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Everything Radionuclides - Nuclear Medicine
1. EVERYTHING
RADIONUCLIDES
PROPERTIES, PRODUCTION, COMPARISONS
E K P O Vi c t o r, A D E D O K U N A d e r o n k e , A D E WA D a r e ,
A D E D E W E N u s i r a t , D AV I D D o r a t h y, A J I B A D E O l u w a f e m i .
A M . S C M E D I C A L P H Y S I C S P R E S E N T A T I O N
C O U R S E O N N U C L E A R M E D I C I N E ( 2 0 1 7 )
C O L L E G E O F M E D I C I N E , U N I V E R S I T Y O F L A G O S ( C M U L ) , N I G E R I A
2. OVERVIEW
Definitions
Properties
Activity
Half-Life
Energy
Decay Process
Production
Cyclotron
Nuclear Reactor
Generator
Radiopharmaceuticals
Characteristics
Applications
Quality Control
2
3. DEFINITION
A radionuclide is a radioactive nuclide with an unstable
nucleus that dissipate its excess energy by spontaneously
emitting ionizing radiation (e.g. alpha, beta or gamma
rays).
It is also called radioisotope, radioactive isotope or
radioactive nuclide.
In Nuclear Medicine (NM), radionuclides are used for
diagnosis, treatment and research.
3
4. What causes radioactivity?
Radioactivity is caused by instability in the nucleus
due to either:
a. Imbalance in the number of neutrons (N) and
protons (Z) – Natural Radionuclides
b. Excitation due to bombardment of particles –
Artificial Radionuclides
4
5. STABLE & UNSTABLE NUCLIDES
Odd Z - Odd N nuclei are usually unstable
(exceptions are: 2H, 6Li, 10B, 14N).
For A<20, Z = N nuclei are usually stable.
For A>20, Z = N nuclei are usually unstable.
These nuclei require N>Z for stability.
There are no stable nuclei with Z>83.
5
7. ACTIVITY
Radioactive materials experience an exponential decay.
The decay rate (called activity) is the number of disintegrations
occurring each second.
Activity (A) is the change in number of radioactive atoms (dN)
per unit time (dt).
A = –dN/dt ,
and, can be expressed as:
A = λN
After time t, A (t) = Aoe-λt or N (t) = Noe-λt
where Ao , No = initial activity, number of radioactive atoms resp.
λ = decay constant
7
8. ACTIVITY (UNITS)
SI Unit: Becquerel
1 Becquerel (Bq) = 1 disintegration per second (dps)
1 milliCurie (mCi) = 37 MBq
Typical values of Activity in Nuclear Medicine:
0.1 – 30mCi for diagnostics, and
up to 300mCi for therapy.
8
9. CUMULATIVE ACTIVITY
The total number of nuclear transformations in an organ or tissue is
called cumulative activity (Ā).
Cumulative activity values are often different for healthy patients
and patients with certain diseases.
where Ao = initial activity in the organ
Te = effective half-life
Organ Dose, D = Ā x S-factor (in Gy)
Total Body / Eff. Dose, E = ∑D (for all organs) (in mSv)
Ā = 1.44 x Ao x Te
9
10. SPECIFIC ACTIVITY
Specific Activity (a) is the Activity of a given radionuclide per
unit mass. It is a physical property of the radionuclide.
where NA is Avogadro’s constant, and M is molar mass
Its unit is in Bq/g or Ci/g.
Relatively high specific activity is preferred in NM.
99mTc is considered to have high a of 5.2x106 Ci/g .
a =
Activity
mass
=
λN
MN/NA
a =
λNA
M
10
11. HALF-LIFE (T½ )
Half-Life is the time taken for number of radioactive atoms
to decay by half.
It is a constant for each radionuclide, and given by the
equation.
N (t) = Noe-λt
At half-life (t=T1/2), N (t) = ½ No ,
We can thus show that:
T½ = In 2/λ
T½ =
𝟎.𝟔𝟗𝟑
𝝀
11
12. Half-Life (contd.)
There are 3 types of Half-Lives
Physical Half-Life (Tp or T1/2): The time taken for number of
radioactive atoms to decay by half.
Biological Half-Life (Tb): The time required for the body to
biologically eliminate half of a radionuclide’s activity or amount
(through metabolic turnover and excretion).
Effective Half-Life (Te): The time required for radioactivity
distributed in organs to decrease to half its original value due to
radioactive decay and biological elimination.
Te < Tp ,Tb
𝟏
𝑻 𝒆
=
𝟏
𝑻 𝒑
+
𝟏
𝑻 𝒃
12
15. Half – Life of 99mTc
15
99mTc with half-life of 6 hours, will reduce to only 6.25% of its
original value within 24 hours (4 half-lives).
:
16. ENERGY
Preferred radionuclides should emit gamma rays of energy
50 – 300 keV.
This energy range is high enough to exit the patient but low
enough to be collimated and easily measured.
Radionuclides emitting mono-energetic gamma rays are
preferred.
16
17. MODES OF DECAY
17
There are four main modes of radioactive decay:
Alpha decay
Beta decay
Beta plus decay
Beta minus decay
Electron capture
Gamma decay
Pure gamma decay
Internal conversion
Spontaneous fission
18. MODES OF DECAY (CONTD.)
18
DECAY EMITTED PARTICLE
α decay α particle
β- decay β- , anti-neutrino
β+ decay β+ , neutrino
Electron Capture Neutrino
Pure Gamma Decay Gamma rays
Internal Conversion Orbital Electron
Spontaneous fission Fission products
21. DESIRABLE PROPERTIES OF RADIONUCLIDES
1. Physical half-life of a few hours.
2. Decay to a stable daughter (or one with very long T1/2).
3. Emit γ-rays but no α & β – rays.
4. Decay by isomeric transition and electron capture is preferred.
5. Emit γ-rays of energy 50 – 300 keV.
6. Emit mono-energetic γ-rays.
7. Have high specific activity.
8. Be easily and firmly attached to the radiopharmaceutical at
room temperature, and does not affect its metabolism.
9. Be affordable and readily available at hospital site.
21
22. COMMONLY USED RADIONUCLIDES
The primary radionuclide used for diagnostic nuclear medicine is
Technetium-99m.
The primary radionuclide used for therapeutic nuclear medicine is
Iodine-131.
The primary radionuclide used for Positron Emission Tomography
(PET) is Fluorine-18-labelled De-oxyglucose (FDG).
22
24. CYCLOTRON-PRODUCED RADIONUCLIDES
Radionuclides can be produced in cyclotrons (or other
particle accelerators) by accelerating heavy charged
particles (e.g. p,α, d) to bombard stable nuclei.
Examples of cyclotron-produced radionuclides are:
18F, 67Ga, 123I, 57Co, 201Tl.
68Zn + p 67Ga + 2n
Protons are accelerated to approx. 20MeV to bombard 68Zn nuclei.
i.e. 68Zn (p, 2n) 67Ga
24
25. CYCLOTRON-PRODUCED RADIONUCLIDES (contd.)
Some radionuclides produced by cyclotrons (such as 123Cs)
decay further to the more clinically useful radionuclide
(123I).
Most cyclotron-produced radionuclides are neutron-poor,
and thus decay by β+ decay or electron capture (EC).
25
27. WORKING PRINCIPLE OF A CYCLOTRON
A cyclotron is a circular accelerator with semi-circular
electrodes (called D’s or dees because of their shape).
An ion source (hydrogen ion, i.e. proton) is introduced at
the centre between the ‘D’s and accelerated to very high
energy.
The accelerated proton hits the target with a very high
speed releasing neutron and the desired daughter
radionuclide.
18O + p 18F + n
27
28. CYCLOTRON-PRODUCED RADIONUCLIDES (contd.)
As cyclotron-produced radionuclides are very expensive. there are
now smaller specialized hospital-based cyclotrons to produce
clinically used radionuclides, such as 18F for PET.
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Industrial
cyclotron
Medical
Cyclotron
30. NUCLEAR REACTOR-PRODUCED RADIONUCLIDES
2 methods:
Nuclear Fission
Neutron Activation
Here, radionuclides are produced using neutrons to bombard either:
• Unstable target nuclei, leading to nuclear fission, OR
• Stable target material, via neutron activation
Nuclear reactor-produced radionuclides are usually neutron-rich, and
thus decay mainly by β- decay.
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31. NUCLEAR FISSION-PRODUCED RADIONUCLIDES:
o Most common target fissile material is 235U.
o When bombarded by neutrons, it splits into smaller nuclei
called fission fragments.
The desired radionuclide can be separated from the other
fissile fragments using chemical separation techniques.
31
NUCLEAR REACTOR PRODUCED RADIONUCLIDES (contd.)
32. CHARACTERISTICS OF NUCLEAR FISSION–PRODUCED
RADIONUCLIDES
Radionuclide Gamma ray energy
(keV)
Physical half-life
99Mo 740 66 h
133Xe 364 8.1 d
131I 81 5.27 d
137Cs 662 30 y
32
Commonly NM radionuclides produced by fission are:
99Mo, 133Xe, 131I, 137Cs.
33. NEUTRON ACTIVATED – PRODUCED RADIONUCLIDES:
o In Neutron Activation, an accelerated neutron is
captured by a stable nuclide, inducing radioactivity.
o Reactions are usually (n,γ); (n,p) or (n,α).
o (n,γ) is the most common, thus producing isotopes of the
target material.
33
NUCLEAR REACTOR PRODUCED NUCLIDES (contd.)
34. Thus, since their chemistry are alike, the daughter
radionuclide CANNOT be separated from its parent
(carrier) using chemical techniques.
The produced daughter radionuclide is NOT carrier-free.
34
NUCLEAR REACTOR PRODUCED NUCLIDES (contd.)
35. The presence of carrier in the mixture limits the ability to
concentrate the radionuclide of interest and therefore
lowers the specific activity.
Because of this, nuclear fission is mainly preferred to
neutron activation. An exception is 125I.
35
NUCLEAR REACTOR PRODUCED NUCLIDES (contd.)
37. 99mTc is produced using a radionuclide generator.
Because of the relatively low half-life of 99mTc (6 hours), it
cannot be feasibly stored for days (93.75 % of it decays
within 24 hours).
Therefore, its parent nuclide 99Mo (T1/2 = 66 hours) is
stored and transported in the form of portable lead-
shielded radionuclide generators, and supplied to
hospitals.
The 99Mo / 99mTc generators are fondly called moly cows.
GENERATORS
37
39. Radionuclide generators:-
• are constructed on the principle of the decay-growth
relationship between a long-lived parent and its short-
lived daughter radionuclide.
• i.e. a long-lived parent nuclide is allowed to decay to
its short-lived daughter nuclide and the latter is
then chemically separated.
99Mo 99mTc + β-
(T1/2 = 66hrs ) (T1/2 = 6hrs)
GENERATORS (contd.)
39
41. 99Mo - 99mTc process
99Mo
87.6% 99mTc
140 keV
T½ = 6 h
99Tc
ß-
T½ = 2*105 y
99Ru
(stable)
12.4%
ß- , ṽ
T½ = 66 h
41
ß- , ṽ
T½ = 66 h
Isomeric Transition
42. PROCEDURE FOR PRODUCTION OF 99mTc
1. Nuclear Fission: Molybdenum produced as nuclear fission
product of 235U in nuclear reactor.
2. Molybdenum in compound form as Ammonium Molybdenate
(NH4
+)(MoO4
-) is loaded to column of inorganic alumina
(Al2O3) resin in the generator, and shipped.
3. Adsorption Occurs: Molybdenum compound attaches to the
surface of the alumina molecules.
The generator makes use of the fact that Molybdenum likes to
bond with Alumina, but Technetium does not.
42
43. PROCEDURE FOR PRODUCTION OF 99mTc
4. Elution: 99Mo decays to 99mTc, and an isotonic saline*
(called “eluant”, e.g. NaCl) is added to the column to
remove the 99mTc (“eluate”) when it is needed.
Chemical technique mainly used for separation is
Column Chromatography.
The 99Mo is not soluble in saline and therefore remains in the
column, while the 99mTc is soluble and thus extracted.
43
45. As air filter is opened, atmospheric pressure forces saline into the
column.
Saline passes through the column to elute (wash off). The Cl- ions
exchange with the 99mTcO4
- forming Sodium Pertechnetate
(Na93mTcO4).
A 99mTc generator is eluted once daily for one week (or
as need be) and then replaced.
The half-life of 99Mo is 66 hours, which allows the generator to
remain useful for approximately 1 week (about 2.5 half-lives).
45
PROCEDURE FOR PRODUCTION OF 99mTc
46. TRANSIENT vs SECULAR EQUILIBRIUM
(TE) (SE)
Equilibrium occurs when ratio
of activity of parent and
daughter reach a constant.
99mTc is produced as 99Mo
decays.
For TE, Tp > Td
e.g. 99Mo – 99mTc generator
For SE, Tp >>> Td
e.g. 81Rb – 81mKr generator
46
For 99mTc, TE occurs at ~ 22-23
hours (~4 half-lives of 99mTc).
Elution is done at this time.
47. TRANSIENT AND SECULAR EQUILIBRIUM
SECULAR EQUILIBRIUM (SE)
For T1/2 (parent) >> T1/2 (daughter),
e.g. 81Rb – 81mKr generator
T ½ (4.58 hr) (13 secs)
SE occurs at approx. 5 to 6 half-
lives of the daughter.
SE lasts longer.
47
48. Recall that activity, A = λN
The formula that governs the ratios of the activities is:
where AP, λP are activity and decay constant of the parent, and
AD, λD are activity and decay constant of the daughter
Maximum activity of daughter nuclide occurs at time, tmax given by:
48
TRANSIENT vs SECULAR EQUILIBRIUM (contd.)
49. For TRANSIENT EQUILIBRIUM, t ½D < t ½P and λD > λP ,
For SECULAR EQUILIBRIUM, t ½D << t ½P and λD >> λP ,
AD / AP ≈ 1
49
TRANSIENT vs SECULAR EQUILIBRIUM (contd.)
50. Types of Generators
2 types of generators:
• Dry type: this has a separate container of saline
solution that is changed every time a new elution
will be made. The column is thus dry between elutions.
• Wet type: it has a built-in container with enough
volume of saline solution for all elutions.
Transient Equilibrium generators and Secular
Equilibrium generators are also sometimes considered
types of generators.
50
51. ACTIVITY OF DAUGHTER
The activity of the daughter (e.g. 99mTc) at the time of elution
depends on the following:
1. The activity of the parent.
2. The rate of formation of the daughter, which is equal to the rate of
decay of the parent (i.e. Aoe-λt).
3. The time since the last elution.
4. The elution efficiency (typically 80% to 90%).
51
54. ADVANTAGES AND DISADVANTAGES OF
DIFFERENT PRODUCTION METHODS
METHOD OF RADIONUCLIDE
PRODUCTION
ADVANTAGES DISADVANTAGES
Cyclotron i. High specific activity
ii. Fewer radioisotopes are
produced
iii. It is easily accessible than
nuclear reactor
i. Expensive to purchase and
operate
Nuclear fission i. The fission process is a
source of a number of
widely used radioisotopes
(90Sr, 99Mo, 131I and 133Xe)
ii. High specific activity
i. Large quantities of
radioactive materials
generated
Neutron activation - i. It is difficult to separate
chemically
ii. Low specific activity
Generator i. It is cheap
ii. It is portable
iii. High specific activity
iv. It is easy to operate
i. It cannot be stored for
future use.
54
55. • Physical half-life: 6 hours;
• Biological half-life: 24 hours;
• the absence of β radiation permits the administration of GBq
activities for diagnostic purposes without significant radiation
dose to the patient.
• emits 140 keV photons which can be readily collimated to give
images of superior spatial resolution;
• Readily available in a sterile, pyrogen free and carrier free state
from 99Mo - 99mTc generators.
• 99mTc can easily be labelled with several radiopharmaceuticals, as
shown in table later.
Technetium-99m Properties
99mTc has the following favorable characteristics:
55
56. RADIOPHARMACEUTICALS
Pharmaceuticals are attached (labelled) to the radionuclide
in order to send it to desired target within the body. The
resultant mixture is called radiopharmaceuticals.
They compose of a radionuclide bond to an organic molecule.
Radiopharmaceuticals are designed to concentrate on a
particular organ/tissue.
They mimic a natural physiologic process.
They evaluate function rather than anatomy.
56
57. DESIRABLE PROPERTIES OF
RADIOPHARMACEUTICALS
Localize largely and quickly in target organ.
Eliminated from the body with effective T1/2 similar to duration of examination.
Effective T1/2 should be long enough to complete the study, but short
enough to minimize patient dose.
Have low toxicity.
Form stable product in vivo and in vitro.
Minimal electron contamination.
Contain no chemical or radionuclide contaminants.
Be readily and cheaply available.
57
58. MIXING OF RADIOPHARMACEUTICALS
Radiopharmaceuticals can be produced by simple mixing
and shaking at room temperature.
e.g. 99mTc + MDP + other chemicals.
Room is under positive pressure of sterile air.
The radiopharmaceutical is usually sterilized and anti-
microbial preservatives added.
58
59. Technetium-99m RADIOPHARMACEUTICALS
59
S/N COMPOUND ORGAN
1. Hexamethyl propylene amine oxime
(HMPAO)
Cerebral imaging
2. Dimercaptosuccinic acid (DMSA) -
Mercaptoacetyletriglycine (MAG3), DTPA
Renal study
3. Human serum albumin (HSA) colloidal
particles / Sulfur Colloid
Liver, spleen, red bone
marrow imaging
4. Iminodiacetic acid (HIDA) Biliary studies
5. HSA Macroaggregates Lung perfusion imaging
6. Diethylene Triamine Pentacetic Acid (DTPA) Lung ventilation studies
7. Methylene diphosphonate (MDP) Bone imaging
8. Autologous red cells Cardiac function
9. Heat-damaged autologous red cells Spleen imaging
10. Sestamibi (MIBI) or tetrofosmin Cardiac perfusion
imaging, for parathyroid
adenoma, breast
60. OTHER RADIOPHARMACEUTICALS AND ORGANS
S/N COMPOUND ORGAN
1. 133Xe Lung ventilation imaging
2. 201Thallium Cardiac (myocardial perfusion)
3. Radioiodine or 99mTc-NaI Thyroid imaging
4. 123I or 131I- labelled hippuran Renal study
5. 51Cr – labelled RBC Liver, spleen, kidneys
6. 67Ga – labelled citrate Tumour detection and infection
7. 111In-labelled leukocytes Detect acute infection
8. 75Se- selenomethionine Pancreas localization
9. 75Se – Cholesterol Suprarenal cortex localization
10. 81mKrypton- gas Lung ventilation
60
61. RADIONUCLIDES FOR THERAPY
61
131I treatment of thyroid cancer,
131I treatment of hyperthyroidism
Radioimmunotherapy with 90Y
ibritumomab tiuxetan (Zevalin) & 131I
tositumomab (Bexxar) therapy of low-grade
non-Hodgkin's lymphoma.
They can be administered in capsule or
liquid solution form.
63. PHYSICAL TESTS
pH and Ionic Strength
Ideal pH of radiopharmaceutical should be 7.4
The pH of radiopharmaceutical is measured by a pH
meter
Correct ionic strength is achieved by the addition of acid
or alkali.
Particle Size
The size of particles aid to determine the site where
radiopharmaceutical will get localized.
63
64. CHEMICAL TESTS
RADIONUCLIDE PURITY
It is the percentage of the total radioactivity in the form of the
desired radionuclide present in the radiopharmaceutical.
Impurities arise from fission of heavy elements in the reactor.
Multi-Channel Analyser (MCA) or well counter is used for
test.
Beta Spectrometer or a liquid scintillator may also be used to
test in pure beta emission radionuclides.
64
65. CHEMICAL TEST (CONTD.)
Radionuclide impurities could give rise to instability of
radiopharmaceutical, increasing the dose and degrading the
image quality.
Sodium ascorbate, sodium sulphite, and ascorbic acid are often
added to maintain stability.
65
66. CHEMICAL TEST (CONTD.)
RADIOCHEMICAL PURITY
It refers to the percentage of total radioactivity in a sample
that is present in the desired chemical form.
Radiochemical impurities may arise from decomposition due
to change in temperature or pH, and light.
Presence of radiochemical impurities could alter the
bio-distribution of radiopharmaceutical.
66
67. CHEMICAL TEST (CONTD.)
Methods used to detect radiochemical impurities in a given
radiopharmaceutical include;
Gel chromatography
Precipitation
Solvent extraction
High performance liquid chromatography (HPLC)
Distillation
67
68. CHEMICAL TEST (CONTD.)
CHEMICAL PURITY
Whereas radiochemical purity deals with the purity of the
starting materials for radiopharmaceuticals, chemical
purity checks the final material, to ascertain it has not
been affected by the process (milking).
e.g. Presence of Al ions in Tc radiopharms, gotten from the
alumina in the 99mTc generator.
A simple colorimetric limit test (spot colour test) is used for
alumina.
68
69. CHEMICAL TEST (CONTD.)
ACTIVITY
Measures the amount of radioactivity of a radiopharm of
each dose before administration to patients.
The determination of activity is carried out by means of
an isotope dose calibrator.
The Dose Calibrator is used to determine content of Mo
each time the 99mTc generator is eluted.
69
70. BIOLOGICAL TEST
To examine the sterility, apyrogenicity and toxicity.
STERILITY
It indicates the absence of micro-organisms in a
radiopharmaceutical preparation.
70
71. BIOLOGICAL TEST (CONTD.)
METHODS OF STERILIZATION
1. Autoclaving
Radiopharmaceutical is sterilized by heating steam at
121oc under a pressure of 18 psi for 15-20 minutes.
Suitable for thermostable radiopharmaceutical (such as
99mTc - pertechnetate, 111 In-indium chloride).
Not suitable for heat labile radiopharms (e.g. I-131) and
short- lived radionuclides (e.g. F-18) because it takes too
long .
71
72. BIOLOGICAL TEST (CONTD.)
2. Membrane filtration
Radiopharmaceutical is filtered through a membrane filter
that remove various organisms by sieving mechanism.
It is suitable for short lived radionuclides and heat-labile
radiopharmaceutical.
72
74. BIOLOGICAL TEST (CONTD.)
STERILITY TEST
It is performed by incubating the radiopharmaceutical
sample in fluid Thioglycollate medium or soybean-casein
digest at 300C to 350C and 200C to 250C for 14 days
respectively.
74
75. BIOLOGICAL TEST (CONTD.)
APYROGENICITY TEST
All radiopharmaceuticals for human administration are required
to be pyrogen-free.
Pyrogens are either polysaccharides or proteins produced by
metabolism of microorganism.
Pyrogenic contamination may be prevented by the use of sterile
glassware, solutions, and equipment under aseptic conditions in
any preparation procedure.
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76. BIOLOGICAL TEST (CONTD.)
Apyrogenicity test (contd.)
Tested by injecting rabbits with test material and
monitoring their rectal temperature over 3 hours.
If the total temperature rise is less than 1.4oC, and none
of the animals shows a temperature rise over 0.60C , then
the material is considered to be non-pyrogenic.
76
77. BIOLOGICAL TEST (CONTD.)
Toxicity test
Toxicity arises from the pharmaceutical part of the
radiopharmaceutical, however it is minimal since the
quantity of radiopharmaceutical used is usually small.
The toxic effect of radiopharmaceutical is described by
L50/60, which describes the dose required to produce
mortality of 50% of a species in 60 days after
administration of a radiopharmaceutical dose.
Toxicity is preferably studied using cell culture and
computer modelling.
77
78. SUMMARY
Radionuclides are produced with cyclotrons, nuclear
reactors or generators.
Their QA involve a Physical test (pH, ionic, etc.), Chemical
test (radionuclide purity, radiochemical purity, etc.) and
Biological test (sterility, apyrogenicity, toxicity tests).
78
79. REFERENCES
B. Saha. Fundamentals of Nuclear Pharmacy. 4th ed. New York: Springer, 2013.
D. L. Bailey. Nuclear Medicine Physics : a handbook for students and teachers. — Vienna:
International Atomic Energy Agency, 2014.
E. B. Podgorsak. Radiation Oncology Physics: A Handbook for Teachers and Students. Vienna: IAEA,
2005.
E. Forster. Equipment for Diagnostic Radiography. New York: Springer, 2012.
IAEA. Nuclear Medicine Resources Manual. Vienna : International Atomic Energy Agency, 2006.
J. A. Pope. Medical Physics Imaging. Heinemann Advanced Science, 1999.
J. T. Bushberg, et al. The Essential Physics of Medical Imaging. 2nd ed. Philadelphia: Lippincott Williams &
Wilkins, 2002.
Marco Silari. Radionuclide Production. African School of Physics, 2010
P. Allisy-Roberts, J. R. Williams. Farr’s Physics of Medical Imaging. Edinburg: Elsevier Health Sciences,
2007
S. Webb. The Physics of Medical Imaging. 2nd ed. Florida: CRC Press, 2012.
W. Huda, R. Sloan. Review of Radiologic Physics. 3rd ed. Philadelphia: Lippincott Williams & Wilkins, 2009.