The AAPM/RSNA Physics Tutorial for Residents

Transcription

1 IMAGING & THERAPEUTIC TECHNOLOGY The AAPM/RSNA Physics Tutorial for Residents Radiation Interactions and Internal Dosimetry in Nuclear Medicine 1 Douglas J. Simpkin, PhD LEARNING OBJECTIVES After reading this article and taking the test, the reader will be able to: Define radiation dose and describe the mechanisms by which charged particles and photons interact with matter to deposit dose. Describe the Medical Internal Radiation Dose (MIRD) formalism for calculating internal radiation dose, including definitions of source and target organs, mean energy emitted per decay, S values, cumulated activity, and effective halftime. Recognize the sources of information necessary to perform radiation dose calculations for common radiopharmaceuticals. The decay of a radioactive nucleus leads to the emission of energy in the form of photons or charged particles. The form and energy of the radiation emitted will depend on the decaying nucleus. Some of the emitted energy will be absorbed by target organs; the ratio of the absorbed energy to the mass of the target is the radiation dose. Charged particles traveling in a medium slow down because of interactions between the electric charge of the particle and that of the orbital electrons and nuclei of the medium. These interactions transfer energy from the charged particle to the orbital electrons and the nuclei of the medium. A photon may be transmitted through a medium or may be attenuated by the medium. Of the four mechanisms by which photons interact with matter, two are important in the energy range of interest in nuclear medicine: the photoelectric effect and Compton scattering. The internal radiation dose from radionuclides used in nuclear medicine can be estimated with the Medical Internal Radiation Dose (MIRD) method. Important aspects of the MIRD method include the concepts of source and target organs, energy emitted per decay, absorbed fraction, S value, cumulated activity, and effective dose equivalent. INTRODUCTION The decay of a radioactive nucleus leads to the emission of energy in the form of gamma or x-ray photons or energetic charged particles. These charged particles include alpha particles, electronlike beta particles, positrons, and energetic Auger or conversion electrons. The latter electrons originate from interactions between the decaying nucleus and the surrounding orbital electrons of the atom. The type and energy of the emitted radiation depend on the type of radionuclide and may vary from decay to decay for radionuclides that have multiple decay pathways. For example, in addition to leading to emission of the well-known 140-keV gamma ray, the decay of technetium-99m may lead to emission of low-energy conversion and Auger electrons, as Abbreviation: MIRD = Medical Internal Radiation Dose Index terms: Dosimetry Radiations, exposure to patients and personnel Radiations, measurement Radionuclides, radiation dose RadioGraphics 1999; 19: From the Department of Radiology, St Luke s Medical Center, 2900 W Oklahoma Ave, Milwaukee, WI From the AAPM/RSNA Physics Tutorial at the 1997 RSNA scientific assembly. Received March 12, 1998; revision requested June 12 and received October 27; accepted November 3. Address reprint requests to the author. RSNA,

2 well as several low-energy x rays (1). For radionuclides that decay by means of multiple beta emission pathways, such as iodine-131, the energy of the emitted beta particle will vary from decay to decay. Each type of radiation will interact with nearby media in a manner unique to the form and energy of the radiation. The absorption by the medium of the energy of the radiation leads to the deposition of radiation dose. Radiation dose is the ratio of the energy deposited to the mass of the medium. Units of dose are the rad (100 erg of energy deposited per gram of medium) or the gray (1 J of energy deposited per kilogram of medium). Because 10 7 erg = 1 J, it follows that 1 Gy = 100 rad, 1 cgy = 1 rad, and 1 mgy = 100 mrad. Also, because 1 MeV = J, a dose of 1 MeV g 1 = Gy. The direction of the emitted radiation from the decay site is random (isotropic). Isotropic emission implies that a point source of a therapeutic radiopharmaceutical immediately adjacent to a target cell will deliver not more than half of its energy to the target. Isotropic emission also implies that, near a point source of radiation in a nonabsorbing medium, the number of emitted radiations per area (the radiation flux) varies with the inverse square of the distance from the point radiation source. Thus, if the radiation flux at distance r 1 is I 1, then the flux I 2 at distance r 2 can be determined with the following formula: I 2 /I 1 = (r 1 /r 2 ) 2. (1) Generally, the radiation dose delivered to a medium increases with the radiation flux through the medium. Thus, the radiation dose is always greatest for locations near the site of radioactive decay. In this article, the interactions of charged particles and photons with matter are reviewed, and the energy-depositing mechanisms and the spatial range of the dose distributed from these radiations are described. The fundamentals of the dosimetry of nuclear medicine radiopharmaceuticals are also discussed. Various aspects of the Medical Internal Radiation Dose (MIRD) method are presented including the concepts of source and target organs, energy emitted per decay, absorbed fraction, S value, cumulated activity, and effective dose equivalent. Sample dose calculations are presented, and the uncertainties involved are discussed. References to recent publications of the International Commission on Radiological Protection and the Nuclear Regulatory Commission illustrate the importance of dose estimates in daily clinical practice for issues related to misadministration of radiopharmaceuticals. Considerations associated with fetal dose estimates are also discussed. CHARGED PARTICLE INTERACTIONS Alpha and beta particles and electrons traveling in a material medium slow down because of interactions between the electric charge of the particle and that of the orbital electrons and nuclei of the medium. These interactions transfer energy from the charged particle to the orbital electrons and (to a lesser degree) the nuclei of the medium. The rate of energy transfer per distance traveled is termed the stopping power and depends on the type and energy of the particle, as well as the medium. There are two general classes of interactions that transfer energy from the charged particle. The rate per distance at which energy is transferred to the orbital electrons of the material is termed the collision stopping power. In the energy range of interest in nuclear medicine, the energy transferred to the orbital electrons manifests as atomic excitations and ionizations with effects that are local to the interaction site. Low-mass, high-energy charged particles traveling in high atomic number media may also lose energy to the production of photons. The rate of such loss is termed the radiative stopping power. This effect is not seen for alpha particles and is of limited importance for beta particles and electrons in biologic materials at nuclear medicine energies. For example, for the 1.71-MeV maximum energy beta particle emitted by phosphorus-32, the radiative stopping power in water is 80 times smaller than the collision 156 Imaging & Therapeutic Technology Volume 19 Number 1

3 stopping power (2). Thus, for charged particles in the energy range of concern in nuclear medicine, the particles give up kinetic energy primarily by means of electrostatic collisions with the orbital electrons of the atoms of the medium. The transfer of energy from the charged particle continues until the particle has exhausted its kinetic energy. The path taken by the particle in the medium is termed the particle track. The track for low-mass particles such as beta particles is usually tortuous, whereas that for massive alpha particles is often straight. The total distance traveled in the medium by the charged particle is termed the path length. The straight-line distance from the starting point of the particle to the stopping point is termed the range. Note that the path length will exceed the range except in cases where the particle travels in a straight path. An alpha particle is approximately 8,000 times more massive than an orbital electron. This extraordinary mass difference means that in an electrostatic interaction with an orbital electron, an alpha particle loses very little energy and is not deflected from its original direction. Therefore, alpha particles lose kinetic energy in small increments in interactions with a very large number of orbital electrons and travel in straight paths in media. Alpha particles travel very short distances in solids and liquids. For example, the range of a typical 5- MeV alpha particle is just 0.05 mm in soft tissue, no more than about a dozen cell diameters. This fact implies that the energy of the alpha particle is deposited in a correspondingly small volume near the decay site. Therefore, the radiation dose from alpha-emitting radionuclides distributed in the body (for therapeutic purposes or as a result of internal contamination) is highly localized; cells near the site of radionuclide concentration receive very high doses, whereas more distant cells receive no dose. Conversely, shielding external sources of alpha emitters is easy because alpha particles will not penetrate a sheet of paper or common examination gloves. In low atomic number media such as tissue, beta particles interact primarily by electrostatically colliding with orbital electrons in the medium. Because the beta particle has the same mass as the orbital electron, each collision will decrease the energy of the beta particle by possibly large fractions. This process will cause redirection or scattering of the beta particle, possibly through a large deflection angle. The paths of beta particles are hence tortuous, with path lengths that may be significantly longer than the ranges. The beta particle orbital electron collision may cause the target orbital electron to be ejected from the atom. Such a secondary electron is termed a knock-on electron or delta ray. Very occasionally, a beta particle will spontaneously decelerate near the nucleus of a target atom. A bremsstrahlung ( braking radiation ) photon is emitted from the interaction site; the energy of this photon is equal to the difference in the energy of the beta particle before and after the event. For beta particles in tissue, bremsstrahlung production is rather rare. On average, about 72 decays of beta-emitting P-32 are necessary before a bremsstrahlung photon (of energy above 50 kev) is created in water (3). The chance of bremsstrahlung production increases with beta energy and the atomic number, Z, of the medium. For example, because of the high atomic number of lead (Z = 82), bremsstrahlung production is much more likely in lead than in a low atomic number medium such as water, tissue, or plastic. Beta-emitting radiopharmaceuticals are usually shipped with the lightest-weight protective shielding by surrounding the source first with low-density plastic (to stop the beta particles by means of collisions and not the bremsstrahlung effect) and then with lead (to stop any bremsstrahlung photons that may have been created in the plastic or the source itself). The range of beta particles in a medium depends on the energy of the particle and the density of target orbital electrons. For all materials except gaseous hydrogen, the electron density is proportional to the physical density (ρ = mass per volume); therefore, a single graph of electron range in all materials is available. Figure 1 shows the product of the electron range x and the density of the medium ρ as a function of beta energy (4). For example, January-February 1999 Simpkin RadioGraphics 157

4 Figure 1. Graph shows the range of electrons or beta particles as a function of the kinetic energy, E, of the particle. The linear range x (in centimeters) traveled by the electron in any medium is obtained by dividing the range from this graph by the density of the medium ρ (in grams per centimeter). from Figure 1, ρx for the 1.71-MeV maximum energy beta particle emitted by P-32 is 0.8 g cm 2. In air (ρ = g cm 3 ), this range is 0.8 g cm 2 / g cm 3 = 615 cm = 6.15 m. In tissue (ρ = 1.0 g cm 3 ), this range is 0.8 g cm 2 /1.0 g cm 3 = 0.8 cm = 8 mm. In general, beta particles travel meters in air and millimeters in tissue. PHOTON INTERACTIONS: TRANSMISSION AND ATTENUATION Photons interact with media much differently than do charged particles. An x ray or gamma ray may tunnel through a medium completely oblivious to the presence of the medium and emerge unchanged in either energy or direction. Such a photon is said to have been transmitted through the medium. Conversely, a photon may undergo a sudden, catastrophic interaction that causes it to cease to exist. Such a photon is said to have been attenuated. A secondary photon may be created as a result of an attenuating event; however, creation of such a photon depends on the type of interaction. This secondary photon may have lower energy than the original photon with a direction usually different from that of the original photon. Owing to conservation of energy, the photon energy not spent overcoming atomic binding energy or given to secondary photons will be deposited locally in the medium. The probability that a photon will be transmitted through (and thereby avoid attenuation) distance x in a medium of density ρ is given by 158 Imaging & Therapeutic Technology Volume 19 Number 1

5 Figure 2. Graph shows the probabilities of transmission of 30- and 140-keV photons in water. the exponential function e µx. The linear attenuation coefficient, µ, is the probability per differential distance of the photon undergoing an attenuating event and depends on the energy of the photon and the atomic number and density of the medium. The density dependence of µ can be eliminated by dividing by the density of the medium, a process that yields the mass attenuation coefficient, µ/ρ. Note that µ = µ/ρ ρ. The value of µ/ρ is appropriate for the medium regardless of its physical state. For example, at a given photon energy, one value of µ/ρ holds for liquid water, ice, and water vapor. A graph of the probability of photon transmission, e µx, as a function of material thickness shows interesting properties common to all exponential functions: (a) The probability of transmission initially decreases rapidly and then flattens out to asymptotically approach (but never reach) zero and (b) the same incremental thickness of medium transmits the same fraction of the photons. The probabilities of transmission of 30-keV photons from iodine- 125 and 140-keV photons from Tc-99m as a function of thickness in liquid water are shown in Figure 2 (5). Exponential transmission of photons means that the same fraction of photons is transmitted through a given thickness of medium. Consider the medium thickness that transmits half of the photons of a given energy. This thickness is a half-value layer (HVL). Therefore, a medium that is two HVLs thick will transmit 1/2 1/2 = 1/4 of the original number of photons. The HVL and the linear attenuation coefficient µ are related by the following formula: HVL = 0.693/µ. (2) For example, for 140-keV photons in water, µ = 0.15 cm 1. From Equation (2), the HVL for 140-keV photons in water is 4.6 cm. Therefore, the probability that a 140-keV gamma ray will be transmitted through 18.4 cm (four HVLs) of water-equivalent tissue is 1/2 4 = = 6.2%. This result explains why radioactive objects in nuclear medicine patients are poorly imaged when they reside deep within the patient. Similarly, the HVL of 140-keV photons in lead is 0.3 mm. Thus, a typical 1/16 inch (1.6-mm) lead thickness for wall shielding will provide approximately five HVLs of protection and thereby decrease the transmitted intensity of 140-keV photons from Tc-99m to 1/2 5 = 1/32 = 3%. Such lead shielding is available conveniently preinstalled on wallboard sheets. January-February 1999 Simpkin RadioGraphics 159

6 Figure 3. Diagram shows the mechanics of the photoelectric effect. KE = kinetic energy of the photoelectron. TYPES OF PHOTON INTERACTIONS Of the four mechanisms by which photons interact with matter, only two are important in the photon energy range of interest in clinical nuclear medicine. The two unimportant mechanisms are quickly dealt with. These are coherent (or Rayleigh) scattering and pair production. In coherent scattering, a low-energy photon is redirected with no change in energy (and no energy deposited in the medium). Coherent scattering occurs only rarely in comparison with the photoelectric effect and Compton scattering. Pair production occurs only for high-energy (>1,022-keV) photons and is thus not routinely encountered in clinical nuclear medicine. The high-energy photon disappears; in its place, an electron-positron pair of particles is produced by a direct application of Einstein s mass-energy relationship. The photoelectric effect is one of the most important mechanisms by which photons interact. In the photoelectric effect, a photon of energy E penetrates an atom in the medium and strikes an inner-shell electron held to the atom with binding energy BE. The photon disappears; the electron is ejected from the atom with kinetic energy equal to E BE and is henceforth called a photoelectron. Figure 3 shows this interaction diagrammatically. The photoelectric effect therefore constitutes conversion of photon energy to electron kinetic energy, which is deposited locally in the medium. The photoelectric effect is both the desirable interaction by which gamma rays are detected in a gamma camera crystal of sodium iodide and the unavoidable mechanism by which radiation dose is delivered to patients and nuclear medicine workers. Radiation shielding is best achieved with materials that stop the radiation by means of the photoelectric effect because the photon energy is given directly to the shielding barrier and not radiated through the material. Figure 4. Diagram shows the mechanics of Compton scattering. e- = electron, KE = kinetic energy of the recoil electron. Because of quantum mechanical considerations, photons prefer to undergo the photoelectric effect with inner-shell electrons in atoms of the absorbing medium. The probability of the photoelectric effect occurring with a K-shell electron is approximately five times greater than with an L-shell electron. However, the energy of the photon must exceed the binding energy BE holding the electron to the atom for the electron to be dislodged by means of the photoelectric effect. On a graph of the probability of a photoelectric effect against photon energy, this fact causes sharp discontinuities or absorption edges at photon energies equal to the various electron shell binding energies in the medium. Let τ/ρ be the probability of the photoelectric effect occurring per distance divided by the density of the material. Quantum mechanics shows that, for the same numbers of electron shells available for the photoelectric effect, the chance of the interaction per distance divided by the density of the medium is proportional to Z 3 /E 3. Thus, the probability of a photoelectric effect increases dramatically with higher atomic number materials and decreases precipitously with increasing photon energy. The photoelectric effect is therefore of most importance at lower photon energies and predominates for high atomic number media such as lead. For example, compare water and lead at 140-keV photon energy. When both the atomic number and density differences are taken into account, the probability per distance of the photoelectric effect in lead is 27,000 times greater than in water. Also, compare the probability per distance of the photoelectric effect in water at 80 kev and at 140 kev. The probability at 80 kev is 6.3 times greater than that at 140 kev. Compton scattering occurs when a photon of energy E interacts with an outer-shell elec- 160 Imaging & Therapeutic Technology Volume 19 Number 1

7 Figure 5. Graph shows the probabilities of coherent scattering, photoelectric effect, and Compton scattering interactions in water. E = photon energy, scatter = scattering. tron in one of the atoms of the medium. The photon is deflected through scattering angle θ at reduced energy E. The electron is dislodged from the atom as a recoil electron with kinetic energy equal to E E. Figure 4 illustrates the mechanics of Compton scattering. The energy of the recoil electron is absorbed locally in the medium. This mechanism is analogous to that occurring on a pool table with the photon representing the cue ball and the electron representing the eight ball. The energy E of the scattered photon is linked to the scattering angle by the following formula: E = E/[(1 + E/511 kev)(1 cos θ)]. (3) Note that the form of the equation requires the photon energy E in the denominator to be in kilo electron volts (kev). Compton scattering may occur at any angle θ from 0 to 180. Grazing Compton interactions occur for θ 0 and cause little photon deviation and minimal energy transfer from the photon to the electron. Backscattering occurs through large angles (θ 180 ) and imparts maximum energy to the recoil electron. The angle through which scattering, and thus energy transfer, occurs is statistically random, with high-energy photons tending to scatter in the forward direction. For low-energy photons, the probabilities for forward scattering and backscattering are approximately equal and are approximately twice that for side scattering. For example, consider a 140-keV gamma ray from Tc-99m. This photon may scatter through 30 to create (from Eq [3]) a 135-keV scattered photon. The energy difference of = 5 kev is given to the recoil electron, which will be absorbed locally in the medium. Had the gamma ray undergone a 180 scattering event, the backscattered photon would have left the interaction site with 90.4 kev of energy and the recoil electron would have headed in the forward direction with = 49.6 kev of energy. The probability per distance that a Compton scattering event will occur is proportional to the density of the medium but is independent of the atomic number of the medium. The reason is that Compton scattering occurs with weakly bound outer-shell electrons, and the density of such target electrons is proportional to the density of the medium. The chance of a Compton scattering event is very weakly dependent on photon energy. This concept is illustrated for water in Figure 5, which shows that the probability of Compton scattering is constant (within a factor of 2) over the range of kev. Compared with the orders of magnitude changes in the probability of photoelectric effect interactions with photon energy, the former change is trivial. January-February 1999 Simpkin RadioGraphics 161

8 Figure 5 shows the probabilities of photoelectric effect and Compton scattering interactions in water. This graph shows that the photoelectric effect is most probable at photon energies below approximately 30 kev, whereas Compton scattering predominates at energies above 30 kev. For example, 140-keV photons in water are 164 times more likely to undergo a Compton scattering event than a photoelectric effect interaction. INTERNAL DOSIMETRY Radioactive materials placed in the human body for diagnostic or therapeutic nuclear medicine distribute through the body following the rules of pharmacokinetics including pathology and not physics. In general, the distribution varies with time and is spatially nonuniform on both the macroscopic and cellular levels. For example, disease of an organ may lead to nonuniform uptake of radionuclide in sections of organs of interest (and is often the target of radionuclide imaging). Even cases of assumed uniform radiopharmaceutical uptake in an organ, such as colloidal uptake in the liver, are in fact very nonuniform at the microscopic level, with the Kupffer cells bearing the bulk of the radioactivity (6). As discussed earlier, radionuclides distributed in the body emit radiation isotropically; that is, in no preferred direction. This fact causes regions near radionuclide concentrations to receive a larger radiation flux than more distant locations. In addition, attenuation and absorption of the radiation in intervening tissues may prevent the radiation from reaching distant sites. These two effects dictate that sites near radionuclide concentrations will receive significantly higher radiation doses than more distant locations. Indeed, alpha and beta particles may be completely absorbed in tissues near the decay site, so that the dose may be nil to locations just centimeters from sites of charged particle emitting radionuclide concentration. Consider an organ of density ρ throughout which a radionuclide has been distributed uniformly with activity concentration C (in becquerels per cubic centimeter). Assume that the size of this organ is large compared with the range of the emitted radiations. This situation describes the condition of radiation equilibrium, in which all energy emitted in a volume is also absorbed in the volume. If each radioactive decay emits average energy, then the radiation dose rate inside the organ is as follows: D = C/ρ, (4) with D given in million electron volts (MeV) per gram per second, in million electron volts per decay, C in decays per cubic centimeter per second, and ρ in grams per cubic centimeter. From symmetry arguments, the dose rate at the surface of this large volume will be half of that inside the organ. The reader may find the mean energy emitted per nuclear transition,, referred to as the equilibrium dose constant in older texts. The internal radiation dose may thus be estimated for extremely simple source distributions. These include isolated point sources and large organs with uniform concentrations of radionuclides emitting nonpenetrating radiations such as charged particles or low-energy photons. However, to address the more general problem of temporally and spatially varying radionuclide concentrations in variously sized organs in nuclear medicine patients, it is necessary to develop more accurate models of radiation transport in realistic models of the human anatomy. THE MIRD METHOD In 1968, the Society of Nuclear Medicine formed the MIRD Committee to investigate and standardize methods of internal dosimetry for nuclear medicine sources. Over the past 3 decades, a number of MIRD Committee publications have dealt with the various aspects of internal dosimetry. The types and energies of radiations emitted in the decay of nuclear medicine radionuclides were reviewed (7). Computer simulations were developed to mimic the transport of these radiations in both idealized and anthropomorphic geometries (8). These simulations are referred to as Monte Carlo computer techniques. The MIRD Committee developed the model of internal dosim- 162 Imaging & Therapeutic Technology Volume 19 Number 1

9 etry that is now the accepted standard (9). The work of the MIRD Committee continues today with investigations ongoing at the Radiation Internal Dose Information Center, Oak Ridge Institute for Science and Education, PO Box 117, MS 51, Oak Ridge, TN (Internet home page: htm). The MIRD method is based on assumptions of time-varying radioactive concentration uniformly distributed in one or more source organs or regions. Radiation originating from decays within one or more source organs is responsible for depositing energy in a target organ. We are interested in knowing the radiation dose in target organs, which may have no radioactive uptake. Note that the target and source may be the same organ. Indeed, the source organ will typically receive the largest radiation dose in the body. The average dose to the target organ is simply the energy transported from the source to the target organ that is deposited in the target organ divided by the mass of the target organ. In the MIRD method, the geometries of the source and target organs and the attenuating properties of the tissues in the body are presumed on the basis of standard anatomic models. Note that although MIRD phantoms have been developed to simulate idealized adults and children, individual patients will rarely match the MIRD assumptions of organ layout, size, and tissue composition. Internal dosimetry requires knowledge of the time-varying radioactive concentrations in source organs in the body. Published dose calculations assume activity distributions gleaned from limited physiologic studies of patients or animals in normal and diseased states. These assumptions will rarely match the spread of radioactivity in individual patients presenting with specific conditions. The time-varying distribution of activity in individual patients could be determined (to within the limited spatial resolution of the modality) by using parallel-opposed head scintigraphy or quantitative single photon emission computed tomography. The mean energy emitted per nuclear transition,, is dependent on the radionuclide and its various decay pathways. For example, I-131 decays via six possible beta pathways, each of which may generate gamma-ray and x-ray photons as well as Auger electrons or conversion electrons. The energy of the emitted beta particle is itself randomly chosen from a broad distribution. The emitted radiations and their energies may be complicated but are well understood from the nuclear physics literature. The units for are gray kilogram per becquerel second, gram rad per microcurie hour, or, more obviously, million electron volts per decay. Note that 1 g rad/(µci h) = Gy kg/(bq sec). Values of for the various decay pathways for common radionuclides are available (7). The fraction of radiation energy emitted from the source organ that is deposited in the target organ is the absorbed fraction, ϕ, with paired arguments (target source). The MIRD Committee determined values of ϕ(target source) using computer Monte Carlo calculations, which simulate the emission, transport, and energy-depositing interactions of radiations in the assumed patient geometry. Note that for weakly penetrating radiations, such as alpha particles or low-energy beta particles, all of the emitted radiation is absorbed locally in the source organ, for which ϕ = 1. For target organs distant from the source, ϕ 0. The specific absorbed fraction, Φ, is defined as ϕ divided by the mass of the target organ. According to these MIRD parameters, the average energy deposited in the target organ due to a radioactive decay in the source organ is simply ϕ, the product of the average energy per decay,, and the absorbed fraction, ϕ. This energy deposition then depends on the radionuclide and its decay pathway, as well as the source organ target organ pairing. The radiation dose to the target organ (of mass m) per decay in the source organ is simply ϕ /m = Φ. The assumed organ masses are based on average man models and are given for average adults of both sexes and children. The dose per decay (averaged over all decay pathways) is termed the S value. S has been evaluated for each radionuclide of interest for a large number of source organs (O s ) and target organs (O t ) by means of the following relationship: S(O t ) = Σ all decay paths ϕ(o t ) /m. (5) Also known as the dose per cumulated activity, S has units of dose per decay or dose rate per activity (eg, rads per microcurie hour [grays January-February 1999 Simpkin RadioGraphics 163

10 per becquerel second]). Values of S for many radionuclides of interest in nuclear medicine are published in MIRD Pamphlet no. 11 (10). The total dose to the target organ due to radioactivity in the source organ is proportional to the product of S and the number of decays occurring in the source organ. The number of decays is proportional to the cumulated activity, Ã, in the source organ. Ã is the area under the time-activity curve for radionuclide activity in the source organ. Thus, the dose to the target organ is as follows: D(O t ) = Ã S(O t ). (6) An equivalent method is to define a residence time, τ, as the ratio of the cumulated activity in the source organ, Ã, to the activity administered to the patient, A 0. The residence time may then be thought of as an effective time that the administered activity resides in the source organ. The equation for the dose to the target organ is then as follows: D(O t ) = Ã S(O t ) = A 0 τ S(O t ). (7) An additional dosimetric value of concern is the effective dose equivalent, H E (11). H E is a weighted sum of doses to radiosensitive organs in the body and is calculated as follows: H E = Σ all organs D organ w organ, (8) Figure 6. Graph shows the cumulated activity in the source organ, Ã, as the area under the time-activity curve. where w organ is the weighting factor assigned to each radiosensitive organ. H E is thought to conservatively best represent the risk to the irradiated individual from nonuniform dose distributions in the body. This concept certainly applies in nuclear medicine. Of concern in the calculation of the effective dose equivalent are the doses to the gonads (w = 0.25), breasts (w = 0.15), lungs (w = 0.12), bone marrow (w = 0.12) and bone surfaces (w = 0.03), thyroid gland (w = 0.03), and any additional five organs (exclusive of the skin and lens [each with w = 0.06]) that receive the highest doses in the body. The concept of H E has recently been updated to the effective dose (12). The effective dose still follows the definition in Equation (8) but with a more complete list of organs and modified organ weighting factors. Effective dose and H E from nuclear medicine radionuclides seem to be quite similar (Toohey RE, Stabin MG, written communication, 1998). The effective dose has not yet been adopted by the Nuclear Regulatory Commission. Note that the effective dose (or the H E ) is not the same as the total body dose typically reported on the package inserts for many radiopharmaceuticals. The total body dose is simply the total energy deposited anywhere in the body divided by the total mass of the body. The effective dose is more than two times (for Tc-99m) to 100 times (for radioiodines) greater than the total body dose for many common radiopharmaceuticals (Toohey RE, Stabin MG, written communication, 1998). Consider a source organ in which the timevarying activity distribution A(t) is present. The cumulated activity in the source organ, Ã = I t A(t) dt, (9) is the area under the time-activity curve (Fig 6). Ã is proportional to the number of decays that occur in the time of interest and is traditionally expressed in microcurie hours. Alternatively, Ã may be expressed in megabecquerel seconds (1 MBq sec = µci h). Note that 1 MBq sec = 10 6 decays, therefore 1 µci h = decays = 133 MBq sec. In special cases, Ã can be estimated simply. Consider a patient into whom activity A 0 is administered. If a fraction f of that activity is irreversibly bound to the source organ and the radionuclide is long-lived (or the time of interest t is short), the cumulated activity is as follows (Fig 7a): Ã(0 t) = f A 0 t. (10) For exponential removal of the radionuclide from the source organ with initial activity fa Imaging & Therapeutic Technology Volume 19 Number 1

11 a. b. Figure 7. (a) Graph shows the time-activity curve for the case of constant activity in the source organ. à is then just the product of fa 0 and the time of interest t. (b, c) Graphs show the activity in a source organ in which the activity is being removed exponentially over time, with effective half-time T 1/2, by a combination of physical decay and biologic washout. In b, the cumulated activity over the limited time of interest, from 0 to t, is the area under the exponential curve. This area is given by the indicated equation. In c, the time of interest has been expanded to t, and the c. area under the whole exponential curve is given by 1.44fA 0 T 1/2. and effective half-time T 1/2, the cumulated activity out to time t is as follows (Fig 7b): à = 1.44 fa 0 T 1/2 1/2 Over all time (t ), the cumulated activity for the exponentially decreasing activity is as follows (Fig 7c): (11) Ã(0 ) = 1.44 fa 0 T 1/2. (12) The two simultaneous mechanisms removing activity from the source organ are radioactive, or physical, decay, and biologic washout. If the metabolic removal occurs with an exponential half-time of T b and the half-life of radionuclide decay is T p, then the effective half-time T 1/2 is as follows: T 1/2 = T b T p /(T b + T p ). (13) Note that the effective half-time T 1/2 is always shorter than the shorter of either T b or T p. In the MIRD technique, source organ target organ pairs are considered individually. A realistic calculation of radiopharmaceutical dose to an organ of interest must accumulate the dose from all possible source organs. In general, such accumulation is a difficult task, even for idealized anatomy, because information on the in vivo kinetics of the administered radiopharmaceutical in an individual patient may be sparse or difficult to apply.. Consider two simple calculations of internal dose performed with the MIRD method. First, consider the dose due to an irreversibly bound liver agent. Assume that f = 85% of the 1-mCi (37.0-MBq) activity of an injected Tc-99m labeled sulfur colloid is instantaneously bound to the liver with no biologic washout. The effective half-time T 1/2 is then equal to T p = 6 hours, and the cumulated activity over all time is à = ,000 µci 6 h = 7,344 µci h ( MBq sec). What is the dose to the liver due to this activity in the liver? From MIRD Pamphlet no. 11, S(liver liver) = rad/µci h ( Gy/MBq sec), so that the dose D = à S = 7,344 µci h rad/µci h = 0.34 rad (3.4 mgy). The dose to the uterus from this cumulated activity in the liver can also be estimated. From MIRD Pamphlet no. 11, S(uterus liver) = rad/µci h ( Gy/MBq sec). The uterine dose from activity in the liver is then D = à S = 7,344 µci h rad/µci h = rad = 2.9 mrad (29 µgy). Of course, a full determination of the dose to the uterus must include contributions from all source organs, especially the excretory organs (and their radioactive contents) more proximal to the uterus. January-February 1999 Simpkin RadioGraphics 165

12 Next consider the dose to the thyroid gland due to ingestion of 10 µci (0.37 MBq) of I-131. Assume a euthyroid uptake of f = 25%. For simplicity, assume that this uptake happens instantaneously. The biologic half-time for iodine in the thyroid is 65 days and the physical half-life of I-131 is 8 days, so that the effective half-time is (65 8)/(65 + 8) = 7.1 days. The cumulated activity over all time is à = µci 7.1 days 24 h/d = 613 µci h ( MBq sec). From MIRD Pamphlet no. 11, S(thyroid thyroid) for I-131 = rad/ µci h ( Gy/MBq sec). The dose is then D = à S = 613 µci h rad/ µci h = 13.5 rad (135 mgy). Compilations of nuclear medicine doses in which all source organs are considered with standard man geometry and typical physiologic models of metabolic transport in the body have been generated in the form of simple tables of dose per administered activity in milligray per megabecquerel or rad per millicurie. Note that 1 mgy MBq 1 = 3.7 rad mci 1. These compilations include Report no. 53 of the International Commission on Radiological Protection (13) and NUREG/CR-6345 (14). The latter document was sent to all Nuclear Regulatory Commission medical licensees in Most of the clinically important radiopharmaceuticals are included. Doses to 24 target organs and the effective dose equivalents are listed in NUREG/CR-6345 for each radiopharmaceutical. The dose information in NUREG/CR-6345 should be available in every nuclear medicine department. Consider again the two dose calculations performed earlier with the MIRD method and crude assumptions about the distribution and retention of the radioactive material. For the 1- mci (37.0-MBq) Tc-99m labeled sulfur colloid injection, the liver dose per administered activity tabulated in NUREG/CR-6345 for a patient with normal liver function is 0.32 rad mci 1 ( mgy/mbq). Hence, the liver dose in this example is estimated to be 0.32 rad mci 1 1 mci = 0.32 rad (3.2 mgy), a result that is in good agreement with that of the MIRD example. However, the uterine dose tabulated in NUREG/CR-6345 for the Tc-99m labeled sulfur colloid injection is rad mci 1 ( mgy/mbq), and rad mci 1 1 mci = rad (0.05 mgy). The uterine dose calculated from activity in the liver was rad (0.029 mgy). This discrepancy is explained by the dose contributions of activity in source organs in addition to the liver. For the 10-µCi (ie, 0.01-mCi) (0.37-MBq) oral administration of I-131, the thyroid dose per administered activity tabulated in NUREG/ CR-6345 is 1,300 rad mci 1 ( mgy/ MBq). The thyroid dose is thus 1,300 rad mci mci = 13 rad (130 mgy). Once again, this result agrees well with that of the MIRD calculation. However, the importance of NUREG/CR lies not in the ability to reproduce simple, single source organ MIRD calculations. Rather, the authors of NUREG/CR-6345 have implemented detailed physiologic models for the time-dependent distribution of radioactive materials in multiple source organs. Thus, it is possible to solve dosimetry problems far more complicated than could be reasonably addressed by a clinician armed only with a table of S factors. Simple dose calculations may be required by regulations. For example, suppose the wrong radioactive material is injected into a patient. The licensee then faces a potential misadministration per Nuclear Regulatory Commission regulations. As of early 1998, the Nuclear Regulatory Commission s definition of a diagnostic misadministration (10 CFR 35.2) requires that the dose to any one organ in the patient exceed 50 rad (0.5 Gy) or the patient s effective dose equivalent exceed 5 rem (50 msv). Consider the case wherein a lung scan was ordered, but the technologist mistakenly made up and injected 4 mci (148 MBq) of the liver scanning agent Tc-99m sulfur colloid. From NUREG/CR-6345, the highest organ dose from Tc-99m sulfur colloid is to the liver and equals rad mci 1 ( mgy/mbq) administered, whereas the effective dose equivalent from this injection is rem mci 1 ( msv MBq 1 ) administered. Multiplying by the 4 mci injected activity, the liver dose is then 1.3 rad (13 mgy) and the effective dose equivalent is 0.2 rem (2 msv). Because these doses do not exceed the Nuclear Regulatory Commission s thresholds, this mistake is not considered a diagnostic misadministration. Calculating the radiation dose to the embryo or fetus of a pregnant nuclear medicine patient may be difficult because surprisingly little infor- 166 Imaging & Therapeutic Technology Volume 19 Number 1

13 mation exists on the distribution of radioactivity in the placenta and fetus. Calculation of the dose to the conceptus is also complicated by the proximity of the maternal bladder. Because urinary excretion is the route of elimination for many radiopharmaceuticals, the contents of the maternal bladder deliver a correspondingly high dose to the conceptus. Early in pregnancy, during the first 6 18 weeks after conception, the dose to the embryo or fetus is the same as that to the maternal uterus and is due to activity in maternal source organs only. Later in pregnancy, placental uptake and transfer to the fetus may occur, but information on this possibility is sketchy. Certainly, absorption of I-131 in the fetal thyroid is of concern. Readers interested in the problem of conceptus dose in nuclear medicine are referred to the recent article by Russell et al (15). Given the simplicity of the MIRD method and its applications, such as NUREG/CR-6345, the user is reminded of the errors implicit in application of the MIRD method to individual patients. Individuals will usually not match the assumptions used in generating the MIRD data. For example, patient size and source organ target organ geometry will vary from the standard man of the MIRD method. The time course of activity distribution in each patient should ideally be measured and may vary widely from the simplifying assumptions used in the MIRD calculations. The MIRD method assumes uniform radionuclide concentration in each source organ. In actuality, the activity may concentrate in individual cells in an organ. Also, nonuniform organ uptake is a prime diagnostic indicator of disease and a fundamental reason for performing nuclear medicine imaging. Radiation dose to a target organ calculated with the MIRD method is an average that may poorly represent the magnitudes of localized maximum doses within the organ and possibly misrepresent the risk to the organ. Despite these caveats, the MIRD schema remains the standard method for calculating internal radiation dose from radiopharmaceuticals. REFERENCES 1. Kocher DC. Radioactive decay data tables. DOE/TIC Springfield, Va: National Technical Information Service, Stopping powers for electrons and positrons. ICRU Report no. 37. Bethesda, Md: International Commission on Radiation Units and Measurements, Simpkin DJ, Cullom SJ, Mackie TR. The spatial and energy dependence of bremsstrahlung production about beta point sources in H 2 O. Med Phys 1992; 19: Photon, electron, proton, and neutron interaction data for body tissues. ICRU Report no. 46. Bethesda, Md: International Commission on Radiation Units and Measurements, 1992; Berger MJ, Hubbell JH. XCOM: photon cross sections on a personal computer. NBSIR Washington, DC: National Bureau of Standards, Makrigioros GM, Ito S, Baranowska-Kortiylewicz J, et al. Inhomogeneous deposition of radiopharmaceuticals at the cellular level: experimental evidence and dosimetric implications. J Nucl Med 1990; 31: Weber DA, Eckerman KF, Dillman LT, Ryman JC. MIRD: radionuclide data and decay schemes. New York, NY: Society of Nuclear Medicine, Snyder WS, Ford MR, Warner GG. Estimates of specific absorbed fractions for photon sources uniformly distributed in various organs of a heterogeneous phantom. MIRD Pamphlet no. 5 (revised). New York, NY: Society of Nuclear Medicine, Loevinger R, Budinger TF, Watson EE. MIRD primer for absorbed dose calculations. Revised edition. New York, NY: Society of Nuclear Medicine, Snyder WS, Ford MR, Warner GG, et al. S absorbed dose per unit cumulated activity for selected radionuclides and organs. MIRD Pamphlet no. 11. New York, NY: Society of Nuclear Medicine, International Commission on Radiological Protection. Recommendations of the International Commission on Radiological Protection. ICRP Publication no. 26. Oxford, England: Pergamon, International Commission on Radiological Protection recommendations of the International Commission on Radiological Protection. ICRP Publication no. 60. Oxford, England: Pergamon, International Commission on Radiological Protection. Radiation dose to patients from radiopharmaceuticals. ICRP Publication no. 53. Oxford, England: Pergamon, Stabin MG, Stubbs JB, Toohey RE. Radiation dose estimates from radiopharmaceuticals. NUREG/CR Oak Ridge, Tenn: Oak Ridge Institute for Science and Education, Russell JR, Stabin MG, Sparks RB, Watson E. Radiation absorbed dose to the embryo/fetus from radiopharmaceuticals. Health Phys 1997; 73: This article meets the criteria for 1.0 credit hour in category 1 of the AMA Physician s Recognition Award. To obtain credit, see the questionnaire on pp January-February 1999 Simpkin RadioGraphics 167