A fast, angle‐dependent, analytical model of CsI detector response for optimization of 3D x‐ray breast imaging systems

Purpose: Accurate models of detector blur are crucial for performing meaningful optimizations of three‐dimensional (3D) x‐ray breast imaging systems as well as for developing reconstruction algorithms that faithfully reproduce the imaged object anatomy. So far, x‐ray detector blur has either been ignored or modeled as a shift‐invariant symmetric function for these applications. The recent development of a Monte Carlo simulation package called MANTIS has allowed detailed modeling of these detector blur functions and demonstrated the magnitude of the anisotropy for both tomosynthesis and breast CT imaging systems. Despite the detailed results that MANTIS produces, the long simulation times required make inclusion of these results impractical in rigorous optimization and reconstruction algorithms. As a result, there is a need for detector blur models that can be rapidly generated. Methods: In this study, the authors have derived an analytical model for deterministic detector blur functions, referred to here as point response functions (PRFs), of columnar CsI phosphor screens. The analytical model is x‐ray energy and incidence angle dependent and draws on results from MANTIS to indirectly include complicated interactions that are not explicitly included in the mathematical model. Once the mathematical expression is derived, values of the coefficients are determined by a two‐dimensional (2D) fit to MANTIS ‐generated results based on a figure‐of‐merit (FOM) that measures the normalized differences between the MANTIS and analytical model results averaged over a region of interest. A smaller FOM indicates a better fit. This analysis was performed for a monochromatic x‐ray energy of 25 keV, a CsI scintillator thickness of 150 μ m , and four incidence angles (0°, 15°, 30°, and 45°). Results: The FOMs comparing the analytical model to MANTIS for these parameters were 0.1951 ± 0.0011 , 0.1915 ± 0.0014 , 0.2266 ± 0.0021 , and 0.2416 ± 0.0074 for 0°, 15°, 30°, and 45°, respectively. As a comparison, the same FOMs comparing MANTIS to 2D symmetric Gaussian fits to the zero‐angle PRF were 0.6234 ± 0.0020 , 0.9058 ± 0.0029 , 1.491 ± 0.012 , and 2.757 ± 0.039 for the same set of incidence angles. Therefore, the analytical model matches MANTIS results much better than a 2D symmetric Gaussian function. A comparison was also made against experimental data for a 170 μ m thick CsI screen and an x‐ray energy of 25.6 keV. The corresponding FOMs were 0.3457 ± 0.0036 , 0.3281 ± 0.0057 , 0.3422 ± 0.0023 , and 0.3677 ± 0.0041 for 0°, 15°, 30°, and 45°, respectively. In a previous study, FOMs comparing the same experimental data to MANTIS PRFs were found to be 0.2944 ± 0.0027 , 0.2387 ± 0.0039 , 0.2816 ± 0.0025 , and 0.2665 ± 0.0032 for the same set of incidence angles. Conclusions: The two sets of derived FOMs, comparing MANTIS ‐generated PRFs and experimental data to the analytical model, demonstrate that the analytical model is able to reproduce experimental data with a FOM of less than two times that comparing MANTIS and experimental data. This performance is achieved in less than one millionth the computation time required to generate a comparable PRF with MANTIS . Such small computation times will allow for the inclusion of detailed detector physics in rigorous optimization and reconstruction algorithms for 3D x‐ray breast imaging systems.