Proof-of-concept demonstration of edge-illumination x-ray phase contrast imaging combined with tomosynthesis

In this note we present the first proof-of-concept results on the potential effectiveness of the edge-illumination x-ray phase contrast method (in its ‘coded-aperture’ based lab implementation) combined with tomosynthesis. We believe that, albeit admittedly preliminary (e.g. we only present phantom work), these results deserve early publication in a note primarily for four reasons. First, we fully modelled the imaging acquisition method, and validated the simulation directly with experimental results. This shows that the implementation of the method in the new geometry is understood, and thus that it will be possible to use the model to simulate more complex scenarios in the future. Secondly, we show that a strong phase contrast signal is preserved in the reconstructed tomosynthesis slices: this was a concern, as the high spatial frequency nature of the signal makes it sensitive to any filtration-related procedure. Third, we show that, despite the non-optimized nature of the imaging prototype used, we can perform a full angular scan at acceptable dose levels and with exposure times not excessively distant from what is required by clinical practice. Finally, we discuss how the proposed phase contrast method, unlike other approaches apart from free-space propagation (which however requires a smaller focal spot, thus reducing the flux and increasing exposure times), can be easily implemented in a tomosynthesis geometry suitable for clinical use. In summary, we find that these technical results indicate a high potential for the combination of the two methods. Combining slice separation with detail enhancement provided by phase effects would substantially increase the detectability of small lesions and/or calcifications, which we aim to demonstrate in the next steps of this study.


Introduction
This note presents preliminary results on the possible combination of two important developments in medical x-ray imaging, namely x-ray phase contrast imaging (XPCi) (Lewis 2004, Bravin et al 2013 and digital tomosynthesis (DTS) (Dobbins andGodfrey 2003, Park et al 2007).
Following its introduction either at synchrotrons (Snigirev et al 1995, Ingal andBeliaevskaya 1995) or with microfocal sources (Davis et al 1995, Wilkins et al 1996, XPCi has progressed significantly over recent years. Most importantly, methods have emerged that enable its implementation with conventional, non-microfocal laboratory sources, such as Talbot-Lau interferometry (Pfeiffer et al 2006) and edge-illumination/coded-aperture approaches (Olivo et al 2001, Olivo andSpeller 2007a). These methods have the potential to enable the transfer of XPCi into clinical practice.
This note focuses on the latter method, primarily because of its simplified set-up , which however does not affect its phase sensitivity (Marenzana et al 2012). Specifically with regards to a tomosynthesis implementation, this set-up simplification is essential as it enables acquiring the various projections simply by 'tracking' the source angular position with a lateral displacement of the pre-sample mask (see below).
The method is based on the 'edge-illumination' principle, i.e. the observation that illuminating only the edge of the detector pixels substantially enhances the phase sensitivity of an x-ray imaging system. It was first introduced in the framework of a synchrotron experiment (Olivo et al 2001), and more recently adapted for use with conventional sources by means of a pair of appropriately designed apertured masks placed either side of the imaged object (Olivo and Speller 2007a; a schematic of the imaging system is presented in the next section). A recent paper reviews the two implementations of the method, and discusses the transition from one to the other (Munro et al 2012b).
The lab-based set up was shown to provide intense XPCi signals also when used with focal spots of up to 100 μm, compatible with current practice in mammography (Olivo and Speller 2007b), to easily tolerate high x-ray energies  and to be resilient to misalignments/vibrations of the order of a few μm . Again this is an essential feature in view of a tomosynthesis implementation, as this sort of tolerance is within reach of current technology; for comparison, Talbot-Lau methods were shown to require tolerances of a few tens of nm (Zambelli et al 2010). Finally, the low aspect ratio of the masks makes them cheap and easy to fabricate, and mask areas sufficient to cover large fields of view are already commercially available.
Edge-illumination XPCi produces differential phase contrast profiles through integration (at the pixel level) of partial free-space propagation profiles, in themselves proportional to the second derivative of the phase shift (Olivo andSpeller 2008, Munro et al 2012b). The final result practically matches the signal that is obtained in analyser based imaging (Davis et al 1995, Ingal and Beliaevskaya 1995, Chapman et al 1997: this was already recognized in the original edge-illumination paper (Olivo et al 2001), and was more recently formally demonstrated . Due to this corpus of previous literature, and in the interest of brevity as required by a note, formal equations expressing the x-ray intensity detected at N2 the pixel level will not be repeated here-explicit expressions can be found in Munro et al 2010, 2012a, Diemoz et al 2013. Phase retrieval (Munro et al 2012a was not performed in the present case, hence the images presented below contain the differential phase signal superimposed on the 'standard' absorption one. This is essentially the strategy followed by the in vivo program underway at the Trieste synchrotron (Castelli et al 2011), and was adopted primarily for its simplicity and because it enabled us to keep dose and exposure time to a minimum. At the same time, it is admittedly a limiting approach, as it prevents the application of promising algorithms like, for example, the one recently introduced by Köhler et al (2011), as they require the prior separation of phase and absorption signals. Phase retrieval methods are a relatively recent development for our method (Munro et al 2012a, and more research in this direction will be undertaken in the next stages of this preliminary study. DTS provides separated volumetric image slices of the sample in planes perpendicular to the 'main' x-ray direction (bisector of the angle spanned by the source during the scan) through limited view tomography. This enables removing, or at least suppressing, the 'structural noise' due to the superposition of multiple anatomic structures projected onto the same region of the image, which could mask the details of interest (Dobbins andGodfrey 2003, Park et al 2007). While DTS finds several applications in diagnostic radiology, breast imaging is considered one of the most significant as DTS can at least partially solve the wellknown 'dense breast' problem, in which the superposition of fibroglandular structures can make it difficult to visualize faint tumours in individual 2D projection images (Niklason et al 1997).
While several acquisition geometries exist for DTS, such as fully (Dobbins and Godfrey 2003) and partially isocentric (Dobbins andGodfrey 2003, Niklason et al 1997), in this preliminary study conducted with a proof-of-concept prototype we have decided to rotate the sample over a limited angular range, while keeping source, aperture masks and detector stationary. This effectively corresponds to the fully isocentric geometry, and the adaptation to more sophisticated geometries (as well as direct testing of the case in which the sample is kept stationary and the tube rotated) will be the subject of future research. Figure 1 shows a schematic of the imaging prototype. This uses the Rigaku M007 rotating target x-ray source, with a molybdenum anode and a focal spot size of approximately 75 μm. For this experiment, it was operated at 40 kVp and 25 mA with 30 μm Mo filtration. The detector is the ANRAD 'SMAM' amorphous selenium flat panel, with a pixel size of 85 μm.

Materials and methods
Both detector and pre-sample aperture masks were manufactured to the authors' design by Creatv Microtech (Potomac, MD, USA). The detector mask consists of a series of 720 × 6 cm long vertical 20 μm wide apertures, with 83.5 μm pitch, obtained in an approximately 30 μm thick gold layer electroplated on a graphite substrate. The pre-sample mask has the same design demagnified by a factor 1.25 to account for the beam divergence-source-to-sample and sample-to-detector distances were 1.6 and 0.4 m respectively in this case. Both masks are mounted on a stack of Newport translators and Kohzu cradles which allows the alignment of each aperture with a pixel column in the detector (Ignatyev et al 2013). Images were obtained at '50% illumination' (Olivo and Speller 2007b), which means that the two masks were misaligned by half an aperture size along x (see figure 1(b)). The sample stage features translation along x, rotation around y for the tomosynthesis acquisitions, and cradles allowing rotation along z and x to enable alignment of the tomosynthesis rotation axis (y) with the pixel columns.  Two phantoms were imaged-one aimed at experimentally verifying the developed simulations and the other at testing the imaging system on a sample of sufficient thickness. The 'simulation' phantom ('wire phantom' in the following) consisted of two polyethylene wires (roughly) aligned in the y direction, separated by 2 cm, with thicknesses of 210 and 470 μm respectively. This was mounted on the sample stage with the centre of rotation (approximately) between the two wires. The second phantom ('double TORMAM' in the following) was obtained by superimposing two TORMAM mammography phantoms (Leeds Test Objects Ltd, Boroughbridge, Yorkshire, UK) and shifting them one with respect to the other, so that different details overlapped in an individual projection image. Each phantom is 1.6 cm thick, for an overall sample thickness of 3.2 cm. Figure 2 shows the sample and the region of interest (ROI) imaged in this experiment.
Two different strategies were followed (and ultimately compared) to simulate the wire phantom. The first one was based on an extension of the ray optics model described in Olivo and Speller (2007b). This extension allows following each ray after interaction with the first object, calculating possible interactions with the second object and tracking the (twice) modified trajectory to verify whether it hits a detector aperture or the solid septa between N4 apertures (e.g. see trajectory '3' in figure 1(b)). By changing the position of the centres of the two wires (which are given as input to the code), the double wire combination can be rotated, thus simulating the various projections forming the tomosynthesis scan. The second strategy consisted in implementing the appropriate geometry through the modular Monte Carlo 'McXtrace' program (Knudsen et al 2011). Considering that the Olivo and Speller model had been experimentally verified a number of times in the past (Olivo and Speller 2007b, this also enabled us to 'benchmark' the McXtrace software, which means that in the future we will be able to reliably exploit its modular nature and flexibility to simulate more complex scenarios. The measurement of the entrance dose was obtained with a calibrated ionization chamber (Keithley 35050A) placed behind the pre-sample mask and in contact with the phantom. A value of 0.76 mGy was measured at zero degree projection angle for a 7 s exposure (see figures 5 and 6 below and related discussion), and multiplied by the number of angles to obtain a total air kerma used in the tomosynthesis scan. As the key results presented below for the 3.2 cm thick 'double TORMAM' phantom were obtained using 15 projections, this corresponds to a total entrance dose of 11.4 mGy for the entire DTS scan, which is within the limits of quality assurance protocols in mammography (Gennaro et al 2004).
Images were reconstructed using an iterative algorithm based on the separable paraboidal surrogates method developed by Sotthivirat and Fessler, a full description of which can be found in Erdogan and Fessler (1999), Fessler and Erdogan (1999) and Sotthivirat and Fessler (2000). The convergence check was performed visually: we observed that ten iterations were typically sufficient to enhance the phase contrast signal without compromising image quality through excessively increased noise. The resolution in the z direction was set to 0.5 mm. Prior to reconstruction, all projections were dark-and bright-field corrected, i.e. the 'dark' image acquired with the beam off was subtracted, and the result was then normalized to the 'bright' field image acquired with the beam on but without the sample present. The reconstruction method was chosen because its use resulted in better image quality and preservation of the phase-induced edge-enhancement compared to the other methods we tested (e.g. filtered backprojections).
As done above for the expressions of x-ray intensity at the pixel level, due to the brevity constraints imposed by a note we avoid repeating the reconstruction equations here, and refer the reader to the quoted literature. It should be noted that the development of a dedicated reconstruction algorithm was not among the aims of the present proof-of-concept work, although this might be pursued as a future direction (e.g. along the lines described by Köhler et al (2011), following incorporation of phase retrieval in an efficient tomosynthesis acquisition scheme). Our aim thus far was to implement the edge-illumination XPCi method in the tomosynthesis geometry while choosing the reconstruction algorithm providing the best performance for 'mixed' phase/absorption images (Castelli et al 2011) among the ones available. Figure 3 shows the comparison between experimental and simulated (with both the Olivo and Speller ray tracing and McXtrace models) profiles extracted from projection images of the wire phantom, rotated at different angles.

Results and discussion
As can be seen, the two simulation models provide practically indistinguishable results, which enables us to benchmark McXtrace against an existing model that was previously experimentally verified. Most importantly, there is good match with the experimental results. In the interest of brevity, only two examples are reported, but the full tomosynthesis scan was simulated, and the same agreement was observed at all angles. In (a), the rotation angle is such that the small wire is projected roughly at the centre of the large one. In (b), the right edges almost match, and as a consequence the positive peak on the right-hand side of the profile is amplified. The small insets show the (simulated) images for each case. Figure 4 shows the slices reconstructed from simulated (panels (a) and (d) and experimental (panels (b) and (e)) tomosynthesis scans of the wire phantom. The scan was limited to angular positions where wires overlap, i.e. broadly speaking from the position represented in figure 3(b) to the symmetric one where the left edges of the wires overlap. This required an angular span of approximately 1.5 • , which was covered through 15 angular steps of approximately 0.1 • each.
Despite the limited angular range and the fact that the two wires are always completely overlapping in the individual projections, they are fully separated in the tomosynthesis reconstruction. Most importantly, the phase-induced edge-enhancement is preserved, and despite the additional steps of acquiring multiple projections and performing a tomosynthesis reconstruction, there is still optimal agreement between simulated and experimental data extracted from reconstructed slices (profiles in figures 4(c) and (f)), although the noise is increased and some reconstruction artefacts can be observed. This further validates the robustness and reliability of the simulation model(s).
Due to the small dimensions of the imaged details, and for the sake of a better comparison between simulation and experiment, the sample was 'dithered' in four steps for each angular projection, i.e. the sample was laterally displaced by a quarter of a (demagnified) pixel, and an image with increased resolution was obtained for each projection by recombining the four sub-pixel images. This means that 4 (dithering steps) × 15 (angular projection) = 60 images were acquired in total, for an overall scan time of 3 (the exposure time for each frame being 3 s). This 'dithering' process was not applied to the 'double TORMAM' images presented below, which enabled us to reduce both exposure time and delivered dose.
The 'double TORMAM' phantom was acquired in 15 projections of 1 • each, with a 7 s exposure per projection and no dithering, i.e. a single projection was acquired at each angular position. This corresponds to a total scan time of 105 s and a total entrance dose of 11.4 mGy (see above), compatible with quality assurance protocols in mammography (Gennaro et al 2004). The exposure time per frame was increased with respect to the wire phantom to compensate for the higher absorption of the 3.2 cm thick 'double TORMAM' phantom. However, it should be noted that this has not been optimized, and strategies exist to reduce the exposure time (e.g. we have evidence that the system length could be reduced from the current 2 m to at least 1.5 m (Olivo and Speller 2007b)). A significant detail showing effective separation of features while preserving strong phase-related edge enhancement is shown in figure 5; for completeness' sake, figure 6 shows the full area of the phantom that has been imaged. Admittedly, the imaged phantom represents a highly simplified imaging task compared to real breast tissue. However, we find that this study reaches its preliminary aim which was to demonstrate that our XPCi method can be implemented in tomosynthesis geometry while maintaining substantial phase-induced edge-enhancement and delivering radiation doses compatible with clinical requirements. While the phantom's simple geometrical structure is likely to have played a role in enabling a limited angular span, it should be noted that wider spans (and larger frame numbers) could be coupled to a lower exposure per frame to reach the same overall dosage, and therefore potentially similar statistics in the reconstructed slices. This will be the subject of further investigations.
Finally, we point out the simple way in which edge-illumination could be implemented in a tomosynthesis system in which the object is kept stationary and the source moves in an arc above it. The edge-illumination method requires only that the illuminated pixel fraction (i.e. the portion of each beamlet in figure 1(b) falling outside the absorbing septa of the detector mask) is kept constant at all projections. As the source position is moved along an arc, this is obtained by a lateral displacement of the pre-sample aperture. This displacement can be easily calculated in advance, and needs to be realized with a tolerance of 1-2 μm, which is within reach of current technology . Most importantly, the detector output (e.g. outside the sample) is in itself a measure of the pre-sample mask position: this can be used in a feedback mechanism that tracks the pre-sample mask position and keeps the system dynamically aligned, as discussed in Ignatyev et al (2013).

Conclusions
We have conducted a preliminary phantom study on the possible implementation of the edgeillumination x-ray phase contrast imaging method in the tomosynthesis geometry. The goal was to use simple masks and a commercially available x-ray source and detector to perform a scan with exposure times and dose values not too distant from clinical requirements. The target was met in terms of delivered dose; however, it was only partially met in terms of exposure N8 time. Nevertheless, strategies can be implemented (reduction of the overall system length, use of different anode material/design, etc), which could make the required ∼10× reduction in exposure time possible. In addition to this, we show that significant phase-induced edge enhancement is preserved in the reconstructed slices, and we discuss strategies to design a clinical system in which the source rotates and the patient is kept stationary. Finally, we have fully modelled the system using two different simulation codes, and demonstrated excellent agreement with the experimental results. These models will support the developments of the next stages (more complex phantoms, increased angular range/number of projections, etc) of what is admittedly a preliminary, yet encouraging, proof-of-concept investigation.