10‐MV x‐ray primary and scatter dose calculation using convolutions

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Abstract
Three-dimensional (3-D) forward and backward primary dose spread functions in water were developed for 10-MV X rays. Three-dimensional forward and backward primary dose spread functions in a heterogeneous medium were constructed from the ones in water using the density scaling theorem. Each of the forward and backward primary dose components were calculated using a method of convolving the primary water collision kerma distribution with the forward or backward primary dose spread function. Scatter dose was separated into forward and backward components. Each scatter dose component was calculated using a differential scatter method, a kind of convolution method, where the primary water collision kerma distribution was convolved with a differential scatter-maximum ratio or differential backscatter factor equation. From the dose calculation and measurement results obtained for water phantoms containing a cork or aluminum slab, it was found that the 3-D forward and backward primary dose functions were effective especially in regions where there was a loss of longitudinal and/or lateral electronic equilibrium.