Monte Carlo kilovoltage X-ray tube simulation: A statistical analysis and compact simulation method.

INTRODUCTION: Monte Carlo (MC) simulations are a powerful tool for improving image quality in X-ray based imaging modalities. An accurate X-ray source model is essential to MC modeling for CBCT but can be difficult to implement on a GPU while maintaining efficiency and memory limitations. A statistical analysis of the photon distribution from a MC X-ray tube simulation is conducted in hopes of building a compact source model. MATERIALS & METHODS: MC simulations of an X-ray tube were carried out using BEAMnrc. The resulting photons were sorted into four categories: primary, scatter, off-focal radiation (OFR), and both (scatter and OFR). A statistical analysis of the photon components (energy, position, direction) was completed. A novel method for a compact (memory efficient) representation of the PHSP data was implemented and tested using different statistical based linear transformations (PCA, ZCA, ICA), as well as a geometrical transformation. RESULTS: The statistical analysis showed all photon groupings had strong correlations between position and direction, with the largest correlation in the primary data. The novel method was successful in compactly representing the primary (error < 2%) and scatter (error < 6%) photon groupings by reducing the component correlations. DISCUSSION & CONCLUSION: Statistical linear transforms provide a method of reducing the memory required to accurately simulate an X-ray source in a GPU MC system. If all photon types are required, the proposed method reduces the memory requirements by 3.8 times. When only primary and scatter data is needed, the memory requirement is reduced from gigabytes to kilobytes.

Efficient scatter distribution estimation and correction in CBCT using concurrent Monte Carlo fitting.

PURPOSE: X-ray scatter is a significant impediment to image quality improvements in cone-beam CT (CBCT). The authors present and demonstrate a novel scatter correction algorithm using a scatter estimation method that simultaneously combines multiple Monte Carlo (MC) CBCT simulations through the use of a concurrently evaluated fitting function, referred to as concurrent MC fitting (CMCF). METHODS: The CMCF method uses concurrently run MC CBCT scatter projection simulations that are a subset of the projection angles used in the projection set, P, to be corrected. The scattered photons reaching the detector in each MC simulation are simultaneously aggregated by an algorithm which computes the scatter detector response, SMC. SMC is fit to a function, SF, and if the fit of SF is within a specified goodness of fit (GOF), the simulations are terminated. The fit, SF, is then used to interpolate the scatter distribution over all pixel locations for every projection angle in the set P. The CMCF algorithm was tested using a frequency limited sum of sines and cosines as the fitting function on both simulated and measured data. The simulated data consisted of an anthropomorphic head and a pelvis phantom created from CT data, simulated with and without the use of a compensator. The measured data were a pelvis scan of a phantom and patient taken on an Elekta Synergy platform. The simulated data were used to evaluate various GOF metrics as well as determine a suitable fitness value. The simulated data were also used to quantitatively evaluate the image quality improvements provided by the CMCF method. A qualitative analysis was performed on the measured data by comparing the CMCF scatter corrected reconstruction to the original uncorrected and corrected by a constant scatter correction reconstruction, as well as a reconstruction created using a set of projections taken with a small cone angle. RESULTS: Pearson's correlation, r, proved to be a suitable GOF metric with strong correlation with the actual error of the scatter fit, SF. Fitting the scatter distribution to a limited sum of sine and cosine functions using a low-pass filtered fast Fourier transform provided a computationally efficient and accurate fit. The CMCF algorithm reduces the number of photon histories required by over four orders of magnitude. The simulated experiments showed that using a compensator reduced the computational time by a factor between 1.5 and 1.75. The scatter estimates for the simulated and measured data were computed between 35-93 s and 114-122 s, respectively, using 16 Intel Xeon cores (3.0 GHz). The CMCF scatter correction improved the contrast-to-noise ratio by 10%-50% and reduced the reconstruction error to under 3% for the simulated phantoms. CONCLUSIONS: The novel CMCF algorithm significantly reduces the computation time required to estimate the scatter distribution by reducing the statistical noise in the MC scatter estimate and limiting the number of projection angles that must be simulated. Using the scatter estimate provided by the CMCF algorithm to correct both simulated and real projection data showed improved reconstruction image quality.

Spatial frequency spectrum of the x-ray scatter distribution in CBCT projections.

PURPOSE: X-ray scatter is a source of significant image quality loss in cone-beam computed tomography (CBCT). The use of Monte Carlo (MC) simulations separating primary and scattered photons has allowed the structure and nature of the scatter distribution in CBCT to become better elucidated. This work seeks to quantify the structure and determine a suitable basis function for the scatter distribution by examining its spectral components using Fourier analysis. METHODS: The scatter distribution projection data were simulated using a CBCT MC model based on the EGSnrc code. CBCT projection data, with separated primary and scatter signal, were generated for a 30.6 cm diameter water cylinder [single angle projection with varying axis-to-detector distance (ADD) and bowtie filters] and two anthropomorphic phantoms (head and pelvis, 360 projections sampled every 1°, with and without a compensator). The Fourier transform of the resulting scatter distributions was computed and analyzed both qualitatively and quantitatively. A novel metric called the scatter frequency width (SFW) is introduced to determine the scatter distribution's frequency content. The frequency content results are used to determine a set basis functions, consisting of low-frequency sine and cosine functions, to fit and denoise the scatter distribution generated from MC simulations using a reduced number of photons and projections. The signal recovery is implemented using Fourier filtering (low-pass Butterworth filter) and interpolation. Estimates of the scatter distribution are used to correct and reconstruct simulated projections. RESULTS: The spatial and angular frequencies are contained within a maximum frequency of 0.1 cm(-1) and 7/(2π) rad(-1) for the imaging scenarios examined, with these values varying depending on the object and imaging setup (e.g., ADD and compensator). These data indicate spatial and angular sampling every 5 cm and π/7 rad (~25°) can be used to properly capture the scatter distribution, with reduced sampling possible depending on the imaging scenario. Using a low-pass Butterworth filter, tuned with the SFW values, to denoise the scatter projection data generated from MC simulations using 10(6) photons resulted in an error reduction of greater than 85% for the estimating scatter in single and multiple projections. Analysis showed that the use of a compensator helped reduce the error in estimating the scatter distribution from limited photon simulations by more than 37% when compared to the case without a compensator for the head and pelvis phantoms. Reconstructions of simulated head phantom projections corrected by the filtered and interpolated scatter estimates showed improvements in overall image quality. CONCLUSIONS: The spatial frequency content of the scatter distribution in CBCT is found to be contained within the low frequency domain. The frequency content is modulated both by object and imaging parameters (ADD and compensator). The low-frequency nature of the scatter distribution allows for a limited set of sine and cosine basis functions to be used to accurately represent the scatter signal in the presence of noise and reduced data sampling decreasing MC based scatter estimation time. Compensator induced modulation of the scatter distribution reduces the frequency content and improves the fitting results.

The effects of compensator and imaging geometry on the distribution of x-ray scatter in CBCT.

PURPOSE: X-ray scatter contributes significantly to image degradation in cone-beam CT (CBCT) reconstructed images in the form of CT number inaccuracy image artifacts and loss of contrast. The need for an understanding of the relationship between the scatter distribution and common imaging parameters (cone angle, air gap, filtration, object size) is an essential element to developing methods for efficiently correcting for the effects of scatter in CBCT. The first objective of this study is to validate the scatter distributions calculated using a CBCT Monte Carlo (MC) model against measured scatter estimates. The second objective is to use the CBCT MC model to investigate the effects of common imaging parameters and bowtie compensators on the resulting scatter distribution. METHODS: This investigation employs the use of a CBCT MC model, developed using the EGSnrc code, to simulate the primary and scatter fluence arriving at the detector. The simulation is validated against projection images, scatter-to-open field ratio (SOR), and scatter-to-primary ratio (SPR) measurements taken using a bench-top CBCT system. The CBCT MC model is used to simulate the scatter distribution arriving at the detector for different cone angles {1.4 degrees, 2.8 degrees, 5.7 degrees, and 11.3 degrees}, source-to-axis distances (SADs) {50, 75 and 100 cm}, and axis-to-detector distances (ADDs) {9, 18, 30, 44, 56 cm} for both a 16.4 and 30.6 cm diameter water cylinder. The effects of different bowtie filters are also simulated using the CBCT MC model for the aforementioned cylinder sizes. RESULTS: Profiles of the simulated and measured projection images agree within 6%. The measurements of the SOR and SPR, taken using beam stop techniques, show good agreement with the simulated results. Limitations of current beam stop techniques in estimating scatter profiles of objects with varying thickness are also demonstrated. A functional relationship between scatter (SOR, SPR) and air gap, cone angle is reported. The bowtie filter was found to have the beneficial effect of decreasing the magnitude of scatter in the projection images (SPR decreased by 56%) as well as altering the spatial distribution of the scatter. CONCLUSIONS: The CBCT MC model accurately simulates scatter and primary fluences in the CBCT imaging components and geometry. The CBCT MC model provides a useful tool in investigating the effects of varying CBCT imaging parameters on the scatter distribution. Increasing the air gap, decreasing the cone angle, and the use of bowtie filtration were all found to be effective ways to minimize scatter in CBCT. The bowtie filter was particularly effective in both minimizing the magnitude and modifying the spatial distribution of the scattered photons. This observation directs further research in optimizing bowtie filter design in an effort to minimize scatter induced artifacts.