Article

# Evaluation of scatter-to-primary ratio, grid performance and normalized average glandular dose in mammography by Monte Carlo simulation including interference and energy broadening effects.

Departamento de Física e Matemática, FFCLRP, Universidade de São Paulo, 14040-901, Ribeirão Preto, São Paulo, Brazil.

Physics in Medicine and Biology (Impact Factor: 2.7). 08/2010; 55(15):4335-59. DOI: 10.1088/0031-9155/55/15/010 Source: PubMed

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**ABSTRACT:**In this study the generalized Modulation Transfer Function (GMTF) and the geometric sharpness (Sgeo) were used (i) to study the effects of various focal spot sizes (0.04 mm-0.3 mm), x-ray intensity distributions (Gaussian and double Gaussian), breast thicknesses (2-7 cm) and magnifications M (1.0-2.0) on the spatial resolution of an a-Se digital mammography system, (ii) to identify suitable focal spots for magnification mammography and (iii) derive optimum magnifications. For the calculation of GMTF the required components were: focal spot MTF, obtained from theory, detector MTF, scatter MTF and scatter fraction obtained from Monte Carlo simulations. The results showed that focal spots with sizes up to 0.18 mm are suitable for magnification mammography offering a GMTF which is >50% and >20% at the respective object frequencies of 6.5 mm(-1) and 9 mm(-1). Focal spots with sizes < 0.16 mm and Gaussian. intensity distribution, or sizes ≤ 0.1 mm and double Gaussian, offer a system resolution which improves or does not deteriorate with magnification for most object frequencies. For larger focal spots, i.e. 0.16-0.18 mm for a Gaussian and 0.12-0.18 mm for a double Gaussian. intensity distribution, optimum magnifications exist which depend on the object frequency and breast thickness. System resolution (in terms of Sgeo) is maximized at M = 1.8-2.0 (all breast thicknesses) for Gaussian intensity distribution, and at M = 1.4-1.6 (breast thicknesses ≤ 4 cm) and M = 1.6-1.8 (thicker breasts) for double Gaussian.Physica Medica 09/2013; · 1.17 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**One of the benefits of photon counting (PC) detectors over energy integrating (EI) detectors is the absence of many additive noise sources, such as electronic noise and secondary quantum noise. The purpose of this work is to demonstrate that thresholding voltage gains to detect individual x rays actually generates an unexpected source of white noise in photon counters. To distinguish the two detector types, their point spread function (PSF) is interpreted differently. The PSF of the energy integrating detector is treated as a weighting function for counting x rays, while the PSF of the photon counting detector is interpreted as a probability. Although this model ignores some subtleties of real imaging systems, such as scatter and the energy-dependent amplification of secondary quanta in indirect-converting detectors, it is useful for demonstrating fundamental differences between the two detector types. From first principles, the optical transfer function (OTF) is calculated as the continuous Fourier transform of the PSF, the noise power spectra (NPS) is determined by the discrete space Fourier transform (DSFT) of the autocovariance of signal intensity, and the detective quantum efficiency (DQE) is found from combined knowledge of the OTF and NPS. To illustrate the calculation of the transfer functions, the PSF is modeled as the convolution of a Gaussian with the product of rect functions. The Gaussian reflects the blurring of the x-ray converter, while the rect functions model the sampling of the detector. The transfer functions are first calculated assuming outside noise sources such as electronic noise and secondary quantum noise are negligible. It is demonstrated that while OTF is the same for two detector types possessing an equivalent PSF, a frequency-independent (i.e., "white") difference in their NPS exists such that NPS(PC) > or = NPS(EI) and hence DQE(PC) < or = DQE(EI). The necessary and sufficient condition for equality is that the PSF is a binary function given as zero or unity everywhere. In analyzing the model detector with Gaussian blurring, the difference in NPS and DQE between the two detector types is found to increase with the blurring of the x-ray converter. Ultimately, the expression for the additive white noise of the photon counter is compared against the expression for electronic noise and secondary quantum noise in an energy integrator. Thus, a method is provided to determine the average secondary quanta that the energy integrator must produce for each x ray to have superior DQE to a photon counter with the same PSF. This article develops analytical models of OTF, NPS, and DQE for energy integrating and photon counting digital x-ray detectors. While many subtleties of real imaging systems have not been modeled, this work is illustrative in demonstrating an additive source of white noise in photon counting detectors which has not yet been described in the literature. One benefit of this analysis is a framework for determining the average secondary quanta that an energy integrating detector must produce for each x ray to have superior DQE to competing photon counting technology.Medical Physics 12/2010; 37(12):6480-95. · 2.91 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**Purpose: The proliferation of cone-beam CT (CBCT) has created interest in performance optimization, with x-ray scatter identified among the main limitations to image quality. CBCT often contends with elevated scatter, but the wide variety of imaging geometry in different CBCT configurations suggests that not all configurations are affected to the same extent. Graphics processing unit (GPU) accelerated Monte Carlo (MC) simulations are employed over a range of imaging geometries to elucidate the factors governing scatter characteristics, efficacy of antiscatter grids, guide system design, and augment development of scatter correction.Methods: A MC x-ray simulator implemented on GPU was accelerated by inclusion of variance reduction techniques (interaction splitting, forced scattering, and forced detection) and extended to include x-ray spectra and analytical models of antiscatter grids and flat-panel detectors. The simulator was applied to small animal (SA), musculoskeletal (MSK) extremity, otolaryngology (Head), breast, interventional C-arm, and on-board (kilovoltage) linear accelerator (Linac) imaging, with an axis-to-detector distance (ADD) of 5, 12, 22, 32, 60, and 50 cm, respectively. Each configuration was modeled with and without an antiscatter grid and with (i) an elliptical cylinder varying 70-280 mm in major axis; and (ii) digital murine and anthropomorphic models. The effects of scatter were evaluated in terms of the angular distribution of scatter incident upon the detector, scatter-to-primary ratio (SPR), artifact magnitude, contrast, contrast-to-noise ratio (CNR), and visual assessment.Results: Variance reduction yielded improvements in MC simulation efficiency ranging from ∼17-fold (for SA CBCT) to ∼35-fold (for Head and C-arm), with the most significant acceleration due to interaction splitting (∼6 to ∼10-fold increase in efficiency). The benefit of a more extended geometry was evident by virtue of a larger air gap-e.g., for a 16 cm diameter object, the SPR reduced from 1.5 for ADD = 12 cm (MSK geometry) to 1.1 for ADD = 22 cm (Head) and to 0.5 for ADD = 60 cm (C-arm). Grid efficiency was higher for configurations with shorter air gap due to a broader angular distribution of scattered photons-e.g., scatter rejection factor ∼0.8 for MSK geometry versus ∼0.65 for C-arm. Grids reduced cupping for all configurations but had limited improvement on scatter-induced streaks and resulted in a loss of CNR for the SA, Breast, and C-arm. Relative contribution of forward-directed scatter increased with a grid (e.g., Rayleigh scatter fraction increasing from ∼0.15 without a grid to ∼0.25 with a grid for the MSK configuration), resulting in scatter distributions with greater spatial variation (the form of which depended on grid orientation).Conclusions: A fast MC simulator combining GPU acceleration with variance reduction provided a systematic examination of a range of CBCT configurations in relation to scatter, highlighting the magnitude and spatial uniformity of individual scatter components, illustrating tradeoffs in CNR and artifacts and identifying the system geometries for which grids are more beneficial (e.g., MSK) from those in which an extended geometry is the better defense (e.g., C-arm head imaging). Compact geometries with an antiscatter grid challenge assumptions of slowly varying scatter distributions due to increased contribution of Rayleigh scatter.Medical Physics 05/2013; 40(5):051915. · 2.91 Impact Factor

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