Transcript Slide 1

Photon and Energy Fluence
Particle fluence
dN
Φ
dA
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
dA
dE
Ψ
dA
where dE is the radiant energy incident upon a sphere of cross-sectional
area dA. The unit of energy fluence is J/m2.
dN
Ψ
E  ΦE
dA
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
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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
dΦ
Φ (E) 
(E)
E
dE
and
Ψ (E) 
E
dΨ
dΦ
(E) 
(E) E
dE
dE
where ΦE (E) and ΨE (E) are the particle fluence spectrum differential and
the energy fluence spectrum differentials respectively.
Particle Fluence Rate
dΦ

Φ
dt
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
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dΨ

Ψ
dt
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
K
dE
tr
dm
The unit of kerma is J·Kg-1 and is called the Gray.
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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
C
dE
c
dm
The unit of cema is J·Kg-1 and is called the Gray.
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Absorbed Dose
Absorbed dose is a measure of the amount of energy imparted
ε by ionising radiation to a finite mass dm and volume V
dε
D
dm
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
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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=DxQ
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
1
Thermal Neutrons
3
Fast Neutrons
10
Alpha particles and Ions
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10-20
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
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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.
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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=λxN
The unit of activity is the Becquerel (Bq) and one disintegration
per second = 1 Bq
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Background Dose
In the UK the average background effective dose is 2.2 mSv
per year.
Effective Dose (mSv)
0.26
Radon in air
0.33
Building materials and
rocks
1.3
0.35
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Food
Cosmic Radiation
Radiation Effects
The effects of ionising radiation can be broken into two groups
• Acute effects, and
• Late effects.
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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.
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The Thimble Ionisation Chamber
Graphite
Aluminium
Air Vent
Aluminium Stem
Insulator
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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)
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