Optimal kVp Selection for Contrast CT Imaging Based on a Projection-domain Method

Abstract

Computed Tomography (CT) has been in clinical use for several decades. The number of CT scans has increased significantly worldwide, which results in increased radiation dose delivered to the general population. Many technologies have been developed to minimize the dose from CT scans, including scanner hardware improvements, task-specific protocol design and advanced reconstruction algorithms. In this study, we focused on selection of X-ray tube voltage and filtration to achieve optimal dose efficiency given required image quality, more specifically the contrast to noise ratio. Our approach differs from previous studies in two aspects. Typically, Monte-Carlo simulation is used to estimate dose in simulations, but this is computationally costly. We instead use a projection-domain dose estimation method. No image reconstruction is required for the projection-domain method, which further simplifies the analysis. This study also includes tantalum, a new contrast agent, in addition to soft tissue (water), bone and iodine contrast. Optimal tube voltages and filtration are identified as a function of phantom size. The simulation analysis is confirmed with a limited phantom study.

I. Introduction

CT is widely used in various clinical applications, such as cardiac imaging, colonography, angiography and urology [1]–[3]. The number of CT scans performed every year has dramatically increased, resulting in an increase in radiation dose delivered to the population. This dose increase has led to great concern within the medical community In 2010, the Food and Drug Administration announced the regulation towards the CT manufacturers to avoid unnecessary radiation exposures during scans [4] to lower the radiation risk to patients especially for those exposed to multiple CT scans.

Many technologies have been developed to optimize components of image quality and minimize patient dose, through improved hardware, scanning protocol design and reconstruction algorithms. Dose reduction techniques such as tube-current modulation and low- voltage protocols have been developed [5]. Iterative reconstruction algorithms show a great advantage in providing high quality images with much lower dose [6]–[8]. A computer assisted scan protocol and reconstruction method has been proposed to achieve the best tradeoff between radiation dose and image quality for task- and patient-specific cases [9]. With the combination of the all these advanced techniques, it is expected to see the averaged effective dose decrease by 2 to 3 fold compared to the current value of about 10 mSv [10].

In this study, we focus on the selection of optimal X-ray tube voltage considering the dose efficiency of different contrast materials. Typically, contrast to noise ratio (CNR) is chosen to represent the required image quality. The dose-normalized CNR (CNRD) therefore can be used to evaluate the dose efficiency given the desired CNR [11]. To accurately calculate the CNR and dose in the analysis usually requires image reconstruction and Monte Carlo dose simulation, which are both time-consuming. A projection-domain dose estimation method has been proposed and compared with Monte Carlo dose simulation [12]. In this paper, we use the projection-domain screening method which uses relatively simple analytical estimates of contrast, noise and dose. Contrasting material such as iodine is often injected into the patient to enhance the vasculature. Recently, tantalum has been evaluated as a contrast agent. Tantalum has several potential performance advantages over iodine as a contrast agent, and is hoped to offer an alternative to avoid known issues associated with iodine [13]–[15]. We used our projection-domain screening method to estimate the optimal X-ray tube voltage for the highest CNRD within soft tissue, and between soft tissue and bone, iodine and tantalum. The simulations included electronic noise and quantum noise. The simulation results were confirmed with measurements on a clinical CT scanner.

II. Method: Projection Domain Analysis

A. Analytical Representation for the Noise in the Projection Measurement

We first consider a projection ray passing through the object with a path length of L and attenuation coefficient of μ. Assming the incoming photon counts is a Poisson random variable I₀ with the mean of N₀, then the transmitted photon count is a Poisson random variable I_t with mean and variance of N_t = N₀e^−μL.

For an energy-integrating detector, the variance of the noise in the transmitted projection ray I_t prior to the log operation is

$${\sigma }_{me}^2\approx g^2{E}^2{N}_t+{\sigma }_e^2,$$

where g is the system gain and represents the conversion factor from energy to the number of electrons, E is the energy of X-ray photons detected by the detector, and ${\sigma }_e^2$ is the variance of the electronic noise associated with the detector cell.

For a polychromatic beam, the noise in the projection can be obtained by viewing the polychromatic spectrum as a summation over finite energy bins,

$$I_t=\sum _k{I}_k=\sum _k{I}_{k0}{e}^{-{\mu }_{k}L}.$$

where for energy bin E_k, I_ko is the incoming photon count with mean and variance of N_ko, I_k is the transmitted photon count with mean an variance of N_k, and μ_k is the attenuation coefficient of the object.

The noise in the pre-log data can therefore be written as

$${\sigma }_{photon}^2=\sum _k{g}^2{E}_k^2{N}_k+{\sigma }_e^2.$$

For a polychromatic beam, the signal detected for the transmitted X-ray photons is a summation across all the energy bins. Therefore, the projection value p after the logarithm operation is

$$p=-ln\frac{\Sigma E_k{I}_k}{\Sigma E_k{I}_{ko}}.$$

Using the Taylor expansion, the variance of p can be derived from the variance of the pre-log data based on approximately linearizing the logarithm operation.

$${\sigma }_{proj}^2\approx \left(\frac{{\Sigma }_k{g}^2{E}_k^2{N}_k+{\sigma }_e^2}{{\left({\Sigma }_{k}g{E}_k{N}_k\right)}^2}\right).$$

B. Analytical Representation of the Contrast for Different Materials

The contrast used in this analysis is also obtained from the projection domain. It is defined as the difference in attenuation coefficients between the object of interest and background. In the simulation, along the path of the projection ray, a small amount of the contrast material is inserted in place of the background material (typically, water is used as a background material in this simulation). Water and iodine contrast is analyzed as an example.

We used water contrast as a representative contrast for soft-tissue to soft-tissue contrast. By applying a small perturbation of the normal background water density, the water contrast is computed as:

$$C_{water}\left(E\right)=(1+∊){\mu }_{water}\left(E\right)-{\mu }_{water}\left(E\right),$$

where ∈ is a small constant (we used 0.05).

The iodine contrast is defined as:

$$C_{iodine}\left(E\right)={\mu }_{iodine}\left(E\right)-{\mu }_{water}\left(E\right).$$

Bone and tantalum contrast mechanisms are defined the same way as iodine. For a polychromatic beam, the contrast is defined as the flux-weighted average of the monochromatic contrast,

$$C=\frac{{\Sigma }_k{C}_k{N}_k}{{\Sigma }_k{N}_k}.$$

C. Dose Estimation

An accurate estimation of dose such as can be achieved with Monte Carlo simulation is always computationally costly. In our method, to simplify the calculation but still provide a reasonable estimate of the dose, we calculate the energy of the X-ray photons absorbed by the subject. In our previous publication, this method was demonstrated to be a reasonable approximation of the dose absorbed in the subject [12].

For a monochromatic beam with energy E, the deposited energy of the projection ray is

$$D_e=E{N}_0(1-e^{-{\mu }_{e}L})=E{N}_0-E{N}_t,$$

where μ_e is the attenuation coefficient of the object.

The dose for polychromatic beam is simply calculated as a summation of the energy for absorbed X-ray photons in all energy bins.

$$D_e=\sum _k{D}_{ek}.$$

D. Overall evaluation

The figure-of-merit used in the study is dose weighted contrast-to-noise ratio (CNRD):

$$CNRD=\frac{C}{\sigma \sqrt{D}},$$

where C is the contrast, σ represents the noise in the measurement, and D is the dose delivered to the patient.

III. Simulation Conditions and phantom Measurement

A. Simulation Conditions

We chose a circular water cylinder as our simulation object. For the contrast analysis, the center pixel is replaced by the contrasting material to introduce a small change in the projection value. Three sizes of the water cylinder were used, with diameters of 20 cm, 24 cm and 35 cm chosen to respectively represent pediatric, small adult and large adult abdomen scans.

Four different types of contrast were evaluated in the simulation, including water, bone, iodine and tantalum. We also evaluated the effect of extra filtration of the spectrum on the dose efficiency curve. Since the mA level does not affect the shape of the dose efficiency curve, we only simulated at one mA level.

The spectrum files used in this study are produced by the XSPECT package (v3.5), and then filtered with the nominal intrinsic filtration of a typical X-ray tube. We evaluated spectra with X-ray tube voltages ranging from 60 kVp to 160 kVp, which is a slightly broader range than the typically-used clinical X-ray tube voltages, which range from 80 kVp to 140 kVp. Each spectrum is represented in 0.5 keV increments. In this study, we applied a 0.5mm Cu filter to the X-ray spectrum and compared its performance with the original spectrum.

B. Phantom Measurements

To verify the simulation results, we measured a 24 cm CTDI phantom (fabricated in-house from a commercial 32 cm CTDI phantom, made of PMMA (Plexiglas)) with contrast material inserted at the center using a GE Healthcare Lightspeed VCT scanner. The concentrations of iodine and tantalum contrast were both 20 mg/cc. The contrast agent was installed in a custom-made vial, which was inserted in the modified CTDI phantom. The vial provided a 13 mm diameter cross-section of contrast agent, of which a 10 mm diameter region of interest (ROI) was used. For the background, an annular ROI was used, with a 20 mm inside diameter and a 24 mm diameter outside diameter. For the water contrast we inserted a vial with water and measured the contrast relative to the PMMA. This is not quite the same as the simulated water contrast with only a density perturbation. The contrast was determined as the difference in the average CT number in the contrast agent ROI and the background ROI; the noise was determined as the standard deviation in the background ROI. We measured the water, iodine, and tantalum contrast material at four tube voltages: 80, 100, 120, and 140 kVp; the tube current (mA) was selected to achieve approximately the same dose level, represented by CTDI as measured in that phantom. The scanning parameters are included in Table 1. We did not explore the effect of electronic noise at very low tube current [16].

TABLE I.

Phantom Measurement Parameters

Voltage (kVp)	Current (mA)	CTDI (mGy)
80	300	1.536
100	165	1.553
120	105	1.558
140	75	1.561

IV. Results and Discussion

A. Simulation Results

The simulated dose efficiency curves for water (soft tissue), bone, iodine and tantalum are plotted in Figure 1 for the three different phantom sizes. The CNRD curves are normalized to 1.0 at their maximum values for all cases (i.e. with and without filtration).

Figure 1.

The simulation results for the Dose efficiency (CNRD) curves at different phantom sizes: (a) 20 cm, (b) 24 cm, and (c) 35 cm phantoms respectively. Four contrast mechanisms (water, bone, iodine, and tantalum) show distinctive dose efficiency curves. An optional 0.5 mm Cu filter is used to harden the spectra.

For the simulation based on the 20 cm phantom, low kVp produces the highest dose efficiency for bone and iodine imaging. For tantalum, the optimal voltage is around 100 kVp. The CNRD curve for water is rather flat, with a decrease below 80kVp.

When the phantom size becomes larger, soft tissue imaging is more dose efficient at higher kVp compared with the smaller phantom size. For the 24 cm phantom, the optimal voltage for soft tissue is around 140 kVp. For bone and iodine contrast, lower kVp is still more dose efficient. The optimal value for tantalum is between 100 to 120 kVp. For the 35 cm phantom, the soft tissue requires higher tube voltage for better dose efficiency. Iodine contrast still requires low kVp. The optimal tube voltage for bone contrast is around 80 kVp. For tantalum, the most dose-efficient voltage increased to 120 kVp. With the 0.5 mm Cu filter added, the dose efficiency at a given tube voltage is improved for soft tissue and tantalum imaging. For the 20 cm phantom, the dose efficiency for bone and iodine decreases with the Cu filter, since the lower energy photons are filtered out from the spectrum.

B. Phantom Measurements

The 24 cm CTDI phantom measurement results from the clinical scanner are shown in Figure 2. At the same dose, iodine has the highest CNR at 80 kVp, water has the highest CNR at 140 kVp, and tantalum has the highest CNR at 100 kVp. These equal dose CNR curves match our simulation screening method (Figure 1) reasonably well: the iodine CNR curve drops by about 50% in the 80-140kVp range, the tantalum CNR curve peaks at 100-120kVp and the water CNR curve monotonically increases. As expected, the latter shows a significantly higher increase in the measurements since they actually reflect PMMA to water contrast.

Figure 2.

The CNR curves for iodine, tantalum and water contrast for equal dose measurement, using a 24 cm CTDI phantom.

V. Conclusion

In this study, we used a projection-domain screening method to evaluate the dose efficiency over a range of X-ray tube voltages for different contrast materials, including soft tissue, bone, iodine and tantalum at different phantom sizes.For bone and iodine contrast, low kVp is always more dose efficient (as has been previously shown), and some filtration will improve dose-efficiency at that low kVp, for larger phantoms only. For soft tissue imaging, with small phantom sizes, the optimal value of the tube voltage is around 100~120 kVp, but the curve is very flat, so there is no clear preference. With increasing phantom size, this optimal tube voltage increases. Filtration can improve dose-efficiency by 5-10%. The most dose efficient tube voltage for tantalum contrast imaging is between 100~120 kVp, depending on the phantom size. This value is closer to that of soft tissue contrast, thus making it easier to develop scanning protocols considering both materials.

To verify our simulation results, CTDI phantom measurements were performed on a GE Lightspeed VCT scanner to determine CNRD for water, iodine and tantalum. The measurements (Figure 2) confirmed that the project-domain analysis (Figure 1) gave a very good prediction of the relative performance of various spectra for all contrast mechanisms and phantom sizes. The projection domain method provides a quick screening method for selection of the spectrum, with much less computational cost compared to full image reconstruction and Monte-Carlo dose simulation. The study did not include very low tube currents where electronic noise would start to dominate, hence the conclusions should not be extrapolated to very low signal scenarios. Similarly, the study did not take into account practical upper limits on tube current: the most dose-efficient spectrum may not always achieve the desired image quality. Finally, this study did not take into account algorithmic noise reduction techniques. To first order, we expect that those will not change our conclusions, although it is conceivable that they might favor low kVp protocols, combining high iodine and bone contrast with good noise suppression.