The viability of ADVANTG deterministic method for synthetic radiography generation

Abstract

Fast simulation techniques to generate synthetic radiographic images of high resolution are helpful when new radiation imaging systems are designed. However, the standard stochastic approach requires lengthy run time with poorer statistics at higher resolution. The investigation of the viability of a deterministic approach to synthetic radiography image generation was explored. The aim was to analyze a computational time decrease over the stochastic method. ADVANTG was compared to MCNP in multiple scenarios including a small radiography system prototype, to simulate high resolution radiography images. By using ADVANTG deterministic code to simulate radiography images the computational time was found to decrease 10 to 13 times compared to the MCNP stochastic approach while retaining image quality.

Introduction

Radiation transport problems have been solved by using transport codes for decades. Of these transport codes MCNP (Monte Carlo N-Particle) stochastic method has been the most widely accepted transport code due to its proven ability to realistically model radiation transport problems. It has been used for design of detectors and X-ray sources as well [1]. While MCNP can certainly model a radiography system and create synthetic radiographs, the problem lies with the nature of the code. The main concern with the code is the computational time of a standard radiography simulation. An MCNP simulation of a radiographic image can take days to complete, which is problematic if time sensitive situations call for a more immediate result. It would be impractical to use MCNP to generate synthetic images for CT applications which require hundreds of projection images to reconstruct CT images. Stochastic methods also have another adverse effect of decrease in accuracy as the number of meshes increases while the number of photons for the simulation remains the same. In pursuit of finding methods to decrease the computational time while improving the accuracy for synthetic radiography generation a deterministic approach was researched and compared with MCNP.

A three dimensional discrete ordinates deterministic method discretizes the transport equation and solves a linear system of equations through iterations [2]. Discrete ordinates rely on quadrature sets which define the angular coordinates required to simulate the direction of a photon travel. In the case of ADVANTG, this direction is defined using polar and azimuthal angles. Eq. (1) is the general three-dimensional discrete ordinates equation [3].

$${\Omega }_n\ast \nabla \Psi (\overrightarrow{r},{\Omega }_n)+\sigma \left(\overrightarrow{r}\right)\Psi (\overrightarrow{r},{\Omega }_n)=q(\overrightarrow{r},{\Omega }_n)$$

where, $\Omega$ is a unit vector defined by the directional cosines, $q$ is the emission density, $\Psi$ is the angular flux, and $r$ is the direction in $x,y,z$.

The Stochastic method simulates individual particle behavior and uses a statistical sampling process based on random number generation. MCNP uses particle weights for computational efficiency, weights can be applied to particles to simulate a number of particles emitted from a source. A particle weight is essentially a correction for deviation from the physical transport [4]. Monte Carlo methods primarily rely on two base equations to solve the transport equation, the probability density function, Eq. (2), and the path length, Eq. (3).

$$g\left(F\right)=f\left(x\right)|dx∕dF|$$

$$f\left(x\right)=e^{-x}.$$

Using Eqs. (2), (3), MCNP can simulate particle track lengths from the mean free path and the probability of that interaction using the cumulative probability density function and solve for the flux of the system in particles/${\mathrm{cm}}^2∕\mathrm{s}$ [3].

In MCNP as the volume of a FMESH cell decreases the fraction of particles contributing to the flux decreases, as such the uncertainty will increase, thus Monte Carlo calculations may not be as appropriate as deterministic methods in these cases as describes in Ref. [3]. ADVANTG specifically uses Denovo, a 3-D discrete ordinates transport code developed at Oak Ridge National Laboratory [5]. ADVANTG discretizes the transport problem from a user supplied mesh grid and executes the deterministic code (Denovo) to solve the transport equation. ADVANTG solves the transport equation in multiple steps. First an MCNP first collision source is preformed to mitigate ray effects, then a ray trace using the specified polar and azimuthal angles for photon travel is performed. Finally Denovo iterates through a Krylov subspace solving a linear system of equations for each user defined energy group. ADVANTG was chosen over other deterministic methods such as DORT, TORT, or other proprietary codes due to the robustness and flexibility of the code. DORT only performed 2-D simulations and did not meet the requirement of 3-D transport modeling [6]. TORT, while being a 3-D discrete ordinates solver, is outdated and was replaced by Denovo from Oak Ridge National Laboratory in their Exnihilo package which is shared by ADVANTG [[7], [8]]. Other codes were proprietary or not cost effective for the specific application.