The Potential of Utilizing Mid-Energy X-Rays for In-Line Phase Sensitive Breast Cancer Imaging

Abstract

OBJECTIVE:

The objective of this study is to demonstrate the potential of utilizing mid-energy x-rays for in-line phase-sensitive breast cancer imaging by phantom studies.

METHODS

The midenergy (50–80kV) in-line phase sensitive imaging prototype was used to acquire images of the contrast-detail mammography (CDMAM) phantom, an ACR accreditation phantom, and an acrylic edge phantom. The low-dose mid-energy phase-sensitive images were acquired at 60 kV with a radiation dose of 0.9 mGy, while the high-energy phase-sensitive images were acquired at 90 kV with a radiation dose of 1.2 mGy. The Phase-Attenuation Duality (PAD) principle for soft tissue was used for the phase retrieval. A blind observer study was conducted and paired-sample T-test were performed to compare the mean differences in the two imaging systems.

RESULTS:

The correct detection ratio for the CDMAM phantom for phase-contrast images acquired by the low-dose mid-energy system was 56.91%, whereas images acquired by the high-energy system correctly revealed only 40.97% of discs. The correct detection ratios were 57.88% and 43.41% for phase-retrieved images acquired by the low-dose mid-energy and high-energy imaging systems, respectively. The reading scores for all three groups of objects in the ACR phantom were higher for the mid energy imaging system as compared to the high-energy system for both phase-contrast and phase- retrieved images. The calculated edge enhancement index (EEI) from the acrylic edge phantom image for the mid-energy system was higher than that calculated for the high-energy imaging system. The quantitative analyses showed a higher Contrast to Noise Ratio (CNR) as well as a higher Figure of Merit (FOM) in images acquired by the low-dose mid-energy imaging system.

CONCLUSION:

The PAD based retrieval method can be applied in mid-energy system without remarkably affecting the image quality, and in fact, it improves the lesion detectability with a patient dose saving of 25%.

I. Introduction

Phase-sensitive x-ray imaging has received intense research interest in the last two decades [1–14]. Full Field digital mammography (FFDM) is yet the “gold standard” of breast cancer screening, but its reliability is sometimes controversial [15]. Many studies [16–20] showed that the phase-sensitive imaging technique would have essential advantages in breast cancer screening as a potential alternative to conventional mammography. Among several types of phase-sensitive x-ray imaging, in-line phase-sensitive imaging is experimentally straightforward and applicable for the clinical settings. The requirements for an in-line phase-contrast imaging system are small pixel pitch digital detectors and relatively high coherence width (L_coh) in the x-ray beam [21–23], both of which are satisfactorily achievable by utilizing a microfocus x-ray source.

In the phase-sensitive imaging system, x-ray absorption and phase shift are entangled. We can derive the phase shift map by applying the general x-ray transport equation as follows [24]:

$$\text{I}\left(\overrightarrow{r_D}\right)=\frac{I_{in}}{M^2}\{\text{cos}\left(\frac{\lambda R_2}{4\pi M}{\nabla }^2\right)[A^2(\overrightarrow{r})+\frac{\lambda R_2}{2\pi M}(\nabla \cdot \left(\varphi (\overrightarrow{r})\nabla A^2(\overrightarrow{r})\right))]-2\text{sin}\left(\frac{\lambda R_2}{4\pi M}{\nabla }^2\right)\left[A^2(\overrightarrow{r})\varnothing (\overrightarrow{r})\right]\}$$

where λ is the x-ray wavelength, I_in is the entrance intensity at the object plane, R₂ is the object to detector distance, and M represents the system’s geometric magnification factor while $A^2(\overrightarrow{r})$ and $\varnothing \left(\overrightarrow{r}\right)$ are the attenuation and phase shift maps, respectively. This equation requires at least two different projections with varying R₂ to assess two unknowns, $A^2(\overrightarrow{r})$ and $\varnothing \left(\overrightarrow{r}\right).$ The double projection would not be desirable in a clinical setting due to concerns of unnecessary additional radiation dose. However, there are four single-projection phase retrieval methods that have been introduced with adequate phase map estimation [24–29]. In this study, we used the PAD-based (Phase-Attenuation Duality) method for phase retrieval. The PAD condition exists when imaging tissue with a low effective atomic number, acquired at higher x-ray energies where the x-ray phase shift and the x-ray attenuation are both related to the electron density of the tissue and the x-ray and matter interaction isdominated by Compton scattering. As explained in detail by X. Wu et al. [27], the following equation can map the x-ray phase shift utilizing the PAD-based algorithm:

$$\varphi (\overrightarrow{r})=\frac{\lambda r_e}{{\sigma }_{KN}}\cdot \text{ln}{A}_{KN}^2(\overrightarrow{r})$$

where r_e=2.818×10⁻¹⁵ m (the classical electron radius), σ_KN is the total cross-section for x-ray Compton scattering with a free electron, and $A_{KN}^2$ is the tissue attenuation that can be estimated by the following equation:

$$A_{KN}^2=\left\{{\left[1-\left(\frac{{\lambda }^2{R}_2{r}_e}{2\pi M{\sigma }_{KN}}{\nabla }^2\right)\right]}^{-1}\left(\frac{M^2}{I_{in}}I\left(\overrightarrow{r_d}\right)\right)\right\}$$

The x-ray beams in diagnostic radiology are usually classified into the low, mid, and high energy beams based on measured first half value layer (HVL) under narrow beam conditions. There is wide variation in the HVL for the same generating potential. Therefore, an x-ray up to the energy of 50 KeV is generally considered a low-energy beam and the x-ray beams carrying the photons with the energy of 80–100 KeV or above are usually considered as a high-energy x-ray beam. It might be some overlapping among the categories, but the x-ray beam carrying the photons above 50 KeV and below the 80 KeV is usually considered as a mid-energy x-ray beam. Recent studies have focused on high-energy phase-sensitive imaging because the PAD phase retrieval algorithm operates more efficiently for higher x-ray energies [17,20,30]. Although the phase-attenuation duality does not hold with x-ray energies below 60 keV, a minimal error might be introduced in phase shift estimation, especially for very light elements, if the x-ray energy is not too low. Therefore, the image quality of phase retrieved images is less affected when using the PAD-base algorithm in mid-energy imaging systems for soft tissue. In this study, we investigate the performance and the detectability of the mid-energy phase-contrast and phase-retreived images, using the PAD-base phase retrieval method.

II. Materials and Methods

II-a. Imaging prototype:

We used a micro-focus X-ray source (Hamamatsu Photonics, Model L9181–06), which can provide up to 300 μA tube current and 130 kV tube voltage. The x-ray source has a tungsten (W) anode target, Beryllium output window, and provides a focal spot size of 50 μm or smaller, depending on the tube output power. The detector used in this study was a flat panel sensor (Hamamatsu Photonics, Model C7942SK-25) with a photodiode area of 120 mm by 120 mm, Gadolinium oxysulfide (GOS) scintillator, and providing a pixel pitch of 50 μm. We applied the maximum voltage of 60 kV in the mid-energy, and 90 kV in the high-energy imaging system. We used 2.5 mm and 1.2 mm Aluminum filters for beam hardening in the high-energy and mid-energy imaging, respectively. We applied an R₁ distance of 68.6 cm and an R₂ distance of 82.55 cm to deliver approximate geometric magnification (M) of 2.2 for both the mid-energy and high-energy imaging.

II-b. Dose calculation:

The X-ray spectra under experimental conditions were measured with a CdTe x-ray detector (Amptek Incorporated, Bedford, Massachusetts). The normalized glandular dose coefficient values (D_gN) were estimated with computer-based Monte-Carlo simulations using multiple parameters, including the x-ray spectrum, HVL (Half Value Layer), x-ray source target material, external filter material and thickness used for beam hardening, breast thickness and glandularity, through the procedures detailed in the literature [31–34] to calculate the Average Glandular Dose (AGD) for each imaging condition based on the following equation [35]:

$$\mathit{\text{AGD}}=D_{\mathit{\text{gN}}}\cdot X_{\mathit{\text{ESE}}}$$

where X_ESE is the entrance exposure rate at the object plane for the given experimental conditions. The entrance exposures are measured at 68.6 cm from the x-ray source with an ionization chamber. (The Radcal Leackage and Low Level Measurments Chamber – 10X6−180).

We hypothesized that the mid-energy in-line phase-sensitive imaging system would outperform the high-energy imaging system in terms of image quality and/or radiation dose. Therefore, to reduce the radiation dose in addition to exposure time in the mid-energy imaging system, we set the experimental glandular dose to 0.9 mGy at 60 kV. The high-energy imaging system provides a relatively higher radiation dose of 1.2 mGy at a tube potential of 90 kV.

II-c. Imaging objects:

One measure for the quantitative evaluation of the phase-sensitive imaging system is the Edge Enhancement Index (EEI). We used a 4 mm thick acrylic edge to evaluate the EEI for two different x-ray energies in this study. EEI measures the degree of edge enhancement relative to the absolute change in the pixel intensity for a system [5,36–37]. The EEI is given as:

$$\text{EEI=}\raisebox{1ex}{$\text{(P - T) /(P + T)}$}\!\left/ \!\raisebox{-1ex}{$\text{(}H\text{ - }L\text{) /(}H\text{ + }L\text{)}$}\right.$$

where P and T are the peak and trough intensities at the edge and H and L are the average intensities at the high-intensity and low-intensity regions next to P and T, respectively.

The CDMAM and ACR accreditation phantoms are widely-accepted breast tissue simulating phantoms and were therefore used to investigate the relative performance of the two imaging systems. The CDMAM phantom was initially developed for quality control in conventional mammography systems. The observer bias is reduced if not eliminated in the CDMAM phantom because the locations of discs are unknown to the observer. Additionally, numerous size and contrast levels of target discs provide a comprehensive way to compare the performance of the imaging systems. The gold disk targets on the CDMAM phantom (Fluke Biomedical - type 3.2) are arranged in a matrix of 16 rows and columns with a total number of 205 cells. Within each row, the diameters of the discs are constant while the disc thicknesses logarithmically increase from 0.05 to 1.60 μm. Within each column, the disc thicknesses are constant while the diameters logarithmically increase from 0.10 to 3.20 mm. The CDMAM phantom simulates a compressed breast of 1 cm thickness under standard mammography exposure conditions. Two 50–50 glandular-adipose equivalent homogenous CIRS slabs with a thickness of 2 cm each were added distal to the phantom with respect to the x-ray beam to simulate compressed breast tissue with a total thickness of 5 cm under experimental conditions. We were not able to cover the entire area of the CDMAM phantom with a single image acquisition due to the magnification in the imaging system, which increased the output image size larger than the field of view. Thus, a total number of 14 images were required to thoroughly scan all of the rows and the columns of the CDMAM phantom.

To provide a second phantom comparison of the imaging systems, we also used the Gammex 156D Stereotactic Mammographic Accreditation Phantom, which is equivalent to a 4.2 cm thick compressed 50–50 adipose-glandular breast tissue. This phantom consists of 4 fibers of varying diameters (0.4 to 0.93 mm) mimicking the fibrous structures of the breast, four groups of specks mimicking the breast tissue micro-calcification with varying sizes (0.20 to 0.54 mm), and four tumor simulating masses with diameters of 0.25 to 1.0 mm.

II-d. Observer study:

We asked three experienced observers to review the images independently. To facilitate a blind study and avoid the reading bias, all images of the CDMAM and the ACR phantoms were unlabeled and randomly mixed. Observers were not aware of the utilized kVp in the images of the CDMAM phantom or the ACR phantom. The same 5MP diagnostic monochrome mammography display with high resolution and pixel pitch of 165μm (Sony LMD_DM50) was used by all three observers to review the images in this study.

The CDMAM correction scheme [38] was applied after the observers reported the reading results for the CDMAM phantom. Two main rules within the correction scheme regulate the readout scoring: (a) A True observation result needs two or more correctly indicated nearest neighbors to remain a True and (b) A False or Not indicated disk will be considered as a “True” when it has 3 or 4 correctly indicated nearest neighbors. There are three exceptions for the rules explained above: (a) A True which has only two nearest neighbors at the edge of phantom needs only one correctly indicated nearest neighbors to remain a True, (b) A False or Not indicated disk which has only two nearest neighbors at the edge of the phantom will be treated as a True if both nearest neighbors are correctly identified, and (c) the absent corners of the phantom (0.05 μm/3.20 mm and 1.60 μm/0.10 mm) will be regarded a True when both nearest neighbors are correctly indicated.

The geometric mean calculation between the three observers was applied to determine the final results, since the diameters and thicknesses of the discs on the CDMAM phantom increase logarithmically rather than linearly. A paired sample t-test was employed to analyze and compare the reported mean for the two populations.

Two other quantitative parameters were also used for image quality analysis in the CDMAM phantom imaging: (a) Correct Observation (CO), and (b) Image Quality Figure (IQF). First, correct observation is derived from the following formula [38]:

$$\text{Correct Observation}(\%)=\frac{\text{ the number of correctly identified disk position }}{\mathit{\text{Total cell numbers in the CDMAM phantom}}}\times 100$$

IQF measures the image quality by using the equation below [38]:

$$IQF={\sum }_1^{16}C\times D_{i,min}$$

where C_i is the corresponding thickness (contrast) of column i and D_{i, min} is the minimum detectable disk diameter in the contrast column i. For the IQF calculation two additional rules are also applied: (a) A completely invisible column for disk thicknesses between 0.05 and 0.40 μm will result in a D_{i, min} of 4 mm (next logarithmic value, since the biggest disc in column with diameter of 3.2 mm is still invisible), and (b) A completely visible column for disk thicknesses between 0.25 and 1.6 μm will result in a D_{i, min} of 0.10 mm [38–39]. Smaller IQF values indicate the detection of smaller and thinner discs, which therefore directly implies superior image quality. For intuitive conception, the inverse image quality figure (IQF_inv) is usually adopted in place of IQF. Thus, greater IQF_inv values indicate higher image quality.

II-e. Contrast to Noise Ratio (CNR) and Figure of Merit (FOM):

For a quantitative comparison of two different imaging systems, the CNR and FOM were also determined in this study. The CNR of the target object in the imaging system can be estimated according to the Rose Model defined as follows [40–41]:

$$CNR=\frac{{\overline{I}}_A-{\overline{I}}_B}{\sqrt{\frac{\left({\sigma }_A^2+{\sigma }_B^2\right)}{2}}}\times \sqrt{\frac{a_D}{a_p}}$$

where ${\overline{I}}_A$ is the mean pixel intensity over the target region, ${\overline{I}}_B$ denotes the mean pixel intensity of the background over the same size area, ${\sigma }_A^2$ and ${\sigma }_B^2$ are the corresponding pixel value variances, and a_D and a_p are the target region area and the pixel area, respectively.

In clinical x-ray imaging, dose efficiency is always a big concern due to the potential side effects of ionizing radiation. We acquired the images in the mid-energy x-ray system at a relatively lower radiation dose to simultaneously evaluate the dose efficiency of the mid-energy system. Since two different imaging systems were operated at two different radiation doses, to eliminate the exposure parameter from analytical comparison [42] and make the results analytically dose-independent, FOM was determined for any imaging system by the given equation as follow:

$$\mathit{\text{FOM}}=\frac{\mathit{\text{CN}}{R}^2}{\mathit{\text{Dose}}}$$

III. Results

III-a. Edge Enhancement Index (EEI)

Figure 1(a) shows the comparison images of the laser-cut acrylic edge acquired with both imaging systems. The over-shooting at the boundaries is visible in the edge profiles for both x-ray energies, as shown in Fig. 1(b). The calculated EEI for 60 and 90 kV are 1.53 and 1.32, respectively, which indicate that the higher edge enhancement index is given by the mid-energy x-ray imaging system.

Fig. 1:

The phase-contrast images of the acrylic edge acquired at (a) 60 kV, and (b) 90 kV, and (c) comparison of the edge profiles drawn across the dotted white ROIs for the two different x-ray beams.

III-b. Phantom images without phase retrieval:

As previously mentioned, since the image of the entire CDMAM phantom was too large to fit on the utilized detector, Figure 2 shows the phase-contrast images of the CDMAM phantom for two consistent regions acquired at 60 kV-7.5 mAs and 90 kV-6.5 mAs.

Fig. 2:

Arbitrary-selected ROIs (Top row from area with larg diameter and medium contrast discs, and bottom row from area with small diameter and higher contrast dics) from the phase-contrast images of the CDMAM phantom at (a) 60 kV, AGD=0.9 mGy, and (b) 90 kV, 1.2 mGy.

The contrast-detail curves generated from the CDMAM phase-contrast images at two different tube potentials and shown in Figure 3. All data are geometrically averaged over three observers. The error bars represent a 95% confidence interval with the two degrees of freedom. As can be seen in the graph, lesions with lower contrast for specified disk diameters are visible on the mid-energy phase-sensitive images as compared to the high-energy images. Figure 4 shows the phase-contrast images of the ACR phantoms that were acquired at 60 kV-7.5 mAs and 90 kV-6.5mAs.

Fig. 3:

Contrast-detail curves generated from the phase-contrast images of the CDMAM phantom acquired at 60 (AGD=0.9 mGy) and 90 kV (AGD=1.2mGy).

Fig. 4:

The phase-contrast images of the ACR-156D Phantom at 60 kV-0.9 mGy (left), 90 kV-1.2 mGy (right).

Table 1 shows the correct observation rate and IQF_inv for the CDMAM phantom and the reading scores for the ACR accreditation phantom images acquired by the two imaging systems.

Table 1:

Quantitative analysis of phase-contrast images for CDMAM and ACR phantoms conducted by 3 observers. The CDMAM phantom consists of gold disks with varying diameters and thicknesses in 205 cells. The ACR phantom contains 4 varying sizes for each group of fibers, specks, and masses.

	60 kV (0. 9 mGy)	90 kV (1.2 mGy)	t-Stat	P- value
Total number of detected gold disc (CDMAM)	116.67	84	8.31	0.01
Correct Observation Ratio (CDMAM)	56.91%	40.97%	8.31	0.01
Inverse Image Quality Figure (CDMAM)	0.3836	0.2381	17.04	0.003
Tumor-simulating Masses (ACR)	3.50	3.33	1.0	0.42
Specks, simulating microcalcification (ACR)	3.167	2.33	2.0	0.03
Fibers, mimicking fibrous tissue (ACR)	3.667	3.33	2.0	0.18

The statistical analyses revealed that the mid-energy system outperforms the high-energy system and the difference is statistically significant for the correct observation ratio in the CDMAM phantom (μ_60kv=56.9%, μ_90kv=41.0%, t-stat=8.31, α=0.05, P-value=0.01). Statistical analysis also showed meaningful differences between calculated IQF_inv values for the mid-energy and high-energy imaging systems. The calculated IQF_inv for the mid-energy system was greater than the calculated IQF_inv for the high-energy system ((μ_60kv=0.384 μ_90kv=0.238, t-stat=17.04, α=0.05, P-value=0.003). Although the ACR mammography phantoms are essentially designed for the quality control (QC) testing, the total number of visible structures is commonly used to compare the performance of imaging systems [43–44]. The total number of visible structure for the ACR phantom image acquired by the mid-energy system was greater compared with the image acquired by the high-energy system, but the statistical analysis did not show a significant difference (μ_60kv=10.33/12, μ_90kv=9/12 t-stat=4.0, α=0.05, P-value=0.057). This outcome could be because of low statistical power due to the limited sample size (The Gammex 156D Stereotactic phantom consists of only 12 objects embedded in the phantom).

III-c. Phantom images after phase retrieval:

Figure 5 provides the phase-retrieved images for the selected regions of the CDMAM phantom and ACR phantom images acquired at 60 kV,7.5 mAs, and 90 kV, 6.5 mAs.

Fig. 5:

The phase-retrieved images of the selected ROIs from the CDMAM phantom at (a) 60 kV, (b) 90 kV, and phase-retrieved images of the ACR phantom at (c) 60 kV, and (d) 90 kV.

Figure 6 illustrates the contrast-detail curves generated from geometrically averaged data from three observers for the CDMAM phase retrieved images at two different tube potentials. As shown in the graph, objects with lower contrast for the corresponding diameter are visible in the mid-energy phase-retrieved images as compared to high-energy phase-retrieved images. The only exception is for small discs in the diameter range from 0.1 mm to 0.16 mm. This result could be because of the performance of the phase retrieval algorithm in the mid-energy x-ray range. The PAD-base phase retrieval algorithm ideally works in a high-energy x-ray range, and its consistency starts to degrade as x-ray energy falls below 60 keV. Regardless of impacted performance in the mid-energy system for the PAD-base phase retrieval method, the phase retrieved images acquired by a mid-energy imaging system still provide higher detectability and image quality, as shown in Table 2.

Fig. 6:

Contrast-detail curves generated from phase retrieved images of the CDMAM phantom acquired at 60 and 90 kVs. The radiation dose at 60kV was set to 0.9 mGy where the images at 90kV were acquired with an average glandular dose of 1.2 mGy.

Table 2:

Quantitative analysis of phase retrieved images for CDMAM and ACR phantoms conducted by 3 observers. The CDMAM phantom consists of gold disks with varying diameters and thicknesses in 205 cells. The ACR phantom contains four varying sizes from each group of fibers, specks, and masses.

	60kV (0.9 mGy)	90kV (1.2 mGy)	t-Stat	P-value
Total number of detected gold disc (CDMAM)	118.67	89	10.20	0.009
Correct Observation Ratio (CDMAM)	57.88%	43.41%	10.20	0.009
Inverse Image Quality Figure (CDMAM)	0.3886	0.2443	12.81	0.006
Tumor-simulating Masses (ACR)	3.66	3.33	2.0	0.18
Specks, simulating microcalcification (ACR)	3.16	3	1.0	0.42
Fibers, mimicking fibrous tissue (ACR)	3.66	3	4.0	0.057

The statistical analysis showed significant difference between two systems’ Correct Observation rate in phase retrieved images (μ_60kv=57.9%, μ_90kv=43.4%, t-stat=10.21, α=0.05, P-value=0.009) as well as the IQF_inv (μ_60kv=0.389 μ_90kv=0.244, t-stat=12.81, α=0.05, P-value=0.006). Again, despite better reading scores for the ACR phantom acquired by the mid-energy phase-sensitive imaging system, the statistical analyses do not reveal any significant differences between the two systems (μ_60kv=10.5/12, μ_90kv=9.33/12 t-stat=2.64, α=0.05, P-value=0.11). This might be due the same reason, discussed previously for the ACR phase-contrast images.

III-d. Contrast to Noise Ratio and Figure of Merit:

Although the contrast-detail curve provides the informative perception for the spatial and contrast resolution in the acquired images, it is also highly objective. The CNR and FOM ratio are widely accepted in the literatures as the quantitavie tools for comparing the image quality in different imaging systems. Table 3 provides the measured CNR and FOM ratios for a target disk in the two ROIs of the CDMAM phantom represented in Figure 2 and the tumor-mimicking mass in the ACR accreditation mammography phantom in Figure 4, acquired by both the mid-energy (M) and high-energy (H) x-ray systems.

Table 3:

Quantified CNRs and FOMs from two gold discs with varying diameters/thicknesses in CDMAM phantom and one tumor-simulating mass in ACR phantom for mid-energy (M) and high-energy (H) systems.

	CNR (M)	CNR (H)	FOM (M)	FOM (H)
Disk Size 2.5 mm×0.5μm (CDMAM phantom)	2.46	1.48	6.74	1.85
Disk Size 0.8 mm×0.63μm (CDMAM phantom)	3.59	2.55	14.40	5.43
Mass Thickness: 1mm (ACR Phantom)	2.01	1.61	4.46	2.16

The results showed a higher contrast to noise ratios for both gold discs in the CDMAM phantom image acquired by the mid-energy imaging system. The calculated CNR for the tumor-mimicking mass of 1 mm thickness in the ACR phantom was also greater in the image acquired by the mid-energy imaging system. The higher mid-energy to high-energy FOM ratios for the both CDMAM phantom and ACR phantom images also indicate the superior image quality with relatively lower radiation dose in the image acquired by the mid-energy system.

IV. Discussion and Conclusion

As discussed in the literature as well as indicated in this study, PAD-based phase retrieval is a practical approach in non-grating-based phase-sensitive x-ray imaging systems. The phase-attenuation duality is only valid for higher x-ray energies, where utilizing the high x-ray energy obliterates the attenuation-based image contrast. Hence, high energy in-line phase-sensitive x-ray imaging has mostly been studied in breast imaging to quantify the phase shift, whereas the attenuation-base image contrast is demolished. But in light elements such as soft tissue, the introduced error in phase shift mapping is not considerable, especially when the x-ray beam is not too soft. As demonstrated by the results of this study, the 60kV x-ray beam in the various breast phantoms provides higher detectability and image quality for both phase contrast and phase retrieved images.

As the results indicate, mid energy phase-contrast images of both CDMAM and ACR accreditation phantoms provide higher detection ability and better image quality compared with images acquired at the higher x-ray energy. Phase retrieval improves the detectability of both imaging systems, but its effect is more enhanced in the high-energy imaging system. The accuracy of quantitative values for phase shift within the sample, determined by the PAD-based method in mid-energy systems, are presumably erroneous because the phase-attenuation duality does not hold with relatively lower x-ray energies. However, the objective results still demonstrate the potential advantages of mid-energy phase-sensitive x-ray systems in breast imaging.

The calculated EEI also confirms the broader overshooting phenomenon in the mid-energy x-ray system. The larger overshooting ultimately results in increased edge enhancement in the image. The intra-tissue heterogeneity is usually an indicator of possibilities of malignancy within the breast tissue. Therefore, the higher EEI expands the capability of the radiologist to detect the potential intra-tissue heterogeneity.

Due to low output power in microfocus x-ray sources, the exposure time could be a concern in patient imaging, but more powerful x-ray tubes are recently emerging. We keep the exposure time constant in this study for both imaging systems, and therefore mid-energy imaging system delivers 25% less glandular dose compared with the high-energy system. With the CDMAM phantom, the image acquired at 60 kV with a glandular radiation dose of 0.9 mGy resolves smaller and thinner discs than the high-energy x-ray image does with a glandular radiation dose of 1.2 mGy. It also shows a better inverse image quality figure (IQF_inv) compared with the high-energy x-ray imaging system. The mid-energy phase-sensitive x-ray imaging system also reveals greater total number of visible structures for the ACR Stereotactic Mammographic Accreditation Phantom compared with the high-energy system.

Although the quantitative values for the phase mapping in the mid-energy system are not as accurate as of the value for the phase mapping in the high energy system, the objective evaluation of the mid-energy phase-sensitive x-ray imaging system shows promising results when utilizing the mid-energy x-ray (e.g., approximately 60 kV) for phase-sensitive x-ray imaging, specifically in soft tissues. Mid-energy x-rays provide higher attenuation-based contrast while the phase retrieved images are not substantially impacted by the inconsistency in phase-attenuation duality. Therefore, we believe that mid energy phase-sensitive x-ray imaging has the potential to improve the image quality and lesion detectability with relatively lower dose.

Ultimately, the accuracy of the screening or diagnostic devices not only depends on the sensitivity of the system but also depends on the specificity of the system. In CDMAM imaging, the observer may identify a gold disc in a wrong place within the cell, however, we only focused on the correct detection ratio, IQF_inv and provided the contrast-detail curve in this study. An additional investigation might be required to evaluate the False Positive rates in the images acquired by two imaging systems to demonstrate the accuracy of the mid-energy phase sensitive system for the breast x-ray imaging.