# Assessment of a Patient Dose Monitoring System for Average
## 2 Materials and Methods
\begin{array}{l}D_{gN}=\gamma_{0}+\gamma_{1}\cdot X_{1}^{3}+\gamma_{2}\cdot X _{2}^{3}+\gamma_{3}\cdot X_{3}^{3}+\gamma_{4}\cdot X_{4}^{3}+\gamma_{5}\cdot X _{1}^{2}+\gamma_{6}\cdot X_{2}^{2}+\gamma_{7}\cdot X_{3}^{2}+\gamma_{8}\cdot X _{4}^{2}+\\ \gamma_{9}\cdot X_{1}^{2}\cdot X_{2}+\gamma_{10}\cdot X_{1}^{2}\cdot X_{3}+ \gamma_{11}\cdot X_{1}^{2}\cdot X_{4}+\gamma_{12}\cdot X_{1}\cdot X_{2}^{2}+ \gamma_{13}\cdot X_{1}\cdot X_{3}^{2}+\gamma_{14}\cdot X_{1}\cdot X_{2}^{4}+\\ \gamma_{15}\cdot X_{2}^{2}\cdot X_{3}+\gamma_{16}\cdot X_{2}^{2}\cdot X_{4}+ \gamma_{17}\cdot X_{2}\cdot X_{2}^{3}+\gamma_{18}\cdot X_{2}\cdot X_{4}^{2}+ \gamma_{19}\cdot X_{3}^{2}\cdot X_{4}+\gamma_{20}\cdot X_{3}\cdot X_{4}^{2}+ \\ \gamma_{21}\cdot X_{1}+\gamma_{22}\cdot X_{2}+\gamma_{23}\cdot X_{3}+\gamma_{24} \cdot X_{4}+\gamma_{25}\cdot X_{1}\cdot X_{2}+\gamma_{26}\cdot X_{1}\cdot X_{3 }+\gamma_{27}\cdot X_{1}\cdot X_{4}+\gamma_{28}\\ X_{2}\cdot X_{3}+\gamma_{29}\cdot X_{2}\cdot X_{4}+\gamma_{30}\cdot X_{3}\cdot X _{4}+\gamma_{31}\cdot X_{1}\cdot X_{2}\cdot X_{3}+\gamma_{32}\cdot X_{1}\cdot X _{2}\cdot X_{4}+\gamma_{33}\cdot X_{1}\cdot X_{3}\\ X_{4}+\gamma_{34}\cdot X_{2}\cdot X_{3}\cdot X_{4}\end{array}  \tag{5}\]  
where \(X_{1}\) = HVL (mm Al), \(X_{2}\) = thickness (mm), \(X_{3}\) = glandularity (%), and \(X_{4}\) = kVp. Polynomial regressions were performed using the curve-fitting function from the scipy.optimize module (version 1.7.3). F tests were conducted for both c and g fits to evaluate the overall significance of the regression models. The aim was to determine whether the chosen model significantly contributes to explaining the variability in the data compared to a simpler or null model. A notably high value of the F statistic leads to the rejection of the null hypothesis, indicating that at least one coefficient in the model significantly differs from zero at a statistically significant level. The uncertainties in the AGD calculation were estimated to be 14-20% [23; 29; 30], taking into account uncertainties in air kerma, HVL, compressed breast thickness, and breast glandularity. The calculated and displayed AGD values were compared with each other and with the achievable and acceptable dose levels according to guidelines for quality assurance in breast screening and diagnosis [16; 17; 18; 19; 20; 21; 22]. The breast density used in these AGD calculation formalisms represented a generalization of glandularity that was not based on actual breast composition, but rather on a polynomial fit, which estimated the average breast composition for different breast thicknesses in British women, grouped by two age ranges: 40-49 and 50-64 years [2]. To estimate the effective mammographic breast density, the images were processed using Laboratory for Individualized Breast Radiodensity Assessment (LIBRA) software (version 1.0.4; University of Pennsylvania, Philadelphia, PA, USA; [[https://librasoftwaregroup.com/](https://librasoftwaregroup.com/)]([https://librasoftwaregroup.com/](https://librasoftwaregroup.com/)) (accessed on 7 March 2024) [31; 32]. LIBRA uses a fully automated algorithm to calculate breast percentage density in digital mammography and provides breast segmentation masks, which indicate the dense (i.e., fibroglandular) regions in relation to the fatty tissue. Breast percentage density is defined as the ratio of dense tissue area to the total breast area, as seen in the mammographic image. The advantages of this glandularity estimation software are that it is freely available and works on both raw and post-processed images. LIBRA's performance has been validated for GE and Hologic systems by trained breast-imaging radiologists [31] and compared to other commercially available software [33]. A new version of the software called Deep-LIBRA is still under development and aims to provide a more precise estimate of glandularity based on deep learning and artificial intelligence [34].