A model of primary and scattered photon fluence for mammographic x-ray image quantification.

We present an efficient method to calculate the primary and scattered x-ray photon fluence component of a mammographic image. This can be used for a range of clinically important purposes, including estimation of breast density, personalized image display, and quantitative mammogram analysis. The method is based on models of: the x-ray tube; the digital detector; and a novel ray tracer which models the diverging beam emanating from the focal spot. The tube model includes consideration of the anode heel effect, and empirical corrections for wear and manufacturing tolerances. The detector model is empirical, being based on a family of transfer functions that cover the range of beam qualities and compressed breast thicknesses which are encountered clinically. The scatter estimation utilizes optimal information sampling and interpolation (to yield a clinical usable computation time) of scatter calculated using fundamental physics relations. A scatter kernel arising around each primary ray is calculated, and these are summed by superposition to form the scatter image. Beam quality, spatial position in the field (in particular that arising at the air-boundary due to the depletion of scatter contribution from the surroundings), and the possible presence of a grid, are considered, as is tissue composition using an iterative refinement procedure. We present numerous validation results that use a purpose designed tissue equivalent step wedge phantom. The average differences between actual acquisitions and modelled pixel intensities observed across the adipose to fibroglandular attenuation range vary between 5% and 7%, depending on beam quality and, for a single beam quality are 2.09% and 3.36% respectively with and without a grid.