Modeling Silicon Diode Dose Response in Radiotherapy Fields using Fluence Pencil Kernels

Abstract: In radiotherapy, cancer is treated with ionizing radiation, most commonly bremsstrahlung photons from electrons of several MeV. Secondary electrons produced in photon-interactions results in dose deposition. The treatment response is low for low doses, raises sharply for normal treatment doses and saturates at higher doses. This response pattern applies to both eradication of tumors and to complications in healthy tissues. Well controlled treatments require accurate dosimetry since the uncertainty in delivered dose will be magnified 1 to 5 times in treatment response variations. Techniques that superpose many small radiation fields to concentrate the dose to a localized target are becoming increasingly used. A detector with high spatial resolution suitable for such fields is a silicon diode. To maintain the current accuracy of the dosimetric calibration of 1.5%, diode measurements relative to this calibration should preferably be possible at 0.5% accuracy level.The main limitation of silicon diodes is their over-response to low-energy photons. This problem has been adressed with the insertion of a high atomic number filter in diodes. For modeling diode detector response one must quantify the spectral variations in the irradiated medium resulting from variations of the beam parameters. This requires understanding of the particle transport and can be achieved by Monte Carlo simulations. However, the small dimensions of the detector geometry compared to surrounding medium makes a direct application of Monte Carlo impractical due to the large amount of CPU time necessary to reach statistically satisfactory results.In this work a fast method for spectra calculations is used, based on superposition of mono-energetic fluence pencil kernels. Building on this base a general model for silicon response functions in photon fields is developed. The incident photons are bipartitioned into a low and a high energy component. The high energy part is treated with the Spencer-Attic cavity theory while the low energy part and scattered photons are treated with large cavity theory. The deviations from electron equilibrium are investigated and handled with correction factors. The result is used to correct unshielded diode measurements, with an overall uncertainty less than 0.5%, except for very small fields where the precision is around 1-2%, thus eliminating the need for less predictable shielded diodes for measurements in photon fields.