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

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[ D s ( 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[ z peak ( 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.