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IMAGING & THERAPEUTIC TECHNOLOGY |
1 From the Radiation Internal Dose Information Center, Oak Ridge Institute for Science and Education, 140 E Vance Rd, Oak Ridge, TN 37831-0117. From the AAPM/RSNA Physics Tutorial at the 1998 RSNA scientific assembly. Received October 4, 1999; revisions requested October 15 and received December 23; accepted December 30. Supported by the U.S. Department of Energy under a contract with Oak Ridge Associated Universities. Address reprint requests to R.E.T. (e-mail: tooheyr@orau.gov).
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Abstract |
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 Top Abstract IntroductionBasic ConceptsThe MIRDose ProgramConclusionsReferences |
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Index Terms: Dosimetry • Radiations, measurement • Radionuclides, radiation dose
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Introduction |
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TopAbstractIntroductionBasic ConceptsThe MIRDose ProgramConclusionsReferences |
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This article provides an overview of the theoretical basis of the MIRD technique and its practical applications. The basic MIRD equation and its components are reviewed, followed by calculations of internal doses (both organ and effective doses) with use of the MIRD technique. Examples of the dose estimates for some commonly used radiopharmaceuticals are provided. Special concerns for the pregnant or lactating patient are addressed, with explanations of available tools for fetal dose calculations and of current recommendations for the nursing infant. Modification of dose estimates for the standardized individual to make them more patient-specific is explained, and current trends in internal dosimetry for radiopharmaceuticals, particularly for therapy agents, toward true patient-specific models are briefly discussed.
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Basic Concepts |
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TopAbstractIntroductionBasic ConceptsThe MIRDose ProgramConclusionsReferences |
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Calculating Absorbed Dose Rate
The MIRD method for calculating dose rate has been described by Loevinger et al (1) and is explored herein, beginning with determining the absorbed dose rate for an extremely large volume (almost infinite dimensions) of tissue-equivalent material containing a uniform distribution of radioactive material throughout. The MIRD schema uses numerous symbols, and a summary of these symbols, the quantities they represent, and their units is provided in Table 1.
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Because activity is the number of transitions per unit time,
If all of the energy emitted is absorbed in the material,
The terms that represent the components of dose rate can be replaced by the symbols used in the MIRD schema— = absorbed dose rate, A = amount of activity, m = tissue mass, A/m = activity per unit mass or concentration, and E = the average energy emitted per nuclear transition—and are shown as follows:
A constant to remove the proportionality can be used to give the following equation:
For example, to calculate dose rate in rad per hour if A is in microcuries (µCi), m is in grams (g), and E is in megaelectron volts (MeV) per transition, k has a value of 2.13, derived as follows:
The mean energy E for a given radionuclide is a constant and can be multiplied by the constant k to yield a new constant designated in the MIRD schema by the uppercase Greek letter 
.
For example,
Therefore, the dose rate can be expressed as follows:
Dose values can be converted from these traditional units to the international system (SI) units by the following relationship: 1 gray (Gy) equals 100 rad, so 1 rad equals 1 cGy. Similarly, activity can be converted to SI units by the following relationship: 1 µCi equals 3.7 x 104 becquerel (Bq).
When most radionuclides decay, a number of different types of radiation (particles and photons) will be emitted. Table 2 gives a partial listing of the radiations emitted by technetium-99m. Frequently, a specific radiation (particle or photon) is not emitted in every nuclear transformation; the fraction of transformations in which the radiation is emitted is called its abundance and is indicated by the symbol ni. Thus, for a given radiation i, i = k ni Ei.
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The range of these radiations in soft tissue will vary greatly according to their unique characteristics as shown in Table 3. For the huge volume of tissue we have been discussing, these ranges are not important; however, the human body and its individual organs do not fulfill the criteria of an infinite volume in terms of the ranges of some types of radiation. A large fraction of photon radiation emitted will escape from the body without giving up any energy to tissue.
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In the MIRD schema, this factor is designated by the lowercase Greek letter 
. The dose rate equation for a target being irradiated by a source becomes the following:
The dose rate for a target from all sources can be expressed as follows:
A separate absorbed fraction is required for each type of radiation emitted from a source and irradiating a given target; however, simplifications can sometimes be made. When an average organ dose is adequate, radiations can be divided according to two types for convenience: (a) nonpenetrating, which refers to all forms of radiation that are readily attenuated; that is, the energy is deposited in the immediate vicinity of the source, and (b) penetrating, which refers to radiations that can travel long distances before interacting and depositing their energies.
Alpha particles, beta particles, and electrons are usually classified as nonpenetrating radiations because of their short ranges in tissue. Although for most organs, beta particles and electrons give up their energies within the source organ where the emission occurs, some special cases exist, such as small blood vessels or marrow spaces.
Because of the way photons (gamma rays and x rays with energies greater than 10 keV) interact with tissue, some energy may be given up outside the source organ. These radiations are classified as penetrating. X rays with energy greater than or equal to 10 keV are treated as gamma rays in determining absorbed fractions. X rays with energy less than 10 keV are considered to be nonpenetrating.
For nonpenetrating radiations, all of the energy emitted from activity in an organ is assumed to be absorbed in that organ. Thus, no energy from that organ would be absorbed in any other organ. The absorbed fraction when the source and target organs are the same would be equal to one. The absorbed fraction for any other target would be zero.
For penetrating radiations, only a fraction of the energy emitted in a source organ is absorbed in that organ. Thus, some of the energy emitted in that organ will be absorbed in other organs. Some will escape from the body completely. The absorbed fractions for all targets will have some value between zero and one.
To determine absorbed fractions for photons, a model of the source-target configuration must be developed. Several different anatomic models and methods for making these calculations have been proposed. Normally geometric volumes such as spheres and ellipsoids are used as "phantoms" for the human body and its organs. The sizes and shapes of the volumes that resemble the organs and tissues of an average person at different stages of life are defined by mathematical equations. Table 4 is a partial listing of absorbed fractions from MIRD pamphlet number 5 (2). The complete listing shows absorbed fractions for 12 energies from 10 keV to 4 MeV.
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; therefore, the specific absorbed fraction for a target being irradiated by a source can be represented by (rk 
rh) = (rk rh)/mk.
For a particular mathematical model, the masses of the targets are constants. For example, the liver in the reference man phantom of MIRD pamphlet number 5 has a mass of 1,800 g. The dose rate equation for a target in a given model being irradiated by a source in the model can then be written as follows:
Absorbed fractions are usually determined by Monte Carlo methods because of the complicated geometric configurations that must be considered in the calculations. The Monte Carlo methodology uses a computer program that follows the histories of a large number (typically more than 1 million) of photons. Each photon is emitted from a random point in the source organ in a random direction. The photon travels a distance equal to its mean free path length and undergoes an interaction wherein some energy may be absorbed, and the photon may be scattered in a new, random direction. Each photon is followed until it is completely absorbed or escapes the body. The total energy deposited in the target organ is tallied, and the absorbed fraction is then calculated (3). Multiple computer runs are typically performed, and the results of the runs are compared to determine the variance of the calculated absorbed fraction. When the coefficient of variation is greater than 50%, the Monte Carlo results are not used, as is the case for the thyroid being irradiated by the liver; thus there is no entry in Table 4 for this combination.
The specific absorbed fraction has a useful property that makes it possible to calculate absorbed fractions when Monte Carlo results are not statistically reliable. If the activity is uniformly distributed in the source and if the source and target organs are in a homogeneous absorbing material large enough that edge effects are negligible, the specific absorbed fraction is independent of which organ is designated as source and which is target.
This reciprocity relationship can be expressed by symbols as follows:
Another technique used to calculate absorbed fractions when Monte Carlo calculations have large coefficients of variation has been called the buildup factor method. This method employs the energy-absorption buildup factors and the linear photon attenuation and absorption coefficients associated with a given energy and density of medium to determine specific absorbed fractions.
Table 5 lists specific absorbed fractions for a source in the liver of the reference man phantom. The full table as published by the MIRD Committee shows specific absorbed fractions for activity in 20 source organs irradiating 20 target organs, with photons of 12 energies from 10 keV to 4 MeV.
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For a given radionuclide and a specific source-target organ combination in a mathematical model, the quantity 
i i is a constant. The MIRD Committee has called these values S factors and has tabulated them for 117 radionuclides and all the source-target organ combinations in the reference man phantom. The S factor is defined as follows:
The dose-rate equation can be simplified as follows:
Table 6 lists S factors for Tc-99m in five source organs irradiating 20 target organs of the reference man phantom. The full table includes 20 source organs.
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If the amount of activity in a source does not remain constant, the absorbed dose equals the integral of the (varying) dose rate over the period of interest, expressed as follows:
Dose rate depends on activity, which varies with time. The activity in a source is determined by the biodistribution of the radiopharmaceutical, the metabolism of the person, and the radioactive decay of the radionuclide. The assumption is usually made that the S factor does not change over the time period of interest; therefore, the equation for absorbed dose can be written as follows:
The MIRD schema uses the term cumulated activity à to represent 
A(t)dt, the integral of activity over time, expressed as follows:
Let us examine a simple model of activity A0 introduced into a single compartment (eg, blood) and eliminated by both a biologic mechanism and radioactive decay to get a basic understanding of the determination of cumulated activity by integrating the activity as a function of time.
The fraction of a material that is removed from a source per unit time by biologic processes is called the biologic disappearance constant 
b and is considered to be the same whether the material is stable or radioactive. The following equation shows the number of atoms remaining in a compartment as a result of biologic disappearance of the material as a function of time. From this equation, the biologic half-time Tb (the time at which the number of atoms N is one-half of the initial number N0) can be derived. The relationship of the biologic half-time and the biologic disappearance constant is shown as follows:
The following equation shows the activity remaining as a result of radioactive (or physical) decay as a function of time. From this equation, the physical half-life Tp—that is, the time at which the activity A is one-half of the initial activity A0—can be derived. The relationship of the physical half-life and the physical decay constant, p, is also shown:
The activity remaining in a compartment as a function of time after administration as a result of both physical decay and biologic disappearance can be expressed as follows:
The two decay constants are added to show the effective clearance as a result of physical decay and biologic disappearance, and from that relationship, the equation for the effective half-time Te is derived as follows:
Equation (22) can be integrated to give cumulated activity Ã. The effective disappearance constant e can be substituted wherever the sum b + p appears, as follows:
The dose to a target organ from all source organs is estimated by using Equation (19):
The residence time 
of a radionuclide in a source can be used instead of cumulated activity in estimating the absorbed dose to a target. The residence time is defined as follows:
h, without decay or biologic removal. Therefore, the residence time can be thought of as a "mean" or "effective" life of the administered activity A0 in the source organ h. It is important to remember that residence time accounts for both physical decay and biologic removal.
The MIRD equation for absorbed dose can be written as shown in Equation (19) or as follows:
The schema developed by the MIRD Committee is applicable to calculating absorbed dose estimates for almost any situation, although information has been provided in tabular form primarily for the calculation of average organ doses. However, by determining the appropriate absorbed fractions and cumulated activities, one can estimate the absorbed dose for other configurations and for nonuniform distributions of activity.
Whole-Body Dose and Effective Dose Equivalent
Thus far, the absorbed doses calculated have been to single target organs, and, depending on the biokinetics of the administered radiopharmaceutical, the individual organ doses can range over several orders of magnitude. Consequently, a single parameter that relates to the radiation dose delivered to the body as a whole is needed to evaluate and compare the radiation risks of different procedures. Historically, the parameter used for this function is the whole-body dose or total-body dose. This quantity is defined as the total radiation energy absorbed in the body divided by the mass of the body, which is taken as 70 kg for the reference man phantom. The whole-body dose is calculated in the MIRD schema by using the published S factor for the combination of whole body as source organ and whole body as target organ. The ratio of whole-body dose to the highest single organ absorbed dose varies from near unity for radiopharmaceuticals that tend to be uniformly distributed in the body (eg, tritiated water) to less than 1% for radiopharmaceuticals that have a highly nonuniform distribution (eg, all radioiodine compounds).
In 1977, the International Commission on Radiological Protection (ICRP) introduced the parameter effective dose equivalent, which is a weighted sum of the individual organ absorbed doses (4). The tissue weighting factor for each organ was defined as the ratio between the absorbed dose delivered to the whole body, which would confer a certain probability of cancer induction, and the absorbed dose in a single organ (HT), which would confer the same probability of cancer induction in that organ. For example, a dose of 12 rad to the whole body confers some probability of cancer induction; a dose of 100 rad to the lungs results in the same numerical probability of lung cancer induction; thus, the tissue weighting factor for lung is set equal to 0.12. The product of the tissue weighting factor WT and the absorbed dose equivalent in an organ is called the organ effective dose equivalent; the sum of organ effective dose equivalents is called the effective dose equivalent HE and is calculated as follows:
(The ICRP uses the symbol HT for the absorbed dose in an organ or tissue, which is the same quantity as D[rk] in the MIRD formalism.)
The 1977 ICRP tissue weighting factors are given in Table 7. In this fashion, an overall cancer risk can be computed for a situation in which different organs receive different doses, with or without external irradiation of the whole body. The ICRP developed this method for use in a risk-based system of occupational radiation protection and not for application to patient dosimetry in nuclear medicine procedures. However, if we wish to compare procedures and the resulting patient doses for assessment of risk versus benefit, effective dose equivalent is a more appropriate parameter than whole-body dose, because it takes into account the different sensitivities of the organs. In 1990, the ICRP adopted a different set of tissue weighting factors and renamed the weighted sum of organ absorbed doses as the effective dose; however, the concept and formalism are identical to that for computing effective dose equivalent (5). As is the case for whole-body dose, the ratio of the effective dose equivalent to the largest organ absorbed dose varies widely, with values less than 1% for the radioiodines (6).
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The MIRDose Program |
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TopAbstractIntroductionBasic ConceptsThe MIRDose ProgramConclusionsReferences |
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Various improvements to the phantom have been published, each of which was considered to be a more realistic representation of the three-dimensional structure of the human body. One of the more significant of these improvements is the revised model for bone and marrow developed by Eckerman (9), which defined, for dosimetric purposes, the distribution of the cells at risk in the skeleton—that is, the osteogenic cells on endosteal surfaces of bone and hematopoietic stem cells in red marrow. Although not yet officially adopted by the MIRD Committee, Eckerman's model has been incorporated into the MIRDose program.
Pediatric and Pregnancy Phantoms
The Fisher-Snyder adult phantom was scaled for pediatric use by choosing three orthogonal scaling factors for each major region of the phantom (head, trunk, and legs) to reduce the body size to that appropriate for a child. However, this process did not allow for the different relative sizes of the internal organs in pediatric patients. Cristy (10) developed a series of phantoms that describes not only the external dimensions but also more realistic sizes and shapes of the internal organs for newborns and for children aged 1, 5, 10, and 15 years. The revised pediatric phantoms have been incorporated into the MIRDose program.
For many years, fetal doses were estimated to be the same as the dose calculated to the nongravid uterus. Cloutier et al (11) published a model that tried to account for the changing size and shape of the fetus throughout the course of pregnancy. This model was used primarily to calculate the photon dose to the fetus from activity in the mother's urinary bladder, which is normally the maternal source organ contributing the largest fraction of fetal dose. Stabin et al (12) subsequently published a set of mathematical phantoms developed to represent the pregnant mother at 3, 6, and 9 months gestation. The uterus is represented by different geometric shapes at different times, and the displacement of the other abdominal organs as the uterus increases in size is also taken into account. However, the embryo-fetus is represented as a uniformly distributed mass of tissue that completely fills the uterus. Because of the variable positioning of the fetus during pregnancy, no effort was made to model the various fetal organs, and the entire embryo-fetus was considered to be uniformly irradiated by photons originating from the various source organs in the mother's body. For early pregnancy (the first 6–7 weeks), the fetal dose is still considered to be equal to the dose to the nongravid uterus. These pregnancy models have also been incorporated into the MIRDose program.
Fetal Dosimetry
The pregnancy models enabled fetal dose calculations to be performed for all radiopharmaceuticals, but they did not take into account cross-placental transport of radioactivity, which results in fetal self-irradiation. Russell and colleagues (13, 14) performed an extensive literature search and analysis of experimental data from animal models and published compilations of fetal dose tables for all common radiopharmaceuticals, including fetal self-doses where data permitted reasonable estimates of fetal uptake.
In almost every case, the diagnostic benefit to the mother outweighs the risk of any irradiation of the fetus. However, there is one situation in which severe fetal injury can be incurred from administering a radiopharmaceutical to the mother, and that is use of iodine-131 therapy for ablation of the thyroid in cases of hyperthyroidism or carcinoma. Radioactive iodine readily crosses the placenta and concentrates in the fetal thyroid, where, because of its small organ mass, high radiation doses are received. Watson (15) has published a model and dose tables for the fetal thyroid, beginning at 3 months gestation, the onset of fetal thyroid function. Fetal thyroid dose conversion factors for I-131 sodium iodide range up to 2,150 rad/mCi (580 mGy/MBq) administered to the mother, and fetal thyroid ablation results from typical doses. Consequently, pregnancy testing is absolutely indicated for all women of child-bearing age before they undergo I-131 sodium iodide therapy. Unfortunately, one or two cases of inadvertent fetal thyroid ablation continue to occur each year in the United States.
Lactating Patients
Some radiopharmaceuticals are excreted in breast milk, and nursing mothers who require nuclear medicine procedures must be counseled about the need to interrupt or, in some cases, discontinue breast feeding. Infant doses have been computed from a standard model of breast feeding, which assumes that the infant nurses at 3-hour intervals and consumes 1 L of milk per day. Literature-reported values of radiopharmaceutical excretion in breast milk provide an estimate of the radioactivity ingested by the infant, which is assumed to be rapidly and completed absorbed from the gastrointestinal tract and to have biokinetics similar to those in an adult. The U.S. Nuclear Regulatory Commission (16) advises that infant doses from breast feeding should be less than 1 mSv effective dose equivalent. To meet this goal, complete cessation of breast feeding is indicated for mothers scheduled to undergo gallium-67 citrate and I-131 sodium iodide therapy. Interruption for 12 hours is indicated for those who will be given Tc-99m macroaggregated albumin, Tc-99m–labeled red blood cells (in vivo labeling), Tc-99m sulfur colloid, and indium-111–labeled white blood cells. Interruption for 24 hours is indicated for women who will receive Tc-99m pertechnetate, I-123 metaiodobenzylguanidine, and Tc-99m–labeled white blood cells, and, for those receiving thallium-210 chloride, an interruption of 168 hours is recommended. In all cases in which nursing is interrupted, the breasts may be pumped and the milk refrigerated and used after the radioactivity has decayed.
Patient-specific Dosimetry
The ultimate goal of radiopharmaceutical internal dosimetry is to develop a method whereby the radiation doses to the organs of a specific patient may be estimated, rather than those of a standard phantom. As more and more therapeutic applications of radiopharmaceuticals are developed, patient-specific dosimetry will be needed to estimate both the probabilities of tumor control and of complications arising in normal tissue, as is standard practice in external beam radiation therapy.
Patient-specific radiopharmaceutical dosimetry requires two sets of information: patient-specific biokinetic data for the radiopharmaceutical of interest and a three-dimensional voxel phantom conforming to the individual patient to derive S factors by means of the usual Monte Carlo approach. The former is easily obtained by administering a tracer dose to the patient and by using normal imaging and excretion data to develop an individual biokinetic model. The latter must be obtained by digitizing magnetic resonance or computed tomographic (CT) images of the patient.
In current radiation therapy planning, patient organ boundaries are essentially identified in hands-on displays of scan data by using commercially available treatment planning software. In an attempt to automate this process, Sparks (17) has demonstrated the feasibility of using a Bayesian classifier to identify organs and tissues from CT data. Sparks used 30–40 CT sections from different subjects at approximately the same anatomic position to generate multidimensional probability distributions from a randomly selected group of images in which the organs and tissues had been previously defined. The remaining images were then used as "test" images to determine the efficiency of the algorithm. In this feasibility study, approximately 90% of the organ pixels were correctly identified. This method can be easily generalized into three dimensions by simply including one additional probability density function for pixels in the z direction. The classified images can then be used as the basis for the automated implementation of a voxelized Monte Carlo transport phantom for each individual patient undergoing radiopharmaceutical therapy. This organ identification method seems promising and could possibly be extended to a complete and useful status.
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Conclusions |
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TopAbstractIntroductionBasic ConceptsThe MIRDose ProgramConclusionsReferences |
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Footnotes |
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LEARNING OBJECTIVES After reading this article and taking the test, the reader will be able to: • Define the parameters used in the MIRD dose schema. • Use MIRD tables to compute patient doses from typical nuclear medicine procedures. • Describe special considerations appropriate for pregnant and lactating patients.
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References |
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TopAbstractIntroductionBasic ConceptsThe MIRDose ProgramConclusionsReferences |
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This article has been cited by other articles:
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  S. A. Rivkees and C. Dinauer An Optimal Treatment for Pediatric Graves' Disease Is Radioiodine J. Clin. Endocrinol. Metab., March 1, 2007; 92(3): 797 - 800. [Abstract] [Full Text] [PDF]
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S. Rivkees Radioactive Iodine Use in Childhood Graves' Disease: Time to Wake Up and Smell the I-131 J. Clin. Endocrinol. Metab., September 1, 2004; 89(9): 4227 - 4228. [Full Text] [PDF]
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 S. A. Rivkees and E. A. Cornelius Influence of Iodine-131 Dose on the Outcome of Hyperthyroidism in Children Pediatrics, April 1, 2003; 111(4): 745 - 749. [Abstract] [Full Text] [PDF]
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