chapter 2. dosimetric principles, quantities and units - IRSN

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Chapter 2. Dosimetric Principles, Quantities and Units• Multiplying the collision kerma by ( e/W )air, the number of coulombs of chargecreated per joule of energy deposited, gives the charge created per unit mass of airor exposure:X( K )⎛e⎞=col air ⎜ ⎟Wair⎝⎠. (2.29)• The relationship between total kerma and exposure is obtained by combiningEq. 2.25 and Eq. 2.29 to get:Kair⎛W⎝ e⎞air= X ⎜ ⎟⎠11−g. (2.30)2.8 CAVITY THEORYIn order to measure the absorbed dose in a medium, it is necessary to introduce a radiationsensitive device (dosimeter) into the medium. Generally, the sensitive medium of thedosimeter will not be of the same material as the medium in which it is embedded. Cavitytheory relates the absorbed dose in the dosimeter sensitive medium (cavity) to the absorbeddose in the surrounding medium containing the cavity. Cavity sizes are referred to as small,intermediate or large in comparison with the ranges of secondary charged particles producedby photons in the cavity medium. If, for example, the range of charged particles (electrons) ismuch larger than the cavity dimensions, the cavity is regarded as small. Various cavitytheories for photon beams have been developed depending on the size of the cavity, such asthe Bragg-Gray and Spencer-Attix theories for small cavities and the Burlin theory for cavitiesof intermediate sizes.2.8.1. The Bragg-Gray cavity theoryThe Bragg-Gray (B-G) cavity theory was the first cavity theory developed to provide arelationship between absorbed dose in a dosimeter and the absorbed dose in the mediumcontaining the dosimeter.• The conditions for application of the Bragg-Gray cavity theory are:(1) the cavity must be small when compared with the range of charged particlesincident on it so that its presence does not perturb the fluence of chargedparticles in the medium;(2) the absorbed dose in the cavity is deposited solely by charged particlescrossing it, i.e., photon interactions in the cavity are assumed negligible andthus ignored.The result of condition (1) is that the electron fluences in Eq. (2.22) are the sameand equal to the equilibrium fluence established in the surrounding medium. Thiscondition can only be valid in regions of CPE or TCPE. In addition, the presenceof a cavity always causes some degree of fluence perturbation that requires theintroduction of a fluence perturbation correction factor.50
Review of Radiation Oncology Physics: A Handbook for Teachers and StudentsCondition (2) implies that all electrons depositing the dose inside the cavity areproduced outside the cavity and completely cross the cavity. Therefore, nosecondary electrons are produced inside the cavity and no electrons stop withinthe cavity.• Under these two conditions, according to the Bragg-Gray cavity theory, the doseto the medium D med is related to the dose in the cavity D cav as follows:Dmed⎛S⎞= Dcav⎜ ⎟⎝ρ⎠med,cav, (2.31)where (S / ρ) med,cavis the ratio of the average unrestricted mass collision stoppingpowers of the medium and cavity. The use of unrestricted stopping powers rulesout the production of secondary charged particles (or delta electrons) in the cavityand the medium.• Although the cavity size is not explicitly taken into account in the Bragg-Graycavity theory, the fulfillment of the two Bragg-Gray conditions will depend on thecavity size which is based on the range of the electrons in the cavity medium, thecavity medium, and electron energy. A cavity that qualifies as a Bragg-Graycavity for high energy photon beams, for example, may not behave as a Bragg-Gray cavity in a medium-energy or low-energy x-ray beam.2.8.2. The Spencer-Attix cavity theory• The Bragg-Gray cavity theory does not take into account the creation ofsecondary (delta) electrons generated as a result of the slowing down of theprimary electrons in the sensitive volume of the dosimeter. The Spencer-Attix (S-A) cavity theory is a more general formulation that accounts for the creation ofthese electrons which have sufficient energy to produce further ionisation on theirown account. Some of these electrons released in the gas cavity would havesufficient energy to escape from the cavity carrying some of their energy withthem. This reduces the energy absorbed in the cavity and requires modification tothe stopping power of the gas. The Spencer-Attix cavity theory operates under thetwo Bragg-Gray conditions, however, these conditions now even apply to thesecondary particle fluence in addition to the primary charged particle fluence.• The secondary electron fluence in the Spencer-Attix theory is divided into twocomponents based on a user-defined energy threshold ∆. Secondary electronswith kinetic energies KE less than ∆ are considered slow electrons that deposittheir energy locally; secondary electrons with energies larger than or equal to ∆are considered “fast” (slowing down) electrons and are part of the electronspectrum. Consequently, this spectrum has a low energy threshold of ∆ and ahigh-energy threshold of KEo where KE o represents the initial electron kineticenergy. Since the lowest energy in the spectrum is ∆, the maximum energy loss ofa fast electron with kinetic energy KE larger than or equal to 2∆ cannot be largerthan ∆ and the maximum energy loss of a fast electron with kinetic energy lessthan 2∆ cannot be larger than KE/2 (where ∆ ≤ KE < 2∆).51
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