harmonious and acceptable with the results of MIRD model. r 2004 Elsevier Ltd. All rights reserved. Keywords: Absorbed dose; Dosimetry; MIRD; Technetium-99m; Mathematical model
1. Introduction Radiodiagnostic procedures usually involve patient doses of a few cGy or less. Exposures to such low doses are thought to be associated with genetic effects, cancer induction, and damage to the developing embryo or fetus. Direct evidence of radiation effects at low-dose levels in man, however, has not been found; thus, quantification of radiation effects cannot be precise (Kenneth, 1984). Knowledge of the absorbed dose to critical organs, especially the gonad, is of clinical interest. The dose Corresponding author. Tel.: +90-212-548-4050; fax: +90-
212-548-2230. E-mail addresses: [email protected] (D. Yas-ar), [email protected] (A.B. Tug˘rul).
from internal radionuclides can be estimated by calculation schemes or by direct measurement (Roedler and Kaul, 1975; Robertson, 1982; ICRP 53, 1987). Experimental data are useful for the verification of calculation methods (Golikov and Nikitin, 1989; Lanzl, 1973; Huda and Sandison, 1984, Yasar and Tugrul, 2003). The main object of this study was to determine the absorbed dose of the male gonad from the most commonly used Tc-99m in the liver scintigraphy. The determination of the absorbed dose levels in nuclear medicine applications are made with theoretical methods, because experimental measurements are not practical in many cases. The technique for calculating radiation dose as recommended by the Medical Internal Radiation Dose (MIRD) Committee of Society on Nuclear Medicine has now become widely accepted.
0969-8043/$ - see front matter r 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.apradiso.2004.08.001
ARTICLE IN PRESS 406
D. Yas- ar, A.B. Tug˘rul / Applied Radiation and Isotopes 62 (2005) 405–410
The basic principles of calculating radiation dose can be understood by first examining the relationship between dose rate and activity. Imagine a container of almost infinite dimensions filled with soft tissue, throughout which a radioactive material is uniformly distributed (Cloutier et al., 1984). With this study, the feasibility of the most suitable geometry factor for calculation of absorbed dose was investigated and new geometry factors were proposed for the absorbed dose calculation of critical organs. The geometry may affect the measurement in two ways. First, the medium between the source and the detector may scatter and may also absorb some particles. Second, the size and shape of source and the detector and the distance between them determines what fraction of particles will enter the detector and have a chance to be counted. Normally, the medium between the source and detector is air, a medium of low density. For measurements of photons and neutrons, the air has no effect (Tsoulfanidis, 1983). Disc–disc geometry was thought to be applied to this subject that had been frequently used on the radiation measurements. Disc–disc geometry is a shape on the same vertical line as their centers. In this study, the source and target organs’ geometries are evaluated as parallel to each other with two discs.
2. Theory and procedures The absorbed dose levels for live organs and tissues calculated as theoretical with the MIRD model for radionuclides are being used in nuclear medicine. It is also proposed to calculate the absorbed dose for live organs and tissues with the geometrical factor model in scintigraphic applications. In the geometry factor method, it is generally considered to view one component from another component.
can occur for both types of radiation. For radiation processing geometries, it is difficult to calculate dose distributions with high spatial resolution close to interfaces (Mclaughlin et al., 1989). Radioactive sources are exposed radiation at the 4p rigid angles if it has a small size. In nuclear medicine applications, if the organ or the tissue that is thought to be held radiopharmaceutically as a source organ or tissue, every point of the organ will be exposed to radiation with 4p rigid angles. However, the target organ is exposed to radiation that is according to its size and the geometrical position of the source organ. 2.2. Geometry factor Disc–disc geometrical factor is used for the radiation measurements (Tsoulfanidis, 1983). But it is not met at this kind of geometrical factor application in the literature for absorbed dose calculations of an organ or tissue in nuclear medicine. That is, the interpreted disc is plane and circular for both source organ and target organ so discs are designed as plane parallel. To illustrate the concept of geometry factor or solid angle, consider a point isotropic source at a certain distance from a detector as shown in Fig. 1. Since the particles are emitted by the source with equal probability in every direction, only some of the particles have a chance to enter the detector. That portion is equal to the fractional solid angle subtended by the detector at the location of the source. In general, a case of an extended source solid
Source As
A dAs
2.1. Geometrical factor approach in absorbed dose calculation It is never possible to irradiate bulk products to an absolutely uniformly absorbed dose. Dose measurements may also be complicated by displacement of matter by the dosimeter. They are also affected by dose gradients occurring in the dosimeter itself. In a relatively homogeneous medium containing a small dosimeter and irradiated in a nearly isotropic gamma-ray field, dose measurement uncertainties due to this effect are generally insignificant. In the irradiation of products by large sources, there is diffused incidence of photons and secondary electrons on the product. In the case of irradiation of inhomogeneous products, the gradients are apt to be severely close to material interfaces of very different compositions, and considerable uncertainties
ñ
θ
r d
θ
d
dAd c Ad
B Detector
Fig. 1. Plane source and plane detector geometry.
ARTICLE IN PRESS D. Yas- ar, A.B. Tug˘rul / Applied Radiation and Isotopes 62 (2005) 405–410
angle O is defined by Number of particles per second emitted inside the space defined by the contours of the source and the detector aperture O¼ : Number of particles per second emitted by the source
The mathematical expression for O is derived as follows (Fig. 1): A plane source of area As emitting S0 particles/m2 s, isotropically, is located at a distance d away from a detector with an aperture equal to Ad. Applying the definition given by Eq. (1) for the two differential areas dAs and dAd, and integrating, one obtains: R R 2 ^ A A ðS 0 dAs =4pr Þ dAd ðnr=tÞ O¼ s d ; (1) S 0 As where n^ is a unit vector normal to the surface of the detector aperture. Since n^ r=G ¼ cos o; Eq. (1) takes the form Z Z 1 cos o dAs dAd 2 : (2) O¼ 4pAs As r Ad Eq. (2) is valid for any shape of source and detector. As stated earlier, O is equal to the fractional solid angle (0pOp1). In radiation measurements, it is called either solid angle or geometry factor (Tsoulfanidis, 1983). In this report it will be called the geometry factor.
407
Table 1 The geometry factors calculated for every slice of corresponding liver organ obtained from Rando-Phantom d 0 (cm)
Rd (cm)
Rs (cm)
gd
42.5 40.0 37.5 35.0 32.5 30.0
2 2 2 2 2 2
2.7 6.1 6.2 6.4 4.7 3.3
5.5 6.1 7.0 7.9 9.3 1.1
E-04 E-04 E-04 E-04 E-04 E-03
following equation in terms of Bessel functions: Z 1 J 1 ðxÞ O¼s J 1 ðxsÞ; dx exz x 0
(3)
where s ¼ Rd =Rs ; z ¼ d=Rs and J 1 ðxÞ is the first kind of Bessell function. If Rd =d and Rs =d are less than 1, the following algebraic expression is obtained for the solid angle (Tsoulfanidis, 1983): o2 3 15 c4 þ o4 g¼O¼ 1 ðc2 þ o2 Þ þ þ c2 o2 4 8 4 3 35 c6 þ o6 3 2 2 2 þ c o ðc þ o2 Þ ; ð4Þ 16 2 4 where c ¼ Rs =d;
(5)
2.3. The geometry factor for disc source parallel to detector with a circular aperture
o ¼ Rd =d:
(6)
Consider a disc source parallel to a detector with a circular aperture Fig. 2. Starting with Eq. (2), one may obtain an expression involving elliptic integrals or the
2.4. The calculation of disc–disc geometry factor for liver–gonad geometry
Source
Rs
Disc–disc geometry is represented as a disc for both source organ and target organ. According to Fig. 1, liver and gonad’s centers are shown to be not on the axis of body. However, in this study, it is accepted to neglect the difference between source organ’s center and target organ’s center. In this manner, disc–disc geometry factor is calculated with Eq. (4). Firstly, the liver’s position is determined using a rando-phantom (Golikov and Nikitin, 1989). The liver is located in slices numerate 19, 20, 21, 22, 23 and 24. The holding rates and sizes for every slice are calculated for liver. The results are given in Table 1.
dφs
φs
d′
l d′
dφd
Rd
θd
Detector Fig. 2. The position of disc–disc geometry.
3. The calculation of absorbed dose The energy of ionization radiation is absorbed at different rates according to atomic density of the medium. The mean free path (l1 ) is described as a path which has no interaction during travel in absorber through an absorber of gamma rays. The mean free
ARTICLE IN PRESS D. Yas- ar, A.B. Tug˘rul / Applied Radiation and Isotopes 62 (2005) 405–410
408
Table 2 The linear attenuation coefficients of different photon energies for various materials (Cember, 1992) r (g/cm3)
C Al Cu Pb Air Water Concrete
2.25 2.7 8.9 11.3 0.00129 1 2.35
Energy (MeV) 0.1
0.15
0.2
0.3
0.5
0.8
0.335 0.435 3.80 59.7 1.94 104 0.167 0.397
0.301 0.362 1.830 20.8 1.73 104 0.149 0.326
0.274 0.324 1.309 10.15 1.59 104 0.136 0.291
0.238 0.278 0.960 4.02 1.37 104 0.118 0.251
0.196 0.227 0.730 1.64 1.12 104 0.097 0.204
0.159 0.185 0.581 0.945 9.12 105 0.079 0.166
National Bureau of Standards Report No. 1003 (1952). Table 3 Absorbed doses calculated at gonad with disc–disc geometry factor and with MIRD method for liver–gonad geometry Time (h)
Absorbed doses (mGy) Disc–disc geometry (MBq)
1 2 3 4 5 6
MIRD method (MBq)
111
148
185
222
111
148
185
222
2.48 4.69 6.66 8.42 9.98 11.38
3.31 6.26 8.88 11.23 13.31 15.17
4.13 7.82 11.1 14.03 16.64 18.97
4.96 9.38 13.33 16.84 19.97 22.76
2.23 4.21 5.98 7.55 8.96 10.21
2.97 5.61 7.97 10.07 11.95 13.62
3.71 7.02 9.96 12.59 14.93 17.02
4.45 8.42 11.96 15.11 17.92 20.42
path (l1 ) is also shown as (Knoll, 1979): l1 ¼ 1=matt ;
(7)
where matt represents attenuation coefficient. Radionuclides have energies between 100 and 300 keV in nuclear medicine applications. However, the ionization radiation is absorbed at different rates as to their energies in any medium. In this respect, attenuation coefficients for different media were calculated and published for the ionization radiation to have different energies. These are given in Table 2. Tc-99m is considered as a radionuclide, which has maximum gamma energy, 140.2 keV. Thus, attenuation coefficient (matt ) in water for gamma energy, 150 keV is given (matt ¼ 0:149) in Table 2 (Cember, 1992). Therefore, the gamma rays exposed from source organ have no interaction between target organ and source organ, and all energies of gamma rays are accepted to leave on the target organ, which is the gonad. In this manner, absorbed dose formula is again arranged and the disc–disc geometry factor is applied (Shapiro, 1989; Shani, 1991). D¼
A0 r G gd T eff ð1 elt Þ; mh matt
coefficient (1/cm); mh ; target organ mass (g); T eff ; average effective half-life (h); gd ; disc–disc geometry factor; l; disintegration constant; t, time (h). 3.1. Absorbed dose levels calculated with disc–disc geometry factor for liver–gonad geometry Absorbed dose calculations are made due to characteristics of Tc-99m radionuclide that is widely used in nuclear medicine applications. Also, activity levels are chosen in quantities given to patients. Thus, absorbed dose calculations in this study are made for 111, 148, 185 and 222 MBq as activity levels. First, geometry factors were calculated using Eq. (4) for liver separately. Absorbed dose levels for gonad in the event of the source organs, which is liver were calculated using Eq. (8) together with geometry factor for above-mentioned activity levels and a half-life. Calculated absorbed dose levels are given in Table 3.
4. The calculation with MIRD method (8)
where A0, is activity (mCi ); G; gamma dose constant [(rad cm2)/(mCi h)]; r; density (g/cm3); matt attenuation
The dose is calculated by using techniques adopted by the MIRD Committee of the Society of Nuclear Medicine as follows. Dðrk rh Þ; which is the absorbed
ARTICLE IN PRESS D. Yas- ar, A.B. Tug˘rul / Applied Radiation and Isotopes 62 (2005) 405–410
409
25 111 MBq 148 MBq
Absorbed dose (µGy)
20
185 MBq 222 MBq 111 MBq-MIRD 148 MBq-MIRD
15
185 MBq-MIRD 222 MBq-MIRD
10
5
0 0
1
2
4
3
5
6
7
Time (hr)
Fig. 3. The comparison of absorbed doses for disc–disc geometry factor method and MIRD method.
dose expressed in rads to a target organ rk from a radionuclide distributed uniformly in a source organ rh and has been formulated by the MIRD Committee (Stabin, 1996). MIRD formula presupposes that the source is uniformly distributed within a standard-sized organ, which is subject to much patient variation (UNSCEAR, 1982). Dðrk
rh Þ ¼ Ah Sðrk
rh Þ;
(9)
where Ah (mCi/h) is the cumulated activity in source organ and computer calculations of Sðrk rh Þ have been tabulated (Stabin, 1996). Therefore, absorbed dose values of the testis were calculated for source organ, that is, liver, for before-mentioned activity levels and a halflife. The results are given in Table 3.
5. Discussion and results The geometry factor, which is obtained according to the position of the source and the detector are used widely for radiation measurements and calculation procedures. In this study, it is intended to propose a new model to calculate absorbed dose in nuclear medicine applications. Disc–disc geometry that is not used incalculating the absorbed dose in nuclear medicine and dosimetrical assessments is thought to be applied for calculating the absorbed dose in nuclear medicine. The gonads are very sensitive in response to ionization radiation from the genetic and somatic points of view in the body. The organ that is accepted as a critical organ is evaluated as a target organ and the liver that is frequently made their scintigraphics is chosen as a source organ in this study. Absorbed dose calculations are made due to characteristics of Tc-99m radionuclide that is used widely
Table 4 The statistical evaluation of results of absorbed doses calculated with disc–disc geometry factor method and MIRD method for liver–gonad geometry and 222 MBq activities Time (h)
Disc–disc geometry factor method (mGy)
1 4.93 2 9.33 3 13.25 4 16.74 5 19.85 6 22.62 Average value
MIRD method (mGy)
Deviation (%)
4.46 8.42 11.96 15.11 17.92 20.42
9.53 9.75 9.74 9.74 9.72 9.73 9.70
in nuclear medicine applications. Thus, activity levels are chosen in quantities given to patients. It was accepted to be on same axis and has a plane shape of both source and target organs, to represent a disc. Absorbed doses for the gonad were calculated using geometry factor obtained due to disc–disc position. Also, absorbed doses according to MIRD method were calculated for same source organ and activities. Absorbed doses that were obtained using disc–disc geometry factor were compared with results of MIRD method and their deviation curves are shown in Fig. 3. The results are shown to be harmonious and in agreement with each other. The average deviation percent of the results of absorbed doses for disc–disc geometry factor method and MIRD method is found to be less than 10%. The statistical evaluation of results is given in Table 4 for 222 MBq activities. The results are in agreement with each other and the difference between methods is acceptable.
ARTICLE IN PRESS 410
D. Yas- ar, A.B. Tug˘rul / Applied Radiation and Isotopes 62 (2005) 405–410
6. Conclusions With this study, it is concluded that a different calculation can be realized by using disc–disc geometry factor for liver–gonad geometry. This calculation compared the MIRD results and showed that reaching results are acceptable. So, it is understood that if the case determination for the geometry factor would be appropriate to reality, then the geometry factor application for the dose calculation can be appreciable. As a result, the disc–disc geometry factor for dosimetrical calculation methods in nuclear medicine applications is proposed originally.
References Cember, H., 1992. Introduction to Health Physics Northwestern University, second ed. McGraw-Hill, New York. Cloutier, J.R., Watson, E.E., Coffey, J.I., 1984. Radiopharmaceutical dose calculation. Textbook of Nuclear Medicine, vol. I, Basic Science, second ed., Philadelphia. Golikov, V.Y., Nikitin, V.V., 1989. Estimation of the mean organ doses and the effective dose equivalent from rando phantom measurements. Health Phys. 56 (1), 111–115. Huda, W., Sandison, G.A., 1984. Estimation of mean organ doses in diagnostic radiology from rando phantom measurements. Health Phys. 47 (3), 463–467. ICRP 53, 1987. International Commission on Radiological Protection; Radiation Dose to Patients from Radiopharmaceuticals. Pergamon Press, ICRP Publication 53.
Kenneth, L.M., 1984. Radiation effects in nuclear medicine. Textbook of Nuclear Medicine, vol. I, Basic Science, second ed., Philadelphia. Knoll, G., 1979. Radiation Detection and Measurement. Wiley, New York. Lanzl, L.H., 1973. The Rando-Phantom and its Medical Applications; Department of Radiology, The University of Chicago, Illinois, Chicago. McLaughlin, W.L., Boyd, A.W., Chadwick, K.H., McDonald, J.C., Miller, A., 1989. Dosimetry for Radiation Processing. Taylor & Francis, London. Robertson, J.S., 1982. Radiation absorbed dose calculations in diagnostic nuclear medicine. Int. J. Appl. Radiat. Isot. 33, 981–990. Roedler, H.D., Kaul, A., 1975. Radiation absorbed dose from medically administered radiopharmaceuticals. Proceedings of a Symposium, Vienna, 10–14 March, Biomedical Dosimetry, pp. 655–663. Shani, G., 1991. Radiation Dosimetry Instrumentation and Methods. CRC Press, London. Shapiro, J., 1989. Radiation Protection. Harvard University Press, Cambridge, MA. Stabin, M.G., 1996. MIRDOSE, personal computer software for internal dose assessment in nuclear medicine. J. Nucl. Med. 37, 538–546. Tsoulfanidis, N., 1983. Measurement and Detection of Radiation, University of Missouri Rolla. UNSCEAR, 1982. United Nations Scientific Committee on the Effect of Atomic Radiation, Annex G Ionizing Radiation, Source and Biological Effect, UNSCEAR Report 1982. Yasar, D., Tugrul, A.B., 2003. A comparison of TLD measurements to MIRD estimates of the dose to the testes from Tc-99m in liver and spleen. Radiat. Meas. 37 (2), 113–118.
Applied Radiation and Isotopes 62 (2005) 405–410 www.elsevier.com/locate/apradiso
A new approach for the calculation of critical organ dose in nuclear medicine applications Dog˘an Yas-ara,, A. Beril Tug˘rulb a
TAEA, C - ekmece Nuclear Research and Training Center, Health Physics Division, P.O. Box 1, Atatu¨rk Airport, Istanbul 34149, Turkey b Istanbul Technical University, Institute for Energy, Nuclear Research Division, Ayazag˘a Kampu¨su¨ 80626, Maslak, Istanbul, Turkey Received 21 August 2003; received in revised form 10 June 2004; accepted 5 August 2004
Abstract The geometrical factor that is calculated to keep in mind the radiation source and detector position is rather frequently used in radiation measuring and calculating methods. In this study, using the geometrical factor is intended to suggest a new model to measure the absorbed dose in nuclear medicine applications. Therefore, the source and target organ’s geometries are accepted to be disc and parallel to each other. In this manner, a mathematical model for the geometry of these discs is proposed and a disc–disc geometry factor is calculated. Theoretical calculations have been carried out with the MIRD (medical internal absorbed dose) method, which is widely used to the absorbed dose calculations in nuclear medicine. Absorbed radiation dose is separately calculated for a target organ, which is the testis, with disc–disc geometry factor model and MIRD model. Both the results are compared and the results of disc–disc geometry factor model are shown to be harmonious and acceptable with the results of MIRD model. r 2004 Elsevier Ltd. All rights reserved. Keywords: Absorbed dose; Dosimetry; MIRD; Technetium-99m; Mathematical model
1. Introduction Radiodiagnostic procedures usually involve patient doses of a few cGy or less. Exposures to such low doses are thought to be associated with genetic effects, cancer induction, and damage to the developing embryo or fetus. Direct evidence of radiation effects at low-dose levels in man, however, has not been found; thus, quantification of radiation effects cannot be precise (Kenneth, 1984). Knowledge of the absorbed dose to critical organs, especially the gonad, is of clinical interest. The dose Corresponding author. Tel.: +90-212-548-4050; fax: +90-
212-548-2230. E-mail addresses: [email protected] (D. Yas-ar), [email protected] (A.B. Tug˘rul).
from internal radionuclides can be estimated by calculation schemes or by direct measurement (Roedler and Kaul, 1975; Robertson, 1982; ICRP 53, 1987). Experimental data are useful for the verification of calculation methods (Golikov and Nikitin, 1989; Lanzl, 1973; Huda and Sandison, 1984, Yasar and Tugrul, 2003). The main object of this study was to determine the absorbed dose of the male gonad from the most commonly used Tc-99m in the liver scintigraphy. The determination of the absorbed dose levels in nuclear medicine applications are made with theoretical methods, because experimental measurements are not practical in many cases. The technique for calculating radiation dose as recommended by the Medical Internal Radiation Dose (MIRD) Committee of Society on Nuclear Medicine has now become widely accepted.
0969-8043/$ - see front matter r 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.apradiso.2004.08.001
ARTICLE IN PRESS 406
D. Yas- ar, A.B. Tug˘rul / Applied Radiation and Isotopes 62 (2005) 405–410
The basic principles of calculating radiation dose can be understood by first examining the relationship between dose rate and activity. Imagine a container of almost infinite dimensions filled with soft tissue, throughout which a radioactive material is uniformly distributed (Cloutier et al., 1984). With this study, the feasibility of the most suitable geometry factor for calculation of absorbed dose was investigated and new geometry factors were proposed for the absorbed dose calculation of critical organs. The geometry may affect the measurement in two ways. First, the medium between the source and the detector may scatter and may also absorb some particles. Second, the size and shape of source and the detector and the distance between them determines what fraction of particles will enter the detector and have a chance to be counted. Normally, the medium between the source and detector is air, a medium of low density. For measurements of photons and neutrons, the air has no effect (Tsoulfanidis, 1983). Disc–disc geometry was thought to be applied to this subject that had been frequently used on the radiation measurements. Disc–disc geometry is a shape on the same vertical line as their centers. In this study, the source and target organs’ geometries are evaluated as parallel to each other with two discs.
2. Theory and procedures The absorbed dose levels for live organs and tissues calculated as theoretical with the MIRD model for radionuclides are being used in nuclear medicine. It is also proposed to calculate the absorbed dose for live organs and tissues with the geometrical factor model in scintigraphic applications. In the geometry factor method, it is generally considered to view one component from another component.
can occur for both types of radiation. For radiation processing geometries, it is difficult to calculate dose distributions with high spatial resolution close to interfaces (Mclaughlin et al., 1989). Radioactive sources are exposed radiation at the 4p rigid angles if it has a small size. In nuclear medicine applications, if the organ or the tissue that is thought to be held radiopharmaceutically as a source organ or tissue, every point of the organ will be exposed to radiation with 4p rigid angles. However, the target organ is exposed to radiation that is according to its size and the geometrical position of the source organ. 2.2. Geometry factor Disc–disc geometrical factor is used for the radiation measurements (Tsoulfanidis, 1983). But it is not met at this kind of geometrical factor application in the literature for absorbed dose calculations of an organ or tissue in nuclear medicine. That is, the interpreted disc is plane and circular for both source organ and target organ so discs are designed as plane parallel. To illustrate the concept of geometry factor or solid angle, consider a point isotropic source at a certain distance from a detector as shown in Fig. 1. Since the particles are emitted by the source with equal probability in every direction, only some of the particles have a chance to enter the detector. That portion is equal to the fractional solid angle subtended by the detector at the location of the source. In general, a case of an extended source solid
Source As
A dAs
2.1. Geometrical factor approach in absorbed dose calculation It is never possible to irradiate bulk products to an absolutely uniformly absorbed dose. Dose measurements may also be complicated by displacement of matter by the dosimeter. They are also affected by dose gradients occurring in the dosimeter itself. In a relatively homogeneous medium containing a small dosimeter and irradiated in a nearly isotropic gamma-ray field, dose measurement uncertainties due to this effect are generally insignificant. In the irradiation of products by large sources, there is diffused incidence of photons and secondary electrons on the product. In the case of irradiation of inhomogeneous products, the gradients are apt to be severely close to material interfaces of very different compositions, and considerable uncertainties
ñ
θ
r d
θ
d
dAd c Ad
B Detector
Fig. 1. Plane source and plane detector geometry.
ARTICLE IN PRESS D. Yas- ar, A.B. Tug˘rul / Applied Radiation and Isotopes 62 (2005) 405–410
angle O is defined by Number of particles per second emitted inside the space defined by the contours of the source and the detector aperture O¼ : Number of particles per second emitted by the source
The mathematical expression for O is derived as follows (Fig. 1): A plane source of area As emitting S0 particles/m2 s, isotropically, is located at a distance d away from a detector with an aperture equal to Ad. Applying the definition given by Eq. (1) for the two differential areas dAs and dAd, and integrating, one obtains: R R 2 ^ A A ðS 0 dAs =4pr Þ dAd ðnr=tÞ O¼ s d ; (1) S 0 As where n^ is a unit vector normal to the surface of the detector aperture. Since n^ r=G ¼ cos o; Eq. (1) takes the form Z Z 1 cos o dAs dAd 2 : (2) O¼ 4pAs As r Ad Eq. (2) is valid for any shape of source and detector. As stated earlier, O is equal to the fractional solid angle (0pOp1). In radiation measurements, it is called either solid angle or geometry factor (Tsoulfanidis, 1983). In this report it will be called the geometry factor.
407
Table 1 The geometry factors calculated for every slice of corresponding liver organ obtained from Rando-Phantom d 0 (cm)
Rd (cm)
Rs (cm)
gd
42.5 40.0 37.5 35.0 32.5 30.0
2 2 2 2 2 2
2.7 6.1 6.2 6.4 4.7 3.3
5.5 6.1 7.0 7.9 9.3 1.1
E-04 E-04 E-04 E-04 E-04 E-03
following equation in terms of Bessel functions: Z 1 J 1 ðxÞ O¼s J 1 ðxsÞ; dx exz x 0
(3)
where s ¼ Rd =Rs ; z ¼ d=Rs and J 1 ðxÞ is the first kind of Bessell function. If Rd =d and Rs =d are less than 1, the following algebraic expression is obtained for the solid angle (Tsoulfanidis, 1983): o2 3 15 c4 þ o4 g¼O¼ 1 ðc2 þ o2 Þ þ þ c2 o2 4 8 4 3 35 c6 þ o6 3 2 2 2 þ c o ðc þ o2 Þ ; ð4Þ 16 2 4 where c ¼ Rs =d;
(5)
2.3. The geometry factor for disc source parallel to detector with a circular aperture
o ¼ Rd =d:
(6)
Consider a disc source parallel to a detector with a circular aperture Fig. 2. Starting with Eq. (2), one may obtain an expression involving elliptic integrals or the
2.4. The calculation of disc–disc geometry factor for liver–gonad geometry
Source
Rs
Disc–disc geometry is represented as a disc for both source organ and target organ. According to Fig. 1, liver and gonad’s centers are shown to be not on the axis of body. However, in this study, it is accepted to neglect the difference between source organ’s center and target organ’s center. In this manner, disc–disc geometry factor is calculated with Eq. (4). Firstly, the liver’s position is determined using a rando-phantom (Golikov and Nikitin, 1989). The liver is located in slices numerate 19, 20, 21, 22, 23 and 24. The holding rates and sizes for every slice are calculated for liver. The results are given in Table 1.
dφs
φs
d′
l d′
dφd
Rd
θd
Detector Fig. 2. The position of disc–disc geometry.
3. The calculation of absorbed dose The energy of ionization radiation is absorbed at different rates according to atomic density of the medium. The mean free path (l1 ) is described as a path which has no interaction during travel in absorber through an absorber of gamma rays. The mean free
ARTICLE IN PRESS D. Yas- ar, A.B. Tug˘rul / Applied Radiation and Isotopes 62 (2005) 405–410
408
Table 2 The linear attenuation coefficients of different photon energies for various materials (Cember, 1992) r (g/cm3)
C Al Cu Pb Air Water Concrete
2.25 2.7 8.9 11.3 0.00129 1 2.35
Energy (MeV) 0.1
0.15
0.2
0.3
0.5
0.8
0.335 0.435 3.80 59.7 1.94 104 0.167 0.397
0.301 0.362 1.830 20.8 1.73 104 0.149 0.326
0.274 0.324 1.309 10.15 1.59 104 0.136 0.291
0.238 0.278 0.960 4.02 1.37 104 0.118 0.251
0.196 0.227 0.730 1.64 1.12 104 0.097 0.204
0.159 0.185 0.581 0.945 9.12 105 0.079 0.166
National Bureau of Standards Report No. 1003 (1952). Table 3 Absorbed doses calculated at gonad with disc–disc geometry factor and with MIRD method for liver–gonad geometry Time (h)
Absorbed doses (mGy) Disc–disc geometry (MBq)
1 2 3 4 5 6
MIRD method (MBq)
111
148
185
222
111
148
185
222
2.48 4.69 6.66 8.42 9.98 11.38
3.31 6.26 8.88 11.23 13.31 15.17
4.13 7.82 11.1 14.03 16.64 18.97
4.96 9.38 13.33 16.84 19.97 22.76
2.23 4.21 5.98 7.55 8.96 10.21
2.97 5.61 7.97 10.07 11.95 13.62
3.71 7.02 9.96 12.59 14.93 17.02
4.45 8.42 11.96 15.11 17.92 20.42
path (l1 ) is also shown as (Knoll, 1979): l1 ¼ 1=matt ;
(7)
where matt represents attenuation coefficient. Radionuclides have energies between 100 and 300 keV in nuclear medicine applications. However, the ionization radiation is absorbed at different rates as to their energies in any medium. In this respect, attenuation coefficients for different media were calculated and published for the ionization radiation to have different energies. These are given in Table 2. Tc-99m is considered as a radionuclide, which has maximum gamma energy, 140.2 keV. Thus, attenuation coefficient (matt ) in water for gamma energy, 150 keV is given (matt ¼ 0:149) in Table 2 (Cember, 1992). Therefore, the gamma rays exposed from source organ have no interaction between target organ and source organ, and all energies of gamma rays are accepted to leave on the target organ, which is the gonad. In this manner, absorbed dose formula is again arranged and the disc–disc geometry factor is applied (Shapiro, 1989; Shani, 1991). D¼
A0 r G gd T eff ð1 elt Þ; mh matt
coefficient (1/cm); mh ; target organ mass (g); T eff ; average effective half-life (h); gd ; disc–disc geometry factor; l; disintegration constant; t, time (h). 3.1. Absorbed dose levels calculated with disc–disc geometry factor for liver–gonad geometry Absorbed dose calculations are made due to characteristics of Tc-99m radionuclide that is widely used in nuclear medicine applications. Also, activity levels are chosen in quantities given to patients. Thus, absorbed dose calculations in this study are made for 111, 148, 185 and 222 MBq as activity levels. First, geometry factors were calculated using Eq. (4) for liver separately. Absorbed dose levels for gonad in the event of the source organs, which is liver were calculated using Eq. (8) together with geometry factor for above-mentioned activity levels and a half-life. Calculated absorbed dose levels are given in Table 3.
4. The calculation with MIRD method (8)
where A0, is activity (mCi ); G; gamma dose constant [(rad cm2)/(mCi h)]; r; density (g/cm3); matt attenuation
The dose is calculated by using techniques adopted by the MIRD Committee of the Society of Nuclear Medicine as follows. Dðrk rh Þ; which is the absorbed
ARTICLE IN PRESS D. Yas- ar, A.B. Tug˘rul / Applied Radiation and Isotopes 62 (2005) 405–410
409
25 111 MBq 148 MBq
Absorbed dose (µGy)
20
185 MBq 222 MBq 111 MBq-MIRD 148 MBq-MIRD
15
185 MBq-MIRD 222 MBq-MIRD
10
5
0 0
1
2
4
3
5
6
7
Time (hr)
Fig. 3. The comparison of absorbed doses for disc–disc geometry factor method and MIRD method.
dose expressed in rads to a target organ rk from a radionuclide distributed uniformly in a source organ rh and has been formulated by the MIRD Committee (Stabin, 1996). MIRD formula presupposes that the source is uniformly distributed within a standard-sized organ, which is subject to much patient variation (UNSCEAR, 1982). Dðrk
rh Þ ¼ Ah Sðrk
rh Þ;
(9)
where Ah (mCi/h) is the cumulated activity in source organ and computer calculations of Sðrk rh Þ have been tabulated (Stabin, 1996). Therefore, absorbed dose values of the testis were calculated for source organ, that is, liver, for before-mentioned activity levels and a halflife. The results are given in Table 3.
5. Discussion and results The geometry factor, which is obtained according to the position of the source and the detector are used widely for radiation measurements and calculation procedures. In this study, it is intended to propose a new model to calculate absorbed dose in nuclear medicine applications. Disc–disc geometry that is not used incalculating the absorbed dose in nuclear medicine and dosimetrical assessments is thought to be applied for calculating the absorbed dose in nuclear medicine. The gonads are very sensitive in response to ionization radiation from the genetic and somatic points of view in the body. The organ that is accepted as a critical organ is evaluated as a target organ and the liver that is frequently made their scintigraphics is chosen as a source organ in this study. Absorbed dose calculations are made due to characteristics of Tc-99m radionuclide that is used widely
Table 4 The statistical evaluation of results of absorbed doses calculated with disc–disc geometry factor method and MIRD method for liver–gonad geometry and 222 MBq activities Time (h)
Disc–disc geometry factor method (mGy)
1 4.93 2 9.33 3 13.25 4 16.74 5 19.85 6 22.62 Average value
MIRD method (mGy)
Deviation (%)
4.46 8.42 11.96 15.11 17.92 20.42
9.53 9.75 9.74 9.74 9.72 9.73 9.70
in nuclear medicine applications. Thus, activity levels are chosen in quantities given to patients. It was accepted to be on same axis and has a plane shape of both source and target organs, to represent a disc. Absorbed doses for the gonad were calculated using geometry factor obtained due to disc–disc position. Also, absorbed doses according to MIRD method were calculated for same source organ and activities. Absorbed doses that were obtained using disc–disc geometry factor were compared with results of MIRD method and their deviation curves are shown in Fig. 3. The results are shown to be harmonious and in agreement with each other. The average deviation percent of the results of absorbed doses for disc–disc geometry factor method and MIRD method is found to be less than 10%. The statistical evaluation of results is given in Table 4 for 222 MBq activities. The results are in agreement with each other and the difference between methods is acceptable.
ARTICLE IN PRESS 410
D. Yas- ar, A.B. Tug˘rul / Applied Radiation and Isotopes 62 (2005) 405–410
6. Conclusions With this study, it is concluded that a different calculation can be realized by using disc–disc geometry factor for liver–gonad geometry. This calculation compared the MIRD results and showed that reaching results are acceptable. So, it is understood that if the case determination for the geometry factor would be appropriate to reality, then the geometry factor application for the dose calculation can be appreciable. As a result, the disc–disc geometry factor for dosimetrical calculation methods in nuclear medicine applications is proposed originally.
References Cember, H., 1992. Introduction to Health Physics Northwestern University, second ed. McGraw-Hill, New York. Cloutier, J.R., Watson, E.E., Coffey, J.I., 1984. Radiopharmaceutical dose calculation. Textbook of Nuclear Medicine, vol. I, Basic Science, second ed., Philadelphia. Golikov, V.Y., Nikitin, V.V., 1989. Estimation of the mean organ doses and the effective dose equivalent from rando phantom measurements. Health Phys. 56 (1), 111–115. Huda, W., Sandison, G.A., 1984. Estimation of mean organ doses in diagnostic radiology from rando phantom measurements. Health Phys. 47 (3), 463–467. ICRP 53, 1987. International Commission on Radiological Protection; Radiation Dose to Patients from Radiopharmaceuticals. Pergamon Press, ICRP Publication 53.
Kenneth, L.M., 1984. Radiation effects in nuclear medicine. Textbook of Nuclear Medicine, vol. I, Basic Science, second ed., Philadelphia. Knoll, G., 1979. Radiation Detection and Measurement. Wiley, New York. Lanzl, L.H., 1973. The Rando-Phantom and its Medical Applications; Department of Radiology, The University of Chicago, Illinois, Chicago. McLaughlin, W.L., Boyd, A.W., Chadwick, K.H., McDonald, J.C., Miller, A., 1989. Dosimetry for Radiation Processing. Taylor & Francis, London. Robertson, J.S., 1982. Radiation absorbed dose calculations in diagnostic nuclear medicine. Int. J. Appl. Radiat. Isot. 33, 981–990. Roedler, H.D., Kaul, A., 1975. Radiation absorbed dose from medically administered radiopharmaceuticals. Proceedings of a Symposium, Vienna, 10–14 March, Biomedical Dosimetry, pp. 655–663. Shani, G., 1991. Radiation Dosimetry Instrumentation and Methods. CRC Press, London. Shapiro, J., 1989. Radiation Protection. Harvard University Press, Cambridge, MA. Stabin, M.G., 1996. MIRDOSE, personal computer software for internal dose assessment in nuclear medicine. J. Nucl. Med. 37, 538–546. Tsoulfanidis, N., 1983. Measurement and Detection of Radiation, University of Missouri Rolla. UNSCEAR, 1982. United Nations Scientific Committee on the Effect of Atomic Radiation, Annex G Ionizing Radiation, Source and Biological Effect, UNSCEAR Report 1982. Yasar, D., Tugrul, A.B., 2003. A comparison of TLD measurements to MIRD estimates of the dose to the testes from Tc-99m in liver and spleen. Radiat. Meas. 37 (2), 113–118.