Introduction to Physical Science/Excerpts from sources

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 nucleus; 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.