Title:
Monte Carlo assessment of CT dose equilibration in PMMA and water cylinders with diameters from 6 to 55 cm.

Abstract:
In multidetector CT, the dose integral DIL of single scan dose profile over the integration interval (-L/2, L/2) can predict the accumulated dose DL(0) at the center of the scan range (-L/2, L/2) for a helical scan of pitch = 1. Both DIL and DL(0) increase with L until the limiting levels (DI∞ and Deq) are reached. The DL(0) equilibration is related to the DIL equilibration. The aim of this study was to evaluate the DIL∕DI∞ growth curve, and its variations with factors such as phantom diameter, phantom axis (center or periphery), material (PMMA or water), tube voltage, and bowtie filter (head or body).
A Geant4-based Monte Carlo program was used to simulate single axial scans on a clinical CT scanner, and to compute axial dose profiles in the cylinders of 90 cm in length, and 6-50 cm (PMMA) and 6-55 cm (water) in diameters. DIL∕DI∞ ratios were calculated over a range of integration lengths, and were fitted to a mathematical model: f(L) = 1 - α × exp[ - (L/d)(n)], where α, d, and n were fitting parameters. The minimum length required for DIL to approach within 2% of DI∞ was referred to as the equilibrium length Leq. It could be directly derived from data, and was also calculated from the fits.
The Leq results of the above two approaches were consistent (deviation: 1.4% on average, and 3.6% maximum). When the other conditions (such as tube voltage, bowtie filter, and phantom material) were the same, DI∞ increased with the reduced phantom diameters. The center/periphery DI∞ ratio was greater than 1 for small phantoms, and increased with larger phantoms until their diameters were above about 16 cm. Dose to water was substantially higher than that to PMMA, especially at the centers of large phantoms. As phantom diameter increased, α, n, and Leq increased on the central axis, and initially increased and then saturated [α ≈ 0.555 (PMMA and water), n ≈ 0.81 (PMMA) and 0.80 (water), and Leq ≈ 29 cm (PMMA) and 30 cm (water)] on the peripheral axis. Bowtie filter and tube voltage affected dose, but had small effects on α, n, and Leq. Leq was almost constant on the central or peripheral phantom axis for beam widths from 0.1 to 40 mm.
The mathematical model can represent the DIL∕DI∞ curve from a single axial CT scan. Generally, n ≠ 1. The equilibrium dose, α, n, and Leq exhibit strong dependencies on phantom diameter and location in the phantom. On the other hand, α, n, and Leq have relatively weak dependencies on material (PMMA or water), tube voltage (80-140 kVp), and bowtie filter, and Leq is also insensitive to beam width (≤4 cm). A weak dependency of the DIL∕DI∞ curve on CT scanner using 80-140 kVp and beam width up to 4 cm is consistent with the results of this study and previous publications. The dose equilibration data provided in this paper can be useful for CT dose evaluation. A framework is presented for assessing dose at any point in infinitely long PMMA and water cylinders undergoing multidetector CT examinations.