11 chap 08 measurement of absorbed dose
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11 chap 08 measurement of absorbed dose 11 chap 08 measurement of absorbed dose Presentation Transcript

  • Chapter 8 Measurement of Absorbed DoseThe most direct measurement of radiation dose in a medium isto measure the heat generated in the medium due to theradiation. But the temperature increase in the medium isgenerally very small, making this type of measurement verydifficult. 1
  • Commonly used dosimeters• Ionization chambers. • cylindrical: photons, high-energy electrons (>10 MeV) • parallel plate (plane parallel): low energy electrons (<10 MeV)• Diodes.• Thermo luminescent dosimeters (chips, powders).• Film, radiochromic film. 2
  • Ionization ChamberAn ion chamber is a volume of air (cavity), usually surroundedby a layer of material (chamber wall) just thick enough toprovide electron equilibrium. The electrons generated in thewall enter the cavity, causing ionization. The ions produced inthe air cavity are collected and read out through an electrometer.An ion chamber may be sealed (used in machines as monitorchamber) or unsealed (used for routine calibrations).There are 2 major designs of unsealed ion chambers, cylindricaland parallel-plate. wall air cavity wall electrode electrode air cavity 3
  • 8.1 Radiation Absorbed Dose Exposure: applicable only to photon beams, in air, E < 3 MeV Absorbed dose is defined for all types of radiation (charged, uncharged particles); all materials; and all energies.Dose is defined as the mean energy imparted by ionizingradiation to a given material per unit mass. dε dose = dm Old unit: 1 rad = 100 ergs/g = 10-2 J/kg New unit: 1 Gy = 1 J/kg = 100 rad, or 1 cGy = 1 rad 4
  • 8.2-A Relationship Between KERMA, Exposure, andAbsorbed Dose (KERMA)KERMA (K) (kinetic energy released in the medium) isdefined as dEtr/dm, where dEtr is the sum of the kineticenergies of all the charged particles liberated by the neutralparticles (photons) in a material of mass dm. µ  Kcol is the part of the energy loss due to K = Ψ  tr   ρ  collision with the atoms, resulting in   ionization and excitation. K = Kcol + Krad Krad is the part of energy loss in producing bremsstrahlung photons. µ  µ  µ   µ  g  K = Ψ  tr (1 − g ) + Ψ  tr  ρ   ρ  g = Ψ  en  + Ψ  en    ρ   ρ  (1 − g )            5
  • Energy Transfer and Energy AbsorptionThe transfer of energies from a photon beam to the medium is atwo-step process: (1) The photon interacts with the atom,causing one or more electrons ejected from the atom. All or partof the photon energy is transferred to the electron(s). (2) thekinetic energy the ejected electron(s) is absorbed by the mediumthrough ionization and excitation (excluding the bremsstrahlungphotons produced by these electrons). hv’’ e- δ−ray hv hv’ 6
  • Energy Transfer Coefficients EtrEnergy transfer coefficient: µ tr = µ (cm-1) hν Etr is the average energy transferred into the kinetic energyof the charged particles per interaction, hv is the originalphoton energy.µtr is the fraction of energy transferred per unit pathlengthtraversed by the photon.Mass Energy transfer coefficient: µtr/ρ (cm2/g) 7
  • KERMAKERMA (Kinetic Energy Released in the Medium). It occurs ata point. K = <dEtr>/dm, where <dEtr> is the average kineticenergy transferred from photons to electrons in a volumeelement whose mass is dm. Compton scattering Photo-electric effect e- hv K L hv hv’ photo- dEtr= hv- hv’ electron hv- Bk ≤dEtr≤ hv 8
  • µK = Φ •   • Etr ρ  Φ is the photon fluence (# photons /cm2),µ is the linear attenuation coefficient: number of collisions per unitpathlength (cm), per incident photon (# collisions/photon/cm).Φ•µ is the number of collisions per unit volume (# collisions /cm3).Etr is the average kinetic energy transferred to the electron(s) percollision, (MeV/collision).Φ•µ•Etr is the amount of kinetic energy transferred per unit volume(MeV/cm3).Φ• (µ/ρ) •Etr is the amount of kinetic energy transferred per unitmass (MeV/g or J/kg or Gy). 9
  • µ  µ tr   µ tr K = Φ •   • Etr = hν • Φ •  ρ  ρ  = Ψ • ρ          µtr = (Εtr/hν) µ, the fractional energy transferred per unitpathlength (/cm).ψ = hν•Φ , energy fluence (MeV/cm2).ψ •µtr is the energy transferred per unit volume (MeV/cm3).ψ •(µtr/ρ) is the energy transferred per unit mass (MeV/g orJ/kg or Gy) 10
  • For a spectrum of photon energies, the KERMA is defined as: Emax  µ (E) K =∫ Φ( E )  Etr ( E )dE 0  ρ Example: A beam of 10 MeV photons with fluence of 1014/m2is incident on a small block of carbon. Calculate the Kerma:Given (µ/ρ) = 0.00196 m2/kg and Etr = 7.30 MeVK = 1014 (/m2) x 0.00196 (m2/kg) x 7.30 MeV = 1.43x1012 (MeV/kg) = 1.43x1012 (MeV/kg) x 1.602x10-13 (J/MeV) = 0.229 J/kg = 0.229 Gy 11
  • DOSEEnergy is transferred to electron(s) at the point of collision, butnot all of it is retained in the medium; some of it radiated awayas bremsstrahlung. The absorbed dose is the energy actuallydeposited in the medium along the electron track.KERMA (at a point) and energy deposition (over a distance) donot take place at the same location. hv’’ Κr (radiative e kerma) - Kc (collision kerma) hv0 Κ Κ = Κc + Κr hv’ 12
  • Energy Absorption CoefficientEnergy absorption coefficient: µen = µtr (1-g) (cm-1)‘g’ is the fraction of the energy of secondary charged particlesthat is lost to bremsstrahlung in the material.Thus, µen represents the fractional energy absorbed locally in thematerial.Mass Energy absorption coefficient: µen/ρ (cm2/g)In soft tissues (low Z materials), g ≈ 0. Thus, µen ≈ µtr .Sometimes µab is used instead of µen. 13
  • The absorbed dose is defined as D = <dEab>/dm.<dEab> is the mean energy imparted by the electrons to amass dm of the medium.The absorbed dose is also defined at a point, including allelectron tracks coming in and going out of a small volumedV (containing mass dm) at that point. dV dmThe unit for the dose is Gray: 1 Gray = 1 J/kg1 Gy = 100 cGy = 100 rad (old unit, has been phased out). 14
  • Example: Kerma and Dose as a result of a Compton scattering Τ’’ e - hv2 Τ hv0 hv1 m T = initial kinetic V energy of the electron T’ = kinetic energy of K = T / m = (hv0 -hv1) / m the electron when crossing the boundary D = (T-T’-hv2) / m of volume V 15
  • Following the previous example, the average energytransferred to an electron is 7.30 MeV. Of this, 7.04 MeVwill be absorbed along the electron track. The remaining0.26 MeV is dissipated as bremsstrahlung photons.The length of the track of the 7.30 MeV electrons in carbonis about 1.9 cm. Along this track, it produces about ~2x105ion pairs (7.04 MeV/34 eV).In contrast, only one atom is ionized (1 ion pair) at the siteof the photon interaction, whereas ~2x105 ion pairs aredistributed along the electron track. 16
  • Example: Kerma and Dose involving pair production and annihilation hv=0.511 MeV Τ2 e+ hv0 Τ1 e- hv=0.511 MeV m V K = (T1+T2) / m = (hv0-1.022 MeV) / m D = (T1+T2) / m 17
  • 8.2-B Relationship Between KERMA and ExposureExposure defined as ionization produced in air, applicable tophotons up to 3 MeV only. W  X= K ( col ) air   e      µ en  W  X = Ψair   ρ     e     air   W  is the amount of energy required to produce 1 ion   e   pair in air, 33.97 eV/ion-pair, or 33.97 J/C.   18
  • Exposure is defined (only for photons in air) as: X = dQ/dm, wheredQ is the total charge of the ions of either sign produced in air when allof the electrons liberated by photons in a volume element of air having amass dm are completely stopped in air.The unit of exposure is the roentgen (R), defined as the exposure toproduce 1 esu of charge in 1 cm3 of air under STP. hv’’ e- air dm dQ = charges produced along the hv0 track X hv’ 1 R = 1 esu / 1 cm3 of air under STP = 3.33×10-10 C / 0.001293 g of air = 2.58×10-4 C / kg of air 19
  • ( ) Wair e is the mean energy expended in air to produce one ion pair, ~34 eV/ion-pair, or 34 J/C. ( ) ( ) = (K ) µen Ψ• X= = ( K c ) air Wair ρ E ,air / 34 ( ) Wair e e c airExample: calculate the energy fluence and photon fluence per R for hν = 1MeV. Given (µen/ρ)air = 0.0279 m2/kg.1 R = 2.58×10-4 C/kg of air = 2.58×10-4 C/kg of air × (34 J/C) = 0.00876 J/kg of air ( ) ( ) = Ψ • 0.00279( ) • X = Ψ ( J m2 ) • µ en ρ air m2 kg J kg 1R 0.00876 J / kg Ψ 0.00876 = X 0.00279 ( ) = 3.14( ) J m2 R J m2 R Ψ 3.14( J m 2 R ) Φ= = = 1.96 ×1013 photons m2 R hν 1.602 × 10 −13 J 20
  • Relationship between Kerma and Dose (no attenuation of the photon beam) µ K = Φ •   • Etr ρ   kerma Buildup equilibrium dose region regionKerma or dose dose Electron track depth 21
  • Relationship between Kerma and Dose (with attenuation of the photon beam) Buildup transient region equilibrium regionKerma or dose dose 700 kerma dose 800 µ K = Φ •   • Etr ρ 900   1000 Electron track depth 22
  • 8.2-C Relationship Between KERMA and Absorbed Dose Absorbed dose and Kerma cep β = D/Kcol = 1 Dose KERMA β>1 β<1 µ en Buildup (Transient) D =β ρ Ψ region equilibrium region depthUnder (transient) electron equilibrium conditions, β depends on the beamenergy, not material. For Co-60, β=1.005 23
  • 8.3 Calculation of Absorbed Dose from Exposure(A- absorbed dose to air) Under conditions of electron equilibrium: ( Dair = K col ) air =X• W e 1 roentgen (R) of exposure produces 2.58×10-4 coulombs of charges per Kg of air. Dair(J/kg) = X(R) • 2.58×10-4 (C/kg/R) • 33.97 (J/C) Dair(cGy) = 0.876 (cGy/R) • X(R) roentgen-to-rad conversion factor for air 24
  • 8.3 Calculation of Absorbed Dose from Exposure(B- absorbed dose to any medium)Under conditions of charged Dmed = Ψmed ( µ en ρ ) medparticle equilibrium:Dmed Ψmed ( µ en ρ ) med ( µ en ρ ) med = = A• , where A = Ψmed ΨairDair Ψair ( µ en ρ ) air ( µ en ρ ) air Wair ( µ en ρ ) medDmed =X• • •A fmed (f-factor) is the roentgen- e ( µ en ρ ) air to-rad conversion factor (dose- to-air to dose-to-medium  ( µ en ρ ) med  conversion). It is a function of = 0.876 • X • A  ( µ en ρ ) air  the material composition and photon energy. = f med • X • A 25
  • 8.3 Calculation of Absorbed Dose from Exposure(C- dose calibration with ion chamber in air) For megavoltage beams, build-up cap is needed to provide electron Equilibrium equilibrium mass of tissue air air air × × × P P P M X=M•Nx Dfs= ftissue• X•Aeq Nx is the exposure ftissue is the f-factor M is the corrected calibration factor for (exposure-to-dose reading the given chamber conversion factor) for tissue for the same beam Aeq =Ψtissue/Ψair quality 26
  • 8.3 Calculation of Absorbed Dose from Exposure (D- dosemeasurement from exposure with ion chamber in amedium)medium chamber with build-up cap Air cavity Ψb Ψc Ψm × × × P P P M X=M•Nx Dmed= fmed• X•Am Am =Ψm/Ψc med W  µ en  Dmed = M • Nx • •  ρ  • Am  e   air 27
  • 8.4 The Bragg-Gray Cavity Theory (how to convert dose-to-cavity-air to dose-to-medium) E0 ∫ Φ ( E ) S ( E )dE  ρ E0 E0   D = ∫ Φ ( E ) S ( E )dE = ∫ Φ ( E )dE  ρ 0   E0 ∫ Φ( E )dE 0 0 Φ S (energy loss/cm3) 0 Φ S S (# e-/cm2) (energy loss/cm) D = Φ  ρ   Φ is the electron fluence at the point of measurement, ( ) S ρ is the mass collision stopping power averaged over the electron energy spectrum E0 is the maximum electron energy 28
  • 8.4 The Bragg-Gray Cavity Theory (how to convert dose-to-cavity-air to dose-to-medium) S  W S Dg = Φ •   = J g • ρ Dmed = Φ •   g e ρ   med Jg is charge produced per unit mass of air cavity removed, medium assuming Φ not medium affected × × gas Dmed ( S ρ ) med med W S  = or Dmed = Jg • •  Dg (S ρ )g e  ρ g   29
  • Bragg-Gray Conditions• The cavity is so small that it does not perturb the electron fluence, i.e. Φ is not changed• Absorbed dose (energy) deposited in the cavity is entirely due to electrons crossing it, i.e., no electrons produced nor lost in the cavity. air vacuum Φ Φ Φ A B A B A BElectron fluence Φ is The condition remains The situation is nocontinuous and true if a slab of longer true for a slab ofunchanged across the ‘vacuum’ is ‘air’- low energyboundary between A sandwiched between A electrons are stoppedand B, since nothing is and B, since no in and high energy δ-produced nor lost at the interaction takes place rays produced in andinterface inside the vacuum. escaped from the slab 30
  • 8.4 The Bragg-Gray Cavity Theory (A- Stopping power, the Spencer-Attix formulation) E0 L W L med L ∆∫ Φ( E ) ρ ( E )dE     Dmed = Jg • •   = ρ e  ρ g E0     ∫ Φ( E )dE ∆To exclude low-energy electrons (E<∆) thatenter and then stop in the cavity(∆ is the electron energy required to cross the cavity, typically ~10 kev) (L ρ) is the restricted mass collision stopping power with ∆ as the cutoff energy To exclude high-energy δ-rays (E>∆) that are produced and then escape from the cavity 31
  • 8.4 The Bragg-Gray Cavity Theory (B-chamber volume)If chamber volume V is known, then Jg can be obtained from: Q where Q is the charge produced, ρ is theJg = ρ •V density of (cavity) air But V cannot be accurately measured directly. However, it can be indirectly determined from the chamber exposure calibration factor Nx. 32
  • 8.4 The Bragg-Gray Cavity Theory (B-chamber volume) chamber mass of wall with wall material air & buildup air air cap × × × P P P air W  L wall  µ   Dwall = Dcham   ( Φ cav ) air Dair = Dwall  β en  ( Ψcham ) wall airDcham = J air   e  ρ wall  ρ  air   air   air   wallJair= charge Bragg-Gray theoryproduced per unit Electron fluence ratiomass in air in wall L transient electron Dwall = Dcham   ( Ψcav ) air wallchamber volume   air  ρ  air equilibrium exists 33
  • 8.4 The Bragg-Gray Cavity Theory (B-chamber volume) Combining the equations for Dcham-air, Dwall, and Dair, we have: wall air W  L   µ en   ρ  ( Ψcav ) air ( Ψcham ) wall β wall air Dair = J air   e    ρ      air   wallDair can also be measured with a chamber with an exposure calibration factor NX: W  Dair = M • Pion • N x • Aion • k •   e  • β air    chamber reading chamber exposure corrected for calibration factor Converts from kerma to dose recombination corrected for recombination 33.97 J/C exposure (R) 2.58x10-4 C/kg/R 34
  • 8.4 The Bragg-Gray Cavity Theory (B-chamber volume) Combining the two previous equations for Dair, we have: air wall  L   µ en  = M • Pion • N x • Aion • k • β wall     ( Ψcav ) wall ( Ψcham ) air air wallJ air ρ  ρ    wall   air Awall = change of photon energy fluence due to the wall and buildup cap air wall  L   µ en  J air = M • Pion • N x • Aion • k • β wall     ρ   ρ  Awall    wall   air wall and buildup cap made of different materials, α is the fraction of electrons J air = M •P • N • A •k •β generated in wall ion x ion wall   L  air  µ  wall air cap  Aα  L   µ en   ρ   ρ  + (1 − α )  ρ   ρ   Awall α    en         wall    air   cap   air   35
  • 8.4 The Bragg-Gray Cavity Theory (B-chamber volume) From the previous slide: J air = M • Pion • N x • Aion • k • β wall • Aα • Awall Jair is the charge produced per unit mass of air in the chamber: M • Pion where ρair = density of air, J air = ρ air • Vc Vc = chamber volume Combining the two equations above, we have the relationship between Vc and Nx: 1 Vc = k • ρ air • N x • Aion • β wall • Aα • Awall 36
  • 8.4 The Bragg-Gray Cavity Theory (C- effective point of measurement) For parallel plate chambers,Effective point the effective point ofof measurement measurement is at the inner face of the front plate Effective point For cylindrical chambers, of measurement 0.85r the effective point of measurement is displaced 0.85r from the center 37
  • 8.4 The Bragg-Gray Cavity Theory (C- effective point of measurement) π /2 Φ xeff = ∫ 0 x • 2 x • Φ • cos θ • ds π /2 ∫0 2 x • Φ • cos θ • dsArea perpendicular to electron fluence dsNumber of electrons entering the circle θ rthrough ds x dθTracklength of each electron enteringthrough ds ∝ amount of ionization produced 2xTotal amount of ionization produced due toelectrons entering through ds x = r • cos θ Xeff = 8r/3π = 0.85r 38
  • Equipment Needed• Ion chamber and electrometer, need calibration every 2 years.• calibration traceable to standard laboratory (primary standard lab: NIST, secondary standard labs).• cylindrical chamber for photons of all energies and electrons with energies ≥ 10 MeV.• plane-parallel chamber for electrons of all energies (mandatory for energies < 10 MeV).• system to measure air pressure and water temperature 39
  • Press/temperature correction for un-sealed chamber 273.2 + T ( C ) 760(mm Hg )  kTP = × 273.2 + 22 C PThe chamber calibration factor is obtained in the standardlaboratory under ‘standard’ conditions: 22° C, 760 mm Hg.When the chamber is used under conditions with differentroom temperature and pressure, the number of air moleculesin the chamber is different, hence appropriate corrections areneeded. 40
  • 8.5 Calibration of Megavoltage Beams: TG-21 Protocol (A. Cavity-Gas Calibration Factor) The cavity-gas calibration factor Ngas, is defined as the absorbed dose to the cavity gas per unit charge produced in the cavity. It has a unit of Gy/C. Ngas = Dair / Q Co-60 where Dair is the dose to the chamber cavity air, Q is the charge produced in the cavity, or Ngas = Dair / (M‧Pion) chamber with wall where M is the collected charge (or meter & buildup reading), corrected for recombination loss Pion. cap Ngas is unique to each ionization chamber, × determined entirely by its cavity volume. M Dair 1  Q ( W )  ( We ) = 28.379 Gy / C (W e) = 33.97 J CN gas = =  e = Q Q  m  ρ air • Vc Vc (m 3 ) ρ air = 1.197 kg m3 41
  • 8.5 Calibration of Megavoltage Beams: TG-21 Protocol (A. Cavity-Gas Calibration Factor) Dair J • (W e )Conversion from Nx to Ngas: N gas = = air , and M • Pion M • Pion J air = M • Pion • N x • Aion • k • β wall   L  air  µ  wall  L   µ en   air cap α    en  + (1 − α )    ρ  ρ   ρ   ρ   Awall     wall    air   cap   air   N gas = N x • Aion • k • (W e ) • β wall   L  air  µ  wall  L   µ en   air cap α    en  + (1 − α )    ρ  ρ   ρ   ρ   Awall     wall    air   cap   air   42
  • 8.5 Calibration of Megavoltage Beams: TG-21 Protocol (B. Chamber as a Bragg-Gray Cavity) Conversion from Dose-to-air to Dose-to-medium medium wall x Dair Dwall Dmed wall med L LDair = M • Pion • N gas Dwall = Dair •   • Prepl ρ Dmed = Dwall •   • Pwall ρ   air   wall med L Dmed = Dair •   • Pwall • Prepl ρ   air 43
  • Dmed Φ med ( ) L L med Dair = ρ med ( ) Φ air L   ρ   air Dair = Φ air ( ) L ρ air ρ air ( Φ ) med ≈ ( Ψcav ) med Thin-wall approximation air air Dmed = Φ med ( ) L ρ med wall Dairmedium x Dair Dwall Dair = ( ) ( ) L wall wall ρ air Ψcav air Dmed x Thick-wall Dair approximation Dwall ( ) CPE ( ) µ en Dmed Dmed = Ψmed β med = ( Ψchamb ) wall β µ en med med ρ med ρ wall Dwall ( ) CPE µ en Dwall = Ψwall ρ wall β wall 44
  • From the previousslide: Thin-wall approximation: Dmed = D ( ) (Ψ ) L med air ρ air med cav air Thick-wall approximation: Dmed = D ( ) (Ψ ) (Ψ L wall air ρ air wall cav air ) med chamb wall (β ) µ en med ρ wall α= fraction of electrons medium generated in ‘wall’. (1-α) wall x 1-α = fraction of electrons α Dmed generated in ‘medium’. Dair(med) Dair(wall)Dair = α • Dair ( wall ) + (1 − α ) • Dair (med )Dair = Dmed α [ ( ) ( Ψ ) ( Ψ ) ( β ) + (1 − α ) ( ) ( Ψ ) L air ρ wall air cav wall wall chamb med µ en wall ρ med L air ρ med air cav med ] D M • P • N •( ) •(Ψ ) P L med med air ion gas ρ air cav air replDmed = α( ) (Ψ ) (Ψ L med ρ wall ) ( β ) + (1 − α ) 1 / P med cav wall wall chamb med µ en wall ρ med wall 45
  • Alternative approach to Preplmedium cavity air d med L x Dmed ( P ) = Dair •   • Pwall • Prepl ρ Dair Dmed(P)   air effectivemedium point of d med measurement x ηr L Dmed ( P ) = Dair •   • Pwall ρ Dair Dmed(P’)   air D( P) D(d ) Prepl (d ) = = D ( P ) D ( d − ηr ) 46
  • For electron beams: Pwall is assumed to be 1.  L  med medium cavity Dmed = Dair •   ρ • Prepl  or air z   air    Ez x  L  med  Dair Dmed Dmed = Dair •   • ( Φ cav ) air  med ρ   air    Ez where E z is the mean electron energy at zNote :For electron beams, electron energy and thus L ρ( ) med are depth dependent air therefore, when converting from depth - ionization to depth - dose, apply the L ρ ( ) med stopping power ratios airFor photon beams, electron energy and thus ( L ρ ) air are not depth dependent med therefore depth - ionization ≈ depth - dose 47
  • For electron beams:Prepl has two parts: Prepl = Pfl‧ Pgr• Fluence correction (Pfl): accounts for in-scattering effect and obliquity effect.• Gradient correction (Pgr): accounts for displacement in the effective point of measurement. • Calibration made at dmax. (gradient correction = 1) • For depth-dose measurement: – Apply stopping power ratios correction – For parallel-plate chambers, Prepl = 1 – For cylindrical chambers, the gradient correction part of Prepl is handled by shifting the effective point of measurement towards the surface by 0.5r. 48
  • Conversion from dose-to-water to dose-to-muscle muscle  µ en For photon beams: Dmuscle = Dwater •  ρ     water muscle S For electron beams: Dmuscle = Dwater •  ρ   water muscle muscle  µ en  S    ρ   ≈  ρ ≈ 0.99   water   water 49
  • The TG-51 protocol (Med Phys 26, 1847-70, 1999) The TG-51 protocol is based on ‘absorbed dose to water’ calibration (also in a Co-60 beam). 60 The chamber calibration factor is denoted N D ,Co . w The calibrated chamber can be used in any beam modality (photon or electron beams) and any energy, in water. The formalism is simpler than the TG-21, but it is applicable in water only. 50
  • Equipment Needed• Ion chamber and electrometer – calibration traceable to standard laboratory• waterproofing for ion chamber ( if needed) <1mm PMMA• water phantom (at least 30x30x30 cm3)• lead foil for photons 10MV and above – 1 mm ± 20%• system to measure air pressure and water temperature 51
  • 60Obtain an Absorbed-dose to Water Calibration Factor N D ,Co w 60 Co source dmax × D M (corrected) 60 D  Gy  N Co D,w ≡   C or rdg   Dose to water per unit charge (reading) M   52
  • Quality Conversion Factor QIdeally, for a given chamber individual calibration factor N D , w should be obtained for each beam quality used in theclinic. So that: Dw = M N D , w Q QThis is impractical, as the standard laboratory may not havethe particular beam quality Q available, thus a qualityconversion factor kQ is introduced to convert the calibrationfactor for Co-60 to that for the beam quality Q. 60 N Q D,w = kQ N D ,Co w 53
  • General FormalismIn a Co-60 beam: 60 60 Dw Co = M N D ,Co w ( M is corrected )In any other photon beam:(only cylindrical chamber allowed at present) 60 D = M kQ N D ,Co Q w wIn any electron beam:(both cylindrical and parallel-plate chambers allowed) 60 D = M P k kecal N D ,Co Q w Q gr R50 w 54
  • Charge measurement M = Pion PTP Pelec Ppol M raw Polarity correction Ppol = ( + M raw - - M raw ) 2 M raw T + 273.2 101.33 Press/temperature PTP = × 273.2 + 22 P Electrometer correction Pelec VH 1 - VLIon recombination correction Pion (VH ) = H M raw VH L - M raw VL 55
  • kQ values for cylindrical chambers in photon beamsNRC-CNRC 56
  • Point of Measurement and Effective Point of MeasurementEffective point of × measurement r point of measurement rcav cylindrical parallel plate Photon: r = 0.6 rcav electron: r = 0.5 rcav 57
  • Percent Depth-Dose (ionization) for photon beamsPercent depth dose to be measured at SSD = 100 cm for a10× 10 cm2 field size.Parallel-plate chamber: 100 % depth-dose (ionization)measured curve II. II 80 ICylindrical chamber:measured curve I, needsto be shifted by 0.6 rcav 60 %dd(10to get curve II. ) 40Curve II is the percentdose (percent 20ionization) curve,including contaminated 5 10 15 20electrons. Depth in water (cm) 58
  • Beam Quality Specification (photons)For this protocol, the photon beam quality is specified by%dd(10)x, the percent depth-dose at 10 cm depth in water dueto the photon component only, that is, excluding contaminatedelectrons.For low energy photons (<10 MV with %dd(10) < 75%)%dd(10)x = %dd(10) (contaminated electron is negligible)For high energy photons (>10 MV with 75%<%dd(10)<89%)%dd(10)x ≅ 1.267%dd(10) – 20.0A more accurate method requires the use of a 1-mm thick leadfoil placed about 50 cm from the surface.%dd(10)x = [0.8905+0.00150%dd(10)pb] %dd(10)pb [foil at 50 cm, %dd(10)pb>73%] 59
  • Percent depth dose measured at SSD = 100 cm for a 10× 10 cm2 field sizewith a 1mm Pb filter placed at ~50 cm from the surface. 1mm Pb filter 100 II 80 I (% dd)Pb 60 %dd(10)Pb 40 20 ~50 cm 5 10 15 20 Depth in water (cm) Curve II is the (%dd)Pb curve, with the contaminated electrons in the original beam removed, but generates its own contaminated electrons. %dd(10)x = [0.8905+0.00150%dd(10)pb] %dd(10)pb 60
  • Reference conditions for Photon Beams photon source 100 cm 10 cm 10×10 cm2 10×10 cm2 10 cm water water SSD setup SAD setup 61
  • Photon Beam Dosimetry 60 D = M kQ N D ,Co Q w w where M is the fully corrected (temperature, pressure, polarity, recombination) chamber reading, kQ is the quality conversion factor, 60 N D ,Co is the absorbed dose to water chamber calibration factor w 62
  • Reference conditions for Electron BeamsDepth: dref = 0.6 R50 - 0.1 cm Electron sourcewhere R50 is the depth in water atwhich the dose is 50% of the SSDmaximum dose. dref is approx. at dmaxfield size: (why different field sizes fordifferent energies?)> 10x10 cm2 on surface R50<8.5 cm dref > 20x20 cm2 on surface R50>8.5 cmSSD: as used in clinic between 90 cm waterand 110 cm (typically 100 cm) 60 SSD setup D = M P k kecal N Q w Q gr R50 Co D,w 63
  • Percent Depth-ionization for electron beams Percent depth ionization to be measured at SSD = 100 cm for field size ≥ 10× 10 cm2 (or ≥ 20× 20 cm2 for E>20 MeV). Parallel-plate chamber: measured curve II. 100 II I % depth-ionization Cylindrical chamber: 80 measured curve I, needs to be shifted by 0.5 rcav 60 to get curve II. Curve II is the percent 40 ionization curve. 20 I50R50 = 1.029I50 – 0.06 (cm) for 2≤I50 ≤ 10 cm 2 4 6 8R50 = 1.059I50 – 0.37 (cm) Depth in water (cm) for I50 > 10 cm 64
  • Depth-ionization vs. Depth-dose For photon beams, depth-ionization is considered to be equivalent to depth-dose. For electron beams, depth-ionization must be converted to depth-dose by multiplying the stopping power ratio: L water ∫ Φ (d , E )( )L ρ water dE   = ∫ Φ ( d , E )( ) ρ   gas L ρ gas dE Why? 65
  • QElectron Beam Dosimetry ( P ) gr Q Pgr depends on user’s beam must be measured in clinic. Cylindrical chamber: M raw (d ref + 0.5rcav ) P =Q gr Same as shifting the point of M raw (d ref ) measurement upstream by 0.5rcav. parallel plate chamber: Pgr = 1.0 Q 66
  • Electron Beam Dosimetry (Kecal ) 60 Co QecalKecal is the photon-to-electron conversion factor, N D , w →N D , wfor an arbitrary electron beam quality Qecal, taken as R50 = 7.5 cm.The values of Kecal are available in the TG-51 protocol.Parallel-plate chambers: chamber Attix Capintec PTB Exradin Holt Markus NACP kecal 0.883 0.921 0.901 0.888 0.900 0.905 0.888cylindrical chambers: Exradin chamber NE2571 NE2581 PR-06 N23331 N30004 … A12 kecal 0.906 0.903 0.885 0.900 0.896 0.905 … 67
  • Electron Beam Dosimetry ( k R50 ) k R50 is the electron quality conversion factor converting from Qecal to Q. k R50 for a number of cylindrical and parallel-plate chambers are available in Figs. 5-8 in the TG-51 protocol. It can also be calculated from the following expressions: − R50 3.67 Cylindrical: k (cyl ) = 0.9905 + 0.0710e R50 Parallel-plate: k R50 ( pp ) = 1.2239 − 0.145( R50 ) 0.214 68
  • k’R50 for Cylindrical ChambersNRC-CNRC 69
  • k’R50 for Parallel Plate ChambersNRC-CNRC 70
  • Electron Beam Dosimetry 60 D = M P k kecal N D ,Co Q w Q gr R50 w where M is the fully corrected chamber reading, Q Pgr is the correction factor that accounts for the ionization gradient at the point of measurement (for cylindrical chamber only) k R50 is the electron quality conversion factor. kecal is the photon to electron conversion factor, fixed for a given chamber model 60N D ,Co is the absorbed dose to water chamber calibration factor w 71
  • Summary - photons 60 Co • get a traceable N D,w • measure %dd(10)Pb with lead foil (shift depth if necessary) • deduce %dd(10)x for open beam from %dd(10)Pb • measure Mraw at 10 cm depth in water (no depth shift !!!) • M = PionPTPPelecPpol Mraw • lookup kQ for your chamber 60 Co D = M kQ N D , w Q w 72
  • Summary - electrons 60 Co• get a traceable N D , w• measure I50 to give R50 (shift depth if necessary)• deduce dref = 0.6 R50 -0.1 cm (approx. at dmax)• measure Mraw at dref (no depth shift !!!)• M = PionPTPPelecPpol Mraw• lookup kecal for your chamber k R50• determine Q (fig, formula) P gr• establish (Mraw 2 depths) 60 Co D =MP k Q w Q gr R50 kecal N D , w 73
  • 8.8 Exposure from Radioactive SourcesExposure rate from a radioactive source can be determinedfrom the photon energy fluence and the relevant mass energyabsorption coefficients for air, assuming charged particleequilibrium: W  µ  Dair = X •   = Ψ  en  e   ρ     air   air therefore,  µ en   e  X = Ψ  ρ  •     air  W  air 74
  • N 3.7 × 1010 × 3600energy fluence/h at 1m from 1 - Ci source = 4π (1) 2 ∑fE i =1 i i photon fluencewhere fi is the number of photons of energy Ei emitted per decay. exposure/h at 1m from 1 - Ci source = X N 3.7 × 1010 × 3600  µ en   e  = 4π (1) 2 ∑ i =1 f i Ei   ρ    •   air ,i  W  air ( substituting W e ) air = 0.00876 J /(kg • R), 1 MeV = 1.602 ×10-13 J N µ   X ( R / h) = 193.8 ∑ i =1 f i Ei  en  ρ     air ,i 75
  • l2  define the exposure rate constant : Γδ = A X ( )δ N  µ en  2 −1 −1 Γδ ( Rm h Ci ) = 193.8 ∑i =1 f i Ei ( MeV )  ρ   (m 2 / kg )   air ,i The exposure rate constant Γδ is a property of the radioactive isotope. Example: calculate the exposure rate constant for 60Co: Ei(MeV fi ( µ en ρ ) air ,i (m 2 / kg ) Γδ = 193.8(1.17 × 0.00270 + 1.33 × 0.00261) ) 1 1.17 0.00270 = 1.29 Rm 2 h −1Ci −1 1 1.33 0.00261 2   100 Exposure rate (R/min) from X = Γδ A / l 2 = 1.29 × 5000 ×   / 605,000-Ci 60Co source at 80cm:  80  = 168 R / min 76
  • 8.9 Other Methods of Measuring Absorbed Dose A. Calorimetry B. Chemical Dosimetry C. Solid State Methods D. Silicon Diodes E. Radiographic Film 77
  • 8.9 (A-calorimetry & B-chemical dosimetry)Calorimetry is based on the principle that the energyabsorbed in a medium from radiation eventually appears asheat energy, resulting in a small rise in temperature, whichcan be measured with a thermistor. The temperature increasein water produced by 1 Gy is 2.39×10-4°CChemical dosimetry is based on the principle that energyabsorbed from radiation may cause chemical change. Mostdeveloped system is the ferrous sulfate (Fricke dosimetry).The absorbed dose D, can be determined by the measuredchemical change ∆M, and the G-value (# of moleculesproduced per 100 eV of absorbed dose) of the chemical.These methods are used in national standards laboratories. 78
  • 8.9-C Solid State Methods (TLD)When certain crystal is irradiated, a small fraction of theabsorbed energy is stored in the crystal. Some of this energycan be recovered later as visible light when the crystal isheated. This phenomenon is called thermoluminescence (TL). ph TL ot conduction band on energy electron trap g valence band z in n ni atio io di irradiation heating ra The emitted light is amplified by the photomultiplier tube. 79
  • 8.9-C Solid State Methods (TLD)When a previously exposed sample of TLD is heated, the lightoutput as a function of time is called a ‘glow curve’. The areaunder the glow curve can be used to measure dose. 80
  • 8.9-C Solid State Methods (TLD)The most commonly used TLD material is lithium fluoride(LiF). Prior to use, the LiF is annealed for 1 hour at 400° C,followed by 24 hours at 80° C (pre-irradiation annealing).In radiation therapy, TLD is primarily used for in vivomeasurement (if placed on skin, proper build-up is needed, e.g.bolus). TLD is available in different forms (powder, chips,rods) and sizes.For megavoltage dosimetry, TLD can provide accuracy of±3%. 81
  • 82
  • 8.9-D Silicon DiodesDiode is a solid state semi-conductor device which generates acurrent when exposed to radiation.Small size, instantaneous response, ruggedness, and highsensitivity, but is energy, directional, and temperaturedependent, also suffers from radiation damage.Primarily used for relative dose measurement (dose distribution)It can also be used for in-vivo dosimetry (does not require 300 Vhigh voltage).Absolute dose measurement (machine output calibration) is donewith a chamber. 83
  • 8.9-D Silicon Diodes (theory) At equilibrium, a built-inA silicon (14Si) doped with impurities to potential is established in themake p-type (electron receptor, e.g. 5B) depletion zone.and n-type (electron donor, e.g. 15P). - - depletion - + - + + - zone + - + + + - - - + - (built-in + potential) + - - + -- - + + - + V – - + + - + + - - + - + - +- - - - + - + + - + - n-type Silicon diode p-type n-type Silicon diode p-type(donor) (receptor) (donor) (receptor) The ion pairs produced along theCarriers near the interface diffuse electron track are attracted towards toacross the boundary and +/- sides of the depletion zone,recombine with the opposite generating a current that can becarrier, forming a depletion zone measured. 84
  • 8.9-D Silicon Diodes• no bias voltage applied.• diodes are more sensitive than ion chambers – • (W/e)Si ~ 3.5 eV [In contrast, (W/e)air ~ 34 eV ] • ρSi ~ 1800 ρair• energy dependency for photons (due to Z=14 for Si), butnot for electrons (therefore can be used for electron relativedepth-dose measurement).• angular dependency.• temperature dependency, but independent of pressure.• radiation damage – needs periodic calibration.• used for patient dose monitoring and when small detectorsize is needed. 85
  • 8.9-E Radiographic Film Radiation or visible lightEmulsion containingsilver bromide crystals Film base, cellulose acetate or polyester resin, ~0.1 mm. When the film is exposed to ionizing radiation, chemical change takes place in the crystals to form the latent image. When the film is developed, the affected crystals reduced to small grains of metallic silver, and the film is fixed. The unaffected granules are removed by the fixing solution. The metallic silver remains on the film, causing darkness. The degree of blackening depends on the dose. 86
  • 8.9-E Radiographic Film The degree of blackening is measured by optical density, defined as: OD = log10 (I0/It), where I0, It are incident and transmitted light intensities, respectively.In dosimetry, the background fog(OD of unexposed processed (for illustration only)film) should be subtracted to net optical density 3.0 xv-2obtain the net optical density,whose relationship with dose is 2.0 RPM-2called H-D curve, or 1.0sensitometric curve.Each box of films may have 5 10 15 RPM-2different characteristics, prior touse, H-D curve should be obtained 50 100 150 xv-2for samples from the box. Dose (cGy) 87
  • 8.9-E Radiographic Film• Advantages:High spatial resolution ( < 1 mm)Ideal for 1D or 2D relative dose distribution measurement. (beamprofiles, isodose distributions), accurate to within ~ ± 3%.Inexpensive for personnel dosimetry (film badge, accurate towithin ±10%)• Disadvantages:Requires careful calibration prior to use.Over responds to low energy photons (due to increased photo-electric events in silver bromide), not suitable for absolute dosemeasurement. 88
  • Comparison of Calculation and Measurement Film Calc. 89
  • Radiochromic film• large dynamic range (10-2-106 Gy): suitable for brachy sourcedose distribution measurement.• no dark room processing required: the radiochromic film isinsensitive to visible light, the emulsion changes color whenexposed to radiation without any processing.• tissue equivalent (zeff 6.0 to 6.5)• less energy dependency compared to conventional film• film response dependent on room temperature. Acceptablerange of room temperatures 20-30° C.• sensitive to ultraviolet light (do not expose to fluorescent light)• more expensive, requires special densitometer (laser scanner atspecific wavelength 610-670 nm) 90
  • 8.6 Transfer of Absorbed Dose from one Medium to AnotherWater is the primary reference medium for calibration. Plastics arecommonly used for convenience. Thus, dose measured in a plasticmedium needs to be transferred to dose in water. photons electrons  µ en  S Dwater = Ψwater •   ρ   Dwater = Φ water •   ρ   water   water  µ en  S Dmed = Ψmed •   ρ   Dmed = Φ med •   ρ   med   med water water  µ en  S Dwater = Dmed •   ρ   Dwater = Dmed •   ρ • Φ med water   med   med 91