Uncertainty estimation and statistical comparative methodology for mammography x-ray energy spectra

Abstract

Numerical models are an alternative to measurements of x-ray energy spectra when validated by comparative methods that assess the similarity of experimental and calculated spectra. In this work, we compared x-ray energy spectra using several methodologies and determined the methodology with highest statistical power among them. Experiments and Monte Carlo (MC) simulations were used to generate a set of 65 experimental and simulated x-ray mammography spectra pairs typically used in mammography applications. They were generated using Tungsten and Molybdenum targets and Molybdenum and Rhodium filters. The x-ray beams were transmitted through breast tissue equivalent material (bTEM) plates with different glandularities and thicknesses, and the transmitted beam was detected using solid-state x-ray spectrometry with a Cadmium Telluride (CdTe) diode. The MC simulations used the PENELOPE code. Additional uncertainties, beyond that from counting, were propagated using the MC method. Quantitative comparative methods based on the statistics, the first and second half-value layers, the mean energy, the effective energy, and the non-parametric u-test were applied and their specificity (true negative rate) was assessed. The polyenergetic normalized glandular dose (DgNp) to a 6 cm breast of 50/50 glandularity was derived from the spectra. In this work, the statistics attained the highest score; therefore, it is the most indicated metric for the x-ray energy spectra comparative evaluations. The contribution of the additional uncertainties was important, being responsible for up to 98% of the spectra total uncertainty and shifting the mean of the evaluated to 1.2(1), compatible with its expected value. The use of non-parametric test is discouraged by our results, since it failed to distinguish spectra pairs that resulted in up to 72% discrepant DgNp.