A virtual trial framework for quantifying the detectability of masses in breast tomosynthesis projection data

Abstract

Purpose: Digital breast tomosynthesis (DBT) is a promising breast cancer screening tool that has already begun making inroads into clinical practice. However, there is ongoing debate over how to quantitatively evaluate and optimize these systems, because different definitions of image quality can lead to different optimal design strategies. Powerful and accurate tools are desired to extend our understanding of DBT system optimization and validate published design principles.

Methods: The authors developed a virtual trial framework for task-specific DBT assessment that uses digital phantoms, open-source x-ray transport codes, and a projection-space, spatial-domain observer model for quantitative system evaluation. The authors considered evaluation of reconstruction algorithms as a separate problem and focused on the information content in the raw, unfiltered projection images. Specifically, the authors investigated the effects of scan angle and number of angular projections on detectability of a small (3 mm diameter) signal embedded in randomly-varying anatomical backgrounds. Detectability was measured by the area under the receiver-operating characteristic curve (AUC). Experiments were repeated for three test cases where the detectability-limiting factor was anatomical variability, quantum noise, or electronic noise. The authors also juxtaposed the virtual trial framework with other published studies to illustrate its advantages and disadvantages.

Results: The large number of variables in a virtual DBT study make it difficult to directly compare different authors' results, so each result must be interpreted within the context of the specific virtual trial framework. The following results apply to 25% density phantoms with 5.15 cm compressed thickness and 500 μm(3) voxels (larger 500 μm(2) detector pixels were used to avoid voxel-edge artifacts): 1. For raw, unfiltered projection images in the anatomical-variability-limited regime, AUC appeared to remain constant or increase slightly with scan angle. 2. In the same regime, when the authors fixed the scan angle, AUC increased asymptotically with the number of projections. The threshold number of projections for asymptotic AUC performance depended on the scan angle. In the quantum- and electronic-noise dominant regimes, AUC behaviors as a function of scan angle and number of projections sometimes differed from the anatomy-limited regime. For example, with a fixed scan angle, AUC generally decreased with the number of projections in the electronic-noise dominant regime. These results are intended to demonstrate the capabilities of the virtual trial framework, not to be used as optimization rules for DBT.

Conclusions: The authors have demonstrated a novel simulation framework and tools for evaluating DBT systems in an objective, task-specific manner. This framework facilitates further investigation of image quality tradeoffs in DBT.

Figure 1

Breast phantoms (before compression) in sagittal cross-section with randomly-generated compartments of adipose (gray) and fibroglandular tissues (white), showing example tissue structures for the simulated class of patients.

Figure 2

We modeled a partially-isocentric breast tomosynthesis acquisition geometry (schematic not to scale).

Figure 3

From left-to-right: Sagittal slice through a compressed phantom (z = 6 cm) with 3 mm diameter signal (light gray), ray-tracing projection at θ = 0°, and simple back projection reconstruction from 25 equally-spaced ray-tracing projections with θ_scan = 96° (refer to Fig. 2 for geometry).

Figure 4

From left-to-right: Zero-angle projection ROIs (128 × 128 pixels) from scans with P = 1, 5, and 15 total projections. Applying Eq. 3 with fixed total exposure (N₀ = 10¹⁰ source photons) and increasing P leads to increased quantum noise per projection.

Figure 5

The mean glandular dose (in milliGray per source photon) declined slightly with projection angle θ (in degrees). This trend qualitatively agrees with results from Sechopoulos et al. (Ref. 11) for a phantom with similar chest-to-nipple distance (e.g., Figs. 8(c) and 9(c) of Ref. 44). Error bars are ±2σ based on a set of 500 phantoms.

Figure 6

Zoomed ROIs (only the central 24 × 24 pixels shown) from the first six (of C) LG channels used to reduce the dimensionality of g. The LG width parameter a = 6, and the full ROIs were 128 × 128 to match the image dimensions in Fig. 4.

Figure 7

AUC versus the number of channels for θ = 0° and θ = 48° projection angles. We chose C = 6 for approximately asymptotic performance. N₀ = 5 × 10¹¹ and ${\sigma }_{\text{elec}}^2=0$.

Figure 8

AUC map as a function of total MGD for the whole scan and electronic noise variance (${\sigma }_{\mathrm{elec}}^2$) illustrates the tradeoffs in our covariance decomposition noise model. In this case P = 5 and θ_scan = 64°, and the dotted lines are approximate boundaries between different performance-limiting factors.

Figure 9

In the anatomical-variability-limited (A) regime, AUC appears to be independent of scan angle. In the Q and E regimes, the trends appear similar to the A regime trends except at large θ_scan. Error bars are 95% confidence intervals computed from 100 bootstrap samples.

Figure 10

Multiprojection imaging (P > 1) improved AUC for all three scan angles (in the A regime), though the optimal number of projections appears to depend on scan angle. For θ_scan = 96°, there is a threshold number of projections around P = 7 for maximum AUC. Error bars are 95% bootstrap confidence intervals.

Figure 11

Comparison of five virtual DBT trial frameworks (continued on the next page).

Figure 11

Comparison of five virtual DBT trial frameworks (continued on the next page).