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62
Counting Statistics
A graph of sensitivity versus (1-specificity)
A graph of sensitivity versus (1-specificity) is plotted above. The ideal point for a test
result would be the upper left corner of the ROC curve with sensitivity = 100 % and
specificity =100 %.
Suggested Reading
1. Brown PH(1997) Mathematics and Statistics In Nuclear Medicine : Technology and Techniques 4 th
Edition ( Eds) Donald R Bernier, Paul E. Christian, Games K Langan pp 1-35 Mosby St. Louis.
2. Metz CE (1978) Basic Principles of ROC analysis. Sem Nucl Med 8, 283-298.
3. Paul L. Meyer (1970) The Poisson and Other Discrete Random Variables, Introductory Probability
and Statistical Applications, Second Edition, Oxford & IBH Publishing Co. Pvt. Ltd., New Delhi. pp
159-181.
Dosimetry of Internally
Administered Radionuclides
A.R. Reddy
Dosimetry of internal emitters is a mature branch of radiological science with a rich
heritage, a well established present, and holding out bright prospects for the future. It deals
with the quantification of the amount of energy imparted to a target in a biological system
due to different types of radiation emitted from a radionuclide distributed in it or elsewhere
in the system. It also is concerned with the spatial and temporal distribution of this imparted
radiation energy in the target. The target in nuclear medicine procedures could be whole
body, or an organ, or a tissue, or a cell or a sub-cellular structure. The energy imparted to
the target is converted to the absorbed dose. Internal dose computations are done not only in
medicine but also for radiation safety and other environmental issues. The internal dose
estimation utilizes age- and sex-specific reference data for human anatomy and body
composition. In the diagnostic use of a radionuclide, the diagnostic information derived for
the benefit of the patient far outweighs associated risk due to radiation dose. Hence estimation
of an average dose assuming uniform distribution of radioactivity in the target organ is
considered to be sufficient. Number of MIRD (Medical Internal Radiation Dose) pamphlets
giving basic methodology and tables of data required for dosimetry has been published.
Using as far as possible the human biokinetic data (for normals) best estimates of the dose
for several radiopharmaceuticals have been published. At this point it must be emphasized
that all the physical data tabulated (like absorbed fractions or S-factors) so far are for
specific mathematically defined models. Therefore the dose estimates available in the MIRD
pamphlets should be used as guidelines for general population not for a specific individual
or patient.
However, when the activity distribution is examined, at microlevel (for example
distribution of radioiodine in thyroid follicle) or even at organ level sometimes (for example
distribution of radioiodine in human thyroid tissue when it is treated therapeutically for
different diseases); at times there is non-uniformity in its distribution. If the particulate
6 3
64
Dosimetry of Internally Administered Radionuclides
radiations emitted from the radionuclide are penetrating enough as compared to the linear
dimensions of a defined target of interest the dose distribution could still is uniform and
hence the average dose estimate will be sufficient. But if the radiations emitted are of low
energy with smaller range as compared to the target size, the average dose estimate at an
organ or gross tissue level loses its meaning and dosimetry is required to be done at a
microlevel with the knowledge of localisation at microlevel as well as microdistribution of
the radionuclide, its decay characteristics and range-energy or energy loss relationships.
This has become essential in case of radionuclides that decay by electron capture and
isometric transitions resulting in Auger electron emissions (whose ranges are nearer to the
linear dimensions of the subcellular structures). With time-activity details for specific patient
(i.e. availability of patient specific biokinetics of the radiopharmaceutical) in nuclear medicine,
dose estimations to patients are quite reliable. Further since the hopes of radionuclide
therapy in nuclear medicine are intensely increasing it has become necessary to consider the
radionuclide dosimetry to a patient taking into consideration details of the activity distribution
in the target to be therapeutically treated and the normal tissues or organs that may concentrate
part of the administered radionuclide. Also the accuracy of dose estimation for therapeutic
use of radionuclide has to be more stringent as compared to that for diagnostic use to avoid
any normal tissue injury. Patient specific dosimetry refers to the estimation of radiation
doses to the tissues of a patient based on individual radionuclide kinetics and his or her
organ or tissue details rather than that based on average kinetics from normal human beings
and anthropomorphic phantoms for dosimetric computation. Estimation of spatial variation
of dose within a target tissue or tumor of a patient will be useful to arrive at specification of
therapeutic dose to be delivered to the target and computing the isodose contours as well as
dose-volume histograms.
Stochastic nature of radioactive decay and the consequent stochastic nature of energy
deposition in targets of very small dimensions are taken into consideration in microdosimetry
approach. The probability distributions of the specific energy imparted to such targets have
been computed for some electron emitters and alpha emitters. The methodology also computes
the number of targets that would not receive any energy deposition at all, in addition to the
probability distribution mentioned above. Microdosimetry deals with the number, size, and
spatial and temporal distributions of individual energy deposition events, particularly in
submicroscopic structures.
In this Chapter all the above aspects of dosimetry of internally administered radionuclides
are dealt with. First absorbed dose and dose equivalent are defined. Then, a brief description
of different types of radiopharmaceuticals one encounters in nuclear medicine and different
dosimetric phantoms is provided. Chronological development of dosimetry of internal emitters
is also given for information. MIRD formalism is presented in some detail thereafter. A
comparison of MIRD and ICRP approach is also discussed. A brief description of other
software packages for dose estimation in nuclear medicine is also presented.
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65
Basics for absorbed dose estimation
The principal quantity of interest in internal dosimetry is the absorbed dose and the dose
equivalent. Absorbed dose (D) is defined by ICRU as:
D = d / dm
Where d is the mean energy imparted by ionizing radiation to matter of mass dm. The
units of absorbed dose are typically erg/g or J/kg. The special units are rad (100 erg/g) or
the gray (Gy) (1 J/kg = 100 rad = 104 erg/g).
The dose equivalent (H) is the absorbed dose multiplied by a Radiation Weighting
Factor, (WR), the latter accounting for the effectiveness of different types of radiation in
causing biological effects.
H = D × W
R
Because the WR is dimensionless, units of the quantity H are the same as absorbed dose
(i.e. erg/g or J/kg). However, special units for this quantity have unique names, rem and
sievert (Sv). Values for the WR have changed over a period of time, as new information
about radiation effectiveness has become available (Refer Chapter on “ICRP
recommendations” in this book).
The quantity dose equivalent was originally derived for use in radiation protection
programs. Development of the effective dose equivalent (EDE) (1) and the effective dose
(ED) by the ICRP (2), however, allowed nonuniform internal doses in the body to be expressed
as a single value, representing an equivalent whole body dose.
Quantities involved in Absorbed Dose Estimation
Physical Quantities
Radionuclides tagged to appropriate pharmaceuticals are administered to a patient in
diagnostic or therapeutic nuclear medicine procedures. Amount of radioactivity administered
is measured in units, bequerals (Bq), or its multiples megabequeral (MBq) or gegabequeral
(GBq). Distribution of the radioactive substance is dependent on the pharmacokinetics of
the administered radiopharmaceutical. Organs or tissues in which the radioactivity is
concentrated are termed as the source organs. Ionizing radiation emitted by these radioactive
substances in the form of alpha, beta and gamma radiation results in absorption of radiation
energy in the source organs or tissues and also in the other organs, termed as target organs.
For estimating the absorbed dose due to these radioactive substances it is essential to know
the energy imparted to unit mass of the target or source material.
Radiopharmaceuticals
A radiopharmaceutical is a radionuclide labeled pharmaceutical. The pharmaceutical follows
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Dosimetry of Internally Administered Radionuclides
a physiological or pathological pathway in the biological system and radionuclide while
riding along the pharmaceutical facilitates static and dynamic detection, and imaging of the
physiological or pathological state of the subject. Cumulated activity in the source region is
determined using the detection and imaging systems in nuclear medicine and it is an essential
parameter for dose estimation. The decay characteristics of radionuclides can be seen in a
chapter “Radionuclides in medicine and research” in this book.
Energy of radiations emitted from radiopharmaceuticals
The basic unit of the energy of any types of radiation either particulate radiation or photons
emitted by a radionuclide is the electron volt (eV). It is equal to the amount of energy
gained by an electron passing through a potential difference of one volt. Energy of the
emitted radiation is characteristic of the radionuclide. For example, energy of the alpha
particle emitted by
135m
Ba will always be 268 keV. Many radionuclides have more than one decay route. That is,
there may be different possible discrete energies that the radiation may have. However,
when a beta particle is emitted, the energy is divided between the beta and a neutrino. (A
neutrino is a particle with no charge and infinitesimally small mass.) Consequently, a beta
particle from a decaying radionuclide has a spectrum of energies varying in a continuous
manner from zero to a maximum energy (E
The average energy is generally around forty percent of the maximum.
238
Cm will always be 6.52 MeV, and the gamma photons emitted by
), which is characteristic of the radionuclide.
max
Radionuclides placed in the human body for diagnostic or therapeutic nuclear medicine
distribute through the body following the rules of pharmacokinetics. Pharmacokinetics depends
on the chemical nature of the pharmaceutical and on the physiological or pathological state
of the region in which the radionuclide is concentrated. The radionuclides, upon their decay,
emit radiation isotropically; that is, in no preferred direction. Hence regions near radionuclide
concentrations receive a larger radiation flux than more distant locations. In addition,
attenuation and absorption of the radiation in the intervening tissues may prevent the radiation
from reaching distant sites. All these factors, namely, radionuclide concentration,
pharmacokinetics and interaction of radiation with the medium, are important factors in the
assessment of radiation dose.
From the point of view of dosimetry it is sufficient to note that radiation interaction with
matter results in creation of charged particles like electrons, positrons, beta and alpha particles
that impart their kinetic energy to the medium through ionizations and excitations. The
energy imparted to a unit mass of the medium is the absorbed dose.
Anthropometric Phantoms
A series of phantoms representing children at five different ages (newborn, 1-year-old,
5-year-old, ten-year-old, and fifteen-year-old) and an adult were developed by Cristy and
Eckerman (3) from an extensive study of medical and other literature, from which the organ
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67
sizes, locations, compositions, etc. were taken. A series of three phantoms representing a
pregnant female at the end of each trimester of pregnancy were developed by Stabin et al
(4). Specific absorbed fractions for different monoenergetic photons were computed and
included in these publications. A software package MIRDOSE 3 was developed by Stabin
(5) from the Radiation Internal Dose Information Center (RIDIC) in Oak Ridge. It included
S-values for Reference Man, Reference Woman, the pediatric phantoms, and all of the
pregnant female phantoms in a convenient format for dose estimations in nuclear medicine.
Chronology of radiation dose estimation from radioactive substances
1941 Marinelli (6) published the first approach to the problem of radiation dosage from a
radioactive material, viz., 32P. He invented a new unit, which he called the equivalent roentgen,
resulting from total decay of a particular amount of radionuclide in one gram of air which
would result in the same number of ion pairs as would be produced when it is exposed to 1
R of x-rays. In order to obtain the dose to a patient or a particular tissue it is necessary to
determine the number of beta particles released per unit volume (or unit mass) of tissue.
1947 Marinelli et al (7) published the method of dosage calculation for other
radionuclides, wherein they introduced the concept of effective half-life to take into account
the influence of physiological excretion of the nuclide in addition to its physical radioactive
decay. Dose was still expressed in terms of roentgen and it was called as dose delivered (in
present day understanding as exposure). The same authors introduced a new parameter
called specific gamma constant for gamma dosimetry. It was expressed as exposure in
roentgens at 1 cm from a uniform point source of 1 mCi in air during 1 hour and was
calculated for a number of radionuclides.
1950s A new unit called rad, which is equal to 100 ergs absorbed per gram of the
absorbing material, was used to express the parameter dose absorbed. Thus if the radionuclide
concentration in the target of interest is known, absorbed dose from either beta particle or
gamma photons or from both, could be calculated from the above information.
1964 Ellett, Callahan and Brownell (8,9) defined Absorbed Fraction as fraction of emitted
radiation that is absorbed in a region of interest. Its values for a number of geometries of
different sizes and for different photon energies computed by Monte Carlo method have
been published.
1968 A new era of internal dose for biologically distributed radionuclides began with
the acceptance of the schema proposed by Loevinger and Berman (10) to MIRD (Medical
Internal Radiation Dose) Committee of the American Society of Nuclear Medicine, and with
the publication of this MIRD schema, as well as data on dose build-up factors and on
absorbed fractions as MIRD Pamphlets. Subsequently, data on radionuclide decay schemes,
Reference Man, specific absorbed fractions as well as S factors for a large number of source
and target organs of the Reference Man have been published as MIRD Pamphlets. The
MIRD schema has provided a unified approach for dose estimate for any type of radiation
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68
Dosimetry of Internally Administered Radionuclides
and any type of target as well as source organ, thus scoring a great advantage over the
earlier methods.
Physical basis of internal dosimetry
The Marinelli-Quimby-Hine system of internal radiation dose calculation was based
on distinguishing the radiation as penetrating and non-penetrating. Gamma photons are
example of penetrating radiations and electrons are non-penetrating radiations. For nonpenetrating radiations (electrons) all the energy of these radiations is assumed to be absorbed
in the target, unless the target of interest is much smaller than the range of the electrons
emitted. Calculations of
partial absorption of beta radiations (10). For photons, two parameters, viz., gamma ray
exposure rate constant () and average geometric factor (g) are considered. The former
encompasses (roughly) radionuclide decay characteristics as well as the photon energy
absorption coefficient in air or tissue of interest and is expressed in R/mCi-hr at 1 cm from
a point source. The parameter average geometric factor, g, is to take care of shape of the
target in which the source is uniformly distributed. Here it is assumed that the photons (both
primary and secondary) can be represented by an effective absorption coefficient,
to either zero (when the target has linear dimensions less than 10 cm), or 0.028 cm-1 when it
is larger. These assumptions are valid when the emitted photon energy is greater than a few
hundred keV. Focht et al (11) calculated the values of g for spheres and cylinders of different
sizes. Tables of gamma ray exposure constants for commonly used radionuclides are also
available (12).
131
I dosimetry in small spheres have taken into consideration the
eff
equal
Simpler methods refining the parameters of Marinelli et al dose equation have evolved.
One such refinement developed by Gupta et al (13) introduced the modified geometric
factor approach. In this method, using the linear attenuation coefficients of each photon
energy and dose build-up factors for every source-to-target distance, the limitation of the
earlier effective absorption coefficient is minimized. Tables of average geometric factors
and absorbed fractions derived there from have been published for spheroids of a variety of
sizes and eccentricities. Reddy and Mehta (14) have extended the lower limit of the photon
energy to 1 keV and spherical target sizes of micron dimensions.
This system of Marinelli et al (7) has been extensively used for dosimetry of internal
emitters until recently. However, with the increasing use of low energy photon emitters (e.g.
99m
Tc) for nuclear medicine procedures, questions have been asked about the validity of the
assumption of an effective absorption coefficient of either 0 or 0.028 cm-1, whatever the
target size or photon energy is. The argument is valid in view of the rapid variation of the
linear absorption coefficient with energy for photon energies less than 100 keV. Satisfactory
solutions to these arguments have become possible with the availability of detailed photon
interaction data compilations at the National Bureau of Standards, USA (NIST, USA), and
advanced semi-analytical computational techniques on large computers. The pioneering papers
of Ellett, Callahan, Brownell (8,9) and Reddy et al (14) first introduced the concept of
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69
photon absorbed fraction and its computation using Monte Carlo techniques for regular
geometries (such as elliptic cylinders, ellipsoids, spheres, straight cylinders, etc.) of different
sizes having either point or uniform source distributions emitting photons of energies from
20 keV to 2 MeV. Snyder et al (15) at Oak Ridge National Laboratory, using more
sophisticated sampling techniques, obtained absorbed fractions for a mathematically defined
anthropometric phantom.
MIRD System
Dosimetry of internal emitters is a well developed branch of nuclear medicine, particularly
after the introduction of the concept of absorbed fraction and the adoption of MIRD (Medical
Internal Radiation Dosimetry) schema for estimation of mean absorbed dose for biologically
distributed radionuclides. General dose equations in the schema which apply to all types of
radiations and targets are given below:
rr
)(Ã
Dose
h
100
m
where Ãh is the cumulative activity in the source region, i (2.13 niEi) is the equilibrium
dose constant, i (r
r
) is the absorbed fraction and is defined as the ratio of the energy
k
h
absorbed by the target volume rk from the ith radiation to the energy emitted by the ith
radiation from the source volume rh and mk is the mass of target organ. If the radionuclide
has n radiations with energies E1, E2, ..., En with fractional abundances n1, n2, ..., nn then
i the equilibrium dose constant in conventional units will be
n
i
13.2
1
En
i
ii
hkiii
k
(1)
The SI units for radiation dose and activity are Gy and MBq respectively; the equilibrium
dose constant can be detonated by i = 0.576NiEi.
The equation for absorbed dose, D in the MIRD system is deceptively simple:
SAD~
where à is the cumulative activity (Bq.s); and S is called S-factor or S- value.
The value of S is given as
n
i
1
mrrrrS
/)()(
khkiihk
Absorbed fractions and S-factors
The absorbed fraction, , is defined as the ratio of the photon energy absorbed in a target
GSPant\Newbook\Final-2007\5-chp\69
(2)
(3)
70
Dosimetry of Internally Administered Radionuclides
of interest to that emitted from a radioactive source situated either as a point source or
uniformly distributed in the same target or elsewhere in the body. The absorbed fraction
defined as above is thus for a volume. Photon absorbed fractions obtained using Monte
Carlo techniques for tissue equivalent targets of regular geometries (such as elliptic cylinders,
ellipsoids, spheres, straight cylinders, etc.) were reported by Ellett et al (8,9,16). These
photon absorbed fractions were computed for monoenergetic photon sources of energies
ranging from 20 keV to 2 MeV situated either as a point isotropic source or as a uniformly
distributed source in the above geometrical shapes and sizes. Later Reddy and Mehta (14)
extended the lower limit of photon energy to 1 keV and spherical target sizes to milligram
levels. Using more sophisticated sampling techniques in the Monte Carlo computations
Snyder et al (15,17,18) obtained absorbed fractions and specific absorbed fractions and Svalues for homogeneous tissue equivalent mathematically defined anthropometric phantom
representing the Reference Man. S-values for radionuclides uniformly distributed in the suborgans like the heart chambers and heart wall; dynamic urinary bladder; adult head and
brain; Cellular absorbed fractions for monoenergetic electrons and alpha particles incorporated
into different cell compartments were computed and S-factors for selected radionuclides
were obtained (19-21).
To support the calculation of nonuniform absorbed doses and to account for nonuniform
activity distributions at the level of imaging instrumentation voxels, Bolch et al published S
value tabulations for different voxel sizes and source-target voxel distances (22). The resulting
S value tabulations facilitate absorbed dose calculations by separating potentially lengthy
and complex Monte Carlo calculations from the task of estimating absorbed dose. Because
use of previously tabulated S values requires a fixed anatomic model, this approach is not
easily amenable to geometries that deviate substantially from the fixed anatomic models.
Voxel S values overcome this problem and have been adopted in several dose calculation
programs.
The MIRD Committee of the Society of Nuclear Medicine, USA, has brought out a
number of pamphlets that give basic data to calculate radiation dose from internal emitters,
such as, nuclear decay data, absorbed fractions, and S-factors for an anthropomorphic phantom
called Reference Man (MIRD Pamphlets 1-19 listed in Appendix ‘A’). Radionuclide decay
data for computation of ” for more than 100 radionuclides have appeared as MIRD Pamphlet
10. Photon absorbed fraction data for regular geometries of different sizes; homogeneous
tissue equivalent medium and uniform source distribution have been the subject matter of
MIRD Pamphlets 3 and 10. Values of S factors for a heterogeneous anthropometric adult
reference man phantom for different source locations were listed in MIRD Pamphlet 11 for
117 radionuclides. Electron absorbed fraction data for monoenergetic point electron sources
or beta emitters were tabulated in MIRD Pamphlet 7. To facilitate calculation of radiation
doses to different age groups, S factors have been computed for a number of targets containing
radioactivity in mathematical phantoms that had been developed for new-born, 1-, 5-, 10,
15-year age groups.
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71
The MIRD Committee has also brought out Summary Dose Estimate Reports for specific
radiopharmaceuticals of interest in nuclear medicine (MIRD Dose Estimate Reports 1-15, 19
listed in Appendix ‘A’). The most important point to be noted in this schema or in these dose
estimate reports is that the dose estimate is to a defined target (a model), like that to the
Reference Man or to his organs. Dose estimates, however, include the best available values of
cumulated activity for humans. Therefore, the dose estimates in the above MIRD reports should
be used as guidelines for general population not for a specific individual or patient. Appendix A
lists the MIRD Pamphlets and Dose Estimate Reports.
ICRP Schema
ICRP has also brought out number of reports since 1987 on radiopharmaceutical dosimetry
(ICRP 17, 53, and 80 and number of addenda to 53) using its dose calculation methodology
called ICRP Schema. The parameter calculated is the Effective dose, E, expressed in Sv. It
is the sum of the weighted equivalent doses in all tissues and organs in the body and is given
by the equation.
E = TWTHT (Sv) (4)
where WT is the tissue weighting factor, indicative of relative radiosensitivity
(susceptibility) of different tissues. HT is the equivalent dose for tissue or organ T and is
given by the equation.
HT = RWRD
(Sv) (5)
T,R
WR is Radiation Weighting Factor, representative of the relative biological effectiveness
of that radiation.
Equivalent Dose Rate, HT (t, t0) at age, t, in target organ or tissue, T, due to an acute
intake of a radionuclide by an individual at age, t0, at the time of intake, is expressed as
follows:
HT (t, t0) = S qS (t, t0) SEE (T S; t) (6)
Where qS (t, t0) = the activity of the radionuclide in the source region, S, at age t after
intake at age t0 (in Bq)
SEE(T S; t), the Specific Effective Energy (in Sv/Bq) is the equivalent dose in target
T per nuclear transformation in source region, S at age t.
Comparison of ICRP and MIRD Schema
ICRP explicitly mentions that dose is an important parameter for risk evaluation and its
estimation is one of the thrusts in radiological protection. MIRD works on this implicitly
although they have not devoted their efforts towards risk evaluation. A comparison of ICRP
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