Professor Anatoly Rosenfeld, Ph.D.

Transcription

1 Professor Anatoly Rosenfeld, Ph.D.

2 Prof Anatoly Rozenfeld Founder and Director A/Prof Michael Lerch Dr George Takacs Dr Iwan Cornelius Prof Peter Metcalfe Dr Dean Cutajar Dr Marco Petasecca Karen Ford Admin Officer and PA Dr Susanna Guatelli Dr Mitra Safavi-Naieni Dr Yujin Qi Dr Elise Pogson Michael Weaver Dr Engbang Li Dr Alessandra Malaroda

3 EDUCATION AND RESEARCH Knowledge and Training at CMRP 70% of medical physicists in NSW were trained at CMRP Technology Solutions Excellence in Education Partnerships in Business

4 Outline 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

5 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

6 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

7 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

8 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

9 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)

10 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

11 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

12 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

13 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

14 Photons passing through matter will be attenuated j 0 j(x) j(x)=j 0 exp(-mx) Where m is the linear attenuation coefficient (m -1 ) m/r is the mass attenuation coefficient (m 2 kg -1 ) μ ρ = τ ρ + σ coh ρ x + σ C ρ + κ ρ is the photoelectric effect s coh is coherent scattering s C is the Compton effect k is pair production

15 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)

16 Energy is lost relative to the mass stopping power S ρ = 1 de ρ dl (Jm2 kg -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 dl el + 1 ρ de dl rad

17 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)

18 Bethe Formula LETD-restricted stopping power, related to LET limited to energy of d-electrons <t D ev

19 Charged particles are liberated through interactions of photons with matter The total charge liberated in a volume is based on photons 1. Crossers 1 2. Stoppers 3. Starters 4 4. Insiders 3 V 2 Charged particles

20 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 photons V Charged particles 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)

21 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 e i = e in e out + Q Where e in is the kinetic energy of the incident particle e out 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)

22 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 = i ε i

23 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 = R in R out + ΣQ Where R in is the incoming radiation R out is the outgoing radiation Q is the total change in rest mass R in SQ R out

24 The Compton effect: Energy transferred E tr = hn 1 - hn 2 = T hn 1 T T e hn 3 Energy deposited e i = e in e out + ΣQ e i = hn 1 (hn 2 + hn 3 + T ) + 0 hn 2

25 Photoelectric effect Energy transferred E tr = T + E A hn 1 T=hn 1 -E b T E A T e hn 2 Energy deposited e i = e in e out + ΣQ e i = hn 1 (T +hn 2 +E A ) + 0 E A

26 Pair production Energy transferred E tr = T + + T - hn T + T - T + e + Energy deposited e i = e in e out + ΣQ e i = hn (T + +T - )-2mc 2 T - e -

27 Kinetic Energy Released per unit Mass The energy transferred to the medium per unit mass K = de tr dm Where E tr is the energy transferred Units of Joules/kilogram (J/kg) or Gray (Gy)

28 Only defined for indirectly ionising radiation (photons, neutrons) Can be considered as the first collision dose Is composed of collision and radiation components K = K col + K rad

29 For mono-energetic photons or neutrons, KERMA may be calculated by K = Φ E μ tr /ρ Where Φ is the particle fluence (m -2 ) E is the energy (excluding rest mass) μ tr /ρ is the mass energy transferred cross-section (m 2 /kg) E μ tr /ρ is the KERMA coefficient (Gy m 2 )

30 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

31 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 Stochastic No gradient No rate Finite mass Measurable Absorbed Dose Non-stochastic Gradient dd/dx Rate D/dt Point quantity Theoretical Concepts of Radiation Dosimetry, SLAC-153

32 Stochastic nature of event size Z deposited in a small volume of mm size 18-MeV electrons 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= GeV N ions

33 Dose is defined for all types of radiation For mono-energetic photons, assuming charged particle equilibrium D = Φ E μ en ρ Where m en /r is the mass absorption cross section (m 2 kg -1 ) For charged particles D = Φ S el ρ Where S el /r is the collision stopping power (Jm 2 kg -1 )

34 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 C The yearly background radiation dose is ~2mGy

35 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

36 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

37 D air = W air e X Where W air is the mean energy expended in air per electron-ion pair formed e is the elementary charge W air /e = J/C independent on photon energy D air is proportional to X Dair(Gy) = X(C kg-1) Dair(Gy) = X(R) Dair(cGy) = X(R) (confussion...)

38 D mat = CPE ΦE μ en ρ mat D air = CPE ΦE μ en ρ air μ en D mat ρ = mat D μ air en ρ air Dtissue=Kair=Dwater, if CPE exist Courtesy Prof Adrie Bos, SSD16 Summer School Lecture Series

39 and then D air = W air e K = Φ E μ tr /ρ X = CPE ΦE μ en ρ air K air = μ tr ρ air μ en ρ air W air e = 1 1 g W air Where g = for 60 Co gamma rays in air The air KERMA is the energy equivalent of the air ionisation with correction for the production of bremsstrahlung e X X

40 ) Temperature ( C) Used to provide a direct measurement of absorbed dose The temperature change needs to be large enough to measure with accuracy D med = c med ΔT Where c is the thermal capacity of the medium (J kg -1 C -1 ) Radiation Dosimetry Instrumentation and Methods, Shani (a) ΔT (b)

41 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

42 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 x k D k = Φ k dt ρdx col F Assumption all electrons are crossers

43 When the cavity is absent, the dose to the same location in the medium x is D x = Φ dt ρdx col Thus, the dose relationship is Φ dt D x ρdx x x = col dt D k Φ dt = k ρdx col x k ρdx col The Bragg-Gray cavity relation

44 D x = Sk x D m col k 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

45 Consider 3 cavity sizes, small, intermediate and large, of medium g within medium w w w e 1 e 1 w e 1 g e 3 e 4 e 4 g e 2 e 3 g Small Intermediate e 2 Large

46 The small cavity satisfies the Bragg-Gray cavity theory, in that almost all of the dose deposition is due to crossers (e 1 ) w w e 1 e 1 w e 1 g e 3 e 4 e 4 g e 2 e 3 g Small Intermediate e 2 Large

47 The intermediate cavity dose consists of a combination of dose from crossers (e 1 ), insiders (e 4 ), starters that stop in the wall (e 2 ) and stoppers that start in the wall (e 3 ) w w e 1 e 1 w e 1 g e 3 e 4 e 4 g e 2 e 3 g Small Intermediate e 2 Large

48 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 w w e 1 e 1 w e 1 g e 3 e 4 e 4 g e 2 e 3 g Small Intermediate Large Almost all of the dose is deposited from insiders created from g interactions with the medium, g e 2

49 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

50 The Burlin cavity theory in simple form is D g = d Sw g + 1 d D w m 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 g w

51 d is defined as the average of the ratio Φ w 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 Φw e L 0 d Φ w e Φ = Φ w e e βl dl L w Φ e w dl 0 = 1 e βl βl

52 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

53 Other definition of Q are by ICRP 60 and by Kellerer and Hahn (Rad Res 114:480, 1988) ICRP 60 L kev mm -1 Q(L) < 10 = = 0.32L > 100 = 300 L -1/2 Track structures of ionizing radiation in 100 nm water

54 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)

55 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)

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57 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%

58 Special acknowledgements for the contributions : Dr Dean Cutajar, Dr Alex Maloroda (slides preparations ) Prof Adrie J.J. Bos, Introduction to Radiation Dosimetry, 4 th Summer School on Solid State Dosimetry, 2010 Frank Herbert Attix, Introduction to Radiological Physics and Radiation Dosimetry, John Wiley and Sons, 1986