Molybdenum, rhodium, and tungsten anode spectral models using interpolating polynomials with application to mammography

Computer simulation is a convenient and frequently used tool in the study of x-ray mammography, for the design of novel detector systems, the evaluation of dose deposition, x-ray technique optimization, and other applications. An important component in the simulation process is the accurate computer-generation of x-ray spectra. A computer model for the generation of x-ray spectra in the mammographic energy range from 18 kV to 40 kV has been developed. The proposed model requires no assumptions concerning the physics of x-ray production in an x-ray tube, but rather makes use of x-ray spectra recently measured experimentally in the laboratories of the Center for Devices and Radiological Health. Using x-ray spectra measured for molybdenum, rhodium, and tungsten anode x-ray tubes at 13 different kV's (18, 20, 22, ..., 42 kV), a spectral model using interpolating polynomials was developed. At each energy in the spectrum, the x-ray photon fluence was fit using 2, 3, or 4 term (depending on the energy) polynomials as a function of the applied tube voltage (kV). Using the polynomial fit coefficients determined at each 0.5 keV interval in the x-ray spectrum, accurate x-ray spectra can be generated for any arbitrary kV between 18 and 40 kV. Each anode material (Mo, Rh, W) uses a different set of polynomial coefficients. The molybdenum anode spectral model using interpolating polynomials is given the acronym MASMIP, and the rhodium and tungsten spectral models are called RASMIP and TASMIP, respectively. It is shown that the mean differences in photon fluence calculated over the energy channels and over the kV range from 20 to 40 kV were -0.073% (sigma = 1.58%) for MASMIP, -0.145% (sigma = 1.263%) for RASMIP, and 0.611% (sigma = 2.07%) for TASMIP. The polynomial coefficients for all three models are given in an Appendix. A short C subroutine which uses the polynomial coefficients and generates x-ray spectra based on the proposed model is available on the World Wide Web at http:/(/)www.aip.org/epaps/epaps.html.