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Absorbed Dose in Radioactive Media Outline Introduction Radiation Equilibrium Charged-Particle Equilibrium Limiting Cases

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Absorbed Dose in Radioactive Media Outline Introduction Radiation Equilibrium Charged-Particle Equilibrium Limiting Cases Outline • General dose calculation considerations, Absorbed Dose in Radioactive absorbed fraction Media • Radioactive disintegration processes and associated dose deposition – Alpha disintegration Chapter 5 – Beta disintegration – Electron-capture transitions F.A. Attix, Introduction to Radiological – Internal conversion Physics and Radiation Dosimetry • Summary Introduction Radiation equilibrium • We are interested in calculating the absorbed dose in a. The atomic composition radioactive media, applicable to cases of of the medium is – Dose within a radioactive organ homogeneous – Dose in one organ due to radioactive source in another b. The density of the organ medium is • If conditions of CPE or RE are satisfied, dose homogeneous c. The radioactive source calculation is straightforward is uniformly distributed • Intermediate situation is more difficult but can be d. No external electric or handled at least in approximations magnetic fields are present Charged-particle equilibrium Limiting cases • Emitted radiation typically includes both • Each charged particle of a given type and photons (longer range) and charged energy leaving the volume is replaced by an particles (shorter range) identical particle of the same energy entering • Assume the conditions for RE are satisfied the volume • Consider two • Existence of RE is sufficient condition for CPE limited cases based • Even if RE does not exist CPE may still exist on the size of the (for a very large or a very small volume) radioactive object 1 Limiting cases: small object Limiting cases: large object • A radioactive object V having a mean radius not much • A radioactive object V with mean radius » l/m for greater than the maximum charged-particle range d the most penetrating g-rays • CPE is well approximated at any internal point P that is at least a distance d from the boundary of V • RE is well approximated at any internal point P • If d« l/m for the g-rays, the absorbed dose D at P that is far enough from the boundary of V so g-ray approximately equals to the energy per unit mass of penetration through that distance is negligible medium that is given to the charged particles in radioactive decay (less their radiative losses) • The dose at P will then equal the sum of the • The photons escape from the object and are assumed not energy per unit mass of medium that is given to to be scattered back by its surroundings charged particles plus g-rays in radioactive decay Limiting cases: large object Absorbed fraction • Deciding upon a maximum • An intermediate-size radioactive object V g-ray “range” L for this case requires quantitative • Dose at P will then equal the sum of the energy criterion per unit mass of medium that is given to – For primary beam only (m) the charged particles plus dose from some g-rays penetration is < 0.1% through L~7 mean free paths • To estimate the dose from g-rays define – Taking into account scatter, absorbed fraction: (broad beam geometry, m ) g - ray radiant energy absorbed in target volume will increase the required AF object size to satisfy the g - ray radiant energy emitted by source attenuation objectives Attenuation of 1MeV g-rays in water Intermediate-size radioactive object Case 1 • Reciprocity theorem: energy spent • Consider volume V filled by a homogeneous medium and a in dv due to the source in dv’: uniformly distributed g-source d v ,dv dv ,d v and dv ,V V ,dv • The volume may be surrounded by • No source in dv” Case 1: infinite homogeneous medium identical to V, but non- • Define Rdv as the expectation radioactive (an organ in the value of the g-ray radiant energy body) emitted by the source in dv, and Case 2: infinite vacuum (object in dv,V the part of that energy that is air) spent in V (source dv and target V) 2 Case 1 continued Case 1 continued • The absorbed fraction with respect • Reduction in the absorbed dose due to g-rays to source dv and target V is : energy escaping from V • Can estimate AF using mean effective attenuation dv ,V V ,dv AF dv ,V coefficient for g-rays energy fluence through a R dv R dv distance r in the medium source, target 2 • Estimates reduction in absorbed 1 m r AF 1 e sin d d dv ,V dose relative to RE condition 4 • For very small radioactive objects 0 0 (V dv) this absorbed fraction • For poly-energetic sources have to find an average approaches zero; for an infinite value of the absorbed fraction radioactive medium it equals unity Case 1 example Case 2 Radioactive object V surrounded by vacuum • More difficult to calculate radius of sphere • The reciprocity theorem is only approximate due to the lack of backscattering • Energy dependence (max ~80keV) • Dose is lower than in Case 1 (ratios >1) m • Dose calculations published in MIRD (Medical Internal Radiation Dosimetry) reports • The larger the radius, the lower the g-ray energy – the closer to RE condition (AF=1) Case 2 MIRD tables Pamphlet 11, 1975 • To obtain a crude estimate of the dose at some • AF is incorporated in “S-value” point P within a uniformly g-active homogeneous tabulated for each radionuclide object, it may suffice to obtain the average and source-target configuration distance r from the point to the surface of the used in nuclear medicine object by • Dose absorbed in any organ Pamphlet 1 2 (target) due to a source in some r r sin d d other organ is calculated based 5rev, 1978 4 0 0 on cumulative activity, D=AxS • Then one may employ men = m in the straight- • S values are typically calculated ahead approximation to obtain by Monte Carlo technique • Straightforward approach, but m en r AF dv ,V 1 e accuracy is limited 3 MIRD tables MIRD tables Bouchet et al., MIRD Pamphlet No. 19, The Journal of Nuc. Med., Vol. 44, p. 1113, 2003 • The accuracy is continuously improved through revisions and updates • Example: kidneys represent a frequent source of radiopharmaceutical uptake in both diagnostic and therapeutic nuclear medicine Bouchet et al., MIRD Pamphlet No. 19, THE JOURNAL OF NUC. MED., Vol. 44, p. 1113, 2003 Radioactive disintegration processes Alpha disintegration • Radioactive nuclei undergo transformations to a more stable state through expulsion of energetic particles • Occurs mainly in heavy nuclei • Example: decay of radium to radon, presented by the mass-energy balance equation 226 222 4 • The total mass, energy, momentum, and electric 88 Ra 86 Rn 2 He 4 .78 MeV 1602 y charge are conserved parent 1 / 2 daughter • Energy equivalent of the rest mass: • Each of the elemental terms represents the rest 12 mass of a neutral atom of that element – 1 amu=1/12 of the mass of 6C nucleus=931.50 MeV – 1 electron mass=0.51100 MeV • Energy term represents kinetic energy released Absorbed dose from Alpha disintegration - disintegration • Take into account both branches through the average branching ratios • For radium average kinetic energy given to charged particles per disintegration E 0 .946 4 .78 MeV 0.054 4.6 MeV 4.77 MeV • For CPE condition in a small (1 cm) radium-activated object: D=4.77 x n MeV/g, where n – number of • Two branches are available for disintegration disintegrations per gram of the matter • Kinetic + quantum energy released is 4.78MeV • For RE condition (large object): D=4.78 x n MeV/g, • After the -particle slows down it captures two electrons from includes g-ray energy its surroundings, becoming a neutral He atom 4 Beta disintegration Beta disintegration • Nuclei having excess of neutrons typically emit an electron, - particle; atomic number Z is increased by 1 • Nuclei having excess of protons typically emit positron, + particle; atomic number Z is decreased by 1 • Nucleus is left in an exited state, emitting one or more g-rays • Example: 32 32 - 0 • Kinetic energy 1.71 MeV is shared between - and neutrino 15 P 16 S 0 1 .71 MeV 1 / 2 14 .3 d 32 + kinetic energy • Charge balance is realized through initially ion of 16S capturing an electron Beta disintegration Beta disintegration • Average kinetic energy of the - or + particle is typically • In + disintegration valence electron is emitted simultaneously 0.3-0.4 Emax; 1/3 Emax is often used for purposes of roughly 15 15 estimating absorbed dose • Example: 8O -> 7N 15 15 - 0 • Neutrino is not included in dose estimates due to almost zero 8 O 7 N e 0 1 .73 MeV 122 s rest mass energy and no charge 1 / 2 2 positron annihilation yields 2m0c =1.022 MeV Absorbed dose from Example 5.1 - disintegration • Uniformly distributed - and g-ray source • The rest-mass loss is spent • Under CPE condition D=nEavg MeV/g for n – half in 1 -MeV g -ray production and disintegrations per gram of medium - – half in -decay, for which Emax=5 MeV and Eavg=2 MeV • Any additional contributions to energy • The point of interest P is located >5 cm inside_ the deposition due to g-rays must be included boundary of the object, at an average distance r = 20 for RE condition cm from the boundary. -1 -1 • Radiative losses by -rays, such as • men=0.0306 cm and m = 0.0699 cm for the g -rays bremsstrahlung and in-flight annihilation, • A total energy of 10-2 J converted from rest mass in are ignored each kg of the object • Estimate the absorbed dose at P 5 Example 5.1 Example 5.2 • For -ray Emax=5 MeV corresponds to maximum particle range (Appendix E) d ~2.6 cm << 1/m=14.3 cm • CPE exists at P, therefore dose due to -rays: • What is the absorbed dose rate (Gy/h) at the 1 2 2 center of a sphere of water 1 cm in radius, D E avg 10 J/kg 10 J/kg 2 32 homogeneously radioactivated by 15P, 1/m • For g-ray 20cm is not >> 1/m=14.3
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