Application of the Fano theorem in inhomogeneous media using a convolution algorithm

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Abstract
For photon fields, separate dose distribution kernels have been generated for charged particles produced in the first interaction, for single and multiple scattered photons, including bremsstrahlung and annihilation. These kernels are applied in absorbed dose calculations for radiotherapy treatment planning using a convolution technique. The vast amount of kernel data required for 3D calculations can be accurately generated out of a small subset, due to rotational symmetry. Due to the discrete sampling of both the irradiated object and the dose distribution kernels, application of the Fano theorem and O'Connor's scaling theorem is not possible without difficulties. The scaling process has been thoroughly investigated and a density dependent correction factor applied to the central kernel value has been derived. The calculated absorbed dose distributions were found to agree well with Monte Carlo calculated data using the EGS4 program.