INTRODUCTION
I AM honored to give the 2015 Taylor lecture to honor Lauriston S. Taylor. I met Dr. Taylor after his retirement as the president of the National Council on Radiation Protection and Measurements (NCRP). He frequently was in the NCRP office, and at coffee breaks and lunchtime, he would welcome the working group and impart a sense of the benefit that a member’s participation provided to NCRP.

Three previous Taylor lectures have dealt with aspects of the radiation protection issues imposed by internally deposited radionuclides. Newell Stannard in the 14th Taylor Lecture (^{Stannard 1990} ) focused on the research supporting the dosimetric models of radiation protection. William J. Bair in the 21st Taylor Lecture (^{Bair 1997} ) focused on the health effects from exposure to radionuclides as they apply to members of the public and workers. Patricia W. Durbin, in the 31th Taylor Lecturer (^{Durbin 2008} ), summarized the search for chemical agents that might accelerate the elimination of internally deposited radionuclides, particularly actinides, from the body. As noted by Fred A. Mettler, Jr., in his 38th Taylor Lecture (^{Mettler 2015} ), we do indeed stand on the shoulders of giants. I am humbled to be a member of the set of lecturers (Table 1 ) who have honored Dr. Lauriston S Taylor, the NCRP founding President (1929–1977) and President Emeritus (1977–2004).

Table 1: Past Taylor Lecturers.

I will focus on the evolution of the dosimetry system of internal emitters and note the role played by various events and advances in technology.

DOSIMETRY SYSTEM
In 1925, the International Congress of Radiology formed the X-Ray Units Committee that became the International Commission on Radiation Units and Measurements, to which Dr. Taylor was appointed. The impetus for this action was the critical need for an agreed upon physical quantity for ionizing radiation exposure. At the 1928 meeting of the Congress, the roentgen was defined as “the exposure when the x-ray or gamma-ray field produces 1 e.s.u (electrostatic unit) of negative charge in 0.00129 grams of air.” At this meeting, the Congress formed the International Advisory Committee of X-Ray and Radium Protection that was to become the International Commission on Radiological Protection (ICRP). Dr. Taylor, then with the National Bureau of Standards and a U.S. representative to the 1928 meeting of the Congress, formed the U.S. Advisory Committee on X-Ray and Radium Protection, which became the National Council on Radiation Protection and Measurements (NCRP). The U.S. Committee in 1934 set a daily exposure limit of 0.1 R (^{NCRP 1934} ). The unfortunate experience with radium in the 1920s among young women working as dial painters and the use of radium as a tonic were reviewed by the Committee, which in 1941 adopted a radium body burden limit of 0.1 μg (0.1 μCi) (^{NCRP 1941} ).

Procedures evolved for calculations of the internal dose from therapeutic implants of radium and radon as capsules, needles, or seeds. The Manchester System (^{Meredith 1947} ), which consisted of tables providing the exposure-rate values at various distances from different source rays, was one such widely used procedure. Herbert M. Parker, the first Taylor lecturer, was involved in the development of these tables (^{Paterson and Parker, 1934} ). In the late 1930s, manmade radionuclides became available for medical use with the availability of charged particle accelerators and cyclotrons. ^{Marinelli et al. (1948a, 1948b, 1948c)} published three papers detailing a computational dosimetry framework for internal emitters that was widely accepted and formed the beginning of our modern computational dosimetry system for internal emitters.

Marinelli initially considered only the beta particle emission from a uniformly distributed radionuclide. As the roentgen was the only defined physical dose quantity, Marinelli’s expressed the beta dose as equivalent roentgen. The total dose, D _{β} , in equivalent roentgens, due to the completed decay of radionuclide uniformly distributed in a tissue is:

where K _{β} = 88 Ē _{β} T , C is the initial activity concentration of the beta emitter (μCi g−1), Ē _{β} is the average energy (MeV) of the beta particles per decay, and T is the half-life (d) of the radionuclide. This expression assumes that all of the beta energy is absorbed within the tissue containing the radionuclide.

Marinelli et al. also addressed the calculation of the dose to a tissue containing a gamma emitter. Their approach was analogous to that used for implants of gamma-ray sources. The total dose D _{γ} , in roentgens, due to gamma rays emitted in the complete decay of the radionuclide uniformly distributed in a tissue, is:

where K _{γ} = 1.44 t I_{γ} × 10−3 is the number of roentgens at 1 cm distance in air due to the complete decay of the unshielded point source of 1 μCi, 1.14 t is the average life in hours of the radionuclide of half-life t (h), and I _{γ} is the dose rate in roentgens per hour at 1 cm in air from an unshielded point source of 1 mCi. Although one could write a general equation for the geometry factor, at this time it was not possible to evaluate the factor for arbitrary tissues.

For a point at the center of a sphere of radius R , the geometry factor g could be evaluated as

where μ is the linear absorption coefficient (cm^{−1} ). Marinelli et al. were able to approximate g for a right cylinder used to represent the trunk of the body, but it was not possible to do the computations for nonspherical geometries. ^{ICRP Publication 2 (1959)} assumed an effective spherical representation of the organs.

In 1946, the NCRP was reorganized with a subcommittee formed on internal dose, chaired by K. Z. Morgan (Fig. 1 ) of Oak Ridge National Laboratory (ORNL). A series of tripartite conferences with Canada and the United Kingdom were held from 1949–1953 (^{Taylor 1984} ) to exchange information underlying radiation protection practices in the various programs during the war years. The meetings resulted in agreements on the “Standard Man” model representing a typical radiation worker, including parameters of the respiratory and gastrointestinal tract. Morgan, who was chairing a similar task force within ICRP, undertook the responsibility for the calculations of the maximum permissible amounts of radionuclides in the body and the maximum permissible concentrations in air and water for the radionuclides. Thus began ORNL’s long-term involvement in the computational efforts addressing internal emitters. The first set of radiation protection guidelines for internal emitters was published by ^{NCRP (1953)} and then by ^{ICRP (1955)} . By that time, the ICRU (1953) had defined the physical quantity absorbed dose as the energy imparted to matter by ionizing particles per unit mass of irradiated matter. The unit of absorbed dose was the rad; one rad is 100 erg g^{−1} . The initial guidance on internal emitters was revised by the ^{NCRP (1959)} and by ICRP (1960), which served as the basis for occupational radiation protection in the U.S. until 1987.

Fig. 1: K.Z. Morgan, former director of the Health Physics Division of Oak Ridge National Laboratory.

The Society of Nuclear Medicine, formed in 1954, recognized a need to improve the computation of absorbed dose for diagnostic nuclear procedures. It noted that the descriptions of the emissions of the radionuclides were often incomplete, organs and tissues of the body were poorly represented by spheres, and the computation of absorbed dose needed to be made in a more consistent manner. These were all issues and concerns noted by Marinelli et al. Two papers by ^{Ellett et al. (1964, 1965)} made possible the formulation of a computational framework that would be complete and simple. Ellett et al. defined the absorbed fraction quantity as the fraction of the energy emitted by a source of gamma rays that is absorbed in a specific volume of tissue. They performed Monte Carlo calculations for photon sources of various energies and for target volume of various sizes and shapes. The absorbed fraction quantity defined for photons could be extended to other radiations and makes possible formulation of the equations of internal dosimetry in general terms, independent of the radiation type and energy. The Medical Internal Radiation Dose (MIRD) Committee formed by the Society of Nuclear Medicine in 1965 published a series of pamphlets providing guidance on various topics. The first pamphlet, authored by ^{Loevinger and Berman (1968)} , referred to as the MIRD Schema, set forth the unified approach to dosimetry, which revolutionized internal dosimetry. Pamphlet No. 1 was updated in 1976 (^{Loevinger and Berman 1976} ). Pamphlet 3 (^{Brownell et al. 1968} ) addressed the absorbed fraction quantity per ^{Ellett et al. (1964, 1965)} , and Pamphlet 5 (^{Synder et al. 1969} ) tabulated the quantity for a monoenergetic photon source within a heterogeneous mathematical phantom representing an adult. Pamphlet 4 (^{Dillman 1969} ) was the first in a series that addressed the radiations emitted in the decay of radionuclides of interest in nuclear medicine. The first five pamphlets issued by the MIRD Committee, listed in Table 2 , were in direct response to stated concerns within the nuclear medicine community and formed the basis of the computational dosimetry for internal emitters within radiation protection, as in ICRP Publication 30 issued in 1979. Differences in nomenclature existed (^{Bolch et al. 2009} ) within the computational frameworks of nuclear medicine and radiation protection, but they shared a common objective. Dillman’s efforts regarding tabulation of the various radiations emitted by radionuclides were documented in the EDISTR computer program (^{Dillman 1980} ) used to produce ICRP Publication 38 (^{ICRP 1983} ) and later updated in production of ICRP Publication 107 (^{ICRP 2008} ).

Table 2: First five pamphlets published by the MIRD Committee.

COMPUTATIONAL DOSIMETRY FRAMEWORK
The computational framework for assessment of internal emitters involves mathematical models representing the routes of intake of the radionuclide into the body, the spatial and temporal distribution of radionuclide after uptake to blood, and the absorbed energy within tissues of the body. Consider an individual of age t _{0} experiencing an acute intake of a radionuclide. The equivalent dose rate, Ḣ (r _{T} , t _{0} , t ) in tissue or organ r _{T} at time t post the intake due to activity present in region r _{s} of the body can be written as:

where A (r _{s} ,t ) denotes the activity (Bq) of the radionuclide present in source region r _{s} at time t , and the coefficient S_{w} (r _{T} ← r _{s} , t _{0} + t ) is the equivalent dose rate in r _{T} per activity (Sv s^{−1} Bq^{−1} ) in r _{s} . The summation extends over all regions within which the radionuclide resides. These regions include both living tissues as well as the contents of the walled organs; e.g., the segments of the gastrointestinal tract and urinary bladder. Eqn (4) provides a separation of the biokinetic considerations governing the spatial and temporal fate of the radionuclide in the body, embodied in A (r _{s} , t ), from the physical aspects of the radiations emitted by the radionuclide which are embodied in S _{w} , including the radiation weighting factors defining equivalent dose.

The S _{W} coefficient for an individual of age t _{0} is given by:

where the outer summation extends over the types of radiations emitted by the radionuclide and weights the absorbed energy given by the inner summation with the applicable radiation weighting factor, w _{R} . The inner summation is the absorbed energy of radiation of type R (e.g., alpha, electron, photon, etc.) emitted with yield Y _{i} [(Bq s)^{−1} ] and energy E _{i} (joules). The specific absorbed fraction Φ_{R} (r _{T} ← r _{s} , E _{i} , t _{0} ) is the fraction of the energy E _{i} of radiation of type R emitted in source region r _{s} that is imparted per mass to target region r _{T} (kg^{−1} ). The specific absorbed fraction data are derived for reference males and females of fixed ages, as detailed in ICRP Publication 89 (^{ICRP 2002} ).

The specific absorbed fraction Φ_{R} (r _{T} ← r _{s} , E _{i} , t _{0} ) is the absorbed fraction quantity introduced by ^{Ellett et al. (1964, 1965)} divided by the mass of the target tissue r _{T} . MIRD Pamphlet 5 (^{Synder et al. 1969} ) tabulated Monte Carlo-derived specific absorbed fractions for monoenergetic photon emission in a mathematical representation of the adult anatomy, which were used in the dosimetric calculations of ICRP Publication 30. ^{Cristy (1980)} developed an age-specific mathematical representation of the body for newborn, 1, 5, 10, and 15-y olds that, with the adult, were used in ICRP’s series of publications (^{ICRP 1996} ) on age-dependent dose coefficients.

ICRP Publication 60 (^{ICRP 1991} ) renamed the two dose quantities of radiation protection as equivalent dose and effective dose, and Publication 68 (^{ICRP 1994a} ) tabulated dose coefficients representing the committed dose associated with acute intakes of the radionuclides. The committed dose coefficient for the intake of a radionuclide by an individual of age t _{0} , h (r _{T} , t _{0} ), is given by the integral of eqn (4) over the commitment period post the intake:

where A _{0} is the activity intake (Bq) at time zero, and T _{c} is the commitment period; i.e., for non-adults T _{c} = 70 − t _{0} and 50 for adults. For adults, no further changes in time of anatomical parameters is assumed, and thus eqn (6) can be written as:

where

dt is the number of nuclear transformations of the radionuclide occurring in source region r _{s} (Bq s). For short-lived radionuclides commonly used in diagnostic nuclear medicine, the upper limit of the integral can be taken as infinite as one can neglect changes in anatomical parameters while the radionuclide resides in the body even in the younger ages. Thus to derive absorbed dose coefficients, as in the MIRD scheme, replace h with d , S _{w} with S in eqn (7), and remove consideration of the radiation weighting factor w _{R} from Eqn (5). The unit of the absorbed dose coefficient is then Gy Bq^{−1} .

Biokinetic models
The computational approach to internal emitters describes the intake, uptake, and fate of the radionuclide in terms of compartment models collectively referred to as biokinetic models. The complexity of these models has increased with the need to address an increasing number of tissues considered to be at risk, to reflect the varied chemical forms that might be encountered in the workplace or general environment, to derive both dose and bioassay coefficients, and to be applicable to both adults and non-adults. The human alimentary tract model of ICRP Publication 100 (^{ICRP 2006} ) is an example of the increased model complexity (Fig. 2 ). The gastrointestinal model of ICRP Publication 30 (^{ICRP 1979} ) consisted of only five compartments.

Fig. 2: Structure of the human alimentary tract model. The dash compartments are connections with the respiratory tract and systemic tissues. In general, the update to blood of the radionuclide is assumed to occur from the small intestine.

Similarly the human respiratory tract model of ICRP Publication 66 (^{ICRP 1994b} ), also used in ICRP Publications 68 and 71, was considerably more complex than the model used in ICRP Publication 30. However, the model as described in Publication 66 has not been fully supported by available data, and thus the forthcoming ICRP Publication series on occupational radiation protection will use a simplified version of the human respiratory tract model as shown in Fig. 3 .

Fig. 3: Structure of the revised ICRP Publication 66 (^{ICRP 1994b} ) human respiratory tract model.

The models detailing the fate of an element upon absorption to blood (systemic behavior) have also grown in complexity. The increased complexity is in recognition of the models being used to derive both dose and bioassay coefficients. More realistic modeling of radioactive progeny formed within the body was also desirable. In the past, only radioiodine and noble gas elements formed in the decay of the parent radionuclide were treated differently from the precursor (parent). The systemic biokinetic model for the alkaline earth elements used in ICRP Publication 72 (ICRP 1995) is shown in Fig 4 .

Fig. 4: Systemic model for alkaline earth elements used in ICRP Publication 72 (ICRP 1995).

The compartment models of the respiratory and alimentary tract, coupled with those of the systemic biokinetics, define a system of first-order differential equations. The solution to the set of equations is the time-dependent distribution of the radionuclide and its radioactive progeny, if any, in mathematical compartments (pools) associated with anatomical regions of the body. Let A _{i,j} (t ) represent the activity of radionuclide i in compartment j at time t . The rate of change in the activity of member i of the decay chain i =1, 2, …, N with i = 1 being the parent nuclide in compartment j , can be written as:

where M is the number of compartments describing the kinetics, λ_{i,j,k} is the fractional transfer rate of chain member i from compartment j (donor compartment) to compartment k (receiving compartment) in the biokinetic model, λ^{P} _{i} is the physical decay constant of chain member i , and β_{k,i} is the fraction of the decays of chain member k forming member i.

Given the initial conditions specified for the compartments, A _{i,j} (0), eqn (8) defines the dynamic behavior of the radionuclide and its progeny within the human body. The first term on the right-hand side of eqn (8) represents the rate of flow of chain member i into compartment j from all donor compartments. The second term represents the rate of removal of member i from compartment j both by transfer to other compartments and by physical decay. The third term addresses the ingrowth of member i within compartment j due to the presence of its precursors k in the compartment. The members of the decay chain are ordered such that the precursors of member i have indexes less than i . An ordered listing of the chain members can be obtained using the DECDATA software distributed with Publication 107 (^{ICRP 2008} ).

The system of N × M ordinary first-order differential equations must be solved using suitable numerical methods. The system is generally solved for the initial conditions that A _{i,j} (0) = 0 for all compartments with the exception of compartments of intake where nonzero initial conditions applied to content of the parent nuclide; i.e., i = 1.

Dosimetric models
The absorbed fraction quantity introduced by ^{Ellett et al. (1964, 1965)} is the cornerstone of the dosimetric models. The absorbed fraction ϕ(r _{T} ← r _{s} ,E ) is the fraction of energy emitted within region r _{s} that is absorbed in region r _{T} . Dividing the absorbed fraction by the mass of region r _{T} yields the specific absorbed fraction (kg^{−1} ). The specific absorbed fractions tabulated in MIRD Pamphlet 5 for a series of monoenergetic photons were derived by Monte Carlo calculations in a stylized geometric model of the body (phantom) assuming the radiation is emitted uniformly within region r _{s} . For so-called nonpenetrating radiations (electrons and alphas), it was generally assumed that the emitted energy was absorbed within region r _{s} . Thus ϕ(r _{T} ← r _{s} ) = 1 if r _{T} = r _{s} ; otherwise it is zero. For walled organs (segments of the gastrointestinal tract), the specific absorbed fraction in the mucosal layer of the wall due to electrons emitted within the contents was approximated as one-half the reciprocal of the mass of the contents. An additional factor of 0.01 was applied in the case of alpha particles and fission fragments; see ICRP Publication 30, Part 1, for details (^{ICRP 1979} ).

Today computational phantoms are derived from medical diagnostic images and provide more realistic shapes and positions of the organs and tissues of the body. The regions of the body are represented by a set of volume elements, referred to as voxels. ICRP has published the reference computational phantoms for the adult male and female that will be used in deriving dose coefficients based on the recommendations of ICRP Publication 103 (^{ICRP 2007} ). The main characteristics of these computational phantoms are shown in Table 3 . In particular, note the number of voxels representing tissues of the body (e.g., in the female this is about 3.9 million voxels). Absorbed fraction calculations for photon, electron, and neutron radiations emitted within the body can be performed in these phantoms with contemporary Monte Carlo radiation transport code.

Table 3: Characteristics of adult reference computational phantoms.

External factors
Decisions within ICRP, NCRP, and national regulatory bodies have influenced the evolution of the internal emitter dosimetry. Often these decisions are influenced by external events.

ICRP Committee 2 established its Task Group on Dose Calculations in 1974 to assist in the revision of the dosimetric data of ICRP Publication 2 (^{ICRP 1959} ). The DOCAL Task Group was centered at ORNL, and with the completion of Publication 30 and the issuance of Publication 38, the Task Group is expected to be disbanded. However, Committee 2 was concerned about its reliance on a single organization for computational support. ORNL had previously played a major role in the preparation of Publication 2 (^{ICRP 1959} ) and other publications, and thus the Committee requested that DOCAL become international in its membership. Thus Committee 2 expanded DOCAL to include several organizations that collectively had the capability to serve the needs of the Committee in computational dosimetry of incorporated radionuclides. This capability was achieved by inclusion of members from the U.K. National Radiation Protection Board (now Public Health England), the German Federal Office for Radiation Protection (Bundesamt für Strahlenschutz), and the Ukraine Radiation Protection Institute. With this structure, DOCAL served the Committee’s needs in development of age-specific dose coefficients for members of the public and dose coefficients for the workers. During its existence, DOCAL has been chaired by W.S. Snyder (1974-1977), M.R. Ford (1977-1984), K.F. Eckerman (1984-2004), and W.E. Bolch (2004-2010). The two founding chairs of the Task Group are shown in Fig. 5 .

Fig. 5: The founding chair of ICRP Committee 2’s Task Group on Dose Calculations. On the left, W.S. Synder, chairman from 1974-1977, and on the right, Mary Rose Ford, chairman from 1977-1984. Both are among the Mettler giants.

Following the issuance of the ICRP Publication 30 series, ICRP Committee 2 decided not to undertake the development of dose coefficients for members of the public but rather leave this issue to national authorities. However, in the aftermath of the Chernobyl accident (26 April 1986), it became clear that an international agreed upon set of coefficients for members of the public was needed. To develop the needed age-specific biokinetic models, it was necessary to supplement the information on the fate of humans on the specific element with information on other members of its chemical family, to consider information derived in studies with animals, and to view these data in a physiologically meaningful manner. These efforts resulted in improved biokinetic models being available for workers as well as members of the public, and DOCAL undertook the calculation of the public dose coefficients.

Within ICRP, the responsibility for developing guidance on the bioassay of internal emitters was transferred from Committee 4 to Committee 2. Prior to this change, Committee 2’s internal emitter guidance was derived with biokinetic information often with no consideration of the routes of elimination from the body. Committee 4’s guidance on excretion and retention of the radionuclide for bioassay purposes thus had to be derived using a different biokinetic model. Addressing the biokinetic information needs for derivation of both dose and bioassay coefficients placed additional demands on the modeling. Excessive conservatism in the modeling is compounded as an excretion function is applied to a bioassay measurement, which is then multiplied by the dose coefficient. Thus current modeling efforts seek a realistic model to the extent possible.

Changes in computational hardware since the 1980s have contributed significantly to the advancement of computational dosimetry. These developments have made possible the advancements in development of both biokinetic and dosimetric models. Calculations that once had to be carried out on mainframe computers are now performed on a desktop. ^{Killough and Eckerman (1984)} and ^{Birchall (1986)} released software for solving systems of differential equations on a microcomputer, and ^{Leggett et al. (1993)} detailed a flexible numerical method to solve complex biokinetic models. Today’s desktop computers have sufficient hardware and speed to handle most needs in computational dosimetry, including radiation transport calculations using standard Monte Carlo codes.

SUMMARY
Considerable advances in the computational dosimetry of internal emitters have occurred over the years. The full impact of these developments will be evident as ICRP releases publications implementing the primary radiation protection guidance of ICRP Publication 103. These developments have eliminated some of the conservatism present in the earlier guidance that arose from addressing only long-term biological processes. There are internal dosimetry issues beyond those addressed in radiation protection. However, the databases used in the computation of a protection system’s coefficients are of sufficiently high technical rigor to support additional inquiries.

Acknowledgments
The author would like to express his gratitude to the many colleagues who came to his aid when he collapsed after giving the L.S. Taylor Lecture. A special thanks to the NCRP staff, Hyatt Regency employees, the Montgomery County Emergency Squad, and the Suburban Hospital professionals, who all ensured he received superb care while on travel. No long-term health consequences are evident, and the author is making good progress in some lifestyle changes.

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