title: Deterministic absorbed dose estimation in computed tomography using a discrete ordinates method.
abstract: OBJECTIVE
  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.
authors.affiliation: Nuclear Engineering, Missouri University of Science and Technology, Rolla, Missouri 65409.
authors.forename: Edward T
authors.initials: ET
authors.lastname: Norris
authors.affiliation: Nuclear Engineering, Missouri University of Science and Technology, Rolla, Missouri 65409.
authors.forename: Xin
authors.initials: X
authors.lastname: Liu
authors.affiliation: GE Healthcare, Waukesha, Wisconsin 53188.
authors.forename: Jiang
authors.initials: J
authors.lastname: Hsieh
mesh_terms: D003198:Computer Simulation; D008962:Models, Theoretical; D009010:Monte Carlo Method; D019047:Phantoms, Imaging; D017785:Photons; D011874:Radiometry / Q000379:methods*; D012984:Software; D014057:Tomography, X-Ray Computed / Q000295:instrumentation / Q000379:methods*