Dose reduction potential in diagnostic single energy CT through patient‐specific prefilters and a wider range of tube voltages

Abstract

Purpose

Various studies have demonstrated that additional prefilters and/or reduced tube voltages have the potential to significantly increase the contrast‐to‐noise ratios at unit dose (CNRDs) and thereby to significantly reduce patient dose in clinical CT. An exhaustive analysis, accounting for a wide range of filter thicknesses and a wide range of tube voltages extending beyond the 70 to 150 kV range of today's CT systems, including their specific choice depending on the patient size, is, however, missing. Therefore, this work analyzes the dose reduction potential for patient‐specific selectable prefilters combined with a wider range of tube voltages. We do so for soft tissue and iodine contrast in single energy CT. The findings may be helpful to guide further developments of x‐ray tubes and automatic filter changers.

Methods

CT acquisitions were simulated for different patient sizes (semianthropomorphic phantoms for child, adult, and obese patients), tube voltages (35–150 kV), prefilter materials (tin and copper), and prefilter thicknesses (up to 5 mm). For each acquisition soft tissue and iodine CNRDs were determined. Dose was calculated using Monte Carlo simulations of a computed tomography dose index (CTDI) phantom. CNRD values of acquisitions with different parameters were used to evaluate dose reduction.

Results

Dose reduction through patient‐specific prefilters depends on patient size and available tube current among others. With an available tube current time product of 1000 mAs dose reductions of 17% for the child, 32% for the adult and 29% for the obese phantom were achieved for soft tissue contrast. For iodine contrast dose reductions were 57%, 49%, and 39% for child, adult, and obese phantoms, respectively. Here, a tube voltage range extended to lower kV is important.

Conclusions

Substantial dose reduction can be achieved by utilizing patient‐specific prefilters. Tube voltages lower than 70 kV are beneficial for dose reduction with iodine contrast, especially for small patients. The optimal implementation of patient‐specific prefilters benefits from higher tube power. Tin prefilters should be available in 0.1 mm steps or lower, copper prefilter in 0.3 mm steps or lower. At least 10 different prefilter thicknesses should be used to cover the dose optima of all investigated patient sizes and contrast mechanisms. In many cases it would be advantageous to adapt the prefilter thickness rather than the tube current to the patient size, that is, to always use the maximum available tube current and to control the exposure by adjusting the thickness of the prefilter.

1. INTRODUCTION

In diagnostic CT changeable prefilters are mainly used in dual energy CT to achieve a better spectral separation. ¹ Low‐energy photons are filtered stronger than high‐energy photons. ² By using additional prefiltration for the high‐energy spectrum the mean energy of the high‐energy spectrum increases and the overlay with the low‐energy spectrum decreases. ¹ This property is also beneficial in single energy CT. Since low‐energy photons are mostly absorbed in the patient and therefore do not contribute to the CT image, patient dose can be reduced by additional prefiltration. ² Beam hardening artifacts can be reduced as well. ³ Due to the additional filtration tube currents need to be increased to compensate for the loss of photons. ²

Various patient studies have been conducted to investigate dose reduction by using additional tin filters, which are available between 100 kV and 150 kV in multiple Siemens systems. Leyendecker et al. ⁴ were able to achieve 81% dose reduction in contrast‐enhanced abdominal CT. Weis et al. ⁵ found 77% dose reduction in pediatric chest CT. In abdominal scans for urinary stone detection 22% dose reduction was achieved by Dewes et al. ⁶ Mozaffary et al. ⁷ found 28% to 66% dose reduction in CT scans for urinary stone disease. All four studies used the Siemens Force system with its 0.6 mm tin filter. Lee et al. ⁸ found 50% dose reduction in cervical spine CT using the 0.4 mm tin filter of the Siemens SOMATOM Drive. The Siemens SOMATOM Definition Flash also utilizes a 0.4 mm tin filter and was used for validation measurements in our study. Gordic et al. ⁹ showed that low‐dose pulmonary dose detection is possible with 100 kV tin filtered scans. The phantom study conducted by Greffier et al. ¹⁰ showed improvements in image quality for lytic and sclerotic bone lesion, pulmonary ground glass opacity, and high contrast pulmonary lesion detection with the tin filter of the Siemens SOMATOM Force system. Many phantom studies have been conducted to determine the effects of changes in tube voltage and optimal tube voltage on dose depending on patient size and contrast modality. ¹¹ , ¹² , ¹³ , ¹⁴ We aim to combine both optimization of the filter thickness and the tube current and quantify the dose saving potential of this approach depending on the patient size. Most importantly, our study should exceed the range of filter thicknesses, tube voltages, and tube current levels covered in today's clinical CTs. This is the only way to identify new dose reduction options and motivate manufacturers to make hardware adjustments to their CT systems.

The k‐edge energy of tin is 29.20 keV. ¹⁵ Just above the k‐edge the x‐ray attenuation coefficient increases. After this increase the attenuation coefficient decreases monotonously in the energy regime relevant for CT (attenuation coefficients are shown in Figure 4). Since a monotonously decreasing attenuation coefficient results in increasing mean spectral energy, materials with lower k‐edge energy could be beneficial for dose reduction in CT scans with low tube voltage. As an alternative to tin copper was chosen. Copper has a much lower k‐edge energy, namely, 8.98 keV. ¹⁵ Dose reduction capabilities of copper prefilters were demonstrated for breast CT by Hernandez et al. ¹⁶ Instead of copper, one can choose any other material that has no k‐edges in the relevant energy range, say, between 20 keV and 200 keV. We have chosen copper here because it is easily available and easy to process. Using a different material without k‐edge in the relevant energy range should not significantly change the quantitative results reported here.

FIGURE 4.

Attenuation coefficients for water, iodine water mixture (mass mixture of 0.6% iodine and 99.4% water), copper, and tin

The aim of this study is to find out how much dose reduction with patient‐specific prefiltration may be achieved if vendors adopted the concept of patient‐specific prefiltration. Benefits of a further x‐ray tube power increase are investigated as well. To achieve our aim we simulate CT acquisitions for different patient sizes, tube voltages, and filter thicknesses. This allows us to determine the dose reduction potential of additional prefiltration in single energy CT, and to calculate the tube current increase that is necessary to compensate for the higher absorption.

While our evaluation focuses on dose reduction and dose reduction values, we here do not want to give the impression that the filter technology shall be used exclusively for dose reduction. The dose savings can equally well be used to increase the image quality. Whether a dose reduction is called for or a better image quality depends on the application. We focus here on the dose reduction potential, as this figure is more tangible to the reader than improvements in image quality.

2. MATERIALS AND METHODS

2.1. Spectral filtration in CT imaging

Before the x‐ray spectrum generated in the x‐ray anode reaches the patient it passes through several layers of material. These materials attenuate the spectrum resulting in a decrease photon flux depending on the photon energy. Each CT scanner has intrinsic filtration, for example, from the anode itself and from the x‐ray exit window. Additional filtration is used to filter out low‐energy photons, which otherwise would be mostly absorbed in the patient contributing little to the image and increasing patient skin dose.

More photons traveling through the center of the patient are absorbed than photons passing through the patient periphery due to the longer path length inside the patient. As a result image noise in the center is higher than at the periphery. Since a more homogeneous noise distribution is preferred, bowtie filters are used to filter the spectrum depending on the angle $\beta$ in the fan. In the fan center, at $\beta =0$, the bowtie thickness is smallest resulting in the lowest filtration and the highest photon flux. Going off‐center, that is, toward larger $|\beta |$, bowtie thickness increases resulting in stronger filtration and lower photon flux. Consequently the bowtie filtration compensates absorption differences and results in a more homogeneous noise distribution in the CT image. Shaped filtration that changes its shape as a function of the patient and as a function of the scanner's rotation angle $\alpha$ are under development but are not yet deployed clinically. ¹⁷

Some CT systems have additional changeable prefilters, which can be used on a case‐by‐case basis. Larger patients require higher photon flux and consequently higher tube current, which may prohibit the use of the additional prefilter due to tube current limitations. Recent CT systems address this issue with increased mAs limits and therefore enable the use of tin prefiltration also for larger patients. Small patients on the other hand require less tube current and therefore prefiltration could be increased. As we will show in this paper, the prefilter thickness should indeed be increased. Moreover, different body regions differ in x‐ray attenuation and therefore in required tube current. This would make an adaptive prefiltration useful.

Our work only deals with the above‐mentioned additional prefiltration. For convenience we will refer to it as prefilter or prefiltration in the following.

2.2. CT scan simulation

The simulated scanner corresponds to the Siemens SOMATOM Definition Flash CT scanner (Siemens Healthineers, Forchheim, Germany), which is available at our institution for validation measurements. Scanner parameters and geometry were chosen accordingly and are given in Table 1. We simulated polychromatic raw data corresponding to a circle scan.

TABLE 1.

Parameters used in the simulations

Field of view diameter	500.0 mm
Image size in pixels	$1024\times 1024$
Source isocenter distance $R_{\mathrm{F}}$	595.0 mm
Source detector distance $R_{\mathrm{FD}}$	1085.6 mm
Number of detector pixels	736
Detector pixel size	$1.3\mathrm{mm}\times 1.3\mathrm{mm}$
Number of source angles	1152
Detector material	GOS 1.4 mm
Anode material	W
Intrinsic prefilter	Al 6.0 mm
Patient‐specific prefilter	Sn 0.0 to 2.0 mm
	or Cu 0.0 to 5.0 mm
Bowtie filter	Teflon, 0.0 to 38.5 mm

The x‐ray spectrum emitted by the source was simulated using the semiempirical model of Tucker et al. ¹⁸ and discretized in 1 keV bins. The detector was simulated as an energy integrating (EI) detector with a 1.4 mm gadolinium oxysulfide (GOS) layer. The detected signal is the sum over all energies of

$$\begin{array}{ccc}\hfill S(\alpha ,\beta ,E)& =& E(1-e^{-{\mu }_{\mathrm{GOS}}(E)d_{\mathrm{GOS}}})\mathrm{Object}(\alpha ,\beta ,E)\hfill \\ & & \mathrm{Filters}(\beta ,E)\mathrm{Spectrum}(E).\hfill \end{array}$$ (1)

Here, $E$ is the x‐ray energy, $\alpha$ is the projection angle, $\beta$ is the angle within the fan, ${\mu }_{\mathrm{GOS}}(E)$ is the x‐ray absorption coefficient of the sensor material, and $d_{\mathrm{GOS}}$ is the detector thickness. The remaining terms are the object attenuation (here: simulated absorber layers or phantoms), the attenuation of the intrinsic, the bowtie and the additional prefiltration, and the final term is the Tucker spectrum. The filter attenuation is split into three parts

$$\begin{array}{c}\hfill \mathrm{Filters}(\beta ,E)=e^{-\mathrm{Intrinsic}(\beta ,E)}{e}^{-\mathrm{Bowtie}(\beta ,E)}{e}^{-\mathrm{Prefilter}(\beta ,E)}.\end{array}$$ (2)

Intrinsic absorption was simulated as a 6 mm aluminium layer. Additional tin and copper prefilters were used. Additional prefiltration was simulated from 0 to 2 mm for tin and 0 to 5 mm for copper in 0.1 mm steps. Attenuation coefficients for the different materials were taken from Hubbell et al. ¹⁵ Since no specific information on the bowtie filter was available to us, its thickness profile $d_{\mathrm{Bowtie}}(\beta )$ was estimated with the projection data of 747 air images acquired with the Definition Flash CT System. These images were acquired with an empty gantry (i.e., air scans) at a tube voltage of 100 kV, a tube current time product of 100 mAs and a rotation time of 285 ms. Since the variance profile $\mathrm{Var}(\frac{S(\beta )}{S_0(\beta )})$ is related to the bowtie profile with

$$\mathrm{Var}\left(\frac{S(\beta )}{S_0(\beta )}\right)=\frac{{\sum }_E{E}^{2}I(E,\beta )}{{\sum }_{E}EI(E,\beta )}$$ (3)

and

$$I(E,\beta )=I(E)e^{d_{\mathrm{bowtie}}(\beta ){\mu }_{\mathrm{bowtie}}(E)},$$ (4)

for air images the bowtie profile can be fitted to the measured variance profile. Here, $S_0$ is the average signal and $I$ is the photon intensity detected by the detector. The variance profile and the corresponding fit can be seen in Figure 1. We performed a noise analysis across the 747 realizations and from the standard deviations found we did fit a Teflon bowtie filter that would result in the same noise profile. The maximum bowtie thickness was found to be 38.5 mm. Even though most CT systems have two bowtie filter for different patient sizes, we use the same bowtie filter for all simulations. However, this simplification should not impact results significantly since the same bowtie is applied to the basis protocol as well.

FIGURE 1.

Measured noise profile from 747 Definition Flash air images (blue) and variance fit with Gaussian bowtie profile (red). Outliers at high fan angles were not regarded for the fit

The number of photons detected by the detector pixel was sampled from a Poisson distribution with the mean corresponding to the number of photons expected from the Lambert Beer law. This was done individually for each keV bin to simulate detector noise.

First‐order beam hardening correction (water precorrection) was applied to the each raw data value. Please note that the correction function is a function of the angle $\beta$ since the detected spectrum is a function of $\beta$, too. Of course the water precorrection function is also a function of the prefilter and of the prefilter thickness. In a real system this first‐order beam hardening correction may be realized using calibration techniques, among which the methods of Refs. 19, 20, 21 may also be adapted.

The CT images were reconstructed with 2D fan‐beam filtered backprojection using a Ram‐Lak kernel. The voxel size of reconstructed images was chosen to be 1 mm. Even though different kernels are used in the clinical practice, the choice of the reconstruction kernel does not affect relative dose changes. This is due to the fact that filtered backprojection is a linear operation. However, results achieved with iterative reconstruction algorithms can vary.

The tube current was chosen such that the image noise was constant for all acquisitions of the same phantom size. Simulated mAs values are shown in Figure 2. Tube current modulation was implemented according to Gies et al. ²² Tube voltage was simulated from 35 to 150 kV in steps of 5 kV.

FIGURE 2.

Simulated mAs values for the child, adult, and obese phantom depending on tin filter thickness

Semianthropomorphic liver phantoms were simulated in three sizes representing a child, an adult, and an obese patient as shown in Figure 3. Based on the adult phantom of size 30 cm $\times$ 20 cm (24.5 cm effective diameter as used for the size‐specific dose estimate (SSDE) calculation ²³ ) the child phantom was scaled by a factor of 0.5 resulting in a size of 15 cm $\times$ 10 cm (12.2 cm effective diameter). The obese phantom consisted of the adult phantom with an added 10 cm fat ring, which increased its size to 50 cm $\times$ 40 cm (44.7 cm effective diameter). The phantom allows us to determine soft tissue contrast and the corresponding contrast‐to‐noise ratio (CNR). To be able to asses iodine CNR as well an iodine insert was placed into the phantom. Iodine contrast was chosen to be 200 HU at a tube voltage of 120 kV without additional prefiltration, which corresponds to a mass mixture of 0.6% iodine and 99.4% water. For each phantom size‐specific standard protocols as typically applied at our facility without additional prefiltration were used as a reference. Their parameters are listed in Table 2.

FIGURE 3.

Simulated CT images of phantoms used to represent child (a), adult (b), and obese (c) patients. The child phantom was created by scaling down the adult phantom. The obese phantom was generated by adding a 10 cm fat extension layer to the adult phantom. Regions of interest (two soft tissue and one iodine) are indicated (yellow circles). Measured CT image of the semianthropomorphic QRM liver phantom (d). (Gray scale window $C=200\mathrm{HU}$, $W=1000\mathrm{HU})$

TABLE 2.

Individual reference protocols for child, adult, and obese phantoms

	Child (15 cm $\times$ 10 cm)	Adult (30 cm $\times$ 20 cm)	Obese (50 cm $\times$ 40 cm)
Soft tissue basis	30 mAs, 90 kV no prefilter	100 mAs, 130 kV no prefilter	600 mAs, 150 kV no prefilter
Iodine basis	50 mAs, 70 kV no prefilter	120 mAs, 90 kV no prefilter	720 mAs, 120 kV no prefilter

2.3. Dose simulation

As a measure of dose the weighted computed tomography dose index (CTDI) was used. Monte Carlo simulations of a CTDI phantom were used to determine the weighted CTDI. We used our in‐house Monte Carlo simulation that was validated against Geant4. While it was originally developed for scatter simulation as described in Baer et al., ²⁴ it can be applied to dose calculation in a similar way. It takes Rayleigh scattering, Compton scattering and photo effect into account. Secondary electrons and K‐escape are ignored and the energy is assumed to be deposited right at the location of the interaction. The CTDI phantom was simulated as a polymethylmethacrylate (PMMA) cylinder with 32 cm diameter and 15 cm depth with a resolution of 1 mm in all directions. The absorbed energy simulated with the Monte Carlo simulations were assessed at regions of interest (ROIs) in the center and the periphery of the phantom. They were used to calculate the central and peripheral ${\mathrm{CTDI}}_{100}$. Subsequently the weighted CTDI ²⁵ was calculated as

$$D={\mathrm{CTDI}}_{\mathrm{w}}=\frac{1}{3}{\mathrm{CTDI}}_{100}^{\mathrm{central}}+\frac{2}{3}{\mathrm{CTDI}}_{100}^{\mathrm{peripheral}}.$$ (5)

In order to save computation time Monte Carlo simulations with monochromatic spectra were precomputed in 1 keV steps up to 200 keV. For each image acquisition the precomputed monochromatic ${\mathrm{CTDI}}_{\mathrm{w}}$ values were linearly combined according to the polychromatic spectrum used in the image acquisition.

${\mathrm{CTDI}}_{\mathrm{w}}$ values can be easily converted into SSDE values. The conversion factors are dependent on the effective diameter and are listed in the AAPM Task Group 204 report. ²³ The conversion factors are 2.38, 1.48, and 0.71 for child, adult, and obese phantoms, respectively. However, due to the linear conversion, ${\mathrm{CTDI}}_{\mathrm{w}}$ and SSDE give the same relative dose reduction results.

It should be noted that the ${\mathrm{CTDI}}_{\mathrm{w}}$ value is not a measure of patient dose. We chose to use ${\mathrm{CTDI}}_{\mathrm{w}}$ for dose comparisons since it, as well as the derived values dose length product (DLP), SSDE, and so forth, are widely accepted figures of merit when comparing CT imaging protocols across scanners, institutions, and patients.

2.4. Image quality assessment

To assess image quality, ROIs in soft tissue and iodine‐enhanced regions were evaluated using our own C++ function. Image noise was determined in a difference image of two noise realizations in order to avoid that potential artifacts contribute to the noise estimate. The standard deviation (= noise) measured in these difference images was divided by $\sqrt{2}$ to account for the increase of noise due to the subtraction process. The mean values (= signal) were determined by averaging the two images and by taking the mean inside each ROI. As figures of merit soft tissue and iodine contrast‐to‐noise ratios at unit dose (CNRD) were calculated as

$$\mathrm{CNRD}=\frac{\left|S_1-S_2\right|}{\sqrt{N_1^2+N_2^2}\sqrt{D}},$$ (6)

where $S_i$ and $N_i$ are signal and noise in ROI $i$ and $D$ is the dose (weighted CTDI). CNRD was chosen as a figure of merit instead of task‐based observers, which would require coverage of many different potential tasks as we aim to provide the most general result possible. Furthermore, the results of task‐based observers should be very similar to the CNRD results in the linear imaging situation presented here. Therefore, using task‐based observers would provide little to no additional information while drastically reducing the clarity of the dose reduction results. When an image is compared to a reference image the dose reduction can be calculated as

$$\text{dose}\text{reduction}=1-\frac{{\mathrm{CNRD}}_{\mathrm{ref}}^2}{{\mathrm{CNRD}}^2}.$$ (7)

2.5. Measurements

To validate simulation results CT scans of a semianthropomorphic liver phantom (QRM GmbH, Möhrendorf, Germany) were acquired using the Flash CT system. The phantom is similar in shape, size, and attenuation to the adult phantom used in the simulations. The scanner allows to perform scans with and without 0.4 mm tin filter. However, the protocols available strongly limit the possible combinations and thus the space of x‐ray parameters that can be covered is quite limited. Tube voltages were set to 80 kV, 100 kV, 120 kV, and 140 kV, respectively. Additionally an image with 140 kV tube voltage and the built‐in 0.4 mm tin filter was acquired. Images were acquired with a reference mAs of 200 and a rotation time of 500 ms resulting in dose values of 9.93 mGy for 80 kV tube voltage, 19.31 mGy for 100 kV, 30.57 mGy for 120 kV, 45.24 mGy for 140 kV, and 13.95 mGy for 140 kV with tin filter. Images were reconstructed with a Siemens B30f kernel and a slice thickness of 1.5 mm. Soft tissue CNRD was determined in a liver ROI covering 107 slices for all images to calculate

$$\text{relative}\text{dose}=\frac{{\mathrm{CNRD}}_{\mathrm{ref}}^2}{{\mathrm{CNRD}}^2},$$ (8)

at constant dose; 140 kV was used for the reference. Simulations were performed with the same tube voltage and prefilter settings for comparison. Since only relative dose values are compared, results are not affected by the use of different reconstruction kernels.

3. RESULTS

3.1. Differences between tin and copper prefilters

To illustrate the differences between tin and copper prefilters 50 kV and 120 kV example spectra filtered by thick 2 mm tin or 5 mm copper prefilters are shown in Figure 5. At tube voltages above 56 kV spectra filtered by either tin or copper prefilters converge with increasing prefilter thickness to a monochromatic spectrum with an energy corresponding to the tube voltage. Below 56 kV spectra filtered by the tin prefilter converge to a monochromatic spectrum at tin's k‐edge energy at 29.20 keV since here Sn attenuation is lowest (Figure 4). Therefore, differences between tin and copper prefiltration are more prevalent at low tube voltages.

FIGURE 5.

50 kV (left) and 120 kV (right) x‐ray spectra without additional filtration, filtered a by 2 mm additional tin prefilter or filtered by a 5 mm additional copper prefilter. The intensity (number of photons) is normalized such that the integral of each spectrum is 1

Since tin attenuation is stronger for most of the relevant energy range, it is useful to not compare tin and copper prefilters with equal thickness. Instead, one should compare prefilters with the same equivalent filter thickness, meaning that both filters absorb the same number of photons or the same fraction of the detected signal. The equivalent filter thickness depends on the spectrum as filtration is energy dependent and is around three times larger for copper filtration compared to tin for 120 kV spectra. The equivalent filter thickness was determined by increasing the copper filter thickness until the number of absorbed photons was the same in both filters.

3.2. Dose simulation

Results of the dose simulation were compared to available tube voltage and tin prefilter combinations of existing scanners with tin prefiltration. CTDI data from the Siemens SOMATOM Force (Siemens Healthineers, Forchheim, Germany) were available between 70 and 150 kV at 100 mAs without tin prefilter and at 100 and 150 kV with tin prefilter. Figure 6 plots the Monte Carlo–simulated CTDI values against the measured ones that are tabulated on our scanner. The agreement between simulated and tabulated values was high (99.9% correlation).

FIGURE 6.

Simulated CTDI values plotted against the measured CTDI values that are stored on the Force CT system. Without tin filter tube voltages between 70 and 150 kV are available. Additionally 100 and 150 kV are available with tin filter. The dashed line is the corresponding linear fit

3.3. Measurements

Table 3 lists the measured and simulated relative dose values. The 140 kV protocol without additional tin filtration was used as the reference. Discrepancies between measurements and simulations for all protocols are within 10%, which is the typical deviation given by the scanner manufacturer in the system owner manual and well within the maximum tolerances stated (40% for 80 kV, 30% for 100 kV, 120 kV, and 140 kV).

TABLE 3.

Measured and simulated relative doses for the adult phantom. The 140 kV protocol was taken as the reference

Protocol	Measured dose	Simulated dose
80 kV	144%	132%
100 kV	105%	108%
120 kV	94%	101%
140 kV	100%	100%
140 kV Sn	88%	79%

3.4. Soft tissue contrast

The dependence of the soft tissue CNRD on the tube voltage, the filter thickness and material, and on the patient size obtained through simulations is shown in Figure 7. At the same equivalent filter thickness soft tissue CNRD shows no significant difference (less than 3% deviation introduced by finite sampling of filter thickness and tube voltage) between tin and copper prefilters at optimal tube voltage, which is the tube voltage with the optimal CNRD at a given filter thickness. At low tube voltages results differ, due to the effect described above in Section 3.1. Soft tissue CNRD increases with increasing prefilter thickness at optimal filter thickness. The optimal tube voltage depends on the patient size and the prefilter thickness. For small patients the tube voltage should be lower than for large patients. Obese patients could potentially benefit from tube voltages higher than 150 kV since soft tissue CNRD increases throughout the simulated tube voltage range. Increasing the prefilter thickness results in lower optimal tube voltage values as this compensates the increase in mean energy caused by thicker filtration.

FIGURE 7.

Soft tissue CNRD for three patient sizes (top to bottom) and Sn (left) and Cu (right) prefilter as a function of tube voltage $U$ and prefilter thickness $d$. Rectangular regions indicate the locations of the maxima

In practice dose reduction is limited by the maximum tube current of the x‐ray tube. To preserve image quality photons lost in the prefilter have to be compensated for by an increase in tube current. Therefore, the maximal available tube current should be used and filter thickness should be chosen accordingly in order to maximize dose reduction. Since x‐ray absorption in the patient depends on the patient size the tube current is usually adapted to the patient size. To achieve minimum dose a better approach would be to choose an appropriate patient‐specific prefilter thickness. Hence fine gradations of filter thickness are advantageous. Another advantage of this approach for small patients would be that it prevents the tube current from reaching its machine minimum. In this case tube current modulation is effectively disabled ²⁶ resulting in a higher patient dose.

In Table 4 simulation results for tube current time product limits of 1000 mAs and unlimited tube current time product are shown. The finite sampling of filter thicknesses and tube voltages in our numerical simulations results in small errors in the dose reduction values that we estimated to be 3 percentage points. Therefore, differences of up to 3 percentage points may be regarded insignificant. Under the assumption that a tube current time product of 1000 mAs is available, tin prefiltration can achieve 15%, 32%, and 25% dose reduction for the child, adult, and obese phantoms, respectively, compared to the standard protocol without prefilter. In this case copper prefiltration provides 17%, 31%, and 29% dose reduction. In the limit of infinite tube current time product and prefilter thickness dose reductions of 19%, 36%, and 57%, respectively, are reached for both prefilter materials. Using the 16 cm CTDI for the child phantom yields slightly higher dose reduction, for example, 24% without a tube current time product limit compared to 19% with the 32 cm CTDI. This shows that dose reduction potential through prefiltration is higher for larger patients although the implementation is more challenging from a technical perspective. To achieve acceptable image quality in larger patients higher tube currents are required due to the increased photon absorption compared to smaller patients.

TABLE 4.

Soft tissue dose reduction with tin (Sn) and copper (Cu) prefilter. The tube current time product is either limited to 1000 mAs or unlimited. Dose reduction values (percent values) are given in reference to the basis without prefilter. Optimal values for tube current time product, tube voltage, and prefilter thickness are given for each protocol and phantom combination. At unlimited tube current time product tube current time product and prefilter thickness are infinite

	Child (15 cm $\times$ 10 cm)	Adult (30 cm $\times$ 20 cm)	Obese (50 cm $\times$ 40 cm)
Basis	30 mAs, 90 kV no prefilter	100 mAs, 130 kV no prefilter	600 mAs, 150 kV no prefilter
Sn, 1000 mAs Limit	1000 mAs, 75 kV, 0.6 mm, 15%	1000 mAs, 120 kV, 1.0 mm, 32%	1000 mAs, 150 kV, 0.2 mm, 25%
Sn, no mAs Limit	70 kV, 19%	100 kV, 36%	150 kV, 57%
Cu, 1000 mAs Limit	1000 mAs, 70 kV, 1.6 mm, 17%	1000 mAs, 125 kV, 3.4 mm, 31%	1000 mAs, 150 kV, 0.8 mm, 29%
Cu, no mAs Limit	70 kV, 19%	100 kV, 36%	150 kV, 57%

3.5. Iodine contrast

Simulation results for the iodine CNRD dependence on tube voltage, filter thickness, and material and patient size are shown in Figure 8. Since iodine contrast is highest around the iodine k‐edge (33.17 keV ¹⁵ ) the optimal tube voltage is low; 50 kV, 60 kV, and 65 kV are optimal for the child, adult, and obese phantoms without additional prefiltration. In this regime the difference in k‐edge energy between tin and copper results in differences in attenuation profiles. Therefore, iodine CNRD behavior differs significantly between prefilter materials. Using tin prefiltration iodine CNRD is maximal at low prefilter thickness depending on patient size. In contrast iodine CNRD increases with increasing prefilter thickness if copper was used as the prefilter material. If however tube voltages below 70 kV are not available, copper loses its advantage over tin.

FIGURE 8.

Iodine CNRD for three patient sizes (top to bottom) and Sn (left) and Cu (right) prefilter as a function of tube voltage $U$ and prefilter thickness $d$. Rectangular regions indicate the locations of the maxima

Simulations showed that iodine CNRD with tin prefiltration in the child phantom already decreases with a 0.1 mm tin prefilter. In consequence no dose reduction could be achieved. Adult and obese phantoms had their maximum at 0.2 mm and 0.7 mm prefilter thickness. Here, dose is reduced by 14% and 33% requiring a tube current time product increase by factor 13 and 24 compared to the optimal tube voltage protocol without prefilter.

Simulation results for a limit of 1000 mAs and unlimited tube current time product are shown in Table 5. Under the assumption of a tube current time product limit of 1000 mAs dose reduction with tin filter is 39%, 40%, and 39% for the child, adult, and obese phantoms compared to the standard protocols without prefilter. This dose reduction is mostly due to the decrease of tube voltage (70 to 50 kV, 90 to 70 kV, and 120 to 105 kV). Only thin filters (0.1 mm or thinner) should be applied. Using the 16 cm CTDI for the child phantom yields slightly lower dose reduction, for example, 35% without a tube current time product limit compared to 39% with the 32 cm CTDI.

TABLE 5.

Iodine dose reduction with tin (Sn) and copper (Cu) prefilter. The tube current time product is either limited to 1000 mAs or unlimited. Dose reduction values (percent values) are given in reference to the basis without prefilter. Optimal values for the tube current time product, tube voltage, and prefilter thickness are given for each protocol and phantom combination. At unlimited tube current time product tube current time product and prefilter thickness are infinite for the copper prefilter

	Child (15 cm $\times$ 10 cm)	Adult (30 cm $\times$ 20 cm)	Obese (50 cm $\times$ 40 cm)
Basis	50 mAs, 70 kV no prefilter	120 mAs, 90 kV no prefilter	720 mAs, 120 kV no prefilter
Sn, 1000 mAs Limit	210 mAs, 50 kV, 0.0 mm, 39%	1000 mAs, 70 kV, 0.1 mm, 40%	1000 mAs, 105 kV, 0.0 mm, 39%
Sn, no mAs Limit	210 mAs, 50 kV, 0.0 mm, 39%	14500 mAs, 55 kV, 0.2 mm, 53%	3950000 mAs, 60 kV, 0.7 mm, 81%
Cu, 1000 mAs Limit	1000 mAs, 50 kV, 0.4 mm, 57%	1000 mAs, 65 kV, 0.2 mm, 49%	1000 mAs, 105 kV, 0.0 mm, 39%
Cu, no mAs Limit	40 kV, 67%	50 kV, 68%	50 kV, 89%

Copper prefiltration in contrast increases iodine CNRD with increasing thickness. This allows for the same optimization strategy as for soft tissue contrast, using the highest tube current available and adapting the prefilter thickness accordingly. With a tube current time product limit of 5000 mAs dose is reduced by 57%, 49%, and 39% for the child, adult, and obese phantoms due to tube voltage decrease and filtration compared to the standard protocol. Here, dose reduction is higher than with a tin prefilter. In the limit of infinite tube current time product and prefilter thickness dose reduction of 67%, 68%, and 89% is achieved, which is significantly higher than the dose reduction of 39%, 53%, and 81% at optimal tube current time product and filter thickness for tin.

4. DISCUSSION AND CONCLUSIONS

In this study the dose reduction potential of a wider tube voltage range and of patient‐specific prefilters in single energy CT was investigated. Even though dose reduction is the most obvious benefit of using additional prefiltration we want to emphasize again that some applications could benefit more from an increase in image quality, which can be achieved with additional prefiltration instead. Our results show that the dose reduction potential depends on the patient size and on the relevant contrast mechanism (soft tissue vs. iodine enhancement). Today's CT scanners provide tube currents up to about 1300 mA (Siemens Vectron tube, Siemens Healthineers, Forchheim, Germany), thereby being able to achieve tube current time products in the order of 1000 mAs (at low rotation speeds or low pitch values). Tube voltages typically can be selected between 70 kV and 150 kV. In this case dose reduction values for soft tissue contrast can, potentially, be 15% to 32% depending on patient size, given that the required prefilters at the required thicknesses were available. The dose reduction for iodine contrast‐enhanced scans is mainly achieved by lowering the tube voltage. Assuming a limit of 1000 mAs our simulations determined 44% and 39% dose reduction for the adult and obese phantoms. Only insignificant 3% dose reduction with the contrast‐enhanced child phantom is found when tube voltage cannot be set below 70 kV.

If, however, tube voltage could be reduced to 50 kV, a 57% dose reduction is possible for children. Adults could also benefit from lower tube voltages in iodine imaging: up to 49 % can be achieved, then. In this case copper prefilters provide a significant advantage over tin prefilters. One way to prevent the need for such low tube voltages would be the use of contrast agents with higher k‐edge energies such as, for example, hafnium or tungsten, which have their k‐edges at 65.35 keV and 69.53 keV, ¹⁵  respectively.

Such high‐Z contrast agents are currently under consideration, ²⁷ , ²⁸ also driven by the upcoming introduction of photon‐counting CT technology. ²⁹ Note that if tube voltage and filter thickness are optimized for the contrast agent one has to accept nonoptimal soft tissue contrast. High‐Z contrast agents would be advantageous here as well. Due to their higher k‐edge energies than iodine their optimal tube voltage is closer to the optimal tube voltage for soft tissue contrast, as can be seen in Table 6 for hafnium.

TABLE 6.

Hafnium dose reduction with tin (Sn) and copper (Cu) prefilter. The tube current time product is limited to 1000 mAs. Dose reduction values (percent values) are given in reference to the basis without prefilter and with iodine contrast. Iodine and hafnium contrast is normalized to the same number of atoms per volume. Optimal values for the tube current time product, tube voltage, and prefilter thickness are given for each protocol and phantom combination. For convenience iodine dose reduction values from Table 5 are displayed here again

	Child (15 cm $\times$ 10 cm)	Adult (30 cm $\times$ 20 cm)	Obese (50 cm $\times$ 40 cm)
Basis	50 mAs, 70 kV no prefilter, I. cont.	120 mAs, 90 kV no prefilter, I. cont.	720 mAs, 120 kV no prefilter, I. cont.
Sn, 1000 mAs Limit Iodine contrast	210 mAs, 50 kV, 0.0 mm, 39%	1000 mAs, 70 kV, 0.1 mm, 40%	1000 mAs, 105 kV, 0.0 mm, 39%
Sn, 1000 mAs Limit Hafnium contrast	1000 mAs, 85 kV, 1.0 mm, 48%	1000 mAs, 95 kV, 0.7 mm, 82%	1000 mAs, 120 kV, 0.1 mm, 85%
Cu, 1000 mAs Limit Iodine contrast	1000 mAs, 50 kV, 0.4 mm, 57%	1000 mAs, 65 kV, 0.2 mm, 49%	1000 mAs, 105 kV, 0.0 mm, 39%
Cu, 1000 mAs Limit Hafnium contrast	1000 mAs, 85 kV, 3.3 mm, 43%	1000 mAs, 95 kV, 2.3 mm, 79%	1000 mAs, 120 kV, 0.3 mm, 83%

If x‐ray tubes became more powerful and were able to provide higher tube currents the dose reduction potential of CT would increase even further. For example, with a tube current time product limit of 5000 mAs the dose reduction potential is estimated to be between 16% and 50% for unenhanced situations and between 57% and 70% for iodine contrast.

Our optimizations have used the CTDI value as a dose measure. Since here we were interested only in relative improvements, for example, improvement for a child without and with a prefilter, the findings should also be valid for other dose or risk measures. If, however, a vendor is to implement such a technology and to decide upon the filter thickness to use for a specific patient and for a specific protocol, then a patient‐specific dose or risk measure, such as, for example, an SSDE, would be advantageous.

To achieve the dose reductions shown in this paper, it is important to adapt the prefilter thickness on a case‐by‐case basis since the optimal filter thickness varies for the examined scenarios. Our simulations have shown that a deviation of 0.1 mm from the optimal Sn filter thickness or a deviation of 0.3 mm from the optimal Cu filter thickness can lead to a dose penalty of more than 10 %. Therefore not only the range of available filter thicknesses is important, but also that the filter comes in fine gradations, that is, that many different filter thicknesses are available. Alternatively, wedge‐shaped filters may be used in combination with a translational unit that shifts the wedge to the desired thickness at the focal spot position.

Additional prefiltration can be used in conjuncture with other dose‐saving measures such as iterative reconstruction, patient‐specific bowtie filters, and tube current modulation. Combining these measures will lead to optimal results.

In our study we did not simulate scattered radiation when simulating the projection data. The main reason for not simulating scatter is that modern diagnostic CT systems use a 2D antiscatter grid to reject most of the scatter before it could reach the detector. Thus, the influence of the scattered radiation is only a small effect and thus we regard this as being only a small limitation of our study. Another reason is that the effect of scatter actually depends on the type, size, shape, and material of the antiscatter grid as well on the collimation of the scan. While now our results are of very general nature and thus of interest to many readers and, hopefully, to all CT manufacturers, considering scatter would make the results very specific to only one setup, or very confusing, provided it covered a wide variety of scattered beam situations. If vendors were to adapt our ideas and implement a variety of prefilter thicknesses in their scanners and optimize the scan protocols accordingly, then that protocol optimization should certainly consider scatter, be it either through simulations or through measurements or, preferably, both.

In this paper we demonstrated the benefit of selecting the optimal prefilter thickness in a patient‐specific way. This requires prefilters with various thicknesses to be installed. Once a thickness is selected, the prefilter remains static during the scan. A future step could be to consider to dynamically vary the prefilter thickness during the scan. Such a prefilter modulation technique, that may be combined with tube current modulation, could be realized using two prefilter wedges that can be shifted relative to each other and thereby produce any prefilter thickness in continuous rather than discrete steps. Detector and spectral calibration of the scanner may become more challenging, but feasible solutions thereto exist ²¹ , ³⁰ and can be adapted to the case of prefilter modulation.

We have shown that substantial dose reduction values can be achieved by utilizing patient‐specific prefiltration and by providing tube voltages lower than 70 kV. The main technical challenge is to design x‐ray tubes that have such high power and such low kV. With today's x‐ray tubes children and nonobese adults may significantly benefit from patient‐specific prefilters. Even though dose reduction for obese patients could be increased further, they would still benefit from patient‐specific prefilters with current x‐ray tubes.

CONFLICT OF INTEREST

The authors have no conflicts to disclose.

Supporting information

Supporting Information

APPENDIX A.

A.1. Absorber simulation

A.1.1. Method

In addition to the simulations described in Sections 2.2 and 2.3, simple absorber simulations were performed. Since they do not require image reconstruction they are far less computationally demanding. We performed the simulation in order to find out how accurate they are compared with the full CT scan simulations. In our absorber simulations, the patient was approximated as a water layer corresponding to the patient size. Additionally a 0.5 cm iodine layer with a density of 0.039 g cm was added to simulate iodine contrast. This density corresponds to a 200 HU contrast at 120 kV tube voltage.

Again, soft tissue and iodine CNRD were used as a figures of merit. As a measure of dose energy absorbed in the water layer was used. The detected signal described in Equation (1) simplifies to

$$\begin{array}{ccc}\hfill S(E)& =& E(1-e^{-{\mu }_{\mathrm{GOS}}(E)d_{\mathrm{GOS}}})\mathrm{Object}\left(E\right)\hfill \\ & & \mathrm{Filters}(\beta =0,E)\mathrm{Tucker}(E)\hfill \end{array}$$ (A1)

and loses its dependence on $\alpha$ and $\beta$. Noise is calculated by taking the standard deviation of the Poisson distributed detected photons resulting in

$$N(E)=\sqrt{ES(E)}.$$ (A2)

A.1.2. Results

The validity of the absorber simulation can be evaluated by comparing results with the tomographic simulation. As an example soft tissue results from the adult phantom and an absorber simulation with a 30 cm water layer are shown in Figure 9. The results show very similar CNRD dependency on tube voltage and prefilter thickness. The location of maxima differs only slightly.

FIGURE A1.

Comparison of soft tissue CNRD between tomographic simulations (left) (top left) and absorber simulation of a 30 cm water layer (right). Rectangular regions indicate the locations of the maxima

The major advantage of the absorber simulation over the tomographic simulation is computation speed. In this example the absorber simulation was faster by a factor of 100, which could be used to increase sampling accuracy.

DATA AVAILABILITY STATEMENT

Research data are not shared.