Radiation Dosimetry (Measurement of Absorbed Dose) Faiz Khan (Chapter 8) Podgorsak (Chapter 2)

Introduction Dosimetry attempts to quantitatively relate specific radiation measurements to chemical/biological changes that could be produced Essential for quantifying biological changes as a function of radiation received For comparing experiments

Introduction continued Radiation interaction Produces ionized and excited atoms and molecules Secondary electrons Produce additional ionizations and excitations Finally all energies are expended. Initial electronic transitions rapid (<10-15s) Represent the initial physical perturbations from which all effects evolve. So, ionization and energy absorption are the starting point for radiation dosimetry

Quantities and Units Absorbed dose is a measure of the biologically significant effects produced by ionizing radiation Definition of absorbed dose, dEavg/dm dEavg : the mean energy imparted by ionizing radiation to material of mass dm Unit The old unit of dose is rad, 1 rad = 100 ergs/g = 10-2J/kg The SI unit of dose is the gray (Gy), 1 Gy = 1J/Kg

Quantities and Units Exposure Defined for X and gamma radiation In terms of ionization of air Old unit called “roentgen” (R) Initially defined in 1928, current definition is: 1 R  2.58 x 10-4C kg-1 of air, exactly Applies only to electromagnetic radiation; the charge and mass refer only to air.

Roentgen - original definition Amount of radiation that produced 1 esu of charge in 1 cm3 of air at STP 1 esu = 3.335 x 10-10C At STP air has a density of 0.001293 g cm-3 1 kg of air has a volume of 7.734 x 105 cm3 1 R = 3.335 x 10-10 C cm-3 of air How much energy is absorbed in air from 1R?

Absorbed Dose and Exposure What is the absorbed dose in air when the exposure is 1 R? Need to know W for air (energy to produce ion pair in air) 33.7 eV/ip = 33.7 J/C. 1 R  2.58 x 10-4C/kg x 33.7 J/C = 8.8 x 10-3 J kg-1 This equals 8.8 x 10-3 Gy (0.88 rad) Similar calculations show that 1R would produce a dose of 9.5 x10-3 Gy (=0.95 rad) in soft tissue. Why is there a difference between air and tissue??? This is why one can say that 1 R ~ 1 rad in tissue.

Exposure Measurement - Free Air Chamber Feasible to measure exposure at radiation energies between few keV and several MeV Definitive measure is by laboratory device known as free air chamber X-ray beam enters through a portal and interacts with cylindrical column of air defined by entry diaphragm Ions created in defined space are measured

Parallel Plate Free-air Ionization Chambers All the energy of the primary electrons expended in chamber HV Wires scattered photon e4 Diaphragm Xray beam e1 e2 e3 Monitor Electrometer

VTC, Advanced Health Physics Concepts Session 7 - February 7, 1998 Free Air Chamber Photons enter chamber and interact with fixed quantity of air PE, CS Ions from air collected by plates Lead lined (shielded) Electric fields are kept perpendicular to plates by guard rings and guard wires Guard wires assure uniform potential drop across plates © CSI - Radiation Safety Training, 1998 10

Free Air Chamber Field intensity is ~ 100 V/cm VTC, Advanced Health Physics Concepts Session 7 - February 7, 1998 Free Air Chamber Field intensity is ~ 100 V/cm Collect ions prior to recombination Voltage low enough so no secondary ionizations Current flow is measured All energy of primary electrons must be deposited in sensitive volume of air for meter to work properly © CSI - Radiation Safety Training, 1998 11

VTC, Advanced Health Physics Concepts Session 7 - February 7, 1998 Free Air Chamber What if all primary electrons are not collected in sensitive volume? If equal number coming in from outside of sensitive volume as is going out: Electronic Equilibrium © CSI - Radiation Safety Training, 1998 12

Electronic Equilibrium VTC, Advanced Health Physics Concepts Session 7 - February 7, 1998 Electronic Equilibrium + + + + + + + + + + + + + + e- e- e- - - - - - - - - - - - - - - - - - - - - - - © CSI - Radiation Safety Training, 1998 14

Electronic Equilibrium VTC, Advanced Health Physics Concepts Session 7 - February 7, 1998 Electronic Equilibrium For every electron which escapes the sensitive volume, another electron of equal energy enters the sensitive volume and deposits energy in the detector A layer of air between entrance port of free air chamber and the sensitive volume can provide enough air so that electronic equilibrium is attained © CSI - Radiation Safety Training, 1998 13

Free-Air Ionization Chamber http://physics.nist.gov/Divisions/Div846/Gp2/wafac.html

Measuring Exposure Free air chamber practical only as laboratory device Portable instrument needed

Exposure Measurement: Air Wall Chamber Plastic Charging diaphragm Anode Practical alternative to free-air chamber Built as a capacitor Central anode, insulated from rest of chamber Given an initial charge When exposed to photons, 20 electrons neutralize charge & lower potential between anode and wall Change in potential difference is proportional to total ionization (and therefore exposure)

Air Wall Chamber Better for field use than the Free Air Chamber VTC, Advanced Health Physics Concepts Session 7 - February 7, 1998 Air Wall Chamber Better for field use than the Free Air Chamber Simulates compressing air into a small volume by using ‘air equivalent’ material X-ray absorption properties similar to that of air Walls must be thick enough to generate enough primary electrons Walls must be thin enough so that primary radiation is not shielded © CSI - Radiation Safety Training, 1998 19

VTC, Advanced Health Physics Concepts Session 7 - February 7, 1998 Air Wall Chamber Ideal air wall chambers have only primary electrons ionizing the air in the sensitive volume Ideal wall thickness is almost energy independent over a range from 200 keV to almost 2 MeV © CSI - Radiation Safety Training, 1998 20

Air Wall Chamber Greater than 3 MeV primary electrons have long range VTC, Advanced Health Physics Concepts Session 7 - February 7, 1998 Air Wall Chamber Greater than 3 MeV primary electrons have long range Impractical to build air wall chamber of sufficient size When walls are made thick enough to generate primary electrons, radiation is attenuated significantly Radiation intensity will no longer be constant Primary electrons not produced uniformly No electronic equilibrium © CSI - Radiation Safety Training, 1998 21

Exposure-Dose Relationship measures charge produced in a mass of air C/kg Absorbed dose Measures energy absorbed per mass J/kg How to relate measurement in air to absorbed dose in something besides air?

Exposure-Dose Relationship VTC, Advanced Health Physics Concepts Session 7 - February 7, 1998 Exposure-Dose Relationship Energy absorption in air ¹ energy absorption in tissue Dose in air ¹ dose in tissue 1 R = 87.7 ergs/gair = 95 ergs/gtissue 1 rad = 100 ergs/gtissue For regulatory purposes, frequently 1 R is assumed to be equal to 1 rad Conversion can be done if required © CSI - Radiation Safety Training, 1998 22

Exposure to Dose Conversion VTC, Advanced Health Physics Concepts Session 7 - February 7, 1998 Exposure to Dose Conversion mm = Energy absorption coefficient for tissue ma = Energy absorption coefficient for air rm = Tissue density ra = Air density © CSI - Radiation Safety Training, 1998 23

Bragg-Grey Theory How to measure absorbed dose? The best way would be calorimetry...but not very practical. Instead, absorbed dose is measured by: measuring ionization use of correction factors calculating (approximating) dose This is done with BRAGG-GREY CAVITY THEORY

Measurement of Absorbed Dose Bragg-Gray principle relates ionization measurements in a gas to absorbed dose in some material. Consider a gas in a walled enclosure irradiated by photons: e1 Gas Wall e2

Bragg-Gray, cont’d Photons interact in cavity and wall Gas Wall e2 Photons interact in cavity and wall Chose wall material that has similar radiation absorption properties as tissue (e.g., Z) Cavity is very small (doesn’t change angular and velocity distributions of secondary electrons) “Electronic equilibrium” exists in cavity (# e- stopping = # e- starting in cavity) requires wall thickness > range of secondary e

Bragg-Gray cont’d Ionizations in the gas Can measure the charge liberated. If you know the energy required to ionize the gas, Then the dose to the gas is:

Bragg-Gray, cont’d where, Q = coulombs of charge liberated W = average ionization energy for the gas m = kg of gas in the cavity Example: A cavity filled with (1 cm3) air at STP is exposed to a radiation field that liberates 3.336X10-10 C. What is the dose to the air? At STP:

Example, cont’d Know the dose to the gas. What about the dose to the medium surrounding it? Assume our cavity is really small...small enough that it does not disrupt the electron spectrum.

Bragg-Gray, contd e1 Gas Wall e2 Wall thickness must be as great as range as secondary charged particles (not too great to attenuate beam) Then energy absorbed per unit mass of wall is related to that absorbed per unit mass of gas by: Note - this special case is where the wall and gas are the same type of material

Bragg-Gray , contd Dw is the dose to the wall Gas Wall Dw is the dose to the wall Dg is the dose to the gas Nq is the number of ions produced in the gas W is eV required to produce ion pair m is the mass of gas in the cavity

Bragg-Gray , contd e1 e2 Gas Wall If gas and wall don’t have same atomic composition, a slight modification is required: where Sg,w are the mass stopping powers of the wall and the gas the cavity and gas pressure must be small

Example 1 cm3 of air in a block of carbon is exposed to 60Co γ Q=3X10-8 C is produced. What is the absorbed dose to the carbon? Mean mass stopping power ratio for 60Co γ in carbon relative to air = 1.009

Example, continued This equation allows us to measure the ionizations in a gas and relate it to dose to the medium.

Bragg-Gray contd e1 e2 Gas Wall If neutrons are present, the wall must be at least as thick as the maximum energy range of any secondary charged recoil nuclei produced by the nuclear interactions. Chambers that meet these conditions can be used to measure absorbed dose to the medium

VTC, Advanced Health Physics Concepts Session 7 - February 7, 1998 Kerma “Sum of the initial kinetic energies per unit mass of all charged particles produced by the radiation” This is regardless of where the energy is deposited Bremsstrahlung photons are not counted, whether they escape or not Annihilation radiation is not counted, regardless of fate of annihilation photons Initial positron, if primary ionizing particle, is counted © CSI - Radiation Safety Training, 1998 37

Energy Transfer - A Two Stage Process - Kerma and Absorbed Dose h’ Scattered photon h Primary ionizing particle (pe, cs electron, e+e- pairs, scattered nuclei (neutrons) h” Quantity of transferred energy is called Kerma (j/kg)

Kerma Etr is just the kinetic energy received by charged particles in a specified volume V, regardless of where or how they spend the energy Kerma is the expectation value of the energy transferred to charged particles per unit mass at a point of interest, including radiative-loss energy, but excluding energy passed from one charged particle to another

Quantities to Describe a Radiation Beam Fluence # photons/area  = dN/da Energy fluence Energy / area = dN h/da Fluence rate # photons/(time area)  = d/dt Energy fluence rate Energy / (time area) = d /dt

Relationship of Kerma to Photon Fluence gives the number of photon interactions that take place per unit mass of material.  is attenuation coefficient  is density

Relationship of Kerma to Photon Fluence For a spectrum of energies that can be described by dΦ(hv) /d hv, then:

Calculating Kerma What is kerma? Given incident on a block of carbon 10 MeV photons  = 1014 m-2 What is kerma?

Calculating Kerma, cont’d Kerma is easy to calculate - but very difficult to measure!

Relating Kerma & Absorbed Dose a measure of kinetic energy transferred at a point in space. Absorbed dose is more “interesting”. Energy is transferred in the medium not all is retained there. absorbed dose is the energy retained in the medium brought about by the ionizations along the track of the charged particle. Kerma and Absorbed Dose do not take place at the same location

Calculating Absorbed Dose dEab is the mean energy “imparted” by the ionizing radiation into a mass, dm. Mass should be sufficiently small so that the absorbed dose is defined at a point, but not so small that statistical fluctuations become important From the previous example, dEtr = 7.3 MeV fraction of 10 MeV photon energy transferred to the medium. A smaller amount is absorbed along the electron track: dEab = 7.06MeV

Kerma and Absorbed Dose, cont’d dEtr- dEab The difference, 7.30-7.06 = 0.24 MeV, is bremsstrahlung. What is the path length of the 7.3 MeV electron in C? Estimate from graphs or tables of electron ranges from literature, ~ 4.2 g cm-2. Divide by the density of carbon Path length: 1.9 cm.

Dose and Kerma

Important Relationship Relate absorbed dose in air to exposure: assuming CPE (electronic equilibrium) J/kg J/kg C/kg J/C

Electronic (Charged-Particle) Equilibrium The transfer of energy (kerma) occurs upstream from the absorbed dose. Kerma can be easily calculated from fluence Absorbed dose cannot. Why? Kerma remains constant Absorbed dose takes time to build up as upstream electrons increase:

No Attenuation of Photon Beam, Φ Constant Range R 100 100 100 100 A B C D E F G Number of electron tracks set in motion by photon interaction Φ constant with depth (small # interactions) Same # electrons set in motion in each square i.e., interactions per volume constant through target

Absorbed Dose and Kerma 100 100 100 100 A B C D E F G kerma Absorbed dose Build up region Electronic equilibrium depth

Beam Unattenuated Same number of photon tracks set in motion in each square e.g., square D is traversed by 400 tracks ionization in D is the same as total ionization started in A absorbed dose is proportional to ionization produced in each square dose reaches a maximum at R (range of 2ndary electron) kerma constant with depth, equals absorbed dose beyond R

Absorbed Dose and Kerma 100 95 90 86 82 78 kerma Absorbed dose In this region there is not strict electronic equilibrium Equilibrium thickness Build up region depth

Attenuation of Photon Beam Beam attenuation, Φ decreases with depth. Dose increases to a maximum (at maximum range of particle) overshoots, then tracks kerma.

Attenuation of Photons in Tissue CPE will generally exist in a uniform medium at a point more than the maximum range for the secondary charged particles from the boundary of the medium

Relating Energy Fluence and Exposure Radioactive beam incident on an area What is relationship between energy fluence and exposure at point p? Assume small mass of air at p The dose at p is: D= (/)Ēab=  (ab/) Can relate to R as: 1 R = 0.00873 J/kg, then /X = 0.00873 J/ ((ab/)kg R) Complicated variation of energy absorption coefficient for air and energy of beam

Relating photon fluence to exposure Relationship between energy fluence and photon fluence:  = dN/da = dN h/da So, =  h, and