Units of Nuclear Medicinehadron.physics.fsu.edu/.../Calendar/SPRING2020/Nuclear-Medicine_A… · Nuclear Medicine Radiation Therapy Radioactive Tracers Radioactive Imaging Radioactivity:

BiomedicalPhysics II

Types ofIonizingRadiation

BiologicalEffectsUnits ofMeasurement

Effects of Radiation

NuclearMedicineRadiation Therapy

Radioactive Tracers

Radioactive Imaging

Biomedical Physics II - PHZ 4703

Nuclear Medicine

04/14/2020

My Office Hours:Wednesday 11:00 AM - Noon

212 Keen Building






Radioactive Tracers

Radioactive Imaging

Radioactivity

Some nuclei are unstable and decay spontaneously into twoor more particles.

This process is called radioactive decay.• The term radioactivity refers to the process in which a

nucleus spontaneously emits either particles or radiation.

When a nucleus decays, it can emit particles or photons:• The radioactive decay products were originally called

alpha (α), beta (β) and gamma (γ).• Generally, all are called “radiation” even though only

gamma is actually a form of electromagnetic radiation.






Radioactive Tracers

Radioactive Imaging

Outline

1 Types of Ionizing Radiation

2 Biological EffectsUnits of MeasurementEffects of Radiation

3 Nuclear MedicineRadiation TherapyRadioactive TracersRadioactive Imaging






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Radioactivity: α Decay

An α particle is composed of two protons and two neutrons:

• This is a He nucleus and is denoted as 42He.

• The α particle does not carry any electrons: Q = +2e.

• Example: 22688Ra → 222

86Rn + 42He

(The number of nucleons is conserved.)






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Radioactivity: α Decay

An α particle is composed of two protons and two neutrons:

• This is a He nucleus and is denoted as 42He.

• The α particle does not carry any electrons: Q = +2e.

1 Range: In air, about one to two inches.

2 Shielding: Stopped by a few centimeters of air, a sheet ofpaper, or the dead layer of skin (outer layer) on our bodies.

3 Biological hazard: Not considered an external radiationhazard. But if inhaled or ingested, becomes a source ofinternal exposure.






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Radioactivity: β Decay

There are two varieties of β particles:

• The negatively-charged particle is an electron.

• The positively-charged particle is a positron.(same mass as electron; both are point charges.)

• Example: 146C → 14

7N + e− + ν̄






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Radioactive Imaging

Radioactivity: β Decay

There are two varieties of β particles:

• The negatively-charged particle is an electron.

• The positively-charged particle is a positron.(same mass as electron; both are point charges.)

1 Range: In air, typically about 10 feet.

2 Shielding: Stopped by relatively thin layers of plastic, glass,aluminum, or wood.

3 Biological hazard: Externally, potentially hazardous to the skinand eyes, but β particles cannot penetrate to deep tissuessuch as the bone marrow or other internal organs.






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Radioactivity: γ Decay

The excited nucleus can emit γrays with different energies:

• This depends on whichexcited and final states areinvolved.

• Typical gamma rays haveenergies from about 10 keVto 100 MeV or higher.

γ rays versus X -rays:

• γ rays are produced innuclear reactions.

• X -rays are generated byatomic electrons.






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Radioactive Imaging

Radioactivity: γ Decay

The excited nucleus can emit γrays with different energies:

• This depends on whichexcited and final states areinvolved.

• Typical gamma rays haveenergies from about 10 keVto 100 MeV or higher.

1 Range: Very high penetrating power; no distinct maximumrange in matter.

2 Shielding: Stopped by dense material (lead, concrete, steel).

3 Biological hazard: Due to high pentrating power, exposure towhole body (rather than a small area of tissue near source).






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Decay Product: Neutrons

Neutron radiation consists of neutrons that are ejected from nucleiof atoms. Neutrons have no electrical charge and thus, interactionsoccur as the result of a “collision” between a neutron and the nucleusof an atom. A charged particle or other radiation which can causeionization may be emitted during these interactions.

1 Range: High penetrating ability, difficult to stop since neutronsdo not experience electrostatic force.

2 Shielding: Moderate to low energy neutron radiation shieldedby materials with high hydrogen content (H2O, polyethyleneplastic).

3 Biological hazard: External “whole body” hazard due to theirhigh penetrating ability.






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Radioactive Imaging

Decay Product: Neutrons

Neutron radiation consists of neutrons that are ejected from nucleiof atoms. Neutrons have no electrical charge and thus, interactionsoccur as the result of a “collision” between a neutron and the nucleusof an atom. A charged particle or other radiation which can causeionization may be emitted during these interactions.

1 Range: High penetrating ability, difficult to stop since neutronsdo not experience electrostatic force.

2 Shielding: Moderate to low energy neutron radiation shieldedby materials with high hydrogen content (H2O, polyethyleneplastic).

3 Biological hazard: External “whole body” hazard due to theirhigh penetrating ability.






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Radioactive Imaging

Radiation & Contamination

Radiation - Radiation is energy in the form of waves or particles givenoff during radioactive decay, or as a consequence of certain physicalprocesses that we can control. Examples are X-ray machines andparticle accelerators.

Radioactive material - Any material containing radioactive (unstable)atoms. Radioactive materials are everywhere. Usually, we encounterthem only in very small amounts. Since radioactive material containsunstable atoms, it emits radiation.

Radioactive contamination - Contamination is radioactive materialthat has been spread to unwanted locations. Many radioactivesources are sealed or are in a form that isolates the material frompotential spread. Contamination may be fixed, transferable (loose),or airborne.






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Outline









Radioactive Tracers

Radioactive Imaging

Biological Effects

The biological effects of radioactivity result from the way thedecay or reaction products interact with atoms and molecules:• The typical binding energy of an electron in an atom is on

the order of 10 eV.• The energy released in a nuclear reaction is typically

several MeV.• If one of the particles collides with an atomic electron,

there is enough energy to eject the electron from theatom or break a chemical bond in molecules.






Radioactive Tracers

Radioactive Imaging

Biological Effects

The biological effects of radioactivity result from the way thedecay or reaction products interact with atoms and molecules:• The typical binding energy of an electron in an atom is on

the order of 10 eV.• The energy released in a nuclear reaction is typically

several MeV.• If one of the particles collides with an atomic electron,

there is enough energy to eject the electron from theatom or break a chemical bond in molecules.

The amount of damage that a particular particle is capable ofdoing is difficult to predict.Ü α, β and γ radiation all have different masses and charges

and therefore interact with tissue in different ways. Theamount of kinetic energy carried by a particle also varies.






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Radioactive Imaging

Exposure

Exposure and Dose - When people are exposed to radiation, theenergy of the radiation is deposited in the body. This does not makethe person radioactive or cause them to become contaminated.

An analogy would be to shine a bright light upon your body. Thebody absorbs the light (energy), and in some cases the absorptionof the light energy may cause noticeable heating in the body tissue.However, your body does not emit light after it has absorbed it.






Radioactive Tracers

Radioactive Imaging

Exposure

Exposure and Dose - When people are exposed to radiation, theenergy of the radiation is deposited in the body. This does not makethe person radioactive or cause them to become contaminated.

An analogy would be to shine a bright light upon your body. Thebody absorbs the light (energy), and in some cases the absorptionof the light energy may cause noticeable heating in the body tissue.However, your body does not emit light after it has absorbed it.






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Radioactive Imaging

Units of Measurement

1 Source Activity − 1 Bq = 1 disintegration / s (SI)

2 Radiation Absorbed Dose − rad1 rad is the amount of radiation that deposits 10−2 J of energyinto 1 kg of absorbing material.Ü The unit accounts for both the amount of energy carried

by the particle and the efficiency with which the energyis absorbed.(SI unit is Gray: 1 Gray = 1 Gy = 1 J / kg = 100 rad).

3 Relative Biological Effectiveness − RBEThis measures how efficiently a particular type of particledamages tissue.Ü This accounts for the fact that different types of particles

can do different amounts of damage even if they depositthe same amount of energy.






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RBE value tends to increaseas particle mass increases.

Röntgen Equivalent in Man−rem:

Dose in rem =(dose in rad) × RBE

(RBE = 1 for 200 keV X rays)

This combines the amountand also the effectiveness ofthe radiation absorbed.

SI unit is Sievert (Sv):1 rem = 0.01 Sv = 10 mSv






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Radioactive Tracers

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Question

A typical exposure from a dental X-ray is 10 mrem.

1 How much energy is deposited to your head when you get adental X-ray?

2 A weigth of 1 N falls on your head. From how high above yourhead would the weight need to be dropped to impart the sameenergy as the X-ray?






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Radioactive Imaging

Question

A typical exposure from a dental X-ray is 10 mrem.

1 How much energy is deposited to your head when you get adental X-ray?

2 A weigth of 1 N falls on your head. From how high above yourhead would the weight need to be dropped to impart the sameenergy as the X-ray?

Solution:

1 10 mrem = 10 mrad = 10× 10−3 × 10−2 J / kg (RBE = 1.0)Mass of human head is about 5 kg:E = 1× 10−4 J / kg × 5 kg = 5× 10−4 J

2 E = 5× 10−4 J = m g h → h = 0.5 mm






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Radioactive Imaging

Question

An average annual dose from natural radiation sources is about500 mrem, of which about 40 mrem comes from 40K, an isotopefound all around us and in our food. What is the maximum energy(RBE = 1.7) deposited in a 65-kg individual from the emitted β raysof potassium each year?






Radioactive Tracers

Radioactive Imaging

Question

An average annual dose from natural radiation sources is about500 mrem, of which about 40 mrem comes from 40K, an isotopefound all around us and in our food. What is the maximum energy(RBE = 1.7) deposited in a 65-kg individual from the emitted β raysof potassium each year?

Solution:40× 10−3 rem = X [ rad ] × 1.7

X = 23.5 mrad = 2.35 × 10−4 J / kg

Energy deposited in 65 kg: E total = X × 65 kg = 0.0153 J






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Radioactive Imaging

Radiation Dosimetry

But even the same equivalent dose can cause different amount ofdamage on different tissues (tissue weight factors).

The effective dose is (1 rem = 10 mSv):

effective dose (Sv) = dose (Gy) x QF x wT






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Radioactive Imaging


When the radiation dose is low, cells are sometimes able torepair the damage:• Especially if dose is absorbed over long periods of time.• Generally, small amounts of radiation do not cause

significant harm to living cells.

If the radiation dose is very large, then cells can be completelydestroyed.

At intermediate doses, cells survive but often malfunction as aresult of the damage:Ü A typical result is that the affected cells reproduce in an

uncontrolled fashion, leading to cancer.






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Radioactive Imaging


Cells die as a result of the damage

If a cell is extensively damaged by radiation, or damaged in such away that reproduction is affected, the cell may die. However, cellsdie all the time; this is only a problem if a large number of cells diein a relatively short period of time.

All cells are not equally sensitive to radiation damage:

Cells which divide rapidly and/or are relatively non-specializedtend to show effects at lower doses of radiation.Ü Blood-producing cells (hematopoietic system) are the

most sensitive biological indicator of radiation exposure.






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Radioactive Imaging


Cells die as a result of the damage

If a cell is extensively damaged by radiation, or damaged in such away that reproduction is affected, the cell may die. However, cellsdie all the time; this is only a problem if a large number of cells diein a relatively short period of time.

All cells are not equally sensitive to radiation damage:

Cells which divide rapidly and/or are relatively non-specializedtend to show effects at lower doses of radiation.Ü Blood-producing cells (hematopoietic system) are the

most sensitive biological indicator of radiation exposure.






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Radioactive Imaging

Radiation Damage

Radiation damage is usually most severe for quickly dividing cells:

• Many types of blood and bone marrow cells fall into thecategory.

• Cancerous cells are also quickly dividing, so radiation can beused as a tool to selectively destroy cancer cells.

Cancerous cells are also quickly dividing, so radiation can be usedas a tool to selectively destroy cancer cells:

• For example, an α particle outside the body will be stopped inthe outer layer of skin and does relatively little damage.

• If a person ingests an α particle, it can do a great deal ofdamage to nearby cells.






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Radioactive Imaging

Acute Dose

Radiation doses can be grouped into two categories, acute andchronic dose.

Acute Dose

An acute radiation dose is defined as a large dose (10 rad or greaterto the whole body) delivered during a short period of time (on theorder of a few days at the most).

Acute Radiation Syndrome:

• Radiation sickness symptoms following acute doses ≥ 200 rad.

• Acute whole body doses of 400–500 rad may result in astatistical expectation that 50 % of the population exposed willdie within 30 days without medical attention.






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Acute Dose


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Acute Dose


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Acute Dose

Hematopoietic (blood-forming organ / bone marrow) syndrome:

Damage to cells (> 200 rad) that divide at the most rapid pace(bone marrow, spleen, lymphatic tissue)Ü Nausea, vomiting, hair loss (2-3 weeks after exposure);

death can occur 1-2 months after exposure.

Gastrointestinal tract syndrome (> 1000 rad):

Characterized by damage to cells that divide less rapidly (suchas the lining of the intestines)Ü Nausea, vomiting, diarrhea, dehydration, electrolytic

imbalance, loss of digestive ability, bleeding ulcers, andthe symptoms of the above syndrome.Death occurs within weeks of exposure.






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Acute Dose

Hematopoietic (blood-forming organ / bone marrow) syndrome:

Damage to cells (> 200 rad) that divide at the most rapid pace(bone marrow, spleen, lymphatic tissue)Ü Nausea, vomiting, hair loss (2-3 weeks after exposure);

death can occur 1-2 months after exposure.

Central nervous system syndrome (> 2000 rad):

Characterized by damage to cells that do not reproduce, suchas nerve cellsÜ Loss of coordination, confusion, coma, convulsions, shock,

and the symptoms of the above syndromes.(not caused by radiation directly, rather from complications)Death follows within hours to days.






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Radioactive Imaging

Deterministic Effects

Effects from acute doses to localized areas include:

• 200 - 300 rad to the skin can result in reddening of the skin(erythema), similar to a mild sunburn and may result in hairloss due to the damage to hair follicles.

• 300 rad to the ovaries can result in prolonged or permanentsuppression of menstruation.

• 30 rad to the testicles can result in temporary sterilization.

• 200 rad to the eyes can cause cataracts.

As a group, the effects caused by acute doses are deterministic. Theseverity of the effects is determined by the amount of dose received.Ü Effects usually have some threshold level.






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Radioactive Imaging

Deterministic Effects

Effects from acute doses to localized areas include:

• 200 - 300 rad to the skin can result in reddening of the skin(erythema), similar to a mild sunburn and may result in hairloss due to the damage to hair follicles.

• 300 rad to the ovaries can result in prolonged or permanentsuppression of menstruation.

• 30 rad to the testicles can result in temporary sterilization.

• 200 rad to the eyes can cause cataracts.

As a group, the effects caused by acute doses are deterministic. Theseverity of the effects is determined by the amount of dose received.Ü Effects usually have some threshold level.






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Radioactive Imaging

Chronic Dose

Chronic Dose

A chronic dose is a relatively small amount of radiation received overa long period of time. The body has time to repair damage becausea smaller percentage of the cells need repair at any given time. Thebody also has time to replace dead or non-functioning cells with new,healthy cells.

Effects of low levels of radiation are more difficult to determine (nodeterministic effects)Ü Delayed, latent effects (include forms of cancer, genetic effects).

• Chronic dose is type of dose received as occupationalexposure.

• Risks are not directly measurable, risk values are estimates.

Risk model is called stochastic.






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Radioactive Imaging

Chronic Dose

Chronic Dose

A chronic dose is a relatively small amount of radiation received overa long period of time. The body has time to repair damage becausea smaller percentage of the cells need repair at any given time. Thebody also has time to replace dead or non-functioning cells with new,healthy cells.

Effects of low levels of radiation are more difficult to determine (nodeterministic effects)Ü Delayed, latent effects (include forms of cancer, genetic effects).

• Chronic dose is type of dose received as occupationalexposure.

• Risks are not directly measurable, risk values are estimates.

Risk model is called stochastic.






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Radioactive Imaging

Radiation Exposure − Values






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For common medical procedures, benefits usually outweighthe risk of exposure.






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Comparison of Risks

Estimated days of life expectancy lost from various risk factors:

Industry Type or Activity Estimated Days LostSmoking 20 cigarettes a day 2370 (6.5 years)Overweight by 20 % 985 (2.7 years)Mining and Quarrying 328Construction 302Agriculture 277Government 55Manufacturing 43Radiation - 340 mrem/yr for 30 years 49Radiation - 100 mrem/yr for 70 years 34






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Somatic vs. Genetic Effects

Somatic effects appear in the exposed person and can be dividedinto two classes based on the rate at which the dose was received.

Prompt somatic effects are those that occur soon after an acute dose(typically 10 rad or greater to the whole body):

Example is hair loss which occurs about three weeks after adose of 400 rad to the scalp. New hair is expected to growwithin two months after the dose, although the color andtexture may be different.






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Radioactive Imaging

Somatic vs. Genetic Effects

Somatic effects appear in the exposed person and can be dividedinto two classes based on the rate at which the dose was received.

Prompt somatic effects are those that occur soon after an acute dose(typically 10 rad or greater to the whole body):

Example is hair loss which occurs about three weeks after adose of 400 rad to the scalp. New hair is expected to growwithin two months after the dose, although the color andtexture may be different.

Delayed somatic effects are those that occur years after radiationdoses are received:

Examples include increased potential for the development ofcancer and cataracts.

Genetic, or heritable effects are abnormalities that may occur in thefuture generations of exposed individuals (never seen in humans).






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Radioactive Imaging

Prenatal Radiation Exposure

An embryo / fetus is especially sensitive to radiation (rapidly dividingcells), particularly in the first 20 weeks of pregnancy.

Potential effects associated with prenatal radiation doses include:

• Growth retardation

• Small head / brain size

• Mental retardation

• Childhood cancer






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Radioactive Imaging

Natural Radiation

For common medical procedures, benefits usually outweigh the riskof exposure.

Natural exposure occurs from many sources:

• Cosmic rays − A collection of many different types of particlesfrom outer space (galactic and solar). At sea level, averageradiation dose is about 26 mrem / year.

• Radon − Produced by the decay of 23892 U in rocks and soil, α

emitter (terrestrial radiation).In the USA, the average effective whole body dose from radonis about 200 mrem per year.

• Sources in the human body (internal sources): e.g. 40K.The total average dose from internal sources is about40 mrem / year.






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Radiation Dose Limits (DOE)


• Cosmic rays − At sea level, average dose: ∼ 26 mrem / year.

• Radon − In the USA, the average effective whole body dosefrom radon is about 200 mrem per year.

• Total average dose from internal sources: ∼ 40 mrem / year.

The Department of Energy (DOE) radiation dose limit for visitors atNational Labs and the public is 100 mrem / year.

Moreover:

• Whole body dose limit for routine exposures = 5 rem / year.

• Extremities, skin and other organs = 50 rem / year.

• Lens of the eye = 15 rem / year.

• Pregnant women: Efforts should be made to avoid exceeding50 mrem / month.






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Human Sources

Chest X-ray:10 mrem






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For common medical procedures, benefits usually outweigh the riskof exposure.


• Cosmic rays − a collection of many different types of particlesfrom outer space.

• Radon − produced by the decay of 23892 U in rocks and soil.

Cancer Treatment:Ü Radioactive materials emit high energy electrons or γ-rays that

kill nearby cancer cells.Also, accelerators can be used (particle therapy).






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Radioactive Imaging

Outline









Radioactive Tracers

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Detection of Radiation






Radioactive Tracers

Radioactive Imaging

Detection of Radiation






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Radioactive Imaging

Bragg Curve

Energy attenuation as a function of distance traveled in mediumshows “Bragg peak” close to the end of the path where speedis smallest (interesting in cancer therapy).






Radioactive Tracers

Radioactive Imaging

Bragg Curve

Energy attenuation as a function of distance traveled in mediumshows “Bragg peak” close to the end of the path where speedis smallest (interesting in cancer therapy).






Radioactive Tracers

Radioactive Imaging

Proton Therapy

Main side effects (true for all forms of radiation therapy):Damage to normal cells.

• Beam is directed at the tumor and rotated around the tumor.

• Or a radioactive source is implanted in the tumor.

Other applications of radiation: Sterilization of surgical equipment,food preservation.






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Radioactive Imaging

Proton Therapy

Main side effects (true for all forms of radiation therapy):Damage to normal cells.

• Beam is directed at the tumor and rotated around the tumor.

• Or a radioactive source is implanted in the tumor.

Other applications of radiation: Sterilization of surgical equipment,food preservation.






Radioactive Tracers

Radioactive Imaging

Radioactive Tracers

Radioactive isotopes as tracers:

• Radioactive labels to “tag” molecules so that their movementinside a biological body can be traced.

• Digestion of food molecules, metabolic pathways.• Synthesis of amino acids by organisms.• Molecular transport across cell walls.• Candidates: 13C, 15N, 18O, 3H

• Imaging agents for medical diagnosis and imaging.

• Appropriate half-life (hours).• γ-emitter with appropriate energy (50–500 keV).• Can be easily combined with many compounds; a

compound is chosen for a particular organ in which it willconcentrate.

• Candidates: 99mTc, 18F






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Radioactive Imaging

Technetium-99m

Most commonly used radionuclide (80 %):99mTc is the chemical symbol of technetium. 99 is its massnumber. The m denotes ’metastable,’ which means it has astable nucleus (unlike most radioactive material) - but hasextra energy which it gives up as γ-rays.

The isotope is useful for several reasons:

• It can be easily combined with several pharmaceuticals.

• It gives off γ-rays at 140 keV which is a good match to thesensitivity range of the Gamma camera.

• Its half-life of six hours is long enough to allow practicalimaging but not so long that the patient, public andenvironment are over-burdened with radiation.

• It is a pure γ emitter.






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Radioactive Imaging

Technetium-99m Generators

Generators are supplied to hospitals from the nuclear reactor wherethe isotopes are made:

• Lead pot enclosing a glass tube containing the radioisotope.

• Contain molybdenum-99 ( 99Mo ), with a half-life of 66 hours,which prograssively decays to technetium-99 ( 99Tc ).

• Tc-99 is washed out of the lead pot by saline solution when itis required.

• After two weeks or less, generator is returned for recharging.






Radioactive Tracers

Radioactive Imaging

Myocardial Perfusion ImagingMyocardial perfusion imaging under stress and rest conditions. Theapical and mid-short-axis, vertical long-axis and horizontal long-axisimages are shown. Right panel shows three-dimensional perfusionmaps, viewed as the left anterior oblique projection. Large arrowsindicate stress-induced ischemia near the apex.






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Radioactive Imaging

Radioisotope Generators

1 PET imaging uses rubidium-82 ( 82Rb ) produced by a generatorsystem that uses strontium-82 ( 82Sr ) as the ’parent’ – which hasa half-life of 25 days.

2 Myocardial Perfusion Imaging (MPI) uses thallium-201 ( 201Tl )chloride or 99mTc and is important for detection and prognosis ofcoronary artery disease.

3 For PET imaging, the main radiopharmaceutical is Fluorodeoxyglucose (FDG) incorporating 18F – with a half-life of just undertwo hours, as a tracer. The FDG is readily incorporated into thecell without being broken down, and is a good indicator of cellmetabolism.

4 In diagnostic medicine, there is a strong trend to using morecyclotron-produced isotopes such as 18F as PET and CT/PETbecome more widely available. However, the procedure need tobe undertaken within two hours of a cyclotron producing it.






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Radioactive Imaging






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Radioactive Imaging






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SPET (aka SPECT)

Single Photon Emission (Computed) Tomography

Imaging an entire plane or slice:

γ-ray imaging equivalent of X-ray CT scan. Features:

• Tomographic imaging technique using γ-rays.• Very similar to conventional nuclear medicine planar

imaging using a γ-camera.• Provides true 3D information.• Information is typically presented as cross-sectional

slices through the patient, but can be freely reformattedor manipulated a required.

However, inefficient detection of only ∼ 1 /10000 photons.Poor spatial resolution of ∼ 1 cm.






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Radioactive Imaging

PETPositron Emission Tomography (PET):

• Underlying physics: e+ + e− → 2γ

• The two γ-photons are detected in coincidence (no collimator)Ü Much better detection efficiency (∼ 3 mm resolution).

• Uses positron emitters: 13C, 15N, 18O, 18F






Radioactive Tracers

Radioactive Imaging

PETPositron Emission Tomography (PET):

• Underlying physics: e+ + e− → 2γ

• The two γ-photons are detected in coincidence (no collimator)Ü Much better detection efficiency (∼ 3 mm resolution).

• Uses positron emitters: 13C, 15N, 18O, 18F






Radioactive Tracers

Radioactive Imaging






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Cardiac SPECT






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Brain SPECT






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PET

PET/CT images of a 60-year-old male patient diagnosed with non-small cell lung cancer and undergoing radiotherapy. Although a largemass in the right upper lobe was detected on chest CT imaging (A),the differentiation between tumor and normal surrounding structureswould not have been feasible without the aid of PET/CT.http://dx.doi.org/10.1590/S1806-37132015000004479

http://dx.doi.org/10.1590/S1806-37132015000004479

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