In-silico study of the impact of system design parameters on microcalcification detection in wide-angle digital breast tomosynthesis

Abstract.

Purpose

Accurate detection of microcalcifications ($\mu \mathrm{Calcs}$) is crucial for the early detection of breast cancer. Some clinical studies have indicated that digital breast tomosynthesis (DBT) systems with a wide angular range have inferior $\mu \mathrm{Calc}$ detectability compared with those with a narrow angular range. This study aims to (1) provide guidance for optimizing wide-angle (WA) DBT for improving $\mu \mathrm{Calcs}$ detectability and (2) prioritize key optimization factors.

Approach

An in-silico DBT pipeline was constructed to evaluate $\mu \mathrm{Calc}$ detectability of a WA DBT system under various imaging conditions: focal spot motion (FSM), angular dose distribution (ADS), detector pixel pitch, and detector electronic noise (EN). Images were simulated using a digital anthropomorphic breast phantom inserted with $120\mu \mathrm{m}$ $\mu \mathrm{Calc}$ clusters. Evaluation metrics included the signal-to-noise ratio (SNR) of the filtered channel observer and the area under the receiver operator curve (AUC) of multiple-reader multiple-case analysis.

Results

Results showed that FSM degraded $\mu \mathrm{Calcs}$ sharpness and decreased the SNR and AUC by 5.2% and 1.8%, respectively. Non-uniform ADS increased the SNR by 62.8% and the AUC by 10.2% for filtered backprojection reconstruction with a typical clinical filter setting. When EN decreased from 2000 to 200 electrons, the SNR and AUC increased by 21.6% and 5.0%, respectively. Decreasing the detector pixel pitch from 85 to $50\mu \mathrm{m}$ improved the SNR and AUC by 55.6% and 7.5%, respectively. The combined improvement of a $50\mu \mathrm{m}$ pixel pitch and EN200 was 89.2% in the SNR and 12.8% in the AUC.

Conclusions

Based on the magnitude of impact, the priority for enhancing $\mu \mathrm{Calc}$ detectability in WA DBT is as follows: (1) utilizing detectors with a small pixel pitch and low EN level, (2) allocating a higher dose to central projections, and (3) reducing FSM. The results from this study can potentially provide guidance for DBT system optimization in the future.

1. Introduction

Early diagnosis and treatment are crucial for reducing breast cancer mortality rates.^1,2 Microcalcification ($\mu \mathrm{Calc}$) is one of the earliest indicators of breast diseases, especially for $\mu \mathrm{Calc}$ clusters with specks smaller than $500\mu \mathrm{m}$. Such $\mu \mathrm{Calc}$ clusters are strongly associated with malignancy and higher grades of breast cancer.^3–8 On the other hand, round-shaped and large $\mu \mathrm{Calcs}$ ($>500\mu \mathrm{m}$) are less likely to be related to cancerous tissue.¹ Studies have demonstrated that full-field digital mammography (FFDM) is an effective screening modality and helps reduce breast cancer mortality.^9–11 In recent years, digital breast tomosynthesis (DBT) has seen rapid clinical adoption for breast screening. DBT acquires multiple projections over a limited angular range (AR) with a total dose comparable to FFDM, and a quasi-three-dimensional (3D) volume can be reconstructed from these projection images. Several large clinical trials have shown that DBT improves both sensitivity and specificity for mass detection compared with FFDM.^12–19 However, controversy remains for $\mu \mathrm{Calcs}$: some studies show that DBT is less sensitive than FFDM for $\mu \mathrm{Calcs}$ detection.²⁰

Among commercially available DBT systems, the tube rotation AR and the number of projection views vary, with AR ranging from 15 deg (narrowest) to 50 deg (widest).^21–24 Previous clinical studies have shown that lesions other than $\mu \mathrm{Calcs}$ are more conspicuous in wide-angle (WA) DBT than narrow-angle (NA) DBT, especially in dense breasts, due to better inter-plane resolution and tissue separation.^22,25 NA DBT detects $\mu \mathrm{Calc}$ clusters with higher sensitivity and better conspicuity than WA DBT due to better in-plane image resolution and faster scans.^22,23,26,27 To minimize the artifact from under sampling, the angular interval between projections should be smaller than 2 deg; hence, the WA DBT system usually requires more projection views.²⁸ With identical mean glandular dose (MGD), as the number of projections increases, quantum noise increases in projection images and reconstructed volumes. For projection images with large incident angles, image noise further increases due to x-rays penetrating thicker breast tissue. To overcome the limitation of higher image noise in DBT, Nishikawa et al. proposed concentrating half of the total dose at the center projection and divide the rest of the dose among other projections. The central high dose projection was utilized for $\mu \mathrm{Calcs}$ detection, and the reconstructed volume was used for mass detection.²⁹ Based on this work, Das et al. demonstrated that $\mu \mathrm{Calc}$ detectability in central high dose projection image is worse than the reconstructed volume of uniform dose DBT (UD-DBT).³⁰ Hu and Zhao proposed two new non-uniform angular dose distribution (ADS) schemes with more dose distributed to central projections and investigated $\mu \mathrm{Calc}$ detectability in reconstructed volumes using a cascaded linear-system model while keeping the total dose, number of projections, and AR the same as in UD-DBT.³¹ It was found that non-uniform ADS improved the detection of small objects ($<200\mu \mathrm{m}$) when a slice thickness (ST) filter was applied to the filtered backprojection (FBP) reconstruction to suppress noise in peripheral views. Vancoillie et al.³² also investigated $\mu \mathrm{Calc}$ detectability under non-uniform dose distribution. They designed the convex dose distribution, with the highest dose assigned to the central projection and decreasing dose levels assigned to peripheral projections. Results showed that the convex distribution has no significant improvement on $\mu \mathrm{Calc}$ detection for WA DBT.³² Duan et al.^33,34 expanded upon this dose distribution design using virtual clinical trial (VCT) methodology and evaluated object detectability using anthropomorphic breast phantoms with a human observer and a model observer. It was demonstrated that concentrating dose to central projections could improve observers’ accuracy and increase the number of detected $\mu \mathrm{Calcs}$ in one cluster without compromising mass detection in WA DBT.

The influence of x-ray tube motion during exposure has also been investigated. There are two tube motion modes in the Food and Drug Administration (FDA)-approved DBT systems: step-and-shoot and continuous motion.²³ Continuous tube motion during exposure enlarges the effective focal spot of the x-ray and causes focal spot motion (FSM) blur. Previous studies found that FSM degrades in-plane image resolution substantially in the tube motion direction.^35–38 Shaheen et al.³⁹ compared DBT systems with two tube motions modes and showed that $\mu \mathrm{Calcs}$ peak contrast is 8% lower in continuous tube motion mode. Qian et al.⁴⁰ proposed another option to remove FSM blur by replacing the rotating x-ray source tube with a stationary carbon nanotube x-ray source array.

The detection of $\mu \mathrm{Calcs}$ is also influenced by detector characteristics. Compared with an active-matrix flat-panel imager (AMFPI), a direct-conversion complementary metal–oxide–semiconductor (CMOS) active-pixel sensor has the benefit of higher frame rate, smaller pixel pitch, lower electronic noise (EN) level, and higher detective quantum efficiency at all spatial frequencies.^41–44 Duan et al.³⁴ demonstrated improved $\mu \mathrm{Calcs}$ detectability for detectors with lower EN levels and smaller pixel pitch using model observers.

The aim of this study is to provide recommendations for system optimization in WA DBT, with the goal of enhancing $\mu \mathrm{Calcs}$ detectability. Although many studies have investigated factors affecting DBT $\mu \mathrm{Calc}$ detectability and proposed strategies for improvement, methodologies varied across studies on the phantom design, image acquisition, and interpretation, and the results have sometimes been inconsistent. This study fills this gap by utilizing an in-silico experimental pipeline and consistent model observer methodology to compare the influence of different system design parameters on the $\mu \mathrm{Calcs}$ detectability, including the AR, tube motion mode, ADS, detector EN level, and detector pixel pitch. Compared with conventional clinical trials, the in-silico approach in this study offers notable advantages, including a reduced cost, improved efficiency, and preclusion of radiation exposure to live subjects.^45,46 The parameters fixed in the study include the source to imager distance, tube rotation center, x-ray spectrum, total MGD, focal spot size, anthropomorphic digital phantom, and $\mu \mathrm{Calc}$ size. The multiple-reader multiple-case (MRMC) receiver operating characteristic (ROC) study was conducted for statistical analysis.⁴⁷ The results of this study can provide guidance for not only system optimization but also the priority of each factor.

2. Methods

2.1. Digital Phantom

The FDA computer modeling pipeline Virtual Imaging Clinical Trials for Regulatory Evaluation (VICTRE) can be used to simulate digital breast phantoms with anthropomorphic breast texture at selected glandular density, breast size, outline shape, and compressed breast thickness.⁴⁸ In this study, a 49 mm thick breast phantom with 25% volumetric glandular density was generated. A total of $127\mu \mathrm{Calc}$ clusters was inserted at three different heights: 45 clusters at 20 mm, 44 clusters at 30 mm, and 38 clusters at 40 mm from the bottom of the phantom, respectively. Figures 1(a)–1(c) show the cross-section planes of the phantom at heights with inserted $\mu \mathrm{Calcs}$. As shown in the magnified image [Fig. 1(d)], each cluster consisted of $6\mu \mathrm{Calcs}$ in a pentagon pattern. The phantom resolution was $60\mu \mathrm{m}$. All $\mu \mathrm{Calcs}$ were simulated in a cubic shape with dimensions of $120\times 120\times 120\mu {\mathrm{m}}^3$, as $\mu \mathrm{Calcs}$ with smaller sizes are more likely associated with malignancy. Furthermore, this size represents the most challenging $\mu \mathrm{Calcs}$ for detection in DBT.^7,27,31,49 All $\mu \mathrm{Calcs}$ have a chemical composition of calcium oxalate. Although calcium oxalate crystals were found to be more relevant with benign diseases and hydroxyapatite calcifications were found in both benign and malignant lesions,⁵⁰ calcium oxalate was used in this study because it provides a more difficult detection task due to its lower x-ray attenuation.⁵¹

Fig. 1.

Cross section of the anthropomorphic digital phantom with $\mu \mathrm{Calc}$ clusters inserted at (a) 20 mm, (b) 30 mm, and (c) 40 mm in height from the bottom of the breast. (d) Magnified view of one of the $\mu \mathrm{Calc}$ clusters in yellow boxes in panels (a)–(c), with each $\mu \mathrm{Calc}$ speck shown as a bright dot in a pentagon pattern. Inside the breast region, the light grey and dark regions represent glandular and adipose tissue, respectively. Bright fibers are the suspensory ligaments of Cooper.

2.2. Image Acquisition and System Design Parameters

The Monte Carlo simulation tool MCGPU was used to generate projection images with the acquisition geometry shown in Fig. 2.⁵² With the tungsten (W) anode spectral model using interpolating polynomials (TASMIP), the incident x-ray spectrum was generated for 28 kVp with W anode and 0.05 mm Rhodium (Rh) filter (Fig. 3).^53,54 To isolate the impact of individual system design parameters, FSM was not incorporated during exposure unless explicitly stated. The simulation is comprised of 25 projections with an angular interval of 2.083 deg, unless otherwise specified. For each imaging scenario, the simulation maintained an MGD of 1.6 mGy for the DBT scan of the digital phantom outlined in Sec. 2.1. The MGD was determined based on previous publications on clinical DBT systems. It is at the lower end of the clinically relevant dose range, making the detection task in this study more challenging.^22,23,55,56 The radiation dose was uniformly distributed among projections, unless otherwise specified. The detector was a $200\mu \mathrm{m}$ thick amorphous-selenium direct flat-panel detector with a $85\mu \mathrm{m}$ pixel pitch, unless explicitly stated. In addition, scattered radiation was included in the simulated image.

Fig. 2.

Image simulation geometry.

Fig. 3.

Incident x-ray photon spectrum of 28 kVp W/Rh.

2.2.1. Tube AR

As presented in Table 1, projection images were simulated for both WA DBT and NA DBT. The $\mu \mathrm{Calc}$ detectability of WA DBT served as the baseline to evaluate the relative improvements resulting from factors discussed in the subsequent sections. The NA DBT results were utilized as a benchmark, providing a target for WA DBT system optimization. The angular interval for WA DBT and NA DBT is 2.08 and 1.07 deg, respectively.

Table 1.

AR and number of projections for reference groups.

	WA DBT	NA DBT
AR (deg)	50	15
Number of projections	25	15

2.2.2. Tube motion mode

To evaluate the influence of FSM on $\mu \mathrm{Calc}$ detection, WA DBT images were simulated with two tube motion modes as shown in Table 2. The FSM in continuous tube motion was estimated to be $\sim 2.00\mathrm{mm}$ for each projection, based on the tube motion speed and the exposure time of a clinical WA DBT Siemens system.

Table 2.

FSM for two tube motion modes.

Tube motion mode	FSM for each projection image (mm)
Continuous motion	$\sim 2.00$
Step-and-shot	0.00

2.2.3. Angular dose distribution

Four ADS schemes were systematically examined for WA DBT, as detailed in Table 3. ADS-1 corresponds to a uniform dose distribution across all projections. ADS-2, ADS-3, and ADS-4 are non-uniform dose distribution schemes among 25 projections. These non-uniform schemes allocated a higher dose for central projections and a lower dose for peripheral projections, as illustrated in Fig. 4. $I_{\text{cent}}$ is the region of central projections receiving a higher dose; $I_{\text{out}-1}$ and $I_{\text{out}-2}$ are regions of peripheral projections receiving a lower dose. $N_{\text{views}}$ is the number of projection views within either $I_{\text{cent}}$ or $I_{\text{out}-1/2}$; $D$ is the dose of each projection, normalized to the total MGD.

Table 3.

ADS schemes.

Scheme	$N_{\text{views}}$ ($I_{\text{cent}}$)	$D$ ($I_{\text{cent}}$)	$N_{\text{views}}$ ($I_{\text{out}-1}$) + $N_{\text{views}}$ ($I_{\text{out}-2}$)	$D$ ($I_{\text{out}-1/2}$)
ADS-1	0	—	25	1 × 1/25
ADS-2	7	2.33 × 1/25	18	0.5 × 1/25
ADS-3	5	3 × 1/25	20	0.5 × 1/25
ADS-4	3	4.67 × 1/25	22	0.5 × 1/25

Fig. 4.

Diagram showing the non-uniform dose distribution design.

2.2.4. Detector EN level and pixel pitch

Five combinations of detector settings were investigated; these encompassed four EN levels for the AMFPI detector with an $85\mu \mathrm{m}$ pixel pitch [200, 600, 1200, and 2000 electrons per pixel (els)] and a scenario for a CMOS detector with a $50\mu \mathrm{m}$ pixel pitch and 200 els EN (Table 4).

Table 4.

Five combinations of detector settings in the simulation.

	#1	#2	#3	#4	#5
EN (electrons/pixel)	200	600	1200	2000	200
Pixel pitch ($\mu \mathrm{m}$)	85	85	85	85	50

2.3. Image Reconstruction

The image reconstruction was performed using the FBP method.^38,57 The in-plane resolution was set to be identical to the detector pixel pitch, with values of 85 and $50\mu \mathrm{m}$ for AMFPI and CMOS, respectively. The ST for all scenarios was 1 mm. Reconstruction employed the standard ramp (RA) filter [Eq. (1)] and spectral apodization (SA) filter [Eq. (2)]. In addition, an ST filter [Eq. (3)] was applied in the $z$-direction to reduce noise aliasing.

$$H_{\mathrm{RA}}(f_r)=f_r,$$ (1)

$$H_{\mathrm{SA}}(f_x)=0.5[1+\cos (\frac{\pi f_x}{A}\left)\right],$$ (2)

$$H_{\mathrm{ST}}(f_z)=0.5[1+\cos (\frac{\pi f_z}{B}\left)\right],$$ (3)

where $A$ and $B$ define the window width for SA and ST filters, respectively, and were chosen with clinically relevant settings as $A=0.75\times f_{NY}$, $B=0.035\times f_{NY}$.³¹ $f_{NY}$ is the in-plane Nyquist frequency, $5.88\text{cycles}/\mathrm{mm}$ for $85\mu \mathrm{m}$ image resolution and $10\text{cycles}/\mathrm{mm}$ for $50\mu \mathrm{m}$ image resolution.

2.4. Observer Study

2.4.1. Two-dimensional (2D) filtered channel observer (FCO)

Model observers were employed to quantify the detectability of $\mu \mathrm{Calc}$ clusters, mitigating limitations of human observers such as time-consuming assessments and the inter-reader variability.⁴⁵ The reconstructed DBT volume for each scenario was cropped into multiple 2D regions of interest (ROIs) with $\mu \mathrm{Calcs}$ [signal present (SP) ROI] and without [signal absent (SA) ROI]. The active area of each ROI, with in-plane resolutions of 85 and $50\mu \mathrm{m}$, measured $4.335\times 4.335{\mathrm{mm}}^2$ and $4.35\times 4.35{\mathrm{mm}}^2$, respectively. One SP ROI and one SA ROI compose an ROI pair for the model observer. ROI pairs were divided into training and testing groups for the MRMC study, as detailed in Sec. 2.4.3.

The FCO, an extension of the channelized Hotelling observer (CHO) and non-prewhitening observer with an eye filter (NPWE), was selected for this study. Compared with CHO, FCO is capable of detecting irregularly shaped, non-circular symmetric signals, and multiple $\mu \mathrm{Calcs}$ in a cluster. In contrast to NPWE, FCO incorporates background pixel covariance statistics, similar to human observers.^58–60

In the context of lesion characterization in DBT volumes, utilizing a 3D model observer can potentially offer more insights into lesion morphology and distribution compared with a 2D model observer.^59,61 However, a 2D FCO model is adequate in this study for optimizing $\mu \mathrm{Calc}$ detection performance for two primary reasons: (1) the height of all $\mu \mathrm{Calcs}$ is $120\mu \mathrm{m}$, which is smaller than the thickness of each DBT slice. Therefore, a 2D ROI extracted from the $\mu \mathrm{Calc}$ in-focus plane should encompass all of the information regarding this $\mu \mathrm{Calc}$. Enhancing the detectability of individual $\mu \mathrm{Calcs}$ is anticipated to improve the overall performance in detecting the entire cluster. (2) In this study, $\mu \mathrm{Calcs}$ within a cluster were inserted at the same height. Consequently, a 2D ROI extracted from the cluster in-focus plane should include all $\mu \mathrm{Calcs}$ within this cluster.

The FCO comprises two sequential steps.

• 1.
  Convolutional channel response ${\lambda }_i$ is defined by Eq. (4):

  $${\lambda }_i=(u_i\otimes s{)}^{\prime }(u_i\otimes g),$$ (4)

  where $s$ denotes the target signal, calculated as the difference between SP ROI and SA ROI from training ROI pairs. $g$ represents the testing ROI. $u_i$ is the Laguerre–Gauss (LG) channel, defined by Eqs. (5) and (6) as

  $$u_i^{2\mathrm{D}}(a)=\frac{\sqrt{2}}{a}\exp \left(\frac{-\pi r^2}{a^2}\right)L_i\left(\frac{2\pi r^2}{a^2}\right),i=1,\dots ,N,$$ (5)

  $$L_i(x)=\frac{{\sum }_{n=0}^i(-1{)}^n(\frac{i}{n})x^n}{n!},$$ (6)

  where $a$ is the channel width, $i$ is the channel number, $N$ is the total number of channels, and $r$ is the distance of the point of interest to the center of the ROI. In this study, five 2D LG channels were used, and the channel width was set as 1.5 times the detector pixel size based on previous FCO studies.^58,59
• 2.
  A decision variable, $t$, is defined in Eq. (7) for the statistical test of response vector $\lambda =[{\lambda }_1,{\lambda }_2,\dots ,{\lambda }_i{]}^{\prime }$ as

  $$t={\lambda }^{\prime }{K}_{\lambda }^{-1}\lambda ,$$ (7)

  where $K_{\lambda }$ represents the covariance of the channel response vector $\lambda$.

2.4.2. $\mu \mathrm{Calcs}$ detectability and ROC analysis

A distribution overlap of the decision variable $t$ between SA and SP testing ROIs was defined as the signal-to-noise ratio (SNR), serving as the figure of merit for $\mu \mathrm{Calc}$ detectability [Eq. (8)]. It is calculated as

$$\mathrm{SNR}=\frac{|\overline{t_{\mathrm{SP}}}-\overline{t_{\mathrm{SA}}}|}{\sqrt{\frac{{\sigma }_{\mathrm{SP}}^2+{\sigma }_{\mathrm{SA}}^2}{2}}},$$ (8)

where $\overline{t}$ and $\sigma$ represent the mean and standard deviation of decision variable $t$, respectively.

Figure 5 illustrates the workflow for generating the ROC curve and the area under the receiver operator curve (AUC) value for evaluating the accuracy of the model observer. After the generation of decision variables $(t_1,t_2,\dots ,t_j)$ for testing ROIs $({\mathrm{ROI}}_1,{\mathrm{ROI}}_2,\dots ,{\mathrm{ROI}}_j)$, a threshold $h$ was established to classify each testing ROI as either an SP ROI or an SA ROI. By comparing the ground truth with classification results and adjusting the threshold ($h$), a set of sensitivity and specificity pairs were generated, forming the ROC curve of the model observer. AUC values were then computed as the area under the ROC curve.

Fig. 5.

Workflow of generating the receiver operating characteristic curve (ROC curve) and AUC value for evaluating the accuracy of the model observer.

2.4.3. MRMC study

A MRMC study was undertaken to assess the statistical performance of the model observer including the mean and standard error (SE) of the SNR and AUC under each imaging condition.^59,62–64 The workflow is outlined in Fig. 6. For each scenario, 127 (SP + SA) ROI pairs were cropped from the reconstructed image slices, with 63 pairs allocated to the training group and 64 pairs to the testing group. Following the methodology stated in a previous work, the number of readers was determined as 50, so that the SE of AUC for each scenario remains at a low uncertainty level ($<0.01$).⁵⁹ In each reader study, the FCO was trained with 50 randomly selected ROI pairs from the training group and tested with all ROI pairs in the testing group.

Fig. 6.

Workflow of the MRMC study for 2D FCO.

3. Results

3.1. Effect of AR

Results in Fig. 7 and Table 5 show that the SNR of $\mu \mathrm{Calcs}$ in NA DBT is 110% higher (3.213) compared with that in WA DBT (1.530). The model observer exhibits a 14.1% higher proficiency in distinguishing between SP ROI and SA ROI in NA DBT (AUC = 0.988) compared with WA DBT (AUC = 0.866). Figure 8 shows representative examples of $\mu \mathrm{Calc}$ clusters, surrounded by adipose and dense background tissue. The fatty and dense backgrounds surrounding these $\mu \mathrm{Calcs}$ represents two extreme conditions of breast density. Hence, these two examples provide a comprehensive visualization of $\mu \mathrm{Calcs}$ in different breast structural backgrounds. Notably, NA DBT images manifest brighter $\mu \mathrm{Calcs}$ and less noisy backgrounds across all examples.

Fig. 7.

Model observer performance of WA DBT and NA DBT. (a) SNR of $\mu \mathrm{Calcs}$. (b) ROC curves. (c) AUC values.

Table 5.

AUC mean (±SE) and SNR mean (±SE) comparison between WA DBT and NA DBT. A statistically significant difference is indicated when $p<0.05$ in the $t$-test.

	WA DBT	NA DBT	$t$-Test $p$ value
AUC	0.866 (±0.004)	0.988 (±0.001)	$<0.01$
SNR	1.530 (±0.026)	3.213 (±0.023)	$<0.01$

Fig. 8.

Examples of $\mu \mathrm{Calc}$ clusters in fatty and dense tissue background. For each example, the columns (from left to right) correspond to the ground truth from the digital phantom, the lesion seen in the in-focus plane of WA DBT, and the lesion seen in the in-focus plane of NA DBT.

3.2. Effect of FSM

Figure 9 and Table 6 show that the introduction of a 2 mm FSM results in a 5.2% reduction in the SNR (1.450) of $\mu \mathrm{Calcs}$ compared with no FSM (1.530). Moreover, the AUC for the model observer is 1.8% lower in the scenario with a 2 mm FSM (0.851) compared with no FSM (0.866). Figure 10 presents typical $\mu \mathrm{Calc}$ cluster examples. The height of both examples is 40 mm from the bottom of the compressed breast. This is the highest insertion location, where the $\mu \mathrm{Calc}$ detectability is most impacted by the FSM. The $\mu \mathrm{Calc}$ clusters are more conspicuous in images without FSM, especially for those located in a fatty background compared with images with a 2 mm FSM.

Fig. 9.

Model observer performance of scenarios with and without FSM. (a) SNR of $\mu \mathrm{Calcs}$. (b) ROC curves. (c) AUC values.

Table 6.

AUC mean (±SE) and SNR mean (±SE) values and statistical analysis results for scenarios with and without FSM. A statistically significant difference is indicated when $p<0.05$ in the $t$-test.

	Without FSM	With FSM	$t$-Test $p$ value
AUC	0.866 (±0.004)	0.851 (±0.003)	$<0.01$
SNR	1.530 (±0.026)	1.450 (±0.021)	$<0.01$

Fig. 10.

Examples of $\mu \mathrm{Calc}$ clusters in fatty and dense tissue background. For each example, the columns (from left to right) correspond to ground truth from the digital phantom, the lesion seen in the in-focus plane of WA DBT with a 2 mm FSM, and the lesion seen in the in-focus plane of WA DBT without FSM.

3.3. Effect of ADS

Figure 11 and Table 7 indicate that, in comparison with the uniform dose distribution (ADS-1), non-uniform dose distribution schemes ADS-2, 3, and 4 result in an increase of 62.8%, 46.8%, and 33.8%, respectively, in the SNR of $\mu \mathrm{Calcs}$. Similarly, the AUC improved by 10.2%, 8.8%, and 6.8%, respectively. The observed improvement diminishes from ADS-2 to ADS-4, suggesting a tradeoff between the lower quantum noise from central projections and higher quantum noise from peripheral projections. This balance depends on the filter setting for the FBP reconstruction, which determines the filtration of high-frequency signals in each projection image. With the SA filter ($A=0.75\times f_{NY}$) and ST filter ($B=0.035\times f_{NY}$) used in this study, ADS-2 exhibits the highest $\mu \mathrm{Calcs}$ detectability (SNR = 2.490 and AUC = 0.954). Figure 12 shows representative examples of $\mu \mathrm{Calc}$ clusters. For ADS-2, there is an appreciable increase in $\mu \mathrm{Calcs}$ conspicuity and a reduction in image noise. The improvement in $\mu \mathrm{Calcs}$ detection is particularly obvious in a fatty background.

Fig. 11.

Model observer performance of different ADSs. (a) SNR of $\mu \mathrm{Calcs}$. (b) ROC curves. (c) AUC values.

Table 7.

AUC mean (±SE) and SNR mean (±SE) values and statistical analysis results for scenarios of different ADS schemes. A statistically significant difference is indicated when $p<0.05$ in the $t$-test.

	ADS-1	ADS-2	ADS-3	ADS-4
AUC	0.866 (±0.004)	0.954 (±0.002)	0.942 (±0.003)	0.925 (±0.003)
SNR	1.530 (±0.026)	2.490 (±0.031)	2.246 (±0.030)	2.046 (±0.023)
Comparison		AUC $t$-test $p$ value	SNR $t$-test $p$ value
ADS-1 versus ADS-2		$<0.01$	$<0.01$
ADS-2 versus ADS-3		$<0.01$	$<0.01$
ADS-3 versus ADS-4		$<0.01$	$<0.01$

Fig. 12.

Examples of $\mu \mathrm{Calc}$ clusters in fatty and dense backgrounds. For each example, the columns (from left to right) correspond to ground truth from the digital phantom, lesion seen in the in-focus plane of WA DBT with ADS-1, ADS-2, ADS-3, and ADS-4.

3.4. Effect of Detector EN Level and Pixel Pitch

As detailed in Fig. 13 and Table 8, $\mu \mathrm{Calcs}$ SNR increases by 21.6%, and AUC increases by 5.0% as the EN decreases from 2000 to 200 els. However, the detectability between EN600 and EN1200 shows no significant difference. Figure 14 and Table 9 demonstrate a 55.6% and 7.5% improvement in $\mu \mathrm{Calcs}$ SNR and AUC, respectively, when comparing the small detector pixel pitch ($50\mu \mathrm{m}$) with the large one ($85\mu \mathrm{m}$) while keeping EN constant at 200 els. The combined improvement achieved with a $50\mu \mathrm{m}$ pixel pitch and EN200 was 89.2% in the SNR and 12.8% in the AUC. Figure 15 shows typical examples of $\mu \mathrm{Calc}$ clusters, comparing detector settings among large pixel pitch with high EN, large pixel pitch with low EN, and small pixel pitch with low EN. Qualitatively, the difference between EN2000 and EN200 is negligible. The $\mu \mathrm{Calcs}$ are substantially sharper in small pixel pitch images in both fatty and dense backgrounds.

Fig. 13.

Model observer performance of different EN levels. (a) SNR of $\mu \mathrm{Calcs}$. (b) ROC curves. (c) AUC values.

Table 8.

AUC mean (±SE) and SNR mean (±SE) values and statistical analysis results for scenarios of different detector EN levels. A statistically significant difference is indicated when $p<0.05$ in the $t$-test.

	EN200	EN600	EN1200	EN2000
AUC	0.909 (±0.003)	0.901 (±0.004)	0.893 (±0.003)	0.866 (±0.004)
SNR	1.861 (±0.030)	1.750 (±0.033)	1.742 (±0.025)	1.530 (±0.026)
Comparison		AUC $t$-test $p$ value	SNR $t$-test $p$ value
EN200 versus EN600		0.03	$<0.01$
EN600 versus EN1200		0.08	0.85
EN1200 versus EN2000		$<0.01$	$<0.01$

Fig. 14.

Model observer performance of different detector pixel pitches. (a) SNR of $\mu \mathrm{Calcs}$. (b) ROC curves. (c) AUC values.

Table 9.

AUC mean (±SE) and SNR mean (±SE) values and statistical analysis results for scenarios of different detector pixel pitches. A statistically significant difference is indicated when $p<0.05$ in the $t$-test.

	$85\mu \mathrm{m}$	$50\mu \mathrm{m}$	$t$-Test $p$ value
AUC	0.909 (±0.003)	0.977 (±0.001)	$<0.01$
SNR	1.861 (±0.030)	2.895 (±0.029)	$<0.01$

Fig. 15.

Examples of $\mu \mathrm{Calc}$ clusters in fatty and dense backgrounds. For each example, the columns (from left to right) correspond to ground truth from the digital phantom, lesion seen in the in-focus plane of WA DBT with 2000 els EN and $85\mu \mathrm{m}$ pixel pitch, 200 els EN and $85\mu \mathrm{m}$ pixel pitch, and 200 els EN and $50\mu \mathrm{m}$ pixel pitch.

4. Discussion

This study systematically evaluated the impact of different DBT image acquisition strategies on $\mu \mathrm{Calc}$ detection using a VCT framework. The findings of this study are based on the usage of 2D FCO, which adequately evaluated the detectability of the cluster of $\mu \mathrm{Calc}$ with all individual $\mu \mathrm{Calcs}$ located on the same plane.^59,61 However, for tasks reliant on 3D morphology or distribution information, such as characterizing large masses or $\mu \mathrm{Calcs}$ clustered across different planes, employing a 3D model observer is recommended due to its advantage in depth perception.

As detailed in Sec. 3.1, AUC values for WA DBT and NA DBT were 0.8661 and 0.9882, respectively. Our results are consistent with the findings of the four-alternative forced choice (4-AFC) reader study conducted by the FDA, which evaluated the detectability of $\mu \mathrm{Calcs}$ with sizes ranging from $\sim 150$ to $180\mu \mathrm{m}$. $\mu \mathrm{Calcs}$ were embedded in a VICTRE anthropomorphic phantom, which was physically built by inkjet printing. The reported percent correct of $\mu \mathrm{Calc}$ detection was 0.84 for Siemens WA DBT and 0.93 for Hologic NA DBT.²³ In this study, the AR values for WA DBT and NA DBT represent the widest (50 deg) and narrowest (15 deg) AR of commercial systems approved by the FDA.^21–24 For systems with an AR falling between $\sim 15$ and 50 deg, the trend of improvement in $\mu \mathrm{Calcs}$ detectability using strategies proposed in this study should be similar.

As demonstrated in Sec. 3.2, the FSM introduces signal blur, resulting in degradation of $\mu \mathrm{Calc}$ detectability. Despite the variation in FSM among different DBT systems, the findings of this study remain valid. Specifically, increased FSM leads to decreased $\mu \mathrm{Calc}$ detectability. For optimal detection of small-size $\mu \mathrm{Calcs}$, the step-and-shoot mode is recommended; however, this approach may be prone to x-ray tube vibration and patient motion during extended image acquisition times.³⁹ Alternatively, FSM can be mitigated by utilizing a stationary x-ray source array or a flying-focal-spot, enabling FSM-free image acquisition without increasing the total scan time.^65–67 Focal spot blur caused by patient motion was not considered in this study. Previous research has suggested that patient motion might counterbalance the benefit of eliminating FSM.⁶⁸ Consequently, further investigations into the influence of patient motion are imperative.

As shown in Sec. 3.3, non-uniform ADS with higher dose allocation to central projections could enhance $\mu \mathrm{Calc}$ detectability, consistent with findings from previous investigations by Hu and Zhao.³¹ The efficacy of non-uniform ADS is contingent upon the choice of reconstruction methodology and the size of $\mu \mathrm{Calcs}$. For instance, the ST filter in FBP reconstruction suppresses the high-frequency signal and noise in peripheral projection images, minimizing noise aliasing artifacts in the ST direction. However, the ST filter may concurrently suppress the in-plane signal power of $\mu \mathrm{Calcs}$. Another constraint associated with the non-uniform ADS is the practical limitation for the dose delivered to the central projections, which is dictated by the maximum tube loading achievable by the imaging system.

Findings presented in Sec. 3.4 demonstrated that detectors with smaller pixel pitch and lower EN level lead to sharper $\mu \mathrm{Calcs}$ and enhanced detectability. Our results highlight the benefit of a direct conversion CMOS detector capable of a smaller pixel pitch and lower EN. For WA DBT, where the number of projections increases, the quantum noise limited condition could be challenged for each low-dose projection.²⁴ Lower EN could ensure quantum noise limited projections, leading to reduced noise in reconstructed volumes, thereby improving the detectability of $\mu \mathrm{Calcs}$. An additional advantage of a CMOS detector is the higher frame rate, which can minimize blur caused by FSM. Barufaldi et al.⁶⁹ concluded that a smaller detector pixel pitch is only beneficial for $\mu \mathrm{Calc}$ detection under continuous tube motion mode. However, it is worth noting that their reconstructed voxel size differed from their detector pixel pitch. In addition, the extent of improvement attributed to detector pixel pitch depends on the specific imaging task. The size of the $\mu \mathrm{Calcs}$ in Barufaldi et al. is much larger than that in this study.

We did not analyze the impact of scattered radiation. Previous studies have shown that scatter is a low-frequency signal and has a limited impact on the $\mu \mathrm{Calc}$ signal.^33,70,71 However, the quantum noise introduced by scattered radiation will degrade the detectability. System optimization such as the implementation of an anti-scatter grid may improve $\mu \mathrm{Calc}$ detectability.

It is important to clarify that our study focuses on the evaluation of image acquisition parameters, and the influence of reconstruction methods is not within the scope of this study. We used FBP to reconstruct DBT volumes because of its linear process, which reflects the intrinsic imaging performance under various system parameter configurations. More advanced algorithms, such as iterative reconstruction and deep-learning-based denoising methods, could further improve image quality by reducing artifacts and noise of the reconstructed volume.⁷² Strategies introduced in this study are implemented in the image acquisition stage to improve the projection image quality, which can be used as the input to advanced reconstruction methods to further enhance $\mu \mathrm{Calc}$ detection. Evaluating the impact of alternative advanced reconstruction algorithms and denoising techniques will be the subject of future investigations.

5. Conclusion

In summary, this study utilized model observers to evaluate the impact of different DBT system parameters on the detectability of $\mu \mathrm{Calc}$ clusters embedded within an anthropomorphic digital breast phantom. Based on the magnitude of impact, the priority for enhancing $\mu \mathrm{Calc}$ detectability in WA DBT is: (1) utilizing detectors with a small pixel pitch and low EN level, such as a direct conversion CMOS detector; (2) allocating a higher dose to central projections; and (3) reducing FSM. The efficacy of the first two factors is contingent upon the absence of FSM. The results from this study can potentially provide guidance for DBT system optimization in the future.

Biographies

Xiaoyu Duan received her BS degree in physics from Nanjing University, China, in 2016 and her MS degree in medical physics from Duke University in 2018. She received her PhD from Stony Brook University in 2024. Her research interests include the development of techniques to improve image quality and lesion characterization for digital breast tomosynthesis, contrast-enhanced breast imaging, and system optimization with a dual-layer detector for contrast-enhanced breast imaging. She is a member of SPIE.

Hailiang Huang is a postdoctoral associate of radiology at Stony Brook Medicine. He received his PhD in biomedical engineering from Stony Brook University in 2023. His current research interests include the optimization of DBT systems, development of dual-energy DBT and contrast-enhanced DBT with advanced detector techniques, and evaluation of their clinical performance. He is a member of SPIE.

Wei Zhao received her PhD in medical biophysics from the University of Toronto in 1997. She is a professor of radiology at Stony Brook University. Her current research interests include the optimization of imaging system geometry and flat-panel detector performance for DBT and dual-energy contrast-enhanced imaging applications, as well as the development of a-Se-based indirect flat-panel detectors with avalanche gain for low-dose imaging applications. She is a fellow of SPIE.

Disclosures

No conflicts of interest to disclose.

Code and Data Availability

The phantom, images, and model observers in this article were simulated with the publicly available tool, VICTRE. Both code and data could be made available upon written request to the authors.