A mathematical model platform for optimizing a multiprojection breast imaging system

Abstract

Multiprojection imaging is a technique in which a plurality of digital radiographic images of the same patient are acquired within a short interval of time from slightly different angles. Information from each image is combined to determine the final diagnosis. Projection data are either reconstructed into slices as in the case of tomosynthesis or analyzed directly as in the case of multiprojection correlation imaging technique, thereby avoiding reconstruction artifacts. In this study, the authors investigated the optimum geometry of acquisitions of a multiprojection breast correlation imaging system in terms of the number of projections and their total angular span that yield maximum performance in a task that models clinical decision. Twenty-five angular projections of each breast from 82 human subjects in our breast tomosynthesis database were each supplemented with a simulated 3 mm mass. An approach based on Laguerre-Gauss channelized Hotelling observer was developed to assess the detectability of the mass in terms of receiver operating characteristic (ROC) curves. Two methodologies were developed to integrate results from individual projections into one combined ROC curve as the overall figure of merit. To optimize the acquisition geometry, different components of acquisitions were changed to investigate which one of the many possible configurations maximized the area under the combined ROC curve. Optimization was investigated under two acquisition dose conditions corresponding to a fixed total dose delivered to the patient and a variable dose condition, based on the number of projections used. In either case, the detectability was dependent on the number of projections used, the total angular span of those projections, and the acquisition dose level. In the first case, the detectability approximately followed a bell curve as a function of the number of projections with the maximum between 8 and 16 projections spanning angular arcs of about 23 degrees-45 degrees, respectively. In the second case, the detectability increased with the number of projections approaching an asymptote at 11-17 projections for an angular span of about 45 degrees. These results indicate the inherent information content of the multi-projection image data reflecting the relative role of quantum and anatomical noise in multiprojection breast imaging. The optimization scheme presented here may be applied to any multiprojection imaging modalities and may be extended by including reconstruction in the case of digital breast tomosynthesis and breast computed tomography.

Figure 1

The prototype multiprojection breast imaging instrument.

Figure 2

Example images of projections of 3D model of a 3 mm simulated lesion assumed to be 3 cm above the detector. These lesions were embedded on tomographic projections to emulate the lesion-present mammographic background. (a), (b), and (c) show the projections with the tube orientation at +22°, 0°, and −22°, respectively, relative to the CC orientation.

Figure 3

Example projection images of ROIs with 3 mm simulated lesions embedded at the center. (a) shows the ROI of a clinically acquired projection with dose level, D_θ, equal to 1∕25th that of standard mammographic screening. (b) and (c) show the same ROI with noise corresponding to 1∕2 and 1∕25th fraction of D_θ.

Figure 4

ROCs of 25 projections obtained from a multiprojection imaging system and the average of those. Also shown are the ROCs obtained from the two fusion techniques. The angular span of the projections was 44.8°.

Figure 5

Variation of AUC with a number of projections for different dose levels. Isoimage-dose condition was used implying that the dose level of each projection (D_θ) along a curve remains constant (i.e., more projections imply more dose to the patient). This dose level is indicated by the fraction of the clinical dose level in the legend. The Bayesian decision fusion technique was used for this analysis. The angular span of the projections was 44.8°.

Figure 6

Variation of AUC under isoimage-dose conditions for a different number of angular projections spanning a total angular arc in the 3.6°−44.8° range using (a) weighted averaging of test statistics techniques and (b) Bayesian decision fusion. The dose level of each acquisition was equal to 1∕25th of the standard mammographic screening dose level leading to an increased dose level with an increasing number of angular projections considered to reach a maximum of a conventional dual-view screening dose at 25 projections.

Figure 7

Variation of AUC under isostudy-dose conditions using the (a) weighted averaging of the test statistics and (b) Bayesian decision fusion technique. The total dose level, equal to 1∕25th of the standard dual-view mammographic screening dose level, was linearly divided among the different projections and, hence, the total dose delivered remains constant at this dose level.