Soft-tissue lesion and microcalcification detectability in cone-beam breast CT: cascaded system analysis

Abstract.

Purpose

We aim to investigate the performance of dedicated breast computed tomography (CT) for the detection of soft-tissue lesions and compare it to the detection of microcalcification clusters using cascaded systems analysis, with the intent of identifying which lesion type should be used for system optimization.

Approach

Signal and noise were propagated through the imaging chain using a cascaded systems model to obtain the modulation transfer function and noise power spectrum. Two imaging tasks were considered: a soft-tissue mass lesion modeled as a disk of 4 mm diameter and a cluster of microcalcifications modeled as calcium carbonate spheres of $220\mu \mathrm{m}$ diameter. Detectability indices using three numerical observer models were obtained for various scintillator thicknesses and acquisition conditions at a fixed 4.5 mGy mean glandular dose.

Results

Detectability index trends are reversed between soft-tissue lesion and microcalcification cluster for the range of X-ray tube voltages and filtrations studied, indicating a potential need for compromise. However, for each of the 150 combinations studied (6 kV settings $\times 5$ Cu filter thicknesses $\times 5$ CsI:Tl scintillator thicknesses) and for each of the three numerical observer models, the detectability index for soft-tissue lesions always exceeded the microcalcification cluster.

Conclusion

When the lesion type is unknown, such as during breast cancer screening, it is more appropriate to optimize the system parameters for the task of detecting a microcalcification cluster, as the detectability index for the soft-tissue lesion exceeded that for the microcalcification cluster for all conditions investigated.

1. Introduction

Dedicated breast computed tomography (CT), an emerging technique¹ for breast cancer detection and diagnosis, provides the benefit of fully three-dimensional (3D) imaging without the need for breast compression. Several research teams are working toward translating dedicated breast CT for multiple breast imaging applications. Broadly, the imaging findings associated with breast cancer can be categorized as soft-tissue lesions or microcalcifications. Soft-tissue lesions, such as masses with or without spiculations and architectural distortions, can be indicative of invasive ductal carcinoma (IDC) and invasive lobular carcinoma.^2,3 Microcalcifications are an important marker for ductal carcinoma in situ and IDC.^4–6

Breast computed tomography (BCT) has shown superior soft-tissue lesion detection compared with digital mammography (DM).^7,8 An important challenge has been the performance of breast CT for detecting microcalcifications, which has been inferior to DM and digital breast tomosynthesis (DBT),⁹ particularly when the radiation dose is reduced to levels appropriate for breast cancer screening.⁷ A recent small cohort study showed photon-counting helical BCT might be comparable to DBT for microcalcification detection.¹⁰ The importance of microcalcification for diagnosing these diseases and the relatively lower performance of BCT compared with the current reference standards emphasizes the need for improving microcalcification detection. Hence, we previously studied and reported on optimizing dedicated breast CT for improving microcalcification detectability.¹¹ However, it is necessary to balance the needs of detecting microcalcifications and soft-tissue lesions to maintain detection performance. We are developing an upright dedicated breast CT system, and it is important to ensure that when this system is optimized for microcalcification detection, it does not adversely affect the detection of soft-tissue lesions. Hence, in this follow-up study, we investigate the performance of dedicated breast CT for detecting soft-tissue lesions and compare it with the task of detecting microcalcifications to assess how trade-offs might be made to improve the overall diagnostic performance.

This study follows the same framework as in the previous investigation on microcalcification detectability¹¹ by using cascaded system analysis (CSA). CSA provides a method for evaluating a system with specified parameters related to system hardware, operating conditions, and image reconstruction to estimate performance.^12–14 CSA models the imaging chain as a cascade of discrete stages where the signal and noise transfer properties can be described mathematically based on the statistics pertaining to imaging physics for each stage. The analysis is conducted in the spatial-frequency domain, and the results of the analysis are the modulation transfer function (MTF), noise power spectrum (NPS), and detective quantum efficiency (DQE). These metrics provide insight into how an imaging system processes input signal and noise, such as the DQE, which is the ratio of the squared signal-to-noise ratio at the output to that at the input. The CSA model can be integrated with numerical model observers—such as prewhitening (PW), non-prewhitening (NPW), and non-prewhitening with eye filter (NPWE)—to provide detectability indices for a specified imaging task. Detectability indices provide a metric that relates to the quantitative imaging performance with human observers.^15,16

2. Approach

The imaging geometry, acquisition conditions, CSA stages, and their implementation are similar to the previous study.¹¹ For completeness, a concise description is provided below. The key difference is the imaging tasks studied to obtain task-specific performance. The simulation framework is described by the schematic in Fig. 1.

Fig. 1.

Schematic showing the simulation framework. From user-provided inputs, the X-ray spectrum is generated and is used in Monte Carlo simulations and cascaded systems analysis. The detectability index is computed for the specified imaging task using the output from cascaded systems analysis.

2.1. Breast Model

The breast was modeled as a semi-ellipsoid with homogeneous composition and a fibroglandular weight fraction of 15%. The dimensions of the modeled breast were 140 mm diameter at the chest wall and 105 mm length along the chest wall to nipple direction. All dimensions are inclusive of a 1.5 mm thick skin layer. The modeled breast shape, dimensions, and fibroglandular weight fraction approximate an average breast.^8,17–19

2.2. Imaging Tasks

Two imaging tasks were considered for the study: (1) detection of a 4 mm diameter, cylindrical soft-tissue lesion with attenuation coefficients²⁰ corresponding to IDC, and (2) detection of a microcalcification cluster represented as $220\mu \mathrm{m}$ diameter ${\mathrm{CaCO}}_3$ (density: $2.8\mathrm{g}/{\mathrm{cm}}^3$) spheres arranged in a pentagon with an additional central sphere embedded in a semi-ellipsoidal breast. The intersphere spacing of the microcalcification cluster was 2 mm. For both lesions, the positioning was such that they were congruent with the intersection of the central ray and the axis of rotation. Hence, for the central plane (cross-sectional or coronal), the cylindrical soft-tissue lesion is a disk and was modeled as per Burgess et al.²¹ For the microcalcification cluster, all spheres are in the central plane. Figure 2 shows the imaging tasks in the spatial and the spatial-frequency domains. Equation (1) describes the signal function in the spatial domain, where $\rho$ is the normalized distance $(r/R)$, $R$ is the radius, $A$ is the signal amplitude, and $\upsilon$ describes the signal profile.²¹ For soft-tissue lesion, $\nu =0$ is used to model a flat-topped disk, and $\nu =0.5$ is used to model each sphere of the microcalcification cluster.

$$S(\rho )=A*\mathrm{Rect}\left(\frac{\rho }{2}\right)(1-{\rho }^2{)}^{\upsilon }.$$ (1)

Fig. 2.

Spatial domain (a, c) and spatial-frequency domain (b, d) of the two imaging tasks studied; a 4 mm diameter disk (a, b) and a cluster of $220\mu \mathrm{m}$ diameter (c, d) microcalcifications.

Fourier transform of Eq. (1) provides the spatial-frequency-dependent $S(f)$, which is normalized to unit area to obtain $\tilde{S}(f)$.

The amplitude of the task function is the difference in the lesion incident spectrum-weighted linear attenuation coefficients between the lesion (mass or calcification) and the background (homogeneous mixture of 15% fibroglandular and 85% adipose tissues by weight) and is computed as

$$\mathrm{\Delta }\mu ={\mu }_L-{\mu }_b,$$ (2)

where,

$${\mu }_L=\int \{q_{\mathrm{rel}}(E)\exp [-{\mu }_b(E)\left(\frac{d-l}{2}\right)\left]\right\}{\mu }_L(E),$$ (3)

$${\mu }_b=\int \{q_{\mathrm{rel}}(E)\exp [-{\mu }_b(E)\left(\frac{d-l}{2}\right)\left]\right\}{\mu }_b(E).$$ (4)

In Eqs. (3) and (4), the term $\{q_{\mathrm{rel}}(E)\exp [-{\mu }_b(\frac{d-l}{2})]\}$ accounts for X-ray beam hardening from the breast surface to the lesion location, ${\mu }_b(E)$ and ${\mu }_L(E)$ are the energy-dependent linear attenuation coefficients of background tissue and lesion, $d$ is the breast diameter at the chest wall, and $l$ is the lesion diameter. The $\mathrm{\Delta }\mu$ from Eq. (2) is denoted as “Delta Mu” in Fig. 3, which illustrates an example, where the applied tube voltage is varied between 50 and 75 kV with fixed X-ray tube filtration of 0.25 mm of Cu and 2.6 mm of Al.

Fig. 3.

Difference in spectrum-weighted linear attenuation coefficients between the lesion (mass or calcification), denoted as “Delta Mu,” as a function of applied tube voltage. The X-ray beam filtration is fixed with 0.25 mm of Cu and 2.6 mm of Al.

Combining the amplitude and the spatial-frequency-dependent components yields the task function $T(f)$ in spatial-frequency domain:

$$T(f)=(\mathrm{\Delta }\mu )\times \tilde{S}(f).$$ (5)

2.3. Modeled System

The system was modeled for full-scan acquisition with 300 projections over 360 deg. The source to axis of rotation distance and the source to detector distance were 634 and 907 mm, respectively, to approximate the geometry of a prototype breast CT system (Proto 2A, Koning Corp., Norcross, GA, USA). The imaging chain was modeled using a tungsten-anode X-ray tube with 0.3 mm focal spot (M1583, Varex Imaging, Salt Lake City, UT, USA) and a CsI:Tl scintillator-coupled complementary metal-oxide-semiconductor (CMOS) detector (Xineos 3030HS, Teledyne-Dalsa, Waterloo, ON, Canada). The native detector pixel pitch of 0.15 mm and detector electronic noise appropriate for a CMOS detector were used in all simulations. For the simulations, the thickness of CsI:Tl scintillator was varied from 300 to $600\mu \mathrm{m}$. The applied tube voltage (kV) was varied from 50 to 75 kV, in steps of 5 kV. The added X-ray beam filtration was varied from 0.1 to 0.5 mm Cu with an additional 2.6 mm thick Al filter downstream of the Cu filter. The X-ray spectra were simulated using Spektr 3.0 toolkit using the TASMICS interpolation model.²² Each simulated spectrum was normalized to unit area and is represented as $q_{\mathrm{rel}}(E)$.

2.4. Monte Carlo Simulations

Monte Carlo simulations were performed using GEANT4 toolkit²³ to determine the normalized glandular dose coefficient (${\mathrm{DgN}}_{\mathrm{CT}}$) and the scatter-to-primary ratio (SPR). The aforementioned homogeneous breast model was used with the chest wall to nipple dimension coaligned with the axis of rotation and the central X-ray plane aligned with the chest wall of the breast model. Monoenergetic X-ray photons (${10}^6$ photons) from 5 to 100 keV, in 1 keV intervals, were emitted toward the breast to determine the energy-dependent ${\mathrm{DgN}}_{\mathrm{CT}}(E)$ and $\mathrm{SPR}(E)$. For each spectrum, the ${\mathrm{DgN}}_{\mathrm{CT}}$ was obtained by weighting the ${\mathrm{DgN}}_{\mathrm{CT}}(E)$ with the normalized X-ray spectrum, $q_{\mathrm{rel}}(E)$, and using photon fluence to air kerma conversion factor, $\vartheta (E)$, by

$${\mathrm{DgN}}_{\mathrm{CT}}=\frac{\int q_{\mathrm{rel}}(E)\vartheta (E){\mathrm{DgN}}_{\mathrm{CT}}(E)\mathrm{d}E}{\int q_{\mathrm{rel}}(E)\vartheta (E)\mathrm{d}E}.$$ (6)

From the ${\mathrm{DgN}}_{\mathrm{CT}}$, the air kerma at the isocenter and the X-ray photon fluence for each projection needed to achieve a mean glandular dose (MGD) of 4.5 mGy was computed. The MGD of 4.5 mGy approximates the radiation dose reported for standard two-view screening mammography in the DMIST study.²⁴ For DBT with synthesized mammogram, the MGD is comparable to DM, and for DBT with acquired DM, the MGD increases by $\sim 0.5\mathrm{mGy}$ for each view.²⁵ For each spectrum, the $\mathrm{SPR}$ was obtained by weighting the $\mathrm{SPR}(E)$ with the normalized X-ray spectrum, $q_{\mathrm{rel}}(E)$, as

$$\mathrm{SPR}=\int q_{\mathrm{rel}}(E)\mathrm{SPR}(E)\mathrm{d}E.$$ (7)

In the projection space, the contrast of the lesion is reduced due to $\mathrm{SPR}$. Also, both scattered and primary photons contribute to image noise, whereas only the primary photons contribute to the signal. These factors were included in the model.

2.5. CSA Model

The CSA model was implemented on MatLab (version 2024b, MathWorks, Inc., Natick, MA, United States) and comprised the following stages: (0) incident X-ray quanta, (1) X-ray interaction with CsI:Tl scintillator, (2) generation of optical quanta within the scintillator, (3) spreading of optical quanta within the scintillator, (4) optical coupling through a fiberoptic plate between the scintillator and the CMOS detector, (5) absorption of optical quanta by the CMOS detector pixel, (6) discrete sampling by the detector, (7) readout and additive noise, (8) log-normalization, (9) application of ramp and apodization filters, (10) bilinear interpolation, (11) backprojection, and (12) 3D sampling based on voxel pitch. The model accounts for K-fluorescence emission and reabsorption within the scintillator when the X-ray photon energy exceeds the K-absorption edge of the CsI:Tl scintillator.¹⁴ The detector incident spectrum was computed after transmitting through the chest-wall diameter of the breast.

2.6. Numerical Observer Models

For each imaging task, the detectability indices were determined using three numerical observer models: (1) PW, (2) NPW, and (3) NPWE and were computed as per Eqs. (810), respectively.

$$d_{\mathrm{PW}}^{\prime 2}=\iint \frac{T^2(u,v){\mathrm{MTF}}^2(u,v)}{\mathrm{NPS}(u,v)}\mathrm{d}u\mathrm{d}v,$$ (8)

$$d_{\mathrm{NPW}}^{\prime 2}=\frac{[\iint T^2(u,v){\mathrm{MTF}}^2(u,v)\mathrm{d}u\mathrm{d}v{]}^2}{\iint T^2(u,v){\mathrm{MTF}}^2(u,v)\mathrm{NPS}(u,v)\mathrm{d}u\mathrm{d}v},$$ (9)

$$d_{\mathrm{NPWE}}^{\prime 2}=\frac{[\iint T^2(u,v){\mathrm{MTF}}^2(u,v)E^2(u,v)\mathrm{d}u\mathrm{d}v{]}^2}{\iint T^2(u,v){\mathrm{MTF}}^2(u,v)\mathrm{NPS}(u,v)E^4(u,v)\mathrm{d}u\mathrm{d}v}.$$ (10)

In Eqs. (810), $T(u,v)$ is the task function, and $\mathrm{MTF}(u,v)$ and $\mathrm{NPS}(u,v)$ are the system MTF and NPS in the coronal (cross-sectional) plane. In Eq. (10), the eye filter, $E(u,v)$, was computed with $c=3$, corresponding to 50 cm viewing distance as

$$E(u,v)=(\sqrt{u^2+v^2}{)}^{1.3}\exp [-c(u^2+v^2)].$$ (11)

Although the detectability indices were computed for all three numerical observers, for conciseness, the results from the PW observer are reported in detail, followed by summarizing the results for all observer models.

3. Results

Validation of the CSA model using experimental data from an independent group of investigators²⁶ was reported in a prior publication.¹¹ The various sources that contribute to the system MTF are shown in Fig. 4. All major sources of blur are included in the modeling except for X-ray focal spot angular motion. It is relevant to note that the current generation of cone-beam breast CT systems uses a pulsed X-ray source that reduces, but does not eliminate, this blur.

Fig. 4.

Various sources that contribute to the system MTF, ${\mathrm{T}}_{\mathrm{sys}}$, for an example case (70 kV, 0.25 mm Cu, and $525\mu \mathrm{m}$ CsI:Tl). The projection space MTF, ${\mathrm{T}}_{\mathrm{proj}}$, is affected by the finite focal spot size, ${\mathrm{T}}_{\mathrm{focus}}$; optical blurring within the CsI:Tl scintillator, ${\mathrm{T}}_{\mathrm{CsI}-\mathrm{optical}}$; blurring due to emission and reabsorption of K-characteristic X-rays within the CsI:Tl scintillator, ${\mathrm{T}}_{\mathrm{CsI}-\mathrm{K}}$; and pixel aperture function, ${\mathrm{T}}_{\mathrm{pix}}$. Bilinear interpolation, ${\mathrm{T}}_{\mathrm{interpolation}}$, during image reconstruction, degrades the ${\mathrm{T}}_{\mathrm{proj}}$ to provide the system MTF, ${\mathrm{T}}_{\mathrm{sys}}$. Adapted from Ref. 11.

A comparison of the trends in the detectability index across applied tube voltage (kV) range and scintillator thickness range is shown in Fig. 5 for the disk-shaped soft-tissue lesion and for the microcalcification cluster using a PW numerical observer. The X-ray beam filtration is fixed with 0.25 mm of Cu and 2.6 mm of Al in this figure. The trends in detectability indices are reversed between soft-tissue lesions and microcalcifications. Detectability index for microcalcification improves with increasing kV, whereas the detectability index for soft-tissue lesion is better at lower kV. Also, the trends in terms of scintillator thickness are different. For mass lesions, there is a trend of improving the detectability index with increasing scintillator thickness. Whereas for the microcalcification cluster, the detectability index is maximized for 450 to $525\mu \mathrm{m}$ thick CsI:Tl, depending on kV, and is reduced for the $600\mu \mathrm{m}$ thick CsI:Tl.

Fig. 5.

Comparison of the detectability index trends for a range of applied tube voltages and scintillator thicknesses using a prewhitening (PW) numerical observer for (a) microcalcification cluster with $220\mu \mathrm{m}$ ${\mathrm{CaCO}}_3$ spheres, and (b) soft-tissue mass-like lesion modeled as a 4 mm diameter disk. The added X-ray beam filtration was fixed with 0.25 mm of Cu and 2.6 mm of Al. It is important to note that the y-axes are different between the two panels. Although the trends are reversed, for mass-like soft-tissue lesion, the detectability index is substantially higher than that for the microcalcification cluster.

The trends with PW observer for both lesion types across a range of copper filtration are shown in Fig. 6. With increasing copper attenuation, the detectability index generally increases for the microcalcification lesion, whereas it decreases for the mass lesion. In terms of scintillator thickness, a $525\mu \mathrm{m}$ thick CsI:Tl yielded a higher detectability index for microcalcification cluster, and a $600\mu \mathrm{m}$ thick CsI:Tl (maximum thickness studied) yielded a higher detectability index for mass lesion.

Fig. 6.

Detectability index trends for varying copper filtration and scintillator thicknesses using a prewhitening (PW) observer. Applied tube voltage is fixed at 60 kV for these two plots. (a) Shows the trends for the PW detectability of a microcalcification cluster. (b) Shows the trends for PW of a soft-tissue mass. With increasing copper filtration, there is a general trend toward improved detectability index for microcalcification cluster, and a decreasing detectability index for mass lesion. For scintillator thickness, a $525\mu \mathrm{m}$ thick CsI:Tl yielded higher detectability index for microcalcification cluster, and a $600\mu \mathrm{m}$ thick CsI:Tl (maximum thickness studied) yielded higher detectability index for mass lesion.

A comparison of the trends in detectability index using the PW observer between the microcalcification cluster and the soft-tissue lesion is shown in Fig. 7 for 3 kV settings. Each lesion has distinct trends for its detectability, indicating that the specific imaging task must be considered for optimizing or evaluating a system. Also, the detectability index for mass lesions is substantially higher than that for the microcalcification cluster.

Fig. 7.

Detectability index using the PW observer is plotted as a function of scintillator thickness for the mass lesion and the microcalcification cluster. All panels have a fixed copper filtration of 0.25 mm. Applied tube voltage is 50, 60, and 75 kV for each respective panel.

Detectability indices for PW, NPW, and NPWE were calculated for the range of input parameters, and a ratio of soft-tissue mass to microcalcification cluster was calculated for each index. A histogram of the ratios is seen in Fig. 8. The PW and NPW histograms show all ratios above 2, whereas the NPWE shows all ratios above 1. The counts indicate the overall greater detectability for the IDC mimicking soft-tissue lesion compared with a microcalcification cluster.

Fig. 8.

Histogram of the ratio of detectability index between soft-tissue mass-like lesion and microcalcification cluster using three numerical observer models: (a) PW, (b) NPW, and (c) NPWE. All ratios are greater than 2 for PW and NPW observer models, and greater than 1 for NPWE.

4. Discussion

This CSA modeled the image chain similar to the previous study to obtain MTF, NPS, and detectability index. Validation of the model was shown in the previous study¹¹ by comparison with a prone breast CT prototype system.

There have been prior studies reporting on either empirical or theoretical evaluation of breast CT using soft-tissue, mass-like lesions.^27–33 The focus of these studies was to determine the optimal kV. All of these studies report an optimal range of 50 to 70 kV. For the range of scintillator thickness, kV, and Cu filter thickness studied, our results indicate a trend toward thicker scintillator, lower kV, and lower Cu filter thickness. This combination would maximize the zero-frequency detective quantum efficiency due to improved quantum efficiency. Referring to Fig. 2 showing the task function for the mass-like lesion in the spatial frequency domain, it can be observed that the amplitude is predominantly weighted toward low spatial frequencies and provides reasoning for the observed trends for the task of detecting soft-tissue lesions. In addition, in contrast to the aforementioned studies, this work provides a more comprehensive evaluation, including scintillator thickness, kV, and X-ray beam filtration.

The intent of this study is to investigate the detectability of a mass-like soft-tissue lesion and a microcalcification cluster to determine which lesion type should be the primary focus for optimization. One approach would be to weight the lesion type by the prevalence rate. Approximately 50% of non-palpable cancers are detected based on the presence of microcalcifications. Thus, equal weighting for soft-tissue lesions and microcalcification can be justified. Referring to Figs. 5 and 6, where the trends are approximately reversed, this would result in a less-than-optimal detectability index for the task of detecting a microcalcification cluster. In this work, for the 150 combinations studied (6 kV settings $\times 5$ Cu filter thicknesses $\times 5$ CsI:Tl scintillator thicknesses) and for each of the three numerical observer models, there was not a single instance where the detectability index for microcalcifications exceeded that for soft-tissue lesions. Hence, the more appropriate choice is to optimize the system parameters for the task of detecting a microcalcification cluster.

Regarding the microcalcification cluster, the detectability index is calculated for the entire cluster and not for individual microcalcifications. A human observer might not need to detect all calcifications constituting the cluster. Also, the ${\mathrm{CaCO}}_3$ spheres comprising the microcalcification cluster were modeled with a density of $2.8{\mathrm{g}/\mathrm{cm}}^3$. Lower densities of ${\mathrm{CaCO}}_3$ can be modeled by including the packing fraction. Even with a packing fraction of 1.0, the detectability index for microcalcification cluster was lower than soft-tissue lesion. Hence, scaling the density lower will further reduce the detectability index. Also, for the energy range of 5 to 80 keV, the linear attenuation coefficients of calcium oxalate and calcium hydroxyapatite straddle the linear attenuation coefficient of ${\mathrm{CaCO}}_3$. For DM and DBT, American College of Radiology (ACR) accreditation requires visualization of either the $320\mu \mathrm{m}$ speck group made of ${\mathrm{Al}}_2{\mathrm{O}}_3$ spheres or the $230\mu \mathrm{m}$ speck group made of glass beads. Evaluation of DM and DBT systems show that the $240\mu \mathrm{m}$ speck group made of ${\mathrm{Al}}_2{\mathrm{O}}_3$ spheres and the $200\mu \mathrm{m}$ speck group made of glass beads are routinely detected.^34,35 Hence, we used an average of $220\mu \mathrm{m}$ speck group made of ${\mathrm{CaCO}}_3$ spheres.

For soft-tissue lesion, the imaging task modeled the lesion as a cylinder resulting in a circular cross-section in the coronal plane. Neither architectural distortion nor spiculated masses were investigated in the study. Development of lesion models from clinical breast CT datasets is the subject of ongoing research, and the framework used in this study can be adapted for investigating the effect of other lesion types on the detectability index. For DM and DBT, ACR accreditation requirements specify the thickness of mass-like lesion, but not its diameter. We used a 4 mm lesion, as several studies^7,36–38 have reported the ability to visualize 2 to 4 mm lesions with breast CT, even at MGD suitable for screening. If smaller lesions are considered, the detectability index will decrease.

In this study, we did not include anatomical noise, typically modeled as a power-law of the form $K{f}^{-\beta }$, where $f$ is the spatial frequency, and $K$ and $\beta$ are fit coefficients.²¹ Fit coefficients $K$ and $\beta$ for prone-position breast CT have been reported, where the breast is pendant. As mentioned earlier, we are currently developing an upright breast CT system, and this study is partly motivated by finding an optimal combination of kV, filtration, and scintillator thickness. However, there is no knowledge on the fit coefficients for upright breast CT, where the breast is supported by a semi-cylindrical cup. The tissue distribution within the breast will most likely be altered with upright geometry compared with prone geometry as the gravitational force is orthogonal. Hence, rather than making incorrect assumptions, we chose to exclude the anatomical noise in our study. Once data from human subjects are collected with the upright breast CT, the framework used in this study can be modified to include the anatomical noise to revisit the choice of X-ray spectrum (kV and filtration). Also, for the short-scan acquisition with upright breast CT, the data completeness requirement is satisfied for the central plane. As the lesions (soft tissue and microcalcification cluster) are centered at the intersection of the central ray and the axis of rotation, the results from this study are also applicable for upright breast CT. We did not investigate the location dependence of the lesions. However, with increasing radial distance from the axis of rotation, the image blur increases and would preferentially affect the microcalcification cluster more than the soft-tissue lesion. This will result in even higher ratios for the detectability index between soft-tissue lesion and microcalcification cluster. Regarding cone-angle dependence, we had previously shown³⁹ that the cone-beam artifacts are subtle in breast CT as the attenuation differences between adipose and fibroglandular tissue are relatively small compared with other cone-beam CT applications. In addition, the results from this study are strictly valid for linear image reconstruction methods, such as the Feldkamp-Davis-Kress algorithm,⁴⁰ and not necessarily for compressed-sensing,^41,42 and deep-learning^43–47 based algorithms that are being actively investigated.

5. Conclusion

Cascaded systems analysis with parallel cascades and numerical observers were used to evaluate the two common lesion types encountered during breast X-ray imaging: a soft-tissue, mass-like lesion and a microcalcification cluster. For the range of scintillator thickness, kV, and Cu filter thickness studied, our results indicate a trend toward thicker scintillator, lower kV, and lower Cu filter thickness for the task of detecting the soft-tissue lesion. However, for the task of detecting the microcalcification cluster, there is a reversal of trends, favoring higher kV, higher Cu filter thickness, and scintillator thickness in the range of 450 to $525\mu \mathrm{m}$. For the 150 combinations studied (6 kV settings $\times 5$ Cu filter thicknesses $\times 5$ CsI:Tl scintillator thicknesses) and for each of the three numerical observer models, there was not a single instance where the detectability index for the microcalcification cluster exceeded that for the soft-tissue lesion. Hence, when the lesion type is unknown, such as during breast cancer screening, the more appropriate choice is to optimize the system parameters for the task of detecting a microcalcification cluster. However, when the lesion type is known, such as during diagnostic imaging, acquisition factors that maximize the detectability index for the specific lesion type can be beneficial.

Biography

Biographies of the authors are not available.

Funding Statement

This work was supported by the National Cancer Institute (NCI) of the National Institutes of Health (NIH) (Grant Nos. R01 CA241709 and R01 CA199044).

Disclosures

The authors have no financial interest or other conflicts of interest to disclose.

Code and Data Availability

Data sharing is not applicable to this article, as no new data were created or analyzed.