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 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 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.