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. 2008 Jun;35(6):2424-31.
doi: 10.1118/1.2921829.

Monte Carlo Evaluation of CTD(infinity) in Infinitely Long Cylinders of Water, Polyethylene and PMMA With Diameters From 10 Mm to 500 Mm

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Monte Carlo Evaluation of CTD(infinity) in Infinitely Long Cylinders of Water, Polyethylene and PMMA With Diameters From 10 Mm to 500 Mm

Hong Zhou et al. Med Phys. .
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Abstract

Monte Carlo simulations were used to evaluate the radiation dose to infinitely long cylinders of water, polyethylene, and poly(methylmethacrylate) (PMMA) from 10 to 500 mm in diameter. Radiation doses were computed by simulating a 10 mm divergent primary beam striking the cylinder at z = 0, and the scattered radiation in the -z and +z directions was integrated out to infinity. Doses were assessed using the total energy deposited divided by the mass of the 10-mm-thick volume of material in the primary beam. This approach is consistent with the notion of the computed tomography dose index (CTDI) integrated over infinite z, which is equivalent to the dose near the center of an infinitely long CT scan. Monoenergetic x-ray beams were studied from 5 to 140 keV, allowing polyenergetic x-ray spectra to be evaluated using a weighted average. The radiation dose for a 10-mm-thick CT slice was assessed at the center, edge, and over the entire diameter of the phantom. The geometry of a commercial CT scanner was simulated, and the computed results were in good agreement with measured doses. The absorbed dose in water for 120 kVp x-ray spectrum with no bow tie filter for a 50 mm cylinder diameter was about 1.2 mGy per mGy air kerma at isocenter for both the peripheral and center regions, and dropped to 0.84 mGy/mGy for a 500-mm-diam water phantom at the periphery, where the corresponding value for the center location was 0.19 mGy/mGy. The influence of phantom composition was studied. For a diameter of 100 mm, the dose coefficients were 1.23 for water, 1.02 for PMMA, and 0.94 for polyethylene (at 120 kVp). For larger diameter phantoms, the order changed-for a 400 mm phantom, the dose coefficient of polyethylene (0.25) was greater than water (0.21) and PMMA (0.16). The influence of the head and body bow tie filters was also studied. For the peripheral location, the dose coefficients when no bow tie filter was used were high (e.g., for a water phantom at 120 kVp at a diameter of 300 mm, the dose coefficient was 0.97). The body bow tie filter reduces this value to 0.62, and the head bow tie filter (which is not actually designed to be used for a 300 mm object) reduces the dose coefficient to 0.42. The dose in CT is delivered both by the absorption of primary and scattered x-ray photons, and at the center of a water cylinder the ratio of scatter to primary (SPR) doses increased steadily with cylinder diameter. For water, a 120 kVp spectrum and a cylinder diameter of 200 mm, the SPR was 4, and this value grew to 9 for a diameter of 350 mm and to over 16 for a 500-mm-diam cylinder. A freely available spreadsheet was developed to allow the computation of radiation dose as a function of object diameter (10-500 mm), composition (water, polyethylene, PMMA), and beam energy (10-140 keV, 40-140 kVp).

Figures

Figure 1
Figure 1
(a) The geometry of the computer simulations is shown. PMMA, polyethylene, and water were used as phantom compositions. The simulations included the head and body bow tie filters, as well is no bow tie filter. Dose was computed at the center of the cylinder, at the edge, and over the entire 10-mm-thick slab of the cylinder as well. (b) The x, y, z coordinate system typically used in CT is illustrated. The doses computed in this research involved the smooth rotation of the x-ray source 2π around the cylinder, with no advancement along the z axis. The locations of the center, edge, and entire CT volumes for dose computation are shown, and in each case these cylindrical volumes were 10 mm long in the z dimension.
Figure 2
Figure 2
(a) Comparisons are shown between the ImPACT CTDI100 values for the head phantom (16-cm-diam PMMA) and head bow tie filter for the GE Lightspeed 16 slice scanner, and those determined in this work by Monte Carlo evaluation. Good agreement is seen, although there is a slight upward bias by the Monte Carlo data, averaging 8.2%. The four values for each location correspond to 80, 100, 120, and 140 kVp—increasing kVp towards the right in the graph. (b) The CTDI100 values from ImPACT are compared for the body phantom (32-cm-diam PMMA) and body bow tie filter against the Monte Carlo determined values, and again good correspondence between the measured and simulated values is observed. The differences between the CTDI100 values for the body average 4.9%.
Figure 3
Figure 3
The dose (CTDI) in infinitely long water cylinders as a function of diameter for a 120 kVp (HVL=8.3 mm AI) x-ray spectrum, with the body bow tie filter, is shown. The dose coefficients at the edge, center, and averaged over the entirety of the CT slice are illustrated.
Figure 4
Figure 4
The dose (CTDI) as a function of diameter is shown for the periphery and the center regions, for infinitely long water and PMMA cylinders. These data are for a 120 kVp spectrum (HVL=8.3 mm AI). No bow tie filter was used.
Figure 5
Figure 5
This figure illustrates the effect of composition on dose (CTDI) in infinitely long cylindrical phantoms. At 120 kVp and with the body bow tie filter, these curves correspond to the center location in the phantom.
Figure 6
Figure 6
Doses (CTDI) in infinitely long cylindrical phantoms for PMMA and with the body bow tie filter are shown for different monoenergetic x-ray beams. The ability of the lower energy photons to penetrate to the center to contribute to dose decreases with diameter, as expected, however even the 30 keV beam is capable of delivering reasonable radiation dose levels to the edge location on the phantom. The higher energy x-ray beams produce more scattered radiation, and hence a “bump” in the dose coefficient is seen for diameters from 10 to 70 mm.
Figure 7
Figure 7
The phantom dose coefficients (CTDI) for water with no bow tie filter as a function of polyenergetic x-ray spectra at different tube voltages are shown. These doses are computed to the entire diameter of the cylinder, not the edge or center. The spectral filtration used for these data corresponded to the amount of Al necessary to deliver the HVLs reported previously see Ref. for this scanner.
Figure 8
Figure 8
The effect of the bow tie filter is illustrated in water at 120 kVp. Dose coefficients (CTDI) for infinitely long phantoms at the periphery of the cylinder are plotted. The head bow tie filter, being designed for typical 170-mm-diam heads, demonstrates more aggressive attenuation as a function of cylinder diameter, as expected.
Figure 9
Figure 9
This figure illustrates the effect of “chamber length” for a 120 kVp spectrum in PMMA with a body bow tie filter. The length of the phantom in all cases is infinite, while the length of integration was 10 mm, 100 mm, and infinite. Thus, this graph compares CTDI10mm, CTDI10mm, and CTDI for the central measurement position. The inset shows the percent increase in dose coefficient as a function of cylinder diameter, from CTDI100 to CTDI.
Figure 10
Figure 10
The relative contribution to CTDI from scatter and primary photon interactions is illustrated as the scatter to primary ratio (SPR), for three different radii (see inset). The relative dose from scatter is larger in the center of the cylinder compared to the edge, due to solid angle considerations.
Figure 11
Figure 11
A picture of the control box for the dose calculator macro is shown.

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