A 10 MV x-ray zero-area tissue-maximum ratio expression constructed by taking into account depth and off-axis beam...

A 10 MV x-ray zero-area TMR (tissue-maximum ratio) expression was constructed using an attenuation coefficient expression which is a function of depth (z) and off-axis distance (r). The zero-area TMR expression can take into account depth and off-axis beam quality change. The construction is based on a method of convolving one-dimension forward and backward primary dose-spread functions with the primary water collision kerma. Additional information required to construct the zero-area TMR expression for a given fanline at an off-axis distance of r is the zero-area TMR value at z = 0 [Ds(r)] and the v(r) and w(r) values in the backward primary dose-spread function. It was found that the depth of peak zero-area TMR [zpeak(r)] decreases with increasing r and that for large depths, the zero-area TMR expression changes significantly as a function of r. Obtaining an accurate expression for zero-area TMR is important for accurate construction of the three-dimensional (3D) forward and backward primary dose-spread functions needed for a 3D convolution method.