Basic Radiation Interactions, Definition of Dosimetric Quantities, and Data Sources J.V. Siebers Virginia Commonwealth University Richmond, Virginia USA 2009 AAPM Summer School Learninggj Objectives 1. To review and describ e the bas ics of radiation interactions for understanding radiation dosimetry 2. To review definitions of quantities required for understanding radiation dosimetry ©JVS: 2009 AAPM SS Constants Units Conversions ©JVS: 2009 AAPM SS ©JVS: 2009 AAPM SS Scope Radiation Types Ionizing Interactions can remove atomic orbital electrons Non-Ionizing Particulate Electromagnetic -electron -positron -proton -neutron -alpha -etc. ©JVS: 2009 AAPM SS Types of ionizin g radiation Direc tltly ion iz ing radia tion Direct interactions via the Coulomb force along a particles track Charged particles electrons positrons protons heavy charged particles ©JVS: 2009 AAPM SS Direct Ionization Coulombic Interaction e- A charged particle exerts electromagnetic forces on atomic Energy transfer can electrons result in the ejection of an electron (ionization) ©JVS: 2009 AAPM SS Indirectlyyg Ionizing Radiation Uncharged particles that must first transfer energy to a charged particle which can then further ionize matter Two step process Examples Elec tromagne tic radia tions: x- or γ-rays Neutrons ©JVS: 2009 AAPM SS Indirectly Ionizing Radiation Pho toe lec tr ic Effec t e- Ejec te d h electrons further ionize matter ©JVS: 2009 AAPM SS Radiant Energy R R – Total energy, excluding rest mass, carried by particles Photons: E = hν = hc/λ Electrons + other CPs: kinetic energy T ©JVS: 2009 AAPM SS Energy imparted ε ε - Energy imparted RRin out Q Q mass to energy conversion resulilting from interactions or radioactive decay if(m→E), Q>0 e- e- h Rin h Rout if(E→m), Q<0 R RR R Q ©JVS: 2009 AAPM SS incu in out c out u Dose d D Gy dm Energy deposited per unit mass 1 Gy = 1 J/kg Knowledge of D is the object of dosimetry ©JVS: 2009 AAPM SS Equilibrium Part 1: Radi a tion Equ ilibr ium h e- h RRin out e- e- h h e- RE dQ d RE RRinQ out D Q dm dm ©JVS: 2009 AAPM SS Radiation Sources Radioactive decay Alpha-decay Beta-decay Electron capture Isomeric transitions Accelerated charged particles Direct X-ray generators Atomic energy transitions Characteristic X-rays Auger electrons Interaction products ©JVS: 2009 AAPM SS Radioactive Decay General balance equations AP AA RRDR A Q ZZZZ RR QMP MDR M ©JVS: 2009 AAPM SS Q ©JVS: 2009 AAPM SS Radioactive Decay Activity dN AN dt t AAet 0 ln 2 t 1 2 ©JVS: 2009 AAPM SS Radioactive Decay α AA44 ZZP 22DHeQ α ‘s have short range / AA0 ZZP 11DQ AA0 ZZP 11DQ Neutrino ( , ))p results in spectrum of energies Emax and E are tabulated ( , ) are non-ionizing Electron Capture AA0 ZZPDQP 11e D v Q Can occur when energetically prohibited Followed by characteristic x-rays or Auger electron Isosoecmeric Tra asnsiti on AA*0 ZZP PQ0 decay from meta-stable state Internal Conversion AA* 00 ZZPPQP 11e P e Q Competes with isomeric transition Results in ejection of atomic electron ©JVS: 2009 AAPM SS ©JVS: 2009 AAPM SS β+ 15 15 0 0 8710ON 17321.732 MVMeV Electron 15Oe 0 15 N 0 1.732 MeV Capture 8170 ©JVS: 2009 AAPM SS ©JVS: 2009 AAPM SS Accelerated Charged Particles Direct use Electrons, protons, … Indirect via production of electromagnetic radiation Synchrotron radiation Bremmstrahlung ©JVS: 2009 AAPM SS Synchrotron Radiation h Magnetic Field e- Synchrotron image courtesy of http://www-project.slac.stanford.edu/ssrltxrf/spear.htm ©JVS: 2009 AAPM SS Bremmstrahlung h brems e- ©JVS: 2009 AAPM SS Atomic Energy Transition Characteristic x-ray xray h ©JVS: 2009 AAPM SS Atomic Energy Transition Auger Electron e- ©JVS: 2009 AAPM SS QQyguantifying Radiation Fields Thus far R ε D ©JVS: 2009 AAPM SS Radiation Fluence dN particles N is number of particles crossing sphere 2 da m surrounding P with cross- sectional area da Integrated over all directions and energies Single particle type ©JVS: 2009 AAPM SS Equivalent definition of fluence l nTracks l = particle track length through a V volume l need not be straight Volume can be irregular UflUseful for MtMonte Carlo applications ©JVS: 2009 AAPM SS Energy Fluence Definition dR J da m2 Poly-energetic Mono-energetic E EdE E E Differenti al energy fluence E EddE ©JVS: 2009 AAPM SS Attenuation dndlt l 1 l 0e nt m ©JVS: 2009 AAPM SS el l 0 Attenuation coefficient µ represents the in terac tion (remova l) of primaries from the beam No consideration is given to what occurs as a result of the interaction Secondary particles Energy-to-mass conversion … To remove density dependence, tabulated as µ/ρ [cm2/]/g] ©JVS: 2009 AAPM SS TERMA Total Energy Release per unit MAss J * TERMA kg Describes loss of radiant energy from uncharged primaries as they interact in material Energy lost can be absorbed locally or at a distance For poly-energetic spectra * E J TERMA E dE E ©JVS: 2009 AAPM SS E kg Aside: Photon Interactions To understand what happens with the radiant energy removed, understand the interactions (e.g. γ interactions) ©JVS: 2009 AAPM SS Photon interactions contributing to µ -1 Rayleigh m σ = Rayleigh + Compton scattering τ = photo-electric κ = pair production η = photo-nuclear ©JVS: 2009 AAPM SS RayygSleigh Scatterin g Elastic coherent scattering of the photon by an atom Important for low energy photons Cont tibtributes < 20% to ttltotal attenua tion coefficient ©JVS: 2009 AAPM SS Compton Scattering e- h h 2 NZA cm e A g ©JVS: 2009 AAPM SS Compton ©JVS: 2009 AAPM SS Photoelectric Effect e- ThEThET h e bbA ©JVS: 2009 AAPM SS Photo-electric 34 Z Au 23 h τ increases when shell can participate in reaction ©JVS: 2009 AAPM SS Pair Production e- h pair e+ T 2 avail TTee h 2 mce mc2 o radian T ©JVS: 2009 AAPM SS Triplet Production 2 Thmcavail 2 e e- h e- triplet e+ h 2mc2 T e 3 ©JVS: 2009 AAPM SS Photo-nuclear interactions (γ,n), (γ,Xn), (γ,p), … BE (Binding Energies) result in thresholds >~ 10 MeV Cross-section is small (η<0.1µ) Neutrons are ppgenetrating ©JVS: 2009 AAPM SS ©JVS: 2009 AAPM SS Pb attenuation coefficient ©JVS: 2009 AAPM SS Relative importance of interactions ©JVS: 2009 AAPM SS Summary photon interactions ©JVS: 2009 AAPM SS Energy transferred to charged particles per-itinterac tion nonr generalR RQ tr inuu out photo = compton = pair = Average n tr i tr ni ©JVS: 2009 AAPM SS el l 0 Recall Attenuation coefficient µ represents the interaction (removal) of primaries from the beam No consideration is given to what occurs as a result of the interaction Secondary particles Energy-to-mass conversion … To remove density dependence, tabulated as µ/ρ [cm2/g] ©JVS: 2009 AAPM SS Mass-energy transfer coefficient Describes the transfer of energy to charged partic les tr tr h ©JVS: 2009 AAPM SS KERMA Kinetic Energy Release per unit MAss d KERMA K tr dm * tr J kg The transfer of radiant energy from uncharged primaries to charged particles as they interact in a material Energy transferred can be absorbed locally or at a distance ©JVS: 2009 AAPM SS *Mono-energetic, integrate for poly-energetic Net energy transfer netnetRRRRR rr Rnonr nonr R r R r Q Q trtr tr tr out uuu in inuu out out u u out u Accounts for portion of kerma is radiated away T’Te- hvbrems Compton example T net Thv h e- tre brems h ©JVS: 2009 AAPM SS Mass-energy absorption coefficient RditiRadiative loss frac tion g net g 1 tr tr Mass-energy absorp tion coeffic ien t en 1 g tr ©JVS: 2009 AAPM SS Kerma Components K KKcr Colli s ion Kerma net * dtr en K Kc c dm Portion of kerma that remains collisional energy losses (non-radiative) Radiative Kerma Portion of kerma (transported elsewhere) by radiative losses ©JVS: 2009 AAPM SS Exposure and W Exposure Hist ori cal radia tion unit dQ C X Ionization density in air dm kg Related to air collision kerma by mean energy required to produce an ion pair e C XK c air W air kg WevJeVipJ1.602 1019 ( ) 1 33.97 33.97 e ip16021.602 1019 ( C electron ) electron C air ©JVS: 2009 AAPM SS Aside Indirectly ionizing radiation How many ionization events can be initiated by a 10 keV photo-electron? 3 1 ip ?ip 10 10 eV 294 ip 33.97 eV ©JVS: 2009 AAPM SS Equilibrium Part 2: Charged Particle Equilibrium h e- e- e- e- RR h inc out c e- R RR R Q incu in out c out u CPE RR QCPE ... CPE net inuu out tr net d CPE d DKtr dm dm c ©JVS: 2009 AAPM SS Charggpe particles e-, e+, p, α, … Sources Accelerated beams Radioactive decay Reaction products (e,γ) , … (n,p), … (()e,e), … Coulomb force interaction Inverse square dependence Semi-continuous rather than discrete interactions Results in energy loss and directional change Interaction can be classified by impact parameter ©JVS: 2009 AAPM SS CP interactions undisturbed incident trajectory b = impact parameter a = atitomic radius n = nuclear radius b b>>a Soft, atomic interaction b~a Hard, knock-on interaction a b<<a Nuclear interactions possible ©JVS: 2009 AAPM SS SSppgptopping power Energy loss per unit path-lthlength dE MeV SdEMeV cm2 S dx cm dx g StSeparate components bby iittinteraction S SS col rad ©JVS: 2009 AAPM SS SSppgptopping power formulations BdBased on BthBethe-Bloch , Heitl er, … Electrons: ICRU 37 2 2 SZ22 1 2ln rmcNee A 2 F 2 2 Collisional A 2 Imc e v Tmc2 2 e c Srrad e N A 22 Z EmcBr e 2 2 137 A F 11 21ln2 8 Material dependent terms ©JVS: 2009 AAPM