Outline Quantities for Describing the Interaction of Ionizing • Kerma, components of kerma Radiation with Matter • Absorbed dose • Exposure Chapter 2 • Quantities for use in radiation protection F.A. Attix, Introduction to Radiological • Summary Physics and Radiation Dosimetry Introduction Definitions • Need to describe interactions of ionizing • Most of the definitions are by ICRU radiation with matter • Energy transferred by indirectly ionizing • Special interest is in the energy absorbed in radiation leads to the definition of kerma matter, absorbed dose – delivered by • Energy imparted by ionizing radiation leads directly ionizing radiation to the definition of absorbed dose • Two-step process for indirectly ionizing • Energy carried by neutrinos is ignored radiation involves kerma and absorbed dose – Very small mass, no electric charge => negligibly small cross section for interactions with matter Energy transferred Energy transferred •- tr energy transferred in a volume V to • The energy transferred in a volume V charged particles by indirectly ionizing nonr R R Q radiation (photons and neutrons) tr in u out u • Radiant energy R – the energy of particles uncharged nonr emitted, transferred, or received, excluding •Rout u does not include radiative losses of rest mass energy kinetic energy by charged particles • Q - energy delivered from rest mass in V (bremsstrahlung or in-flight annihilation) (positive if m E, negative for E m) • Energy transferred is only the kinetic energy received by charged particles Kerma Relation of Kerma to Energy •Kerma K is the energy transferred to charged fluence for photons particles per unit mass • For mono-energetic photon of energy E and medium of atomic number Z, relation is d tr d K e tr through the mass energy-transfer coefficient: dm dm • Includes radiative losses by charged particles tr K (bremsstrahlung or in-flight annihilation of E,Z positron) • For a spectrum of energy fluence E • Excludes energy passed from one charged EE max particle to another K E tr dE • Units: 1 Gy = 1 J/kg = 102 rad = 104 erg/g E0 E,Z Relation of Kerma to Fluence Energy-transfer coefficient for neutrons • Neutron field is usually described in terms • Linear energy-transfer coefficient , tr of fluence rather than energy fluence units of m-1 or cm-1 tr • Kerma factor is tabulated instead of kerma • Mass energy-transfer coefficient , (units are rad cm2/neutron, Appendix F) units of m2/kg or cm2/g E,Z • Set of numerical values, tabulated for a F tr E n E,Z range of photon energies, Appendix D.3 E,Z • For mono-energetic neutrons K Fn E,Z Components of Kerma Collision Kerma • Energy received by charged particles may be spent • Subtracting radiant energy emitted by in two ways charged particles R r from energy transferred – Collision interactions – local dissipation of energy, u ionization and excitation along electron track results in net energy transferred locally – Radiative interactions, such as bremsstrahlung or net Rr positron annihilation, carry energy away from the track tr tr u nonr r • Kerma may be subdivided in two components, Rin u Rout u Ru Q collision and radiative: • Now collision kerma can be defined K Kc Kr d net K tr • When kerma is due to neutrons, resulting charged c dm particles are much heavier, K=Kc Mass energy-absorption Mass energy-absorption coefficient coefficient • Since collision kerma represents energy • For low Z materials and low energy deposited (absorbed) locally, introduce radiative losses are small, therefore values mass energy-absorption coefficient. For of and are close mono-energetic photon beam tr en en Kc E,Z • Depends on materials present along particle track before reaching point P Kerma rate Absorbed dose • Energy imparted by ionizing radiation to • Kerma rate at point P and time t matter of mass m in volume V dK d d tr K Rin u Rout u Rin c Rout c Q dt dt dm due to uncharged due to charged • Units of J/(kg s), erg/(g s), or rad/s • Absorbed dose is defined as • Knowing kerma rate, kerma d D t1 dm Kt ,t K t dt 0 1 2 4 t0 • Units: 1 Gy = 1 J/kg = 10 rad = 10 erg/g Example 1 R hv Absorbed dose in u 1 nonr 2 Rout u Rout u hv2 1 • D represents the energy per unit mass which Rin c 0, Q 0 remains in the matter at P to produce any Rout c hv3 T r effects attributable to radiation Ru hv3 • The most important quantity in radiological 12 Energy imparted physics Rin u Rout u Rin c Rout c Q • Absorbed dose rate: nonr Energy transferred tr Rin u Rout u Q dD d d D Net energy net nonr r dt dt dm tr Rin u Rout u Ru Q transferred Example 1 Example 2 Rin u hv1 nonr 2 Rout u Rout u hv2 1 Positron has no excess Rin c 0, Q 0 3 kinetic energy to transfer R hv T 12 to photons after out c 3 annihilation r Ru hv3 12 12 3 hv hv hv T 0 r 1 2 3 Rin u Rin c Rout c Ru 0 R R nonr 2hv 1.022MeV tr hv1 hv2 0 T out u out u 2 2 net Q hv1 2m0c 2m0c hv1 pair annihilation tr hv1 hv2 hv3 0 production net T hv3 tr tr hv1 1.022 MeV T1 T2 Example 3 Exposure • Positron transfers excess • Historically, was introduced before kerma and kinetic energy T3 to photons after annihilation. dose, measured in roentgen (R) T3 3 • It generates radiative loss • Defined as a quotient 12 from charged-particle dQ kinetic energy X n • Affects and tr by dm 12 3 subtraction of T3 • dQ is absolute value of the total charge of the ions R R R 0 in u in c out c of one sign produced in air when all electrons Rout u 2hv T3 1.022MeV T3 liberated by photons in air of mass dm are nonr completely stopped in air Rout u 2hv 1.022MeV Rr T • Ionization from the absorption of radiative loss of u 3 kinetic energy by electrons is not included 2 2 Q hv1 2m0c 2m0c hv1 Exposure Relation of exposure to energy fluence • Exposure is the ionization equivalent of the collision kerma in air for x and -rays • Exposure at a point due to energy fluence of mono-energetic photons • Introduce mean energy expended in a gas per e ion pair formed, W , constant for each gas, en X independent of incoming photon energy E,airW air • For dry air e Kc air Kc air /33.97 W 33.97 eV/i.p. W air air 1.602 1019 J/eV e 1.602 1019C/electron • Units of [X]=C/kg in SI 33.97 J/C Units of exposure Exposure rate • The roentgen R is the customary unit • Exposure rate at a point P and time t: • The roentgen is defined as exposure dX producing in air one unit of esu of charge X per 0.001293 g of air irradiated by the dt photons. Conversion • Units are C/(kg-sec) or R/sec 1esu 1C 103 g • Exposure t 1R 9 1 0.001293g 2.99810 esu 1kg X X (t)dt 4 2.58010 C/kg t0 1C/kg 3876 R Significance of exposure Significance of exposure • Energy fluence is proportional to exposure for any given photon energy or spectrum • Due to similarity in effective atomic number – Air can be made a tissue equivalent medium with respect to energy absorption – convenient in measurements – Collision kerma in muscle per unit of exposure is nearly independent of photon energy Ratio of mass energy-absorption coefficients for muscle/air and water/air are nearly constant (within <5%) for energies from 4keV to 10 MeV Significance of exposure Significance of exposure • X-ray field at a point can be characterized by means of exposure regardless of whether there is air actually located at this point • It implies that photon energy fluence at that point is such that it would produce exposure of a stated value • Same is applicable to kerma or collision kerma, except that reference medium (not Ratio of mass energy-absorption coefficients for bone/air and necessarily air) has to be specified acrylic/air are nearly constant for energies above 100keV Radiation protection quantities Radiation protection quantities • Quality factor Q – weighting factor to be applied to absorbed dose to provide an estimate of the relative human hazard of ionizing radiation • It is based on relative biological effectiveness (RBE) of a particular radiation source • Q is dimensionless • Higher-density charged particle tracks (higher collision stopping power) are more damaging per unit dose Radiation protection quantities Summary • Quantities describing the interaction of • Dose equivalent H, is defined as ionizing radiation with matter – Kerma, components of kerma H DQN – Absorbed dose • Here D – dose, Q- quality factor, N-product – Exposure of modifying factors (currently=1) • Relationship with fluence and energy fluence • Units of H: • Quantities for use in radiation protection – severs, Sv, if dose is expressed in J/kg – Quality factor Q – rem, if dose is in rad (10-2 J/kg) – Dose equivalent H.