Professor Anatoly Rosenfeld, Ph.D.
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Professor Anatoly Rosenfeld, Ph.D.
Prof Anatoly Rozenfeld
Founder and Director
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Dr Marco Petasecca
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Karen Ford Admin Officer
and PA
Dr Susanna Guatelli
Dr Mitra Safavi-Naieni
Dr Yujin Qi Dr Elise Pogson Michael Weaver
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Dr Engbang Li Dr Alessandra Malaroda
70% of medical physicists
in NSW were trained at CMRP
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What is dosimetry?
Random nature of radiation
Overview of dosimetric quantities
Radiometric quantities
Interaction coefficients
Interactions of indirectly ionizing radiation
Interactions of idirectly ionizing radiation
Dosimetric quantities
Kerma
Absorbed dose
Exposure
Relations between radiation quantities
Measurement of absorbed dose
Calorimeter
Ionization chamber
Outline
Radiation dosimetry is the measure of the effect of radiation on matter
Radiation dosimetry is used in many fields, including ◦ Radiation therapy
Treatment verification
Critical organ dose
◦ Diagnostic imaging
Patient doses
Operator doses
◦ Personnel monitoring
◦ Mining, nuclear industries
We need quantitative method to determine dose of radiation to predict radiation effect or reproduce irradiation conditions
Radiation can be measured by :
• Change colour of liquid (chemical dosimetry)
• Change temperature (calorimetry)
• Biological cell killing (biological dosimetry)
• Ionization in matter (charge measurements)
• Structural defects in matter( EPR , semiconductor dosimetry)
and many others…
There are many quantities used to describe the effects of radiation on matter, including ◦ Fluence (F)
◦ Energy fluence (Y)
◦ KERMA (K)
◦ Absorbed dose (D)
◦ Exposure (X)
◦ Quality factor (Q)
◦ Dose equivalent (H)
Each quantity has a distinct purpose and application in radiation dosimetry
The fluence of a radiation field, F, is defined as the number of particles, N, passing through an area, a, in the limit that the area is infinitesimally small
F = dN/da
Area, a
Number of particles, N
The flux density, j,or fluence rate, is defined as the rate of fluence passing through an area of infinitesimally small size, da, for an infinitesimally small time, dt
j = dF/dt = d/dt(dN/da)
Energy fluence, y, is similar to fluence, however, the energies of the incident particles are considered
The energy fluence is defined as the total kinetic energy, R, incident on an infinitesimally small area, a
Y = dR/da
For monoenergetic particles of energy E
R = E·N
Y = E·F Similarly, energy flux density, y, is defined as the energy fluence for an infinitesimally small time period, dt
y = dY/dt
y = E·j
Radiation transfers energy to matter through interactions, causing ionisations ◦ Indirectly ionising radiation (e.g . neutrons , gamma)
Transfers energy through two steps
Liberation of charged particle
Coulomb interactions from charged particles
Very few interactions per micron
Large energy transfers per interaction(e.g. (n,p)
◦ Directly ionising radiation Coulomb interactions between charged particles and
bound electrons
Many interactions per micron
Low energy transfer per interaction
Photons interact with matter through ◦ Photoelectric effect
releases100% of original photon energy
◦ Compton scattering
releases a fraction of original photon energy
◦ Coherent scattering
releases zero energy
◦ Pair production
releases 100% of original photon energy
Produces electron-positron pair
◦ Photonuclear interactions
releases 100% of original photon energy
Photons passing through matter will be attenuated
Where m is the linear attenuation coefficient (m-1)
m/r is the mass attenuation coefficient (m2kg-1)
𝜇
𝜌=𝜏
𝜌+𝜎𝑐𝑜ℎ𝜌
+𝜎𝐶𝜌+𝜅
𝜌
x
j0 j(x)
j(x)=j0exp(-mx)
is the photoelectric effect scoh is coherent scattering
sC is the Compton effect k is pair production
Charged particles interact with matter through collisional and radiative interactions
Collisional interactions ◦ Involve inelastic collisions with atomic electrons
◦ Result in excitation or ionisation
Radiative interactions ◦ Involve inelastic collisions with an atomic nucleus
◦ Energy emitted in the form of photons (Bremsstrahlung)
Energy is lost relative to the mass stopping power
𝑆
𝜌=
1
𝜌
𝑑𝐸
𝑑𝑙 (Jm2kg-1)
Where dE is the energy lost after traversing a distance dl
Mass stopping power may be separated into collisional (el) and radiative (rad) components
𝑆
𝜌=1
𝜌
𝑑𝐸
𝑑𝑙𝑒𝑙
+1
𝜌
𝑑𝐸
𝑑𝑙𝑟𝑎𝑑
LET is the measure of the local energy deposition along the track of a charged particle
Is equivalent to the stopping power, S, when radiative energy loss is excluded
Gives an indication of the biological damage caused by the charged particle
a particles and neutron secondary’s have high LET (e.g. LETw 5 MeV alpha about 90KeV/mm, 5 MeV proton -8keV/mm)
Electrons have low LET (unless very low energy) ( 1 MeV electron LETw about 0.1KeV/mm)
Bethe Formula
LETD-restricted stopping power,
related to LET limited to energy of d-electrons <t D eV
Charged particles are liberated through interactions of photons with matter
The total charge liberated in a volume is based on 1. Crossers
2. Stoppers
3. Starters
4. Insiders
1
2
3
4
V photons
Charged particles
CPE exists if every charged particle leaving the volume is replaced by a charged particle of the same type, energy and direction entering the volume
Condition for CPE is the distance of the photon beam into the medium greater than the mean free path of electrons (e.g. for 6MV X-ray about 15 mm in water)
V photons
Charged particles
The Energy Transferred (total kinetic energy in a point from all liberated charged particles in a single interaction )
The Energy Deposited in a single interaction is given by
ei = ein – eout + Q Where ein is the kinetic energy of the incident particle
eout is the sum of the kinetic energies of all of the particles leaving the interaction
Q is the change in rest energies of the particles in the interaction (increases for decay, annihilation,
decreases for pair production)
The total energy imparted to a volume ◦ Is the sum of all energies imparted by the individual
interactions
◦ May involve one or many interactions
◦ Is stochastic in nature (random)
(e.g. the number of ionization in the volume from the same radiation source and the same time interval is different; the specific energy imparted, 𝑧 = 𝜀
𝑚 , is variable as well, see later)
𝜀 = 𝜀𝑖𝑖
The mean energy imparted to a volume is the difference between the incoming radiant energy and the outgoing radiant energy, offset by the total change in rest mass averaged over many deposition events
𝜀 = 𝑅𝑖𝑛 − 𝑅𝑜𝑢𝑡 + Σ𝑄 Where Rin is the incoming radiation
Rout is the outgoing radiation
Q is the total change in rest mass
Rin Rout SQ
The Compton effect:
Energy transferred
Etr = hn1 - hn2 = T
Energy deposited
ei = ein – eout + Σ𝑄
ei = hn1 – (hn2 + hn3 + T’) + 0
hn1
hn2
e
T
hn3
T’
Photoelectric effect
Energy transferred
Etr = T + EA
Energy deposited
ei = ein – eout + Σ𝑄
ei = hn1 – (T’+hn2+E’A) + 0
hn1
e T=hn1-Eb
hn2
T’
T
EA
E’A
Pair production
Energy transferred
Etr = T+ + T-
Energy deposited
ei = ein – eout + Σ𝑄
ei = hn – (T’++T’-)-2mc2
hn
e+ T’+
T+
e-
T-
T’-
Kinetic Energy Released per unit Mass
The energy transferred to the medium per unit mass
𝐾 =𝑑𝐸𝑡𝑟𝑑𝑚
Where Etr is the energy transferred
Units of Joules/kilogram (J/kg) or Gray (Gy)
Only defined for indirectly ionising radiation (photons, neutrons)
Can be considered as the first collision dose
Is composed of collision and radiation components
𝐾 = 𝐾𝑐𝑜𝑙 + 𝐾𝑟𝑎𝑑
For mono-energetic photons or neutrons, KERMA may be calculated by
𝐾 = Φ 𝐸 𝜇𝑡𝑟/𝜌 Where Φ is the particle fluence (m-2)
E is the energy (excluding rest mass)
𝜇𝑡𝑟/𝜌 is the mass energy transferred cross-section (m2/kg)
E 𝜇𝑡𝑟/𝜌 is the KERMA coefficient (Gy m2)
The energy deposited/imparted in a volume per unit mass
𝐷 =𝑑𝜀
𝑑𝑚
Where 𝜀 is the energy imparted
Has units of Gray (Gy) or J/kg
Absorbed dose, as opposed to the specific energy imparted, 𝑧 = 𝜀
𝑚 , is a theoretical concept in the limit that the volume and mass approach zero
Imparted Energy Absorbed Dose
Stochastic Non-stochastic
No gradient Gradient dD/dx
No rate Rate D/dt
Finite mass Point quantity
Measurable Theoretical “Concepts of Radiation Dosimetry”, SLAC-153
18-MeV electrons
0.3-GeV N ions
a) At large doses (n>>1) the
distributions are Gaussian.
b) At low doses (n<1) the
distributions are
independent of dose.
c) At low doses the
distribution shifts vertically
and there is an increasing
probability of z=0.
Stochastic nature of event size Z deposited in a small volume of mm size
Dose is defined for all types of radiation ◦ For mono-energetic photons, assuming charged
particle equilibrium
𝐷 = Φ 𝐸𝜇𝑒𝑛
𝜌
Where men/r is the mass absorption cross section (m2kg-1)
◦ For charged particles
𝐷 = Φ𝑆𝑒𝑙𝜌
Where Sel/r is the collision stopping power (Jm2kg-1)
Dose should always be specified in the medium/material, e.g. ◦ Dose to air
◦ Dose to water
◦ Dose to tissue
How much is 1 Gray? ◦ LD50, the lethal dose to kill 50% of the population,
is ~5Gy (total body, photons, short time interval)
◦ 5Gy to water will raise the temperature by 0.0012°C
◦ The yearly background radiation dose is ~2mGy
Air ionisation per unit mass
𝑋 =𝑑𝑄
𝑑𝑚
Where Q is the absolute value of the total charge of the ions of one sign produced in air when all of the electrons or positrons liberated or created by photons in air are completely stopped
Units of Ckg-1 or R (Roentgen)
1C/kg=3876R
Is only defined for photons in air
Is not measureable for ◦ E < 5 keV
◦ E > 3 MeV ( do not exist CPE)
Charge caused by absorption of bremsstrahlung originating from secondary electrons is not included in dQ
𝐷𝑎𝑖𝑟 =𝑊𝑎𝑖𝑟
𝑒𝑋
Where Wair is the mean energy expended in air per electron-ion pair formed
e is the elementary charge
Wair/e = 33.97 J/C independent on photon energy
Dair is proportional to X
Dair(Gy) = 33.97 X(C kg-1)
Dair(Gy) = 0.00876 X(R)
Dair(cGy) = 0.876 X(R) (confussion....)
𝐷𝑚𝑎𝑡 =𝐶𝑃𝐸 Φ𝐸
𝜇𝑒𝑛𝜌
𝑚𝑎𝑡
𝐷𝑎𝑖𝑟 =𝐶𝑃𝐸 Φ𝐸
𝜇𝑒𝑛𝜌
𝑎𝑖𝑟
𝐷𝑚𝑎𝑡
𝐷𝑎𝑖𝑟=
𝜇𝑒𝑛𝜌
𝑚𝑎𝑡𝜇𝑒𝑛
𝜌 𝑎𝑖𝑟
Dtissue=Kair=Dwater, if CPE exist
Courtesy Prof Adrie Bos, SSD16 Summer School Lecture Series
𝐷𝑎𝑖𝑟 =𝑊𝑎𝑖𝑟
𝑒𝑋 =𝐶𝑃𝐸 Φ𝐸 𝜇𝑒𝑛
𝜌 𝑎𝑖𝑟
and 𝐾 = Φ 𝐸 𝜇𝑡𝑟/𝜌
then
𝐾𝑎𝑖𝑟 =
𝜇𝑡𝑟𝜌 𝑎𝑖𝑟
𝜇𝑒𝑛𝜌 𝑎𝑖𝑟
𝑊𝑎𝑖𝑟
𝑒𝑋
=1
1 − 𝑔
𝑊𝑎𝑖𝑟
𝑒𝑋
Where g = 0.003 for 60Co gamma rays in air
The air KERMA is the energy equivalent of the air ionisation with correction for the production of bremsstrahlung
Used to provide a direct measurement of absorbed dose
The temperature change needs to be large enough to measure with accuracy
𝐷𝑚𝑒𝑑 = 𝑐𝑚𝑒𝑑Δ𝑇
Where c is the thermal capacity of the medium
(J kg-1 °C-1)
“Radiation Dosimetry Instrumentation
and Methods”, Shani (a)
(b)
ΔT
22.349
22.348
22.347
22.346
22.345
22.344
22.343
22.342
22.341
22.380
22.375
22.370
22.365
22.360
22.355
22.350
0 10 20 30 40 50 60 70
0 50 100 200 300 400 500 600
Tem
per
atu
re ( C
)
time(s)
Tem
per
atu
re ( C
)
Dose measurements are generally wanted in water/tissue
However, doses are measured using detectors which ◦ Have a different density
◦ Consist of materials with a different atomic number
Doses may be measured in a detector and transformed to dose in water using ◦ Both measurements and calculations
◦ Knowledge of radiation interactions
Doses within small volumes or volumes of low density may be used to measure equivalent doses in water
For a field of charged particles in a medium, x, with a small cavity, k, inside, with constant fluence across the cavity and wall x
𝐷𝑘 = Φ𝑑𝑇
𝜌𝑑𝑥 𝑐𝑜𝑙
x k
F
k
Assumption all electrons are crossers
When the cavity is absent, the dose to the same location in the medium x is
𝐷𝑥 = Φ𝑑𝑇
𝜌𝑑𝑥 𝑐𝑜𝑙
Thus, the dose relationship is
𝐷𝑥𝐷𝑘
=
Φ𝑑𝑇𝜌𝑑𝑥
𝑐𝑜𝑙
Φ𝑑𝑇𝜌𝑑𝑥 𝑐𝑜𝑙
= 𝑑𝑇
𝜌𝑑𝑥𝑐𝑜𝑙
The Bragg-Gray cavity relation
x
x
k
x
k
𝐷𝑥𝐷𝑘
= 𝑆 𝑘𝑥𝑐𝑜𝑙
The relationship between the dose deposited in the medium and the cavity is dependent on the stopping power relationship
Holds true if ◦ The deposited doses are due to charged particles
◦ The fluence does not change over the cavity
m
Consider 3 cavity sizes, small, intermediate and large, of medium g within medium w
Small Intermediate Large
e1 e1
e1
e2
e4 e4
e3
e3
e2
w
w
w
g g g
The small cavity satisfies the Bragg-Gray cavity theory, in that almost all of the dose deposition is due to crossers (e1)
Small Intermediate Large
e1 e1
e1
e2
e4 e4
e3
e3
e2
w
w
w
g g g
The intermediate cavity dose consists of a combination of dose from crossers (e1), insiders (e4), starters that stop in the wall (e2) and stoppers that start in the wall (e3)
Small Intermediate Large
e1 e1
e1
e2
e4 e4
e3
e3
e2
w
w
w
g g g
The large cavity is large enough that dose deposited from electrons originating in the wall effect only a small volume of the medium, thus are negligible
Almost all of the dose is deposited from insiders created from g interactions with the medium, g
Small Intermediate Large
e1 e1
e1
e2
e4 e4
e3
e3
e2
w
w
w
g g g
Burlin made several assumptions to arrive at a useful cavity theory (1966) ◦ The media w and g are homogenous
◦ A homogenous g field exists across both media
◦ Charged particle equilibrium exists everywhere in w and g except for within the maximum electron range from the cavity boundary
◦ The equilibrium spectra of secondary electrons from both w and g are the same
◦ The fluence of electrons from the cavity wall is attenuated exponentially through the medium, g, with no change in spectral distribution
◦ The fluence of electrons originating in the cavity builds up to equilibrium exponentially as a function of distance into the cavity, with the same attenuation coefficient, b, that applies to electrons entering from the wall
The Burlin cavity theory in simple form is
𝐷 𝑔
𝐷𝑤= 𝑑 ∙ 𝑆 𝑤
𝑔+ 1 − 𝑑
𝜇 𝑒𝑛
𝜌
where d is a parameter representative of the cavity size. d approaches1 for small cavities which satisfy the Bragg-Gray cavity theory and approaches 0 for large cavities
m
g
w
d is defined as the average of the ratio Φ𝑤Φ𝑤𝑒
which may be determined by integrating relative to distance from all points in the volume to the cavity wall, l, over the average chord length through the cavity, L
𝑑 ≡Φ 𝑤
Φ𝑤𝑒 =
Φ𝑤𝑒 𝑒−𝛽𝑙𝑑𝑙
𝐿
0
Φ𝑤𝑒 𝑑𝑙
𝐿
0
=1 − 𝑒−𝛽𝐿
𝛽𝐿
Is a dimensionless variable used to weight absorbed dose to give an estimate of the effect on humans of different types and energies of ionising radiation
Is determined through experimental measurements (cell survival studies) of the relative biological effectiveness (RBE) of radiation
Other definition of Q are by ICRP 60 and by Kellerer and Hahn (Rad Res 114:480, 1988)
L keV mm-1 Q(L)
< 10 = 1
10 - 100 = 0.32L - 2.2
> 100 = 300 L-1/2
ICRP 60
Track structures of ionizing radiation in 100 nm water
Is the Dose Equivalent after the quality factor, Q, is applied to the absorbed dose
𝐻 ≅ 𝑄𝑁𝐷 where N is the product of all other possible modifying factors, however, is considered to be 1
Has the units of J/kg
When applied to absorbed dose, J/kg = Grays (Gy)
When applied to dose equivalent, J/kg = Sieverts (Sv)
Traditional Dosimetry: • Radiation protection
• (average) energy deposited in organs and
tumours, group of cells
Microdosimetry • Energy deposited within cell’s compartments
(i.e. nucleus, mitochondria)
Nanodosimetry: • Energy transferred to cellular
elements (i.e. DNA)
The fundamental quantity in radiation dosimetry is absorbed dose, D
D only has meaning if the energy deposition is due to many interactions
Under charged particle equilibrium (CPE), absorbed dose is described by a field quantity and an interaction coefficient
Under certain conditions, absorbed dose may be approximated by KERMA, which is easier to evaluate
Under charged particle equilibrium (CPE), absorbed dose from gamma radiation in water , tissue and air are different within 10%
Special acknowledgements for the contributions : ◦ Dr Dean Cutajar, Dr Alex Maloroda (slides
preparations )
◦ Prof Adrie J.J. Bos, “Introduction to Radiation Dosimetry”, 4th Summer School on Solid State Dosimetry, 2010
◦ Frank Herbert Attix, “Introduction to Radiological Physics and Radiation Dosimetry”, John Wiley and Sons, 1986
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