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Файл:Ординатура / Хирургия / Библиотека им академика М.И. Перельмана / Книга_5545_Библиотеки_им_академика_М_И_Перельмана.pdf
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- •Preface
- •Contents
- •1: Structure of Matter
- •2: Radioactive Decay
- •2.1 Spontaneous Fission
- •1.1.1 Radiation
- •1.2 The Atom
- •1.2.3 Nuclear Binding Energy
- •1.3 Nuclear Nomenclature
- •1.5 Questions
- •Suggested Readings
- •2.2 Isomeric Transition
- •2.2.1 Gamma (γ)-Ray Emission
- •2.2.2 Internal Conversion
- •2.2.2.1 Problem 2.1
- •2.2.2.2 Answer
- •2.3 Alpha (α)-Decay
- •2.4 Beta (β−)-Decay
- •2.5 Positron (β+)-Decay
- •2.6 Electron Capture
- •2.7 Questions
- •Suggested Readings
- •3.1 Radioactive Decay Equation
- •3.1.1 General Equation
- •3.1.2 Half-Life
- •3.1.3 Mean Life
- •3.1.4 Effective Half-Life
- •3.2 Units of Radioactivity
- •3.3 Specific Activity
- •3.4 Calculation
- •3.5 Successive Decay Equations
- •3.5.1 General Equation
- •3.5.2 Transient Equilibrium
- •3.5.3 Secular Equilibrium
- •3.6 Questions
- •Suggested Readings
- •4.5 Poisson Distribution
- •4.6 Gaussian Distribution
- •4.7 Chi-Square Test
- •4.8 Minimum Detectable Activity
- •4.10 Questions
- •Suggested Readings
- •5.1 Cyclotron-Produced Radionuclides
- •5.2 Reactor-Produced Radionuclides
- •5.2.1 Fission or (n, f) Reaction
- •5.2.2 Neutron Capture or (n, γ) Reaction
- •5.6 Radionuclide Generators
- •5.8 Questions
- •Suggested Readings
- •6.1.1 Specific Ionization
- •6.1.2 Linear Energy Transfer
- •6.1.3 Range
- •6.1.4 Bremsstrahlung
- •6.1.5 Positron Annihilation
- •6.2.1.1 Photoelectric Effect
- •6.2.1.2 Compton Scattering
- •6.2.1.3 Pair Production
- •6.2.1.4 Raleigh Scattering
- •6.2.1.5 Photodisintegration
- •6.3.2 Half-Value Layer
- •6.5 Questions
- •Suggested Readings
- •7: Gas-Filled Detector
- •7.1 Principles of Gas-Filled Detector
- •7.2 Ionization Chamber
- •7.2.1 Ion Chamber Survey Meter
- •7.2.2 Dose Calibrator
- •7.2.2.1 Constancy
- •7.2.2.2 Accuracy
- •7.2.2.3 Linearity
- •7.2.2.4 Geometry
- •7.2.3 Pocket Dosimeter
- •7.3 Proportional Counter
- •7.4 Geiger–Müller Counter
- •7.5 Questions
- •Suggested Readings
- •8.1 Scintillation Counter
- •8.4.3 Characteristic X-Ray Peak
- •8.4.4 Backscatter Peak
- •8.4.5 Iodine Escape Peak
- •8.2 Solid Scintillation Detector
- •8.2.1 NaI (Tl) Detector
- •8.2.2 Bismuth Germanate Detector
- •8.2.3 Barium Fluoride Detector
- •8.2.4 Lutetium Oxyorthosilicate Detector
- •8.2.5 Gadolinium Oxyorthosilicate Detector
- •8.2.6 Yttrium Oxyorthosilicate Detector
- •8.2.7 Yttrium Aluminum Perovskite Detector
- •8.2.8 Lutetium Yttrium Oxyorthosilicate Detector
- •8.2.9 Lanthanum Bromide Detector
- •8.3 Solid-State Detector
- •8.3.2 Cadmium–Zinc–Tellurium Detector
- •8.3.3 Cesium Iodide (CsI(Tl)) Detector
- •8.3.4 Solid Scintillation Counter
- •8.3.4.1 NaI(Tl) Detector
- •8.3.4.2 Photomultiplier Tube
- •8.3.4.3 Preamplifier
- •8.3.4.4 Linear Amplifier
- •8.3.4.5 Pulse-Height Analyzer
- •8.3.4.6 Display or Storage
- •8.4 Gamma-Ray Spectrometry
- •8.4.1 Photopeak
- •8.4.6 Positron Annihilation Peak
- •8.4.7 Coincidence Peak
- •8.5 Liquid Scintillation Counter
- •8.5.1 Quenching
- •8.6.1 Energy Resolution
- •8.6.2 Detection Efficiency
- •8.6.2.1 Intrinsic Efficiency
- •8.6.2.2 Photopeak Efficiency or Photofraction
- •8.6.2.3 Geometric Efficiency
- •8.6.3 Dead Time
- •8.7 Gamma Well Counter
- •8.8 Thyroid Probe
- •8.8.1 Thyroid Uptake Measurement
- •8.9 Questions
- •Suggested Readings
- •9: Gamma Camera
- •9.1 Gamma Camera
- •9.1.2 Detector
- •9.1.3 Collimator
- •9.1.4 Photomultiplier Tube
- •9.1.5 X-, Y-Positioning Circuit
- •9.1.6 Pulse-Height Analyzer
- •9.2 Digital Camera
- •9.2.1 Solid State Digital Camera
- •9.3 Questions
- •Suggested Readings
- •10.1.1 Spatial Resolution
- •10.1.1.1 Intrinsic Resolution
- •10.1.1.2 Collimator Resolution
- •10.1.1.3 Scatter Resolution
- •10.1.2.1 Bar Phantom
- •10.1.2.2 Line-Spread Function
- •10.1.2.3 Modulation Transfer Function
- •10.1.3 Sensitivity
- •10.1.3.1 Collimator Efficiency
- •10.1.4 Uniformity
- •10.1.5 Pulse-Height Variation
- •10.1.6 Nonlinearity
- •10.1.7 Edge Packing
- •10.2 Gamma Camera Tuning
- •10.4 Contrast
- •10.4.1 Count Density
- •10.4.2 Image Noise
- •10.4.4 High Count Rate
- •10.4.6 Patient Motion
- •10.5.1 Daily Checks
- •10.5.1.2 Uniformity
- •10.5.2 Weekly Checks
- •10.5.3 Monthly Checks
- •10.5.3.1 High-Count Uniformity Calibration
- •10.5.3.2 Collimator Integrity
- •10.5.4 Annual, Semiannual, or As-Needed Checks
- •10.6 Questions
- •References and Suggested Readings
- •11.1.1 Central Processing Unit
- •11.1.2 Computer Memory
- •11.1.3 External Storage Device
- •11.1.4 Input/Output Device
- •11.1.7 Digital-to-Analog Conversion
- •11.1.8 Digital Image
- •11.2.1 Digital Data Acquisition
- •11.2.2 Static Study
- •11.2.3 Dynamic Study
- •11.2.4 Gated Study
- •11.2.7 Display
- •11.3.1 PACS
- •11.4 Questions
- •Suggested Readings
- •12: Single Photon Emission Computed Tomography
- •12.1 Tomographic Imaging
- •12.2 Single Photon Emission Computed Tomography
- •12.2.1 Data Acquisition
- •12.2.2 Image Reconstruction
- •12.2.2.1 Simple Backprojection
- •12.2.2.2 Filtered Backprojection
- •12.2.2.3 The Convolution Method
- •12.2.2.4 The Fourier Method
- •12.2.2.6 Iterative Reconstruction
- •12.3 SPECT/CT Scanner
- •12.4 Factors Affecting SPECT
- •12.4.1 Photon Attenuation
- •12.4.2 Attenuation Correction Methods
- •12.5 Partial-Volume Effect
- •12.5.2 Sampling
- •12.5.3 Scattering
- •12.6.1 Spatial Resolution
- •12.6.2 Sensitivity
- •12.6.3 Other Parameters
- •12.7.1 Daily Tests
- •12.7.2 Weekly Tests
- •12.7.2.1 Spatial Resolution
- •12.9 Questions
- •References and Suggested Readings
- •13: Positron Emission Tomography
- •13.1 Introduction
- •13.2 PET Radiopharmaceuticals
- •13.3.2 Block Detector
- •13.5 Coincidence Timing Window
- •13.6 PET/CT Scanner
- •13.7 PET/MR Scanner
- •13.7.2 MR Scanner
- •13.7.3 Commercial PET/MR Scanner
- •13.8 Mobile PET or PET/CT Scanner
- •13.9 Micro-PET Scanner
- •13.11 Data Acquisition
- •13.12 Image Reconstruction
- •13.13 Factors Affecting PET
- •13.13.1 Normalization
- •13.13.2 Photon Attenuation Correction
- •13.13.4 Random Coincidences
- •13.13.5 Scatter Coincidences
- •13.13.6 Dead Time
- •13.13.7 Radial Elongation
- •13.14.1 Spatial Resolution
- •13.14.2 Sensitivity
- •13.14.2.1 Noise Equivalent Count Rate
- •13.15.1 Daily Tests
- •13.15.1.1 Sinogram Check
- •13.15.2 Weekly Tests
- •13.15.2.1 Normalization
- •13.18 Questions
- •References and Suggested Reading
- •14.1 Background
- •14.5 Artificial Neural Network
- •14.7 Machine Learning
- •14.7.1 Decision Tree
- •14.7.2 Random Forest
- •14.7.3 Support Vector Machine
- •14.7.4 Computer Vision
- •14.8 Deep Learning
- •14.8.1 Convolutional Network
- •14.8.2 Recurrent Neural Network
- •14.8.3 Generative Adversarial Network
- •14.8.4 Transfer Learning
- •14.9 Radiomics
- •14.10 Natural Language Processing
- •14.11 Large Language Model
- •14.12 Generative Artificial Intelligence
- •14.13.1 Prompt
- •14.13.2 Token
- •14.13.3 Hallucination
- •14.13.4 Deepfake
- •14.13.5 Overfitting
- •14.15 Chatbot
- •14.18 Legal Implication
- •14.20 Questions
- •References
- •15.1 Introduction
- •15.2.1 Scheduling
- •15.2.2 Image Acquisition
- •15.2.3 Image Processing
- •15.2.4 Interpretation
- •15.2.5 Reporting
- •15.3.1 Oncology
- •15.3.2 Cardiovascular Disease
- •15.3.3 Bone Scintigraphy
- •15.3.4 Thyroid Imaging
- •15.5 Drug Development
- •15.6 Questions
- •References and Suggested Reading
- •16: Internal Radiation Dosimetry
- •16.1 Radiation Unit
- •16.1.1 Roentgen
- •16.1.2 Rad
- •16.1.3 Gray
- •16.1.4 Rem
- •16.1.5 Radiation Weighting Factor
- •16.1.6 Quality Factor
- •16.1.7 Sievert
- •16.2 Dose Calculation
- •16.2.1 Radiation Dose Rate
- •16.2.2 Cumulative Radiation Dose
- •16.2.3 Factors Affecting Ã
- •16.2.4 The S Values
- •16.4 Pediatric Dosage
- •16.5 Questions
- •References and Suggested Readings
- •17: Radiation Biology
- •17.1 The Cell
- •17.2.1 DNA Molecule
- •17.2.2 Chromosome
- •17.5 Cell Survival Curves
- •17.6 Factors Affecting Radiosensitivity
- •17.6.1 Dose Rate
- •17.6.2 Linear Energy Transfer
- •17.6.4 Chemicals
- •17.7 Radiosensitizer
- •17.7.1 Oxygen
- •17.7.2 Pyrimidine
- •17.7.3 Others
- •17.8 Radioprotector
- •17.9 Apoptosis
- •17.13.1 Hematopoietic Syndrome
- •17.13.2 Gastrointestinal Syndrome
- •17.13.3 Cerebrovascular Syndrome
- •17.14.1 Somatic Effects
- •17.14.1.1 Carcinogenesis
- •17.14.1.3 Dose–Response Relationship
- •17.14.1.5 Leukemia
- •17.14.1.6 Breast Cancer
- •17.14.1.7 Other Cancers
- •17.14.1.10 Nonspecific Life-Shortening
- •17.14.1.11 Cataractogenesis
- •17.14.2 Genetic Effects
- •17.14.2.1 Spontaneous Mutation
- •17.14.2.2 Doubling Dose
- •17.14.2.3 Genetically Significant Dose
- •17.17 Questions
- •References and Suggested Readings
- •18.1 Introduction
- •18.2 Radiation Protection
- •18.2.3 Occupational Dose Limits
- •18.2.4 ALARA Program
- •18.2.5.1 Time
- •18.2.5.2 Distance
- •18.2.5.3 Shielding
- •18.2.5.4 Activity
- •18.2.6 Personnel Monitoring
- •18.2.6.1 Film Badge
- •18.2.6.2 Thermoluminescent Dosimeter
- •18.2.6.3 Optically Stimulated Luminescence Dosimeter
- •18.3 Radiation Regulations
- •18.3.1 License
- •18.3.1.1 General License
- •18.3.1.2 Specific License of Limited Scope
- •18.3.1.3 Specific Licenses of Broad Scope
- •18.3.2 Radiation Safety Committee
- •18.3.3 Radiation Safety Officer
- •18.3.4.3 Supervision
- •18.3.4.4 Mobile Nuclear Medicine Service
- •18.3.4.5 Written Directives
- •18.4 Bioassay
- •18.6 Radioactive Waste Disposal
- •18.6.2 Release into Sewerage Systems
- •18.6.4 Other Disposal Methods
- •18.7 Radioactive Spill
- •18.8 Recordkeeping
- •18.10 Dirty Bombs
- •18.11 Types of Accidental Radiation Exposure
- •18.12 Protective Measures in Case of Explosion of a Dirty Bomb
- •18.13 Verification Card for Radioactive Patients
- •18.14 Radiation Phobia
- •18.15 European Regulations Governing Radiation
- •18.16 Questions
- •References and Suggested Readings
- •Index

15.5 Drug Development
287
Currently, the application of AI in drug development has received considerable
attention, so much so that researchers and drug companies are committing a lot of
resources and effort to discover new probes or drugs for diagnostic or therapeutic
purposes. This has cut down the time signicantly in discovering new drugs. AI can
screen millions of drugs for specic diseases and design one or more that are most
useful for diagnosis or therapy at a limited cost. Drug–target interaction can be predicted by AI.AI-designed drugs are presumably more efcacious and safer for
human use.
One advantage of the AI application in drug discovery is the availability of a
massive amount of data in this eld, which is a prime requirement for the implementation of AI.These datasets have been used to carry out AI methods in drug
discovery. Ml, DL, GenAI, and many other AI paradigms have been employed.
Blanco-Gonzalez etal. (2023) reported a comprehensive review of AI applications
in drug discovery, addressing important issues of synthesis, drug interaction, repurposing of approved drugs, etc. The authors took the help of ChatGPT 3.5 for organizing the materials in the review, which was later reorganized with human input.
Similarly, ChatGPT 3.5 was asked for a brieng on the AI application in drug discovery with some appropriate comments. Below are the essential points of the
report provided by ChatGPT 3.5.
The rst step in the drug discovery is the identication of a target, namely, a protein, gene, etc., causing the disease. AI can analyze the large datasets and nd the
appropriate molecule as the target. The next step is to nd a drug molecule that binds
strongly with the target molecule, which AI (machine learning) can help by shing
through the vast datasets that contain millions of molecules to nd an effective one.
GAN has been used to design De Novo (new) drug molecules specic for certain
diseases. AI has the unique capability of predicting efcacy, toxicity, and side effects
of a drug molecule. AI models can be trained to learn the pattern of these parameters
in the datasets and accordingly help decide to accept or reject the drug molecule.
AI can be very helpful to organize a clinical trial of a new drug by recruiting the
appropriate cohort of patients, by predicting an ideal dosage, and monitoring the
protocol at every step of the study. Repurposing of a drug (use of an approved drug
for a new disease) is a unique feature offered by AI through scrutinizing the massive
dataset that is beyond the capacity of human comprehension. Research and development, automation in manufacturing, and marketing of the drug all can be performed
with appropriate AI models. AI can furnish all amenities and guidance in fullling
the regulatory requirements.
A few drugs have been discovered with the help of the AI application. When
prompted, ChatGPT 3.5 provided the following list of drugs AI helped design
(Table15.1).

288
15 Application ofArticial Intelligence inNuclear Medicine
Table 15.1
Drug/
compound
DSP-1181 Ex Scientia OCD Molecule design Phase I (2020)
INS018_055 Insilico Medicine IPF Target + molecule Phase II (2023)
Abaucin MIT/McMaster Bacterial
Halicin MIT Antibiotic Molecule
ISM001–055 Insilico Medicine Fibrotic diseases Full pipeline Early trials
Baricitinib Benevolent AI COVID-19 Drug repurposing Approved use
a
Provided by ChatGPT 3.5, when prompted with a query: List of drugs AI helped design
Drugs made with the help of AI
Company/
institution Disease targeted AI role
a
infection
Molecule
discovery
discovery
Development
stage
Preclinical
Preclinical
15.6 Questions
1. Describe how articial intelligence (AI) is applied to nuclear medicine
operations.
2. Elucidate difculties encountered in the analysis of scan images by AI.
3. Explain how AI helps in image reconstruction in nuclear medicine.
4. Explain how attenuation and scatter corrections are made using AI.
5. Can ChatGPT help in diagnosing human diseases, and if so, how?
6. Describe how AI can guide you through to develop new drugs.
7. What are the advantages and disadvantages of ChatGPT in nuclear medicine?
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15 Application ofArticial Intelligence inNuclear Medicine

4
RCkg=×
−
./
Internal Radiation Dosimetry
16
Radiation can cause detrimental effects on human tissues, and these effects depend
on various factors, such as dose, dose rate, time of exposure, and so on. This chapter
describes the method of calculating absorbed doses in various organs from radionuclides ingested internally either purposely (e.g., medical procedures) or
accidentally.
16.1 Radiation Unit
Three units of measure are related to radiation: the roentgen (R) for exposure, the
rad (radiation absorbed dose) for absorbed dose, and the rem (roentgen equivalent
man) for dose equivalent.
16.1.1 Roentgen
The roentgen is the amount of x- or γ-radiation that produces ionization of one elec-
trostatic unit of either positive or negative charge per cubic centimeter of air at 0°C
and 760 mm Hg, standard temperature and pressure (STP). Because 1 cm3 air
weighs 0.001293 g at STP, and a charge of either sign carries 1.6× 10
4.8×10
It should be noted that the roentgen applies only to air and to x- or γ-radiations.
Because of practical limitations of the measuring instruments, the R unit is applicable only to photons of less than 3MeV energy.
© The Author(s), under exclusive license to Springer Science+Business Media, LLC,
part of Springer Nature 2025
G. B. Saha, Physics and Radiobiology of Nuclear Medicine,
https://doi.org/10.1007/978-1-0716-4816-2_16
−10
electrostatic units, it can be shown that
−19
C or
(16.1)
291

292
2
radJkg=
-
/
= 1J kgabsorber/
4
RJkg in air=×
−
./
0 0096
Rrad
Gy
==.
.
16 Internal Radiation Dosimetry
16.1.2 Rad
The rad is a more universal unit. It is a measure of the energy deposited per unit
mass of any material by any type of radiation. The rad is specically dened as
(16.2)
Since 1joule(J)=107ergs,
(16.3)
Another radiation unit is kerma (acronym for kinetic energy released in matter),
which is dened as the sum of initial kinetic energies of all charged particles liberated by uncharged ionizing radiation per unit mass of material. For all practical
purposes, kerma and rad are identical.
16.1.3 Gray
In SI units, the gray (Gy) is the unit of radiation absorbed dose and kerma and is
given by
(16.4)
(16.5)
It can be shown that the energy absorbed per kilogram of air due to an exposure
of 1 R is
Therefore,
or,
Note that for soft tissue,
The rad is not restricted by the type of radiation or absorber or by the energy or
intensity of the radiation. It should be understood that the rad is independent of the
weight of the material. This means that a radiation dose of 1rad (0.01Gy) is always
1rad (0.01Gy) in 1, 2, or 10g of the material. However, the integral absorbed dose
is given in units of gram-rad (g·rad or g·Gy) and calculated by multiplying the rad

rem rad RBE=x
rem rad=xW
r
e1
e5
16.1 Radiation Unit
293
(Gy) by the mass of material. For example, if the radiation dose to a body of 45g is
10rad (0.1Gy), then the integral radiation dose to the material is 450 g⋅rad (or
4.5g·Gy); however, the radiation dose is still 10rad (0.1Gy).
16.1.4 Rem
The dose equivalent unit, rem, has been developed to account for the differences in
effectiveness of different types of radiation in causing biological damage. In radiobiology, the rem is dened as
(16.6)
where RBE is the relative biological effectiveness of the radiation. It is dened as
the ratio of the dose of a standard radiation to produce a particular biological
response to the dose of the radiation in question to produce the same biological
response. Radiations of 250 KV x-rays are normally chosen as the standard radiation because of their widespread use. RBE varies with the linear energy transfer
(LET) of the radiation, radiation dose, dose rate, and the biological system in which
RBE is determined.
16.1.5 Radiation Weighting Factor
In radiation protection, RBE is replaced by the radiation weighting factor, Wr, to
account for differences in effectiveness of various radiations in causing biological
damage. The rem is then dened as
(16.7)
The International Commission on Radiological Protection has suggested the Wr
values for different radiations, which are listed in Table16.1 (ICRP 103, 2007).
These values depend on the LET of the radiation. When a radiation dose comes
from several radiations, the total dose equivalent is calculated by adding the
absorbed doses from individual radiations, multiplied by the W
ln 2/6,
−
En
()
2.5 +18.2
|
|
5.0 +17.0 e
W
=
r
|
|
2.5 + 3.25
ln 22/6
− ,,
En
()
ln 0.04 2/6,
En−
()
En
1MeV 50 MeV
En
≤≤
En
of each radiation.
r
MeV
<
0MeV
>
(16.8)

294
()
=
16 Internal Radiation Dosimetry
Table 16.1
Radiation type Radiation weighting factor, W
Photons 1
Electrons and muons 1
Protons and charged pions 2
Alpha particles, ssion fragments,
heavy ions
Neutrons A continuous curve as a function of neutron energy
a
All values relate to the radiation incident on the body or, for internal sources, emitted from
the source
Used with permission of Elsevier from ICRP Publication 103, Annals of the ICRP, vol 37: Nos
2–4; 2007: permission conveyed through Copyright Clearance Center, Inc.
Table 16.2
for different radiations
Radiation weighting factors W
Quality factors
a
in 2007 Recommendations, ICRP 103
r
r
20
Eq. (16.8)
Type of radiation QF
X-rays, γ-rays, β-particles 1.0
Neutrons of unknown energy and
high-energy protons
α-Particles 20.0
Heavy ions 20.0
10.0
16.1.6 Quality Factor
In the past, the US Nuclear Regulatory Commission (NRC) used the term quality
factors (QF) for radiation weighting factors, which are somewhat different from the
Wr values. The NRC still adopts these values for regulatory purposes, and the values
are listed in Table16.2.
16.1.7 Sievert
In SI units, the dose equivalent is expressed in sievert, which is dened as
In practical situations, all these radiation units are often expressed in milliroentgens (mR), millirads (mrad), and millirems (mrem), which are 10−3 times the units,
roentgen, rad, and rem, respectively. In SI units, the equivalent quantities are milligrays (mGy) and millisieverts (mSv). A rad is also commonly expressed as centigray (cGy), one-hundredth of a gray.
(16.9)

ii
()=()()
()
()
ii
()=()←()
16.2 Dose Calculation
295
16.2 Dose Calculation
The radiation absorbed dose depends on a number of factors: (1) the amount of
radioactivity administered; (2) the physical and biological half-lives of the radioactivity; (3) the fractional abundance of the radiation in question from the radionuclides; (4) the biodistribution of radioactivity in the body; and (5) the fraction of
energy released from the source organ that is absorbed in the target volume, which
is related to the shape, composition, and location of the target. The physical characteristics of a radionuclide are well established. Information concerning the biodistribution of ingested radioactivity can be obtained from various experimental studies
in humans and animals. Factors four and ve are variable from one individual to
another and, therefore, they are approximated for a “standard” or “average”
70-kg man.
Radiopharmaceuticals administered to patients are distributed in different regions
of the body. A region of interest for which the absorbed dose is to be calculated is
considered the “target,” whereas all other regions contributing to the radiation dose
to the target are considered “sources.” The source and the target become the same
when the radiation dose due to the radioactivity in the target itself is calculated.
16.2.1 Radiation Dose Rate
Suppose a source volume r contains A μCi of a radiopharmaceutical emitting several radiations. If the ith radiation has energy Ei and a fractional abundance Ni per
disintegration, then the energy absorbed per hour (dose rate) by a target of mass m
and volume v from the ith radiation emitted by the source volume r is given by
RAmNE
radh Ci gMeV disintegration
// //
=
µ
4
.
××
37 10
-
./
××
16 10
grad erg
./
×.
001
()
×
./
213 AmNE
s
//
3600
()
()
disint
6
ergMeV
h
ii
i
eegrations
/s.
µ
Ci
The above equation is valid for nonpenetrating radiations only, meaning all
energy is absorbed in the absorber. For penetrating radiations, total or part of the
radiation energy may be absorbed in the absorbing material. If the target and the
source are not the same, then a factor must be introduced to account for the partial
absorption, if any, of the radiation energy. Thus,
RAmNEvr
radh/./
213
φ
ii
(16.10)

296
∆
iii
NE= 213.
mv
ii
()
()
()
mv
()
()
()
16 Internal Radiation Dosimetry
Here ϕi(v←r) is called the absorbed fraction and is dened as the ratio of the
energy absorbed by the target volume v from the ith radiation to the energy emitted
by the ith radiation from the source volume r. This is a critical factor that is difcult
to evaluate, because the absorbed fraction ϕi depends on the type and energy of the
radiation, the shape and size of the source Ἳvolume, and the shape, composition,
and distance of the target volume. However, in the case of β-particles, conversion
electrons, α-particles, and x- and γ-rays of energies less than 11 keV, all of the
energy emitted by a radionuclide is absorbed in the volume r larger than 1cm. Then,
ϕi becomes 0, unless v and r are the same, in which case ϕi=1. For x- and γ-rays
with energies greater than 11keV, the value of decreases with increasing energy and
varies between 0 and 1, depending on the energy. The values of ϕi are calculated by
statistical Monte Carlo methods on the basis of fundamental mechanisms of interaction of radiation with matter, and are available in standard textbooks on radiation
dosimetry, particularly the medical internal radiation dose (MIRD) pamphlets published by the Society of Nuclear Medicine.
The quantity 2.13 NiEi is a constant for the ith radiation and is often denoted by
Δi. Thus,
(16.11)
The quantity Δi is called the equilibrium dose constant for the ith radiation and
has the unit g·rad/(μCi·h) based on the units chosen in Eq. (16.11). It should be
pointed out that since β-particles are emitted with a distribution of energy, the average energy E−β of β-particles, which is equal to one-third of E
of the particle, is
max
used in the calculation of Δi. Thus, Eq. (16.11) becomes
RA
radh//
=
∆
φ
r
←
i
(16.12)
The activity A will change due to the physical decay and biological elimination
of the radiopharmaceutical, and therefore, the dose rate will also change. If Ao is the
initial administered activity, then the activity localized in an organ is a fraction f of
. Assuming an effective exponential change in A with time, Eq. (16.12) can be
A
o
written as
t
−
λ
RfAe
radh/./
i
=
e
0
∆
ii
φ
←
r
(16.13)
Here λe is the effective decay constant of the radiopharmaceutical, and t is the
time over which the original activity has decayed.
16.2.2 Cumulative Radiation Dose
The cumulative radiation dose Di to the target due to the ith radiation of the radionuclide during the period t=0 to t can be obtained by integrating Eq. (16.13). Thus,
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