Introduction to Physical Science/Review

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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[edit]

  • 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[edit]

  • 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[edit]

  • 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[edit]

  • 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[edit]

  • 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[edit]

  • 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[edit]

  • 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[edit]

  • 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[edit]

  • 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[edit]

  • 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.