Deterministic Absorbed Dose Estimation in Computed Tomography Using a Discrete Ordinates Method


Purpose: Organ dose estimation for a patient undergoing computed tomography (CT) scanning is very important. Although Monte Carlo methods are considered gold-standard in patient dose estimation, the computation time required is formidable for routine clinical calculations. Here, the authors instigate a deterministic method for estimating an absorbed dose more efficiently.

Methods: Compared with current Monte Carlo methods, a more efficient approach to estimating the absorbed dose is to solve the linear Boltzmann equation numerically. In this study, an axial CT scan was modeled with a software package, Denovo, which solved the linear Boltzmann equation using the discrete ordinates method. The CT scanning configuration included 16 x-ray source positions, beam collimators, flat filters, and bowtie filters. The phantom was the standard 32 cm CT dose index (CTDI) phantom. Four different Denovo simulations were performed with different simulation parameters, including the number of quadrature sets and the order of Legendre polynomial expansions. A Monte Carlo simulation was also performed for benchmarking the Denovo simulations. A quantitative comparison was made of the simulation results obtained by the Denovo and the Monte Carlo methods.

Results: The difference in the simulation results of the discrete ordinates method and those of the Monte Carlo methods was found to be small, with a root-mean-square difference of around 2.4%. It was found that the discrete ordinates method, with a higher order of Legendre polynomial expansions, underestimated the absorbed dose near the center of the phantom (i.e., low dose region). Simulations of the quadrature set 8 and the first order of the Legendre polynomial expansions proved to be the most efficient computation method in the authors study. The single-thread computation time of the deterministic simulation of the quadrature set 8 and the first order of the Legendre polynomial expansions was 21 min on a personal computer.

Conclusions: The simulation results showed that the deterministic method can be effectively used to estimate the absorbed dose in a CTDI phantom. The accuracy of the discrete ordinates method was close to that of a Monte Carlo simulation, and the primary benefit of the discrete ordinates method lies in its rapid computation speed. It is expected that further optimization of this method in routine clinical CT dose estimation will improve its accuracy and speed.


Nuclear Engineering and Radiation Science


This work is supported by the Faculty Development Grant (Grant No. NRC-HQ-12-G-38-0039), from the U.S. Nuclear Regulatory Commission.

Keywords and Phrases

Article; Boltzmann equation; Computed tomography scanner; Computer assisted tomography; Computer program; Denovo simulation; Dosimetry; Human; Imaging phantom; Monte Carlo method; Quality control; Quantitative analysis; Simulation; X ray; Computer assisted tomography; Computer simulation; Devices; Evaluation study; Image quality; Photons; Procedures; Radiometry; Theoretical model; Computer Simulation; Models; Theoretical; Monte Carlo Method; Phantoms; Imaging; Software; Tomography; X-Ray Computed; Computed tomography; Deterministic simulation; Discrete ordinates; Patient dose

International Standard Serial Number (ISSN)

0094-2405; 2473-4209

Document Type

Article - Journal

Document Version


File Type





© 2015 American Association of Physicists in Medicine (AAPM), All rights reserved.

Publication Date

01 Jul 2015

PubMed ID