Bremsstrahlung Spectrum Reconstruction from Gradient Depth Dose Curves Obtained in a Water Phantom

Abstract

Megavoltage sources are commonly used in radiotherapy treatments, and the determination of the spectral distribution of a photon beam is extremely important for exact dosimetry and for the calculation of therapeutic dose distributions. Since direct measurements of the spectrum are very difficult, we present a technique to accurately calculate the bremsstrahlung spectra based on a numerical reconstruction upon central-axis depth dose data measured in a water tank using inverse methods.

The basic idea of this technique is that the measured depth dose curve can be expressed as a weighted superposition of monoenergetic depth dose curves. While traditional approaches directly use the measured depth dose data, we show the improvement of using the gradient of these data for reconstruction. The inverse problem in terms of gradients is shown to be markedly less ill-conditioned than the usual inverse problem. In each case, a Tikhonov regularization is introduced to minimize the effects of noise due to measurement and computation. We illustrate this theory to calculate a 6-MeV photon beam from an Elekta Precise radiotherapy unit utilizing the gradient of depth dose measurements in a water tank.