Breakdown of Bragg–Gray behaviour for low-density detectors under electronic disequilibrium conditions in small megavoltage photon fields

Abstract

In small photon fields ionisation chambers can exhibit large deviations from Bragg-Gray behaviour; the EGSnrc Monte Carlo (MC) code system has been employed to investigate this 'Bragg-Gray breakdown'. The total electron (+positron) fluence in small water and air cavities in a water phantom has been computed for a full linac beam model as well as for a point source spectrum for 6 MV and 15 MV qualities for field sizes from 0.25 × 0.25 cm(2) to 10 × 10 cm(2). A water-to-air perturbation factor has been derived as the ratio of total electron (+positron) fluence, integrated over all energies, in a tiny water volume to that in a 'PinPoint 3D-chamber-like' air cavity; for the 0.25 × 0.25 cm(2) field size the perturbation factors are 1.323 and 2.139 for 6 MV and 15 MV full linac geometries respectively. For the 15 MV full linac geometry for field sizes of 1 × 1 cm(2) and smaller not only the absolute magnitude but also the 'shape' of the total electron fluence spectrum in the air cavity is significantly different to that in the water 'cavity'. The physics of this 'Bragg-Gray breakdown' is fully explained, making reference to the Fano theorem. For the 15 MV full linac geometry in the 0.25 × 0.25 cm(2) field the directly computed MC dose ratio, water-to-air, differs by 5% from the product of the Spencer-Attix stopping-power ratio (SPR) and the perturbation factor; this 'difference' is explained by the difference in the shapes of the fluence spectra and is also formulated theoretically. We show that the dimensions of an air-cavity with a perturbation factor within 5% of unity would have to be impractically small in these highly non-equilibrium photon fields. In contrast the dose to water in a 0.25 × 0.25 cm(2) field derived by multiplying the dose in the single-crystal diamond dosimeter (SCDDo) by the Spencer-Attix ratio is within 2.9% of the dose computed directly in the water voxel for full linac geometry at both 6 and 15 MV, thereby demonstrating that this detector exhibits quasi Bragg-Gray behaviour over a wide range of field sizes and beam qualities.

Small field dosimetry: What have we learnt?

“…Similar data has been also been reported by other groups (16,19). Figure 1 shows data for Siemens and Elekta machine for various detectors.…”

“…However, when field size deceases to smaller the range of charged particle, electronic equilibrium cannot be established and Bragg-Cavity theory cannot be used. There had been surge of literature (12)(13)(14)(15)(16)(17)(18)(19) searching the solution in such situation. We will not dwell on cavity theory in this paper, however we refer to various published papers on this subject.…”

AAPM‐RSS Medical Physics Practice Guideline 9.a. for SRS‐SBRT

“…As a generalization, even micro‐ion‐chambers are large relative to the field sizes used in SRS‐SBRT due to violation of cavity theory 16, 17. Generalized approaches to the lack of lateral equilibrium and violation of cavity theory have been addressed in the literature 18, 19, 20, 21. Newer solid‐state microdetectors have become available such as diode, plastic scintillators, and synthetic microdiamonds that have shown appropriate characteristics for small‐field dosimetry.…”

Deriving detector‐specific correction factors for rectangular small fields using a scintillator detector

“…The three data points with the largest CE effects belonged to fields with either jaw set at 0.5 cm. This was due to the diminishing source occlusion as the field size exceeds 0.5 cm, as demonstrated by Kumar et al (8) Francescon et al (17) studied small rectangular field OFs in two linacs: Synergy (Elekta, Stockholm, Sweden) and Primus (Siemens, Munich, Germany). Similar CE effects were observed on these linacs as CE observed in this work (Varian Edge).…”

“…These measurements are challenging, and are fundamentally linked to the physics of small fields. Unlike traditional large fields, electronic equilibrium breaks down as the radiation field size drops below the range of the secondary electrons, invalidating the Bragg‐Gray conditions 8 , 9 . Source occlusion also takes place at small fields, resulting in a decrease in the dose deposited (4) .…”