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Radiation Dosimetry Dose Calculations D, LET & H can frequently be obtained reliably by calculations: Alpha & low – Energy Beta Emitters Distributed in Tissue Chemical elements preferentially seeks specific body organs for example: I concentrates in the thyroid Ra and Sr (strontium) are bone seekers 3 H + C s tend to distribute themselves throughout the whole body.

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For & low : they deposit these energy locally: If A denotes the average concentration, in Bq/g, of the radionuclide in the tissue and denotes the average alpha or particles. the rate of energy absorption per gram of tissue is A MeV g -1.s -1 the absorbed dose rate is D = A [D = 1.6 x 10 -10 A Gy/s](12.21) D: average dose …? Hot spot? (Where A in Bq/g and E in MeV) Radiation Dosimetry

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Charged Particle Beams Fig. 12.9 …. To calculate dose rate at a given depth x for a flounce rate cm -2 s -1 Slab thickness x & Area A normal to the beam the rate of energy deposition in the volume elements is = A(-dE/dx) x where –dE/dx is the collision stopping power, we ignore struggling. ~ the dose rate = (12.23) Radiation Dosimetry

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It follows that the dose per unit fluence at any depth is equal to the mass stopping power for the particles at that depth. For example, if the mass stopping power is 3 MeV cm 2 /g, then the dose per unit fluence can be expressed 3 MeV/g. If significant nuclear interaction occur, then accurate depth – dose curves cannot be calculated from eq. 12.23. Once can then resort to Monte Carlo Calculations, in which the rate of individual incident and secondary particles are handled statistically on the bases of the cross sections for various nuclear interactions that occur. Radiation Dosimetry

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C) Point Source of Gamma Rays We next derive a simple formula for computing the exposure rate in air from a point - source of a activity C that emits an average photon energy E per disintegration. The rate of energy released = CE Neglecting attenuation in air, the energy fluence rate or intensity, through the surface of a sphere of radius r centered about the source Radiation Dosimetry

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for monoenergetic photons, it follows from eq. 8.61 (8.61) (12.24) here is the mass energy – absorption coefficient of air for the photons. Inspection of Fig. 8.12 shows that this coefficient has roughly the same value for photons with energies between 60 keV & 2 MeV, 0.027 cm 2 /g 0.0027 m 2 kg -1. Radiation Dosimetry

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Thus we can apply eq. 12.24 to any mixture of photons in this energy range: (12.25) with C in Bq, E in J & r in m,D is in Gy/s For C in Ci & E in MeV, we have [ ] (12.26) Radiation Dosimetry

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Using hours as the unit of time and changing from dose rate to exposure rate [eq.12.4] gives R/h (12.27) This simple formula can be used to estimate the exposure rate from a point source that emits - rays. :The specific -ray constant, for a nuclide is defined by writing (12.28) Radiation Dosimetry

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This constant, which numerically gives the exposure rate per unit activity at unit distance is usually expressed in Rm 2 /Cih. Comparison with eq. 12.27 shows that 0.5 E, with E in MeV.The accuracy of the approximations leading to eq. 12.27 varies from nuclide to nuclide…… The exposure– rate constant of a radionuclide is defined like the specific gamma ray constant, but includes the exposure rate from all photons emitted with energies greater than a specified value …. Radiation Dosimetry

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Neutrons As discussed in Ch 9, fast n’s lose energy primarily by elastic scattering while slow and thermal n’s have high probability of being captured: In tissue The absorbed dose from fast n’s is due to almost entirely to the energy transferred to the atomic nuclei in tissue by elastic scattering: (½ En)in 1H Qmax = (9.3) Radiation Dosimetry

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The relationship facilitate the calculation of a first collision dose from fast n’s in soft tissue. The first collision dose is that delivered by n’s that make only a single collision in the target approximate the actual dose when the mean free path of n’s is large compared with the dimensions of the target. For 5 – MeV n, = 0.051 cm-1 = 20 cm in the body…? Radiation Dosimetry

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The first collision dose is, of course, always a lower bound to the actual dose. + Moreover fast n’s deposit most of their in tissue by means of collisions with Hydrogen Calculating the first collisions dose with tissue hydrogen often provide a simple, lower – bound estimate of fast neutron dose. Detailed analysis shows that hydrogen recoils contribute approximately 85 – 95% of the first collisions soft tissue dose for n’s with energies 10 keV 10 MeV Table 12.6 Fig. 12.10 shows the result of Monte Carlo calculations carried out for 5 MeV n’s incident on a 30cm soft tissue slab [ the thickness of the body] Radiation Dosimetry

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12.10 Other Dosimetric Concepts and Quantities Kerma A quantity related to dose for indirectly ionizing radiation [photons and neutrons] is the initial kinetic energy of all charged particles librated by the radiation per unit mass [unit of dose]. Kerma: Kinetic Energy Released per unit MAss. By definition, Kerma includes energy that may subsequently appear as bremsstrahlung and it also includes Auger electron energies. Radiation Dosimetry

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The absorbed dose generally builds up behind a surface irradiated by a beam of neutral particles to a depth comparable with the range of the secondary charged particles generated [Fig. 12.10]. The Kerma on the other hand decreases steadily because of the attenuation of the primary radiation with increasing depth. The first collision “dose” calculated for n’s in the last section is, more precisely stated, the first collision “Kerma”. The two are identical as long as: All of the initial kinetic energy of the recoil charged particles can be considered as being absorbed locally at the interaction site. Specifically, Kerma and absorbed dose at a point in an irradiated target are equal when charged particle equilibrium exists there and bremsstrahlung losses are negligible. Radiation Dosimetry

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Microdosimetry: Absorbed dose is an average quantity [non stochastic] and as such does not specifically reflect the stochastic, or statistical, nature of energy deposition by ionizing radiation in matter. Statistical aspect are especially important when one consider dose in small regions of an irradiated target, such as cell nuclei or other sub-cellular components. Consider – for example, cell nuclei = D = 5 m WB DoseType of R. Non-Expos. Nuclei Exposed Nuclei 1 m Gy Low LET 2/3 1/3 to ~ 3 m Gy 1 m Gy High LET 99.8 %! 0.2% ~ 500 m Gy 0.500 MeVp + range=8x10 -4 cm = 8 m 1 nuclear diameter 0.500 MeV e - range = 0.174cm = = 350 nuclear diameters Specific Energy: X doses on the microscopic scale (stochastic quantity) Linear Energy: X microscopic LET defined for a single event (Stochastic quantity) END Radiation Dosimetry

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