Radiation Dosimetry PDF

361 12 Radiation Dosimetry 12.1 Introduction Radiation dosimetry is the branch of science that attempts to quantitatively relate specific measurements made in a radiation field to physical, chemical, and/or...

361 12 Radiation Dosimetry 12.1 Introduction Radiation dosimetry is the branch of science that attempts to quantitatively relate specific measurements made in a radiation field to physical, chemical, and/or bio- logical changes that the radiation would produce in a target. Dosimetry is essential for quantifying the incidence of various biological changes as a function of the amount of radiation received (dose–effect relationships), for comparing different experiments, for monitoring the radiation exposure of individuals, and for surveil- lance of the environment. In this chapter we describe the principal concepts upon which radiation dosimetry is based and present methods for their practical utiliza- tion. When radiation interacts with a target it produces excited and ionized atoms and molecules as well as large numbers of secondary electrons. The secondary electrons can produce additional ionizations and excitations until, finally, the energies of all electrons fall below the threshold necessary for exciting the medium. As we shall see in detail in the next chapter, the initial electronic transitions, which produce chemically active species, are completed in very short times (!10–15 s) in local re- gions within the path traversed by a charged particle. These changes, which require the direct absorption of energy from the incident radiation by the target, represent the initial physical perturbations from which subsequent radiation effects evolve. It is natural therefore to consider measurements of ionization and energy absorption as the basis for radiation dosimetry. As experience and knowledge have been gained through the years, basic ideas, philosophy, and concepts behind radiation protection and dosimetry have continu- ally evolved. This process continues today. On a world scale, the recommendations of the International Commission on Radiological Protection (ICRP) have played a major role in establishing protection criteria at many facilities that deal with radia- tion. In the United States, recommendations of the National Council on Radiation protection and Measurements (NCRP) have provided similar guidance. There is close cooperation among these two bodies and also the International Commission on Radiation Units and Measurements (ICRU). As a practical matter, there is a cer- tain time delay between the publication of the recommendations and the official Atoms, Radiation, and Radiation Protection. James E. Turner Copyright © 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 978-3-527-40606-7 362 12 Radiation Dosimetry promulgation of statutory regulations by organizations responsible for radiation protection. As a result, at any point in time, some differences might exist among particular procedures in effect at different locations, even though they are based on publications of the ICRP or NCRP. We shall discuss the implementation of radia- tion protection criteria and exposure limits in Chapter 14. The present chapter will deal with radiation quantities and units of historical and current importance. 12.2 Quantities and Units Exposure Exposure is defined for gamma and X rays in terms of the amount of ionization they produce in air. The unit of exposure is called the roentgen (R) and was intro- duced at the Radiological Congress in Stockholm in 1928 (Chap. 1). It was origi- nally defined as that amount of gamma or X radiation that produces in air 1 esu of charge of either sign per 0.001293 g of air. (This mass of air occupies 1 cm3 at standard temperature and pressure.) The charge involved in the definition of the roentgen includes both the ions produced directly by the incident photons as well as ions produced by all secondary electrons. Since 1962, exposure has been defined by the International Commission on Radiation Units and Measurements (ICRU) as the quotient !Q/!m, where !Q is the sum of all charges of one sign produced in air when all the electrons liberated by photons in a mass !m of air are completely stopped in air. The unit roentgen is now defined as 1 R = 2.58 × 10–4 C kg–1. (12.1) The concept of exposure applies only to electromagnetic radiation; the charge and mass used in its definition, as well as in the definition of the roentgen, refer only to air. Example Show that 1 esu cm–3 in air at STP is equivalent to the definition (12.1) of 1 R of exposure. Solution Since the density of air at STP is 0.001293 g cm–3 and 1 esu = 3.34 × 10–10 C (Appen- dix B), we have 1 esu 3.34 × 10–10 C = = 2.58 × 10–4 C kg–1. (12.2) cm3 0.001293 g × 10–3 kg g–1 Absorbed Dose The concept of exposure and the definition of the roentgen provide a practical, mea- surable standard for electromagnetic radiation in air. However, additional concepts  12.2 Quantities and Units 363 are needed to apply to other kinds of radiation and to other materials, particularly tissue. The primary physical quantity used in dosimetry is the absorbed dose. It is defined as the energy absorbed per unit mass from any kind of ionizing radiation in any target. The unit of absorbed dose, J kg–1 , is called the gray (Gy). The older unit, the rad, is defined as 100 erg g–1. It follows that 1 J 107 erg erg 1 Gy ≡ = 3 = 104 = 100 rad. (12.3) kg 10 g g The absorbed dose is often referred to simply as the dose. It is treated as a point function, having a value at every position in an irradiated object. One can compute the absorbed dose in air when the exposure is 1 R. Photons produce secondary electrons in air, for which the average energy needed to make an ion pair is W = 34 eV ip–1 = 34 J C–1 (Sect. 10.1). Using a more precise W value,1) one finds 2.58 × 10–4 C 33.97 J 1R= × = 8.76 × 10–3 J kg–1. (12.4) kg C Thus, an exposure of 1 R gives a dose in air of 8.76 × 10–3 Gy (= 0.876 rad). Calculations also show that a radiation exposure of 1 R would produce a dose of 9.5 × 10–3 Gy (= 0.95 rad) in soft tissue. This unit is called the rep (“roentgen- equivalent-physical”) and was used in early radiation-protection work as a measure of the change produced in living tissue by radiation. The rep is no longer employed. Dose Equivalent It has long been recognized that the absorbed dose needed to achieve a given level of biological damage (e.g., 50% cell killing) is often different for different kinds of radiation. As discussed in the next chapter, radiation with a high linear energy transfer (LET) (Sect. 7.3) is generally more damaging to a biological system per unit dose than radiation with a low LET (for example, cf. Fig. 13.16). To allow for the different biological effectiveness of different kinds of radiation, the International Commission on Radiological Protection (ICRP), National Coun- cil on Radiation Protection and Measurements (NCRP), and ICRU (Chap. 1) intro- duced the concept of dose equivalent for radiation-protection purposes. The dose equivalent H is defined as the product of the absorbed dose D and a dimensionless quality factor Q, which depends on LET: H = QD. (12.5) In principle, other multiplicative modifying factors can be included along with Q to allow for additional considerations (e.g., dose fractionation), but these are not ordinarily used. Until the 1990 recommendations made in ICRP Publication 60, the dependence of Q on LET was defined as given in Table 12.1. Since then, the 1 See p. 29 in Attix reference, Section 12.11. 364 12 Radiation Dosimetry Table 12.1 Dependence of Quality Factor Q on LET of Radiation as Formerly Recommended by ICRP, NCRP, and ICRU LET (keV µm–1 in Water) Q 3.5 or less 1 3.5–7.0 1–2 7.0–23 2–5 23–53 5–10 53–175 10–20 Gamma rays, X rays, electrons, positrons of any LET 1 Table 12.2 Dependence of Quality Factor Q on LET as Currently Recommended by ICRP, NCRP, and ICRU LET, L (keV µm–1 in Water) Q 100 300/ L ICRP, NCRP, and ICRU have defined Q in accordance with Table 12.2. In the con- text of quality factor, LET is the unrestricted stopping power, L∞ , as discussed in Section 7.3. For incident charged particles, it is the LET of the radiation in water, expressed in keV per µm of travel. For neutrons, photons, and other uncharged radiation, LET refers to that which the secondary charged particles they generate would have in water. Like absorbed dose, dose equivalent is a point function. When dose is expressed in Gy, the (SI) unit of dose equivalent is the sievert (Sv). With the dose in rad, the older unit of dose equivalent is the rem (“roentgen-equivalent- man”). Since 1 Gy = 100 rad, 1 Sv = 100 rem. Dose equivalent has been used extensively in protection programs as the quantity in terms of which radiation limits are specified for the exposure of individuals. Dose equivalents from different types of radiation are simply additive. Example A worker receives a whole-body dose of 0.10 mGy from 2-MeV neutrons. Estimate the dose equivalent, based on Table 12.1. Solution Most of the absorbed dose is due to the elastic scattering of the neutrons by the hydrogen in tissue (cf. Table 12.6). To make a rough estimate of the quality fac- tor, we first find Q for a 1-MeV proton—the average recoil energy for 2-MeV neu- trons. From Table 5.3 we see that the stopping power for a 1-MeV proton in water is 270 MeV cm–1 = 27 keV µm–1. Under the current recommendations of the ICRP, NCRP, and ICRU, Q is defined according to Table 12.2. However, the older recom-  12.3 Measurement of Exposure 365 mendations, which include Table 12.1, are still in effect at a number of installations. We see from Table 12.1 that an estimate of Q ∼ 6 should be reasonable for the re- coil protons. The recoil O, C, and N nuclei have considerably higher LET values, but do not contribute as much to the dose as H. (LET is proportional to the square of a particle’s charge.) Without going into more detail, we take the overall quality factor, Q ∼ 12, to be twice that for the recoil protons alone. Therefore, the estimated dose equivalent is H ∼ 12 × 0.10 = 1.2 mSv. [The value Q = 10 is obtained from detailed calculations (cf. Table 12.5).] We note that Table 12.2 implies a comparable value, Q = 6.4, for the protons. Changes in the recommendations are discussed more fully in Chapter 14. By the early 1990s, the ICRP and NCRP replaced the use of LET-dependent qual- ity factors by radiation weighting factors, w, specified for radiation of a given type and energy. The quantity on the left-hand side of the replacement for Eq. (12.5), H = wD, is then called the equivalent dose. In some regulations the older terminol- ogy, dose equivalent and quality factor, is still employed. However, the latter has come to be specified by radiation type and energy, rather than LET. 12.3 Measurement of Exposure Free-Air Ionization Chamber Based on its definition, exposure can be measured operationally with the “free-air,” or “standard,” ionization chamber, sketched in Fig. 12.1. X rays emerge from the target T of an X-ray tube and enter the free-air chamber through a circular aperture of area A, defining a right circular cone TBC of rays. Parallel plates Q and Q′ in the chamber collect the ions produced in the volume of air between them with center P′. Fig. 12.1 Schematic diagram of the “free-air” or “standard” ionization chamber. 366 12 Radiation Dosimetry The exposure in the volume DEFG in roentgens would be determined directly if the total ionization produced only by those ions that originate from X-ray interac- tions in the truncated conical volume DEFG could be collected and the resulting charge divided by the mass of air in DEFG. This mass is given by M = ρA′ L, where ρ is the density of air, A′ is the cross-sectional area of the truncated cone at its mid- point P′ , and L, the thickness of the cone, is equal to the length of the collecting plates Q and Q′. Unfortunately, the plates collect all of the ions between them, not the particular set that is specified in the definition of the roentgen. Some electrons produced by X-ray interactions in DEFG escape this volume and produce ions that are not collected by the plates Q, Q′. Also, some ions from electrons originally pro- duced outside DEFG are collected. Thus, only part of the ionization of an electron such as e1 in Fig. 12.1 is collected, while ionization from an “outside” electron, such as e2 , is collected. When the distance from P to DG is sufficiently large (e.g., ∼ 10 cm for 300-keV X rays), electronic equilibrium will be realized; that is, there will be almost exact compensation between ionization lost from the volume DEFG by electrons, such as e1 , that escape and ionization gained from electrons, such as e2 , that enter. The distance from P to DG, however, should not be so large as to attenuate the beam significantly between P and P′. Under these conditions, when a charge q is collected, the exposure at P′ is given by q EP′ =. (12.6) ρA′ L In practice, one prefers to know the exposure EP at P, the location where the entrance port is placed, rather than EP′. By the inverse-square law, EP = (d′ /d)2 EP′. Since A = (d/d′ )2 A′ , Eq. (12.6) gives ! ′ "2 d q q EP = ′ =. (12.7) d ρA L ρAL Example The entrance port of a free-air ionization chamber has a diameter of 0.25 cm and the length of the collecting plates is 6 cm. Exposure to an X-ray beam produces a steady current of 2.6 × 10–10 A for 30 s. The temperature is 26◦ C and the pressure is 750 torr. Calculate the exposure rate and the exposure. Solution We can apply Eq. (12.7) to exposure rates as well as to exposure. The rate of charge col- lection is q̇ = 2.6 × 10–10 A = 2.6 × 10–10 C s–1. The density of the air under the stated conditions is ρ = (0.00129)(273/299)(750/760) = 1.16 × 10–3 g cm–3. The entrance- port area is A = π (0.125)2 = 4.91 × 10–2 cm2 and L = 6 cm. Equation (12.7) implies, for the exposure rate, q̇ 2.6 × 10–10 C s–1 ĖP = = ρAL 1.16 × 10–3 × 4.91 × 10–2 × 6 g 1R × = 2.95 R s–1. (12.8) 2.58 × 10–7 C g–1 The total exposure is 88.5 R.  12.3 Measurement of Exposure 367 Measurement of exposure with the free-air chamber requires some care and at- tention to details. For example, the collecting plates Q and Q′ in Fig. 12.1 must be recessed away from the active volume DEFG by a distance not less than the lateral range of electrons produced there. We have already mentioned minimum and maximum restrictions on the distance from P to DG. When the photon energy is increased, the minimum distance required for electronic equilibrium increases rapidly and the dimensions for a free-air chamber become excessively large for photons of high energy. For this and other reasons, the free-air ionization chamber and the roentgen are not used for photon energies above 3 MeV. The Air-Wall Chamber The free-air ionization chamber is not a practical instrument for measuring routine exposure. It is used chiefly as a primary laboratory standard. For routine use, cham- bers can be built with walls of a solid material, having photon response properties similar to those of air. Chambers of this type were discussed in Section 10.1. Such an “air-wall” pocket chamber, built as a capacitor, is shown schematically in Fig. 12.2. A central anode, insulated from the rest of the chamber, is given an initial charge from a charger-reader device to which it is attached before wearing. When exposed to photons, the secondary electrons liberated in the walls and enclosed air tend to neutralize the charge on the anode and lower the potential difference between it and the wall. The change in potential difference is directly proportional to the total ionization produced and hence to the exposure. Thus, after exposure to photons, measurement of the change in potential difference from its original value when the chamber was fully charged can be used to find the exposure. Direct- reading pocket ion chambers are available (Fig. 10.6). Example A pocket air-wall chamber has a volume of 2.5 cm3 and a capacitance of 7 pF. Initially charged at 200 V, the reader showed a potential difference of 170 V after the chamber was worn. What exposure in roentgens can be inferred? Solution The charge lost is !Q = C!V = 7 × 10–12 × (200 – 170) = 2.10 × 10–10 C. The mass of air [we assume standard temperature and pressure (STP)] is M = 0.00129 × 2.5 = 3.23 × 10–3 g. It follows that the exposure is 2.10 × 10–10 C 1R –3 × = 0.252 R. (12.9) 3.23 × 10 g 2.58 × 10–7 C g–1 Fig. 12.2 Air-wall pocket ionization chamber, having a plastic wall with approximately the same response to photons as air. 368 12 Radiation Dosimetry Literally taken, the data given in this problem indicate only that the chamber was partially discharged. Charge loss could occur for reasons other than radiation (e.g., leakage from the central wire). Two pocket ion chambers can be worn simultaneously to improve reliability. In practice, air-wall ionization chambers involve a number of compromises from an ideal instrument that measures exposure accurately. For example, if the wall is too thin, incident photons will produce insufficient ionization inside the chamber. If the wall is too thick, it will significantly attenuate the incident radiation. The optimal thickness is reached when, for a given photon field, the ionization in the chamber gas is a maximum. This value, called the equilibrium wall thickness, is equal to the range of the most energetic secondary electrons produced in the wall. In addition, a solid wall can be only approximately air equivalent. Air-wall chambers can be made with an almost energy-independent response from a few hundred keV to about 2 MeV—the energy range in which Compton scattering is the dominant photon interaction in air and low-Z wall materials. 12.4 Measurement of Absorbed Dose One of the primary goals of dosimetry is the determination of the absorbed dose in tissue exposed to radiation. The Bragg–Gray principle provides a means of relating ionization measurements in a gas to the absorbed dose in some convenient mate- rial from which a dosimeter can be fabricated. To obtain the tissue dose, either the material can be tissue equivalent or else the ratio of the absorbed dose in the ma- terial to that in tissue can be inferred from other information, such as calculations or calibration measurements. Consider a gas in a walled enclosure irradiated by photons, as illustrated in Fig. 12.3. The photons lose energy in the gas by producing secondary electrons there, and the ratio of the energy deposited and the mass of the gas is the absorbed dose in the gas. This energy is proportional to the amount of ionization in the gas Fig. 12.3 Gas in cavity enclosed by wall to illustrate Bragg–Gray principle.  12.4 Measurement of Absorbed Dose 369 when electronic equilibrium exists between the wall and the gas. Then an electron, such as e1 in Fig. 12.3, which is produced by a photon in the gas and enters the wall before losing all of its energy, is compensated by another electron, like e2 , which is produced by a photon in the wall and stops in the gas. When the walls and gas have the same atomic composition, then the energy spectra of such electrons will be the same irrespective of their origin, and a high degree of compensation can be realized. The situation is then analogous to the air-wall chamber just dis- cussed. Electronic equilibrium requires that the wall thickness be at least as great as the maximum range of secondary charged particles. However, as with the air- wall chamber, the wall thickness should not be so great that the incident radiation is appreciably attenuated. The Bragg–Gray principle states that, if a gas is enclosed by a wall of the same atomic composition and if the wall meets the thickness conditions just given, then the energy absorbed per unit mass in the gas is equal to the number of ion pairs produced there times the W value divided by the mass m of the gas. Furthermore, the absorbed dose Dg in the gas is equal to the absorbed dose Dw in the wall. Denoting the number of ions in the gas by Ng , we write Ng W Dw = Dg =. (12.10) m When the wall and gas are of different atomic composition, the absorbed dose in the wall can still be obtained from the ionization in the gas. In this case, the cavity size and gas pressure must be small, so that secondary charged particles lose only a small fraction of their energy in the gas. The absorbed dose then scales as the ratio Sw /Sg of the mass stopping powers of the wall and gas: D g Sw Ng WSw Dw = =. (12.11) Sg mSg If neutrons rather than photons are incident, then in order to satisfy the Bragg– Gray principle the wall must be at least as thick as the maximum range of any secondary charged recoil particle that the neutrons produce in it. As with the air-wall chamber for measuring exposure, condenser-type chambers that satisfy the Bragg–Gray conditions can be used to measure absorbed dose. Prior to exposure, the chamber is charged. The dose can then be inferred from the re- duced potential difference across the instrument after it is exposed to radiation. The determination of dose rate is usually made by measuring the current due to ionization in a chamber that satisfies the Bragg–Gray conditions. As the following example shows, this method is both sensitive and practical. Example A chamber satisfying the Bragg–Gray conditions contains 0.15 g of gas with a W value of 33 eV ip–1. The ratio of the mass stopping power of the wall and the gas is 1.03. What is the current when the absorbed dose rate in the wall is 10 mGy h–1 ? 370 12 Radiation Dosimetry Solution We apply Eq. (12.11) to the dose rate, with Sw /Sg = 1.03. From the given conditions, Ḋw = 10 mGy h–1 = (0.010 J kg–1 )/(3600 s) = 2.78 × 10–6 J kg–1 s–1. The rate of ion- pair production in the gas is, from Eq. (12.11), Ḋw mSg Ṅg = WSw 2.78 × 10–6 J kg–1 s–1 × 0.15 × 10–3 kg = = 7.67 × 107 ip s–1. (12.12) 33 eV ip–1 × 1.60 × 10–19 J eV–1 × 1.03 Since the electronic charge is 1.60 × 10–19 C, the current is 7.67 × 107 × 1.60 × 10–19 = 1.23 × 10–11 C s–1 = 1.23 × 10–11 A. Simple electrometer circuits can be used to mea- sure currents smaller than 10–14 A, corresponding to dose rates much less than 10 mGy h–1 in this example. Note that Eq. (12.12) implies that the current is given by Ḋw meSg I = Ṅg e =. (12.13) WSw Expressing W = 33 J C–1 and remembering that the conversion factor from eV to J is numerically equal to the magnitude of the electronic charge e, we write, in SI units, Ḋw mSg I= (12.14) WSw 2.78 × 10–6 J kg–1 s–1 × 1.5 × 10–4 kg = = 1.23 × 10–11 A. (12.15) 33 J C–1 × 1.03 The arithmetic is thus shortened somewhat by using Eq. (12.14). However, one must be careful to keep units straight. 12.5 Measurement of X- and Gamma-Ray Dose Figure 12.4 shows the cross section of a spherical chamber of graphite that encloses CO2 gas. The chamber satisfies the Bragg–Gray conditions for photons over a wide energy range, and so the dose DC in the carbon wall can be obtained from the measured ionization of the CO2 by means of Eq. (12.11). Since carbon is a major constituent of soft tissue, the wall dose approximates that in soft tissue Dt. Calcu- lations show that, for photon energies between 0.2 MeV and 5 MeV, Dt = 1.1DC to within 5%. Thus soft-tissue dose can be measured with an accuracy of 5% with the carbon chamber. Generally, the dose in low-Z wall materials will approximate that in soft tissue over a wide range of photon energies. This fact leads to the widespread use of plas- tics and a number of other low-Z materials for gamma-dosimeter walls. The ratio of the absorbed dose in many materials relative to that in soft tissue has been cal- culated. Figure 12.5 shows several important examples. For photon energies from