Introduction to Physical Science/Review

This is the final chapter of a wikibook entitled Basics Physics of Nuclear Medicine, written originally by Kieran Maher in 1997.

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 10¹⁰ 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 cm² 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 a Filtered Back Projection method;
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.