Photon and Energy Fluence Particle fluence where dN is the number of particles incident on the surface of a sphere of cross-sectional area dA. The unit of particle fluence is m-2. Energy Fluence where dE is the radiant energy incident upon a sphere of cross-sectional area dA. The unit of energy fluence is J/m2. where E is the energy of the particle and dN is the number of particles of that energy. This however only describes a monoenergetic beam dA

Photon and Energy Rate Fluence We can alter the previous equations to reflect the fact that nearly all photon and particle beams are polyenergetic. They then become and where ΦE (E) and ΨE (E) are the particle fluence spectrum differential and the energy fluence spectrum differentials respectively. Particle Fluence Rate Energy Fluence Rate where dt is the increment in time. The units of particle fluence rate are m-2·s-1 The units of energy fluence rate are J·m-2·s-1 or W·m-2

KERMA KERMA is an acronym for Kinetic Energy Released per unit Mass. It is a measure of the amount of energy transferred from non-ionising radiation (photons and neutrons) into ionising radiation (electrons, protons, α-particles and heavy ions). Limiting our discussion to electrons, we can define kerma as the mean energy transferred to matter from the indirectly ionising radiation to charged particles (electrons) in the medium dĒtr per unit mass dm The unit of kerma is J·Kg-1 and is called the Gray.

CEMA CEMA is an acronym for Converted Energy per unit Mass and is applicable to directly ionising radiation. It is a measure of the amount of energy lost by charged particles (except secondary electrons) dEc in collisions in a mass dm of a material The unit of cema is J·Kg-1 and is called the Gray.

Absorbed Dose Absorbed dose is a measure of the amount of energy imparted by ionising radiation to a finite mass dm and volume V It can be applied to both directly and indirectly radiation. The unit of absorbed dose is J·Kg-1 and is called the Gray. The energy imparted is the sum of all the energy entering the volume minus all the energy leaving the volume, and incorporates any mass energy conversions e.g. pair production inside the volume will decrease the energy in the volume by 1.022 MeV Volume V

Equivalent Dose In assessing the effects of radiation it is important to consider: The type of radiation, and How much energy is deposited. Different types of radiation cause different amounts of ionisations and have different amounts of interactions with matter per unit track length. The average energy deposited per unit track length is called the Linear Energy Transfer (LET). Radiation with a high LET will cause more cellular damage per Gray than radiation with a lower LET. For this reason we use a quality factor to quantify the effect the radiation has with matter. The equivalent dose is the dose multiplied by the quality factor. The unit of equivalent dose is the Sievert (Sv) H = D x Q H = equivalent dose in Sv D = dose in Gy Q = quality factor Radiation Quality Factor Ionising EM Radiation (X- and γ-rays) 1 Beta Particles Thermal Neutrons 3 Fast Neutrons 10 Alpha particles and Ions 10-20

Tissue Weighting Factor WT Effective Dose Ionising radiation has different effects on different types of tissue. To be able to make comparisons of different doses we calculate the effective dose. The effective dose is the equivalent dose multiplied by a tissue weighting factor and is measured in Sieverts. E = Σ WT x HT E = effective dose in Sieverts HT = equivalent dose in Sieverts WT = tissue weighting factor Tissue which is highly sensitive to radiation has a higher weighting factor than that less sensitive. Organ Tissue Weighting Factor WT Bone surface, skin 0.01 Bladder, breast, liver, oesophagus, thyroid, remainder 0.05 Colon, lung, marrow, stomach 0.12 Gonads 0.2

Collective Effective Dose The collective effective dose is the effective dose summed over a population. Collective dose = Σ D x Ni D = mean equivalent dose in Sieverts Ni = total number of people The unit of collective dose is the person sievert.

Activity In nuclear medicine an important measure of a radioactive substance is its activity. N = N0e-λt N = number of nuclei remaining at time t N0 = the initial number of nuclei λ = the decay constant t = time The activity A is defined as the number of disintegrations per unit time. A = λ x N The unit of activity is the Becquerel (Bq) and one disintegration per second = 1 Bq

Background Dose In the UK the average background effective dose is 2.2 mSv per year.

Radiation Effects The effects of ionising radiation can be broken into two groups Acute effects, and Late effects.

Measuring Dose Gas filled ionisation chambers are used to measure dose in radiotherapy. They consist of two electrodes with a potential difference across them, separated by a gas. The radiation enters the detector and ionises a gas atom. The ions are attracted to the electrodes and detected as current. The voltage across the electrodes must be high enough so that all ions are collected, but not so high that the ions are accelerated and collide with other atoms and ionise them. This cascade of ionisation is the principle used in a Geiger-Muller tube to produce a pulse. Vented chambers have a variable amount of gas and so corrections for temperature and pressure are necessary. At low photon energies ~200 keV the chamber can be open to the air. However at increasing photon energies it is necessary to use a wall constructed of material similar to the atomic number of air. This material simulates several cms of air and allows the chamber to be smaller.

The Thimble Ionisation Chamber Graphite Aluminium Air Vent Aluminium Stem Insulator This cylindrical ionisation chamber has a surrounding wall made of graphite (Z = 6) and a central electrode made of very pure aluminium (Z = 13). The dimensions of the chamber are very precise so that the average atomic number is similar to that of air (Z = 7.3)

The Dosimetry Chain Within a hospital it is necessary to calibrate treatment machines. In the UK the National Physical Laboratory has one highly accurate calorimeter that is used as the primary standard. Each major radiotherapy centre throughout the UK has thimble ion chambers that are calibrated against the primary standard. These secondary standards are then used to calibrate dosimeters used on a daily basis in radiotherapy centres. Primary Standard (NPL) Secondary Standard (Major Radiotherapy Centres) Field Instruments (Radiotherapy Departments)