Measurement of radiation Chapter 7 Measurement of Radiation: • Description of radiation beam • Kerma, dose, and electronic equilibrium Dosimetry • Calculation of the absorbed dose Radiation Dosimetry I – Bragg-Grey cavity theory – Practical ion chambers – Determination of absorbed dose for energies Text: H.E Johns and J.R. Cunningham, The above 3 MeV physics of radiology, 4th ed. – Dosimetry of radio-nuclides http://www.utoledo.edu/med/depts/radther

Description of radiation beam Energy transfer

• Photon interaction involves two stages: (a) energy is • Fluence transferred to charged particles and (b) charged particles dN   transfer energy directly through excitations and ionizations da • The initial interaction can be described by kerma (kinetic • Energy fluence energy released in medium): dN hv Kerma dE   K  tr da dm • Fluence rate Dose d • Kerma is related to photon fluence   dt    K    Etr   

Absorbed dose Electronic equilibrium

• Absorbed dose originates in the second interaction • Transfer of energy to charged particles (kerma) stage, describing the energy retained by the does not take place at the same location as the medium absorption of energy deposited by charged dE D  ab particles (dose) dm • Kerma can be directly related to the fluence, but • Units: 1Gy (gray)=1 J/kg dose can be calculated only in the assumption of – Older unit: 1 rad=10-2 Gy=1 cGy the electronic equilibrium: in any volume as many • This absorbed energy causes ionizations along the electrons are stopped as set in motion charged particle track • Under this condition dose is equal to kerma

1 Electronic equilibrium Electronic equilibrium

No photon • In reality dose deposition attenuation at any point is the result of • For approximate kerma upstream electronic • In case of electronic equilibrium, equilibrium: percentage of photons attenuated within the    electron range R D    E  K(1 g) With 5%   ab should be very small photon    attenuation • Becomes >5% for • g- fraction of energy lost to bremsstrahlung photon energies above 3MeV (column 5) • Typically approximate electronic equilibrium is assumed

Example 1 Bragg-Gray cavity theory

• Calculate the kerma given the photon flux 1016/m2, • Most dose measurements are based on a photon energy 10 MeV, linear attenuation measurement of charge produced through 2 coefficient 0.028 cm /g and energy transfer gas ionization: Q 2 attenuation coefficient 0.022 cm /g. Dgas  W mgas  /  K   /  E   /  tr E A. 5 J/kg tr  /  • W – is the average energy B. 15 J/kg 1 104 m2 K 1016 0.022 10MeV  required to cause one C. 25 J/kg m2 103 kg ionization in the gas 2.21014MeV / kg  D. 35 J/kg • In air W=33.85 eV/ion pair 2.21014 1.61013J / kg  35J / kg Cavity does not perturb electron tracks

Bragg-Gray cavity theory Bragg-Gray cavity theory

• Need dose to the surrounding medium (“wall”) • Relate the dose in gas to the dose in the “wall” through the ratio of mean stopping powers in gas and wall • Bragg-Gray formula relates ionization in the gas cavity to absorbed dose in the medium

wall Q wall Dwall  Dgasl  Sgas  W  Sgas mgas • Using restricted stopping powers gives more accurate result wall • Sgas designates stopping power averaging over both • Since the ratio is not very sensitive to the choice of D, photon and electron spectra is used • Cavity is assumed small and not affecting the beam spectrum

2 Absolute ion chamber Determination of absorbed dose • An ionization chamber made of a known material and having a cavity of a known volume • Have three materials involved • The wall thickness has to be greater than the range of electrons to separate the wall from the medium • From measurement can find the dose to the wall • Knowing the ratio of average energy absorption coefficients in m e d  ab  wall and medium   arrive at:    med wall Q    med D W S wall ab     med air   ab m    Dmed  Dwall  wall   wall

Correction factor Correction factor • Both the air cavity and wall introduce perturbations to • Correction factor kc the beam includes properties of • In order to account for the finite size of both the air wall and medium cavity and wall, need to introduce attenuation through replacement factors correction factor kc

kawall kcmed  med kc  Q wall ab  kcwall  Dmed W Sair   kc m   wall • Values of replacement factors k, and correction factor kc are determined approximately

Effect of temperature and pressure Example 2

• Since the volume of an ion chamber is fixed, need • Find the ratio of barometer readings taken at heights to correct for change in gas mass due to change in X and X+500 meters. Molar mass of Earth's air is temperature and pressure 0.029 kg/mol, universal gas constant • Correction factor relative to conditions of 0oC and R=8.31 N·m/(mol·K). 101.3 kPa (760 mm Hg): Barometric formula: gh  273.2  t 101.3 A. 0.98  k    RT TP    P  P0e  273.2  p B. 0.96   gDh 0.0299.8500   C. 0.94 RT 8.31295 o P / P  e  e  • If the instrument is calibrated for 22 C – adjust the D. 0.92 500 temperature in denominator e0.058 1 0.058  0.94

3 Exposure Standard air chamber

• Exposure is a measure of the ability of radiation to ionize the air; defined as dQ X  dm • Defined only for photons, and only for energies below 3 MeV • Exposure can only be measured directly by standard air • Roentgen is defined as: 1R  2.58104 C / kg of air chamber • It has to be large since the sensitive volume is defined by – 1 C/kg=3876 R the range of electrons set in motion: 3MeV photons produce – Equivalent ionization: 3.335x10-10 C/cm3 of air electron tracks up to several meters long

Example 3 Practical ion chambers

• Air kerma is 5 mGy. What is the exposure?

Q Q A. 0.3 R K  W; X  B. 0.6 R m m 3 J  J  • Assume that even for a volume of air small compared to the X  K /W  510 /33.4   C. 0.9 R kg  C  range of electrons the ionization is produced by electrons C within the volume D. 1.2 R 0.15103  0.15103 3.9103 R  0.58R kg • Adding air-equivalent solid wall and two electrodes – obtain a practical device for measurement of exposure • It has to be calibrated against the standard chamber to produce energy dependent calibration factor Nx: get X=MNx

Effective atomic number Effective atomic number • Air-equivalent material has to have appropriate Z to represent photoelectric effect interaction coefficient at low energies (30 to 80 keV)

• The effective atomic number of a mixture with an fractional numbers of electrons/g of materials Zn (typically m=3.5):

m m m m Z  a1Z1  a2Z2 ... anZn

• For high energies only electron density is • Other equations exist in literature important since Compton interaction is dominant

4 Absorbed dose determination Fluence and exposure above 3 MeV • Ion chamber is still used as the basis for measurements • Energy fluence per • A set of correction factors is employed to convert the roentgen: raw measurement to the dose  0.00873 J • AAPM task group protocols for clinical dosimetry of  high-energy photon and electron beams: X ab /  kg R – Older TG-21 (1983) is based on exposure (or air-kerma) • Fluence per roentgen standard and calibration factor (Nx) – New TG-51 (1999, updated protocol in 2014) is based on an  0.00873 J absorbed-dose to water standard and calibration factor (ND,w)  – Parameters are published for ion chambers from different X hvab /  kg R manufacturers C J 1R is equivalent to 2.58104 33.85  0.00873 J kg  0.873cGy in air kg C

Exposure rate from g-emitters Exposure rate from g-emitters

• The exposure rate constant G is the exposure rate in R/hr at a point 1 meter away from a source • Exposure rate having activity of 1 Ci constant in air for a • From the inverse square law the exposure rate at source emitting 1 any point distance d away from a source with photon of energy hv activity A: per disintegration: X G A  2 t d 2 1 1 G 194.5hvab / air Rm hr Ci R m2  • Units of G     hr Ci 

Example 4 Example 5

• Four 30 mCi 1-125 seeds are arranged at the • The exposure rate constant for a radionuclide is corners of a 1 cm square. Neglecting tissue 12.9 R cm2/(mCi h). How many half-value layers attenuation, the exposure rate in tissue at the (HVLs) of shielding are required to reduce the center of the square is: (Exposure rate constant = exposure rate from a 19.5 mCi source at 2 m to 1.46 Rcm2/mCi-hr) less than 1 mR/h? A. 1 A. 3 15 R/hr X G A 12.919.5 B. 2    B. 376 R/h X 4G A 41.4630 2 2    C. 3 t d 200 C. 264 R/hr 2 2 2 t d ( 20.5 ) D. 4 0.00629 R/h  6.3 mR/h D. 192 R/hr E. 6 6.3 ln 6.3 E. 350 R/hr 350.4 R/hr 1  n   2.65  n  3 2n ln 2

5 Effects of filters on x-ray beam Chapter 8 The Quality of X-Rays (Half-Value Layer)

Radiation Dosimetry I

Text: H.E Johns and J.R. Cunningham, The physics of radiology, 4th ed. http://www.utoledo.edu/med/depts/radther Composite filters: highest Z material closest to x-ray tube (to remove characteristic x-rays)

Example 6 Measurement of half-value layer • In the graph below, the two X-ray spectra shown have the same • Measure exposure rate for a Same characteristic series of attenuators placed 1. Filtration peaks = same target in the beam 2. Target material • Setup to measure primary 3. HVL beam only (away from 4. KVp walls, floor, etc.) • Attenuators are placed at A. 1,2,3,4 Pt.B B. 1,3 Same kVp • Machine output is kept C. 2,4 constant D. 3,4 E. 4 only Different intensity – different filtration and HVL

Measurement of half-value layer Measurement of half-value layer

kV beams are often labeled by their HVL in mm of filtration material (Cu, Al, etc.)

Scatter getting to the detector will significantly affect the resulting HVL

6 Measurement of half-value layer Types of spectral distribution

• Fluence or energy fluence as a function of energy • Exposure distribution

MV spectra Conversion of exposure to absorbed dose • Bremsstrahlung spectra • Depends on a photon energy for mono-energetic • Labeled by the energy beam after unit conversion of electron beam striking the target D  X  f • HVL is not typically med med used except for  Gy       f  0.00873  ab   ab  shielding calculations med      R   med   air

• Depends on the spectral distribution of the beam for

Ali, Rogers, Functional forms for photon spectra of poly-energetic beam (need to find average) clinical linacs, Phys. Med. Biol. 57 (2012) 31–50

Conversion of exposure to Conversion of exposure to absorbed dose absorbed dose

• Presence of heterogeneities leads to scatter • Since scatter is lower energy – affects dose to higher Z materials (bone) more

7 Summary

• Measurement of radiation – Description of radiation beam – Kerma, dose, and electronic equilibrium – Calculation of the absorbed dose – Bragg-Grey cavity theory – Practical ion chambers • The quality of X-rays and half-value layer • Conversion of exposure to absorbed dose

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