Dose spread functions in computed tomography: a Monte Carlo study

Abstract

Purpose: Current CT dosimetry employing CTDI methodology has come under fire in recent years, partially in response to the increasing width of collimated x-ray fields in modern CT scanners. This study was conducted to provide a better understanding of the radiation dose distributions in CT.

Methods: Monte Carlo simulations were used to evaluate radiation dose distributions along the z axis arising from CT imaging in cylindrical phantoms. Mathematical cylinders were simulated with compositions of water, polymethyl methacrylate (PMMA), and polyethylene. Cylinder diameters from 10 to 50 cm were studied. X-ray spectra typical of several CT manufacturers (80, 100, 120, and 140 kVp) were used. In addition to no bow tie filter, the head and body bow tie filters from modern General Electric and Siemens CT scanners were evaluated. Each cylinder was divided into three concentric regions of equal volume such that the energy deposited is proportional to dose for each region. Two additional dose assessment regions, central and edge locations 10 mm in diameter, were included for comparisons to CTDI100 measurements. Dose spread functions (DSFs) were computed for a wide number of imaging parameters.

Results: DSFs generally exhibit a biexponential falloff from the z=0 position. For a very narrow primary beam input (<< 1 mm), DSFs demonstrated significant low amplitude long range scatter dose tails. For body imaging conditions (30 cm diameter in water), the DSF at the center showed 160 mm at full width at tenth maximum (FWTM), while at the edge the FWTM was approximately 80 mm. Polyethylene phantoms exhibited wider DSFs than PMMA or water, as did higher tube voltages in any material. The FWTM were 80, 180, and 250 mm for 10, 30, and 50 cm phantom diameters, respectively, at the center in water at 120 kVp with a typical body bow tie filter. Scatter to primary dose ratios (SPRs) increased with phantom diameter from 4 at the center (1 cm diameter) for a 16 cm diameter cylinder to approximately 12.5 for a 32 cm diameter cylinder. The SPRs increased dramatically at the center of the phantom compared to the edge. For the three equal area regions, the edge to center SPRs for a 32 cm diameter phantom were approximately 1.8, 3.5, and 6.3, respectively.

Conclusions: DSFs demonstrate low amplitude long ranging tails which reach considerable distances in cylindrical phantoms. The buildup that results from these long-ranged tails increases at the center of the field (at z=0) with increasing scan length. The DSF distributions lend a better understanding of the trends in CT dose deposition over a range of relevant imaging parameters. The DSFs as well as other related data are available to interested parties using EPAPS at http://www.aip.org/pubservs/epaps.html.

Figures

Figure 1

(a) The geometry of Monte Carlo simulations is illustrated, showing the x-ray source with bow tie filter rotating around the cylindrical phantom. Five regions are indicated for dose assessment in the phantom, with the center and edge locations being the traditional location for pencil chamber measurements and regions R1, R2, and R3 are equal area regions (a central circle with two outer annuli). (b) The geometry in the z-axis dimension is illustrated, and the dose spread functions were computed along the z axis for each of the five regions center, edge, R1, R2, and R3.

Figure 2

The Monte Carlo relative dose results were compared to the published dose values for 16 cm (head) and 32 cm (body) diameter PMMA phantoms. The point with the arrow indicates the data point used for normalization. The Monte Carlo results (excluding the normalization point) were not significantly different from the published values. The solid squares were for the body center, open squares for body edge, solid triangles head center, and open triangles for head edge. The four points for each symbol correspond to 80, 100, 120, and 140 kVp, with these points increasing in this order from left to right for all symbols.

Figure 3

(a) The sDSFs for each of the three regions R1, R2, and R3 are illustrated. These data are normalized to the maximum value at the center of the sDSF to emphasize differences in shape (distribution). Only scatter data are shown. (b) The sDSFs are shown for three phantom compositions, for the center region (R1). These sDSFs were normalized at the maximum central value. It is seen that the sDSF for water and PMMA are very similar; however, that of polyethylene (“poly”) is broader due to its lower density and the corresponding longer range of x-ray photon penetration. (c) The sDSFs (normalized at the center maximum value) are shown for three different phantom diameters. The 50 cm diameter phantom demonstrates a much broader dose distribution than the 30 and 10 cm diameter phantom sDSFs. (d) The sDSFs are shown for three different bow tie conditions: (1) No bow tie filter, (2) a GE body bow tie filter, and (3) a Siemens’ body bow tie filter. With these values normalized at the center, it is seen that there is very little difference in sDSF for the two commercial bow tie filter, but both of these reduce the lateral (z dimension) spread of the sDSF compared to not using a bow tie filter. (e) The sDSFs are shown as a function of x-ray beam spectrum (80 and 140 kVp), and the higher energy spectrum demonstrates a slightly broader distribution as expected. (f) The sDSFs are shown for all five regions assessed in this study, the center and edge as well as regions R1, R2, and R3. For this 32 cm diameter phantom, the R1, R2, and R3 (which are equal volume) regions have 341 times the collection volume as compared to the center and edge locations. This is why the quantum noise is so apparent at the center and edge locations compared to R1–R3.

Figure 4

This figure illustrates the relative dose is a function of position for nine different scan lengths; 10, 50, 100, 150, 200, 300, 400, 500, and 600 mm. In addition to becoming wider, the amplitude of the dose distributions becomes greater as the width increases due to the influence of the very long low amplitude scatter tails in the DSFs, as shown in Fig. 3.

Figure 5

(a) The relative dose at the center of the scan field of view, as a function of scan length, is illustrated for the five regions in the phantom for a 32 cm water phantom imaged at 120 kVp with a Siemens scanner. (b) The rise to the equilibrium dose as a function of scan length is shown for a number of phantom diameters.

Figure 6

(a) The SPR is shown as a function of x-ray energy at each of the five regions (plus the mean SPR for the whole phantom) for a 32 cm PMMA phantom. Trend lines were included to smooth the noisier data of the center and edge regions. The SPR has a maximum around 60 keV. (b) The SPR is shown for a 16 cm PMMA phantom. The same trends in SPR are seen as in Fig. 6a; however, the overall SPR magnitude is lower in this smaller diameter phantom. (c) The SPR is shown as a function of the cylinder diameter for the five regions R1, R2, R3, center, and edge. The SPR here is integrated over infinite z [Eq. 1]. Typical body imaging conditions apply, with a water composition at 120 kVp.