# Basic Physics of Nuclear Medicine/Chapter Review

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## Chapter Review: Atomic & Nuclear Structure

-   The atom consists of two components -- a nucleus (positively
    charged) and an electron cloud (negatively charged);
-   The radius of the nucleus is about 10,000 times smaller than that of
    the atom;
-   The nucleus can have two component particles -- **neutrons** (no
    charge) and **protons** (positively charged) -- collectively called
    **nucleons**;
-   The mass of a proton is about equal to that of a neutron -- and is
    about 1,840 times that of an electron;
-   The number of protons equals the number of electrons in an isolated
    atom;
-   The **Atomic Number** specifies the number of protons in a nucleus;
-   The **Mass Number** specifies the number of nucleons in a nucleus;
-   **Isotopes** of elements have the same atomic number but different
    mass numbers;
-   Isotopes are classified by specifying the element\'s chemical symbol
    preceded by a superscript giving the mass number and a subscript
    giving the atomic number;
-   The **atomic mass unit** is defined as 1/12th the mass of the
    stable, most commonly occurring isotope of carbon (i.e. C-12);
-   **Binding energy** is the energy which holds the nucleons together
    in a nucleus and is measured in **electron volts** (eV);
-   To combat the effect of the increase in electrostatic repulsion as
    the number of protons increases, the number of neutrons increases
    more rapidly -- giving rise to the **Nuclear Stability Curve**;
-   There are \~2450 isotopes of \~100 elements and the unstable
    isotopes lie above or below the Nuclear Stability Curve;
-   Unstable isotopes attempt to reach the stability curve by splitting
    into fragments (**fission**) or by emitting particles/energy
    (**radioactivity**);
-   Unstable isotopes \<=\> radioactive isotopes \<=\> radioisotopes
    \<=\> radionuclides;
-   \~300 of the \~2450 isotopes are found in nature -- the rest are
    produced artificially.

## Chapter Review: Radioactive Decay

-   **Fission**: Some heavy nuclei decay by splitting into 2 or 3
    fragments plus some neutrons. These fragments form new nuclei which
    are usually radioactive;
-   **Alpha Decay**: Two protons and two neutrons leave the nucleus
    together in an assembly known as an **alpha-particle**;
-   An alpha-particle is a He-4 nucleus;
-   **Beta Decay -- Electron Emission**: Certain nuclei with an excess
    of neutrons may reach stability by converting a neutron into a
    proton with the emission of a **beta-minus particle**;
-   A beta-minus particle is an electron;
-   **Beta Decay -- Positron Emission**: When the number of protons in a
    nucleus is in excess, the nucleus may reach stability by converting
    a proton into a neutron with the emission of a **beta-plus
    particle**;
-   A beta-plus particle is a **positron**;
-   Positrons **annihilate** with electrons to produce two back-to-back
    gamma-rays;
-   **Beta Decay -- Electron Capture**: An inner orbital electron is
    attracted into the nucleus where it combines with a proton to form a
    neutron;
-   Electron capture is also known as **K-capture**;
-   Following electron capture, the excited nucleus may give off some
    gamma-rays. In addition, as the vacant electron site is filled, an
    X-ray is emitted;
-   **Gamma Decay -- Isomeric Transition**: A nucleus in an excited
    state may reach its ground state by the emission of a gamma-ray;
-   A gamma-ray is an electromagnetic photon of high energy;
-   **Gamma Decay -- Internal Conversion**: the excitation energy of an
    excited nucleus is given to an atomic electron.

## Chapter Review: The Radioactive Decay Law

-   The radioactive decay law in equation form;
-   Radioactivity is the number of radioactive decays per unit time;
-   The **decay constant** is defined as the fraction of the initial
    number of radioactive nuclei which decay in unit time;
-   **Half Life**: The time taken for the number of radioactive nuclei
    in the sample to reduce by a factor of two;
-   Half Life = (0.693)/(Decay Constant);
-   The SI Unit of radioactivity is the **becquerel** (Bq)
-   1 Bq = one radioactive decay per second;
-   The traditional unit of radioactivity is the **curie** (Ci);
-   1 Ci = 3.7 x 10^10^ radioactive decays per second.

# 

Chapter Review: Units of Radiation Measurement ==

-   **Exposure** expresses the intensity of an X- or gamma-ray beam;
-   The SI unit of exposure is the **coulomb per kilogram** (C/kg);
-   1 C/kg = The quantity of X- or gamma-rays such that the associated
    electrons emitted per kg of air at STP produce in air ions carrying
    1 coulomb of electric charge;
-   The traditional unit of exposure is the **roentgen** (R);
-   1 R = The quantity of X- or gamma-rays such that the associated
    electrons emitted per kg of air at STP produce in air ions carrying
    2.58 x 10^-4^ coulombs of electric charge;
-   The **exposure rate** is the exposure per unit time, e.g. C/kg/s;
-   **Absorbed dose** is the radiation energy absorbed per unit mass of
    absorbing material;
-   The SI unit of absorbed dose is the **gray** (Gy);
-   1 Gy = The absorption of 1 joule of radiation energy per kilogram of
    material;
-   The traditional unit of absorbed dose is the **rad**;
-   1 rad = The absorption of 10^-2^ joules of radiation energy per
    kilogram of material;
-   The **Specific Gamma-Ray Constant** expresses the exposure rate
    produced by the gamma-rays from a radioisotope;
-   The Specific Gamma-Ray Constant is expressed in SI units in
    C/kg/s/Bq at 1 m;
-   Exposure from an X- or gamma-ray source follows the **Inverse Square
    Law** and decreases with the square of the distance from the source.

## Chapter Review: Interaction of Radiation with Matter

-   **Alpha-Particles**:
    -   exert considerable electrostatic attraction on the outer orbital
        electrons of atoms near which they pass and cause ionisations;
    -   travel in straight lines -- except for rare direct collisions
        with nuclei of atoms in their path;
    -   energy is always discrete.
-   **Beta-Minus Particles**:
    -   attracted by nuclei and repelled by electron clouds as they pass
        through matter and cause ionisations;
    -   have a tortuous path;
    -   have a range of energies;
    -   range of energies results because two particles are emitted -- a
        beta-particle and a **neutrino**.
-   **Gamma-Rays**:
    -   energy is always discrete;
    -   have many modes of interaction with matter;
    -   important interactions for nuclear medicine imaging (and
        radiography) are the Photoelectric Effect and the Compton
        Effect.
-   **Photoelectric Effect**:
    -   when a gamma-ray collides with an orbital electron, it may
        transfer all its energy to the electron and cease to exist;
    -   the electron can leave the atom with a kinetic energy equal to
        the energy of the gamma-ray less the orbital binding energy;
    -   a positive ion is formed when the electron leaves the atom;
    -   the electron is called a **photoelectron**;
    -   the photoelectron can cause further ionisations;
    -   subsequent X-ray emission as the orbital vacancy is filled.
-   **Compton Effect**:
    -   A gamma-ray may transfer only part of its energy to a valence
        electron which is essentially free; \*\* gives rise to a
        scattered gamma-ray;
    -   is sometimes called Compton Scatter;
    -   a positive ion results;
-   **Attenuation** is term used to describe both absorption and
    scattering of radiation.

## Chapter Review: Attenuation of Gamma-Rays

-   Attenuation of a narrow-beam of gamma-rays increases as the
    thickness, the density and the atomic number of the absorber
    increases;
-   Attenuation of a narrow-beam of gamma-rays decreases as the energy
    of the gamma-rays increases;
-   Attenuation of a narrow beam is described by an equation;
-   the **Linear Attenuation Coefficient** is defined as the fraction of
    the incident intensity absorbed in a unit distance of the absorber;
-   Linear attenuation coefficients are usually expressed in units of
    cm^-1^;
-   the **Half Value Layer** is the thickness of absorber required to
    reduce the intensity of a radiation beam by a factor of 2;
-   Half Value Layer = (0.693)/(Linear Attenuation Coefficient);
-   the **Mass Attenuation Coefficient** is given by the linear
    attenuation coefficient divided by the density of the absorber;
-   Mass attenuation coefficients are usually expressed in units of
    cm^2^ g^-1^.

## Chapter Review: Gas-Filled Detectors

-   Gas-filled detectors include the **ionisation chamber**, the
    **proportional counter** and the **Geiger counter**;
-   They operate on the basis of ionisation of gas atoms by the incident
    radiation, where the positive ions and electrons produced are
    collected by electrodes;
-   An **ion pair** is the term used to describe a positive ion and an
    electron;
-   The operation of gas-filled detectors is critically dependent on the
    magnitude of the applied dc voltage;
-   The output voltage of an ionisation chamber can be calculated on the
    basis of the capacitance of the chamber;
-   A very sensitive amplifier is required to measure voltage pulses
    produced by an ionisation chamber;
-   The gas in ionisation chambers is usually air;
-   Ionisation chambers are typically used to measure radiation exposure
    (in a device called an **Exposure Meter**) and radioactivity (in a
    device called an **Isotope Calibrator**);
-   The total charge collected in a proportional counter may be up to
    1000 times the charge produced initially by the radiation;
-   The initial ionisation triggers a complete gas breakdown in a Geiger
    counter;
-   The gas in a Geiger counter is usually an inert gas;
-   The gas breakdown must be stopped in order to prepare the Geiger
    counter for a new event by a process called **quenching**;
-   Two types of quenching are possible: electronic quenching and the
    use of a **quenching gas**;
-   Geiger counters suffer from **dead time**, a small period of time
    following the gas breakdown when the counter is inoperative;
-   The true count rate can be determined from the actual count rate and
    the dead time using an equation;
-   The value of the applied dc voltage in a Geiger counter is critical,
    but high stability is not required.

## Chapter Review: Scintillation Detectors

-   NaI(Tl) is a scintillation crystal widely used in nuclear medicine;
-   The crystal is coupled to a **photomultiplier tube** to generate a
    voltage pulse representing the energy deposited in the crystal by
    the radiation;
-   A very sensitive amplifier is needed to measure such voltage pulses;
-   The voltages pulses range in amplitude depending on how the
    radiation interacts with the crystal, i.e. the pulses form a
    spectrum whose shape depends on the interaction mechanisms involved,
    e.g. for medium-energy gamma-rays used in in-vivo nuclear medicine:
    the Compton effect and the Photoelectric effect;
-   A **Gamma-Ray Energy Spectrum** for a medium-energy, monoenergetic
    gamma-ray emitter consists (simply) of a Compton Smear and a
    Photopeak;
-   **Pulse Height Analysis** is used to discriminate the amplitude of
    voltage pulses;
-   A pulse height analyser (PHA) consists of a **lower level
    discriminator** (which passes voltage pulses which are than its
    setting) and an **upper level discriminator** (which passes voltage
    pulses lower than its setting);
-   The result is a variable width window which can be placed anywhere
    along a spectrum, or used to scan a spectrum;
-   A **single channel analyser** (SCA) consists of a single PHA with a
    scaler and a ratemeter;
-   A **multi-channel analyser** (MCA) is a computer-controlled device
    which can acquire data from many windows simultaneously.

## Chapter Review: Nuclear Medicine Imaging Systems

-   A **gamma camera** consists of a large diameter (25-40 cm) NaI(Tl)
    crystal, \~1 cm thick;
-   The crystal is viewed by an array of 37-91 PM tubes;
-   PM tubes signals are processed by a position circuit which generates
    +/- X and +/- Y signals;
-   These position signals are summed to form a **Z signal** which is
    fed to a pulse height analyser;
-   The +/- X, +/- Y and discriminated Z signals are sent to a computer
    for digital image processing;
-   A **collimator** is used to improve the spatial resolution of a
    gamma-camera;
-   Collimators typically consist of a Pb plate containing a large
    number of small holes;
-   The most common type is a **parallel** multi-hole collimator;
-   The most resolvable area is directly in front of a collimator;
-   Parallel-hole collimators vary in terms of the number of holes, the
    hole diameter, the length of each hole and the septum thickness --
    the combination of which affect the sensitivity and spatial
    resolution of the imaging system;
-   Other types include the **diverging**-hole collimator (which
    generates minified images), the **converging**-hole collimator
    (which generates magnified images) and the **pin-hole** collimator
    (which generates magnified inverted images);
-   Conventional imaging with a gamma camera is referred to as **Planar
    Imaging**, i.e. a 2D image portraying a 3D object giving
    superimposed details and no depth information;
-   **Single Photon Emission Computed Tomography** (SPECT) produces
    images of slices through the body;
-   SPECT uses a gamma camera to record images at a series of angles
    around the patient;
-   The resultant data can be processed using **Filtered Back
    Projection** and **Iterative Reconstruction**;
-   SPECT gamma-cameras can have one, two or three camera heads;
-   **Positron Emission Tomography** (PET) also produces images of
    slices through the body;
-   PET exploits the positron annihilation process where two 0.51 MeV
    back-to-back gamma-rays are produced;
-   If these gamma-rays are detected, their origin will lie on a line
    joining two of the detectors of the ring of detectors which
    encircles the patient;
-   A **Time-of-Flight** method can be used to localise their origin;
-   PET systems require on-site or nearby **cyclotron** to produce
    short-lived radioisotopes, such as C-11, N-13, O-15 and F-18.

## Chapter Review: Production of Radioisotopes

-   Naturally-occurring radioisotopes generally have long half lives and
    belong to relatively heavy elements -- and are therefore unsuitable
    for medical diagnostic applications;
-   Medical diagnostic radioisotopes are generally produced
    artificially;
-   The **fission** process can be exploited so that radioisotopes of
    interest can be separated chemically from fission products;
-   A **cyclotron** can be used to accelerate charged particles up to
    high energies so that they to collide into a target of the material
    to be activated;
-   A radioisotope generator is generally used in hospitals to produce
    short-lived radioisotopes;
-   A **technetium-99m generator** consists of an alumina column
    containing Mo-99, which decays into Tc-99m;
-   Saline is passed through the generator to elute the Tc-99m -- the
    resulting solution is called **sodium pertechnetate**;
-   Both positive pressure and negative pressure generators are in use;
-   An **isotope calibrator** is needed when a Tc-99m generator is used
    in order to determine the activity for preparation of patient doses
    and to test whether any Mo-99 is present in the collected solution.

## Exercise Questions

1\. Discuss the process of radioactive decay from the perspective of the
nuclear stability curve.

2\. Describe in detail FOUR common forms of radioactive decay.

3\. Give the equation which expresses the Radioactive Decay Law, and
explain the meaning of each of its terms.

4\. Define each of the following:

:   \(a\) Half life;
:   \(b\) Decay Constant;
:   \(c\) Becquerel.

5\. A sample of radioactive substance is found to have an activity of
100 kBq. Its radioactivity is measured again 82 days later and is found
to be 15 kBq. Calculate:

:   \(a\) the half-life;
:   \(b\) the decay constant.

6\. Define each of the following radiation units:

:   \(a\) Roentgen;
:   \(b\) Becquerel;
:   \(c\) Gray.

7\. Estimate the exposure rate at 1 metre from a 100 MBq source of
radioactivity which has a Specific Gamma Ray Constant of 50 mR per hour
per MBq at 1 cm.

8\. Briefly describe the basic principle of operation of gas-filled
radiation detectors.

9\. Illustrate using a graph how the magnitude of the voltage pulses
from a gas-filled radiation detector varies with applied voltage and
identify on the graph the regions associated with the operation of
Ionisation Chambers and the Geiger Counters.

10\. Describe the construction and principles of operation of a
scintillation spectrometer.

11\. Discuss the components of the energy spectrum from a monoenergetic,
medium energy gamma- emitting radioisotope obtained using a
scintillation spectrometer on the basis of how the gamma-rays interact
with the scintillation crystal.

12\. Describe the construction and principles of operation of a Gamma
Camera.

13\. Compare features of three types of collimator which can be used
with a Gamma Camera.

