Signal extraction in x-ray dark-field imaging
The x-ray dark-field radiography setup is based on a Talbot-Lau interferometer [16] consisting of an x-ray source, three x-ray gratings and one x-ray detector, as illustrated in Fig. 1. A source grating (G0) renders the method accessible with a clinical x-ray source by providing the beam coherence necessary for the method. A phase shifting grating (G1) causes a specific periodic interference pattern, which can be resolved by the analyser grating (G2) in combination with the detector. By laterally scanning one of the gratings (the so-called phase-stepping), one measures an oscillating signal for each single detector pixel. Comparing a sample scan to a reference scan without sample yields three complementary signals for the sample simultaneously: the conventional attenuation; the differential phase shift; and the dark-field signal. In this study, we focus mainly on the attenuation and the dark-field signal. A more detailed description of this method was previously given [14, 17,18,19].
Technical parameters
The preclinical x-ray dark-field setup used a tungsten target x-ray tube (x-ray WorX SE 160, Garbsen, Germany), operating at 60 kVp and a power of 150 W. The detector was a Varian Paxscan 2520DX flatpanel detector with a CsI scintillator and a pixel size of 127 μm (Varian medical systems, Palo Alto, CA, USA). Due to cone-beam magnification, the effective pixel size was 110 μm. The interferometer was designed for a mean energy of 45 keV with grating periods of 10.0/5.0/10.0 μm for G0/G1/G2, respectively. The full field-of-view needed for the radiography of the hand was stitched together from 3 × 3 single images as the currently available size of the gratings is limited. The radiation exposure for the hand was 87.5 mAs distributed over seven grating steps for 5 s of exposure per step. The exposure time was varied between 1, 2, and 5 s. The incident air kerma at the position of the sample was measured with a PTW NOMEX dosimeter (PTW Freiburg GmbH, Germany). Considering all gratings and the setup geometry, a measured value of 0.22 mGy corresponds to an estimated image receptor dose of about 25 μGy for 1-s exposure time.
Foreign-body phantom
The phantom was specifically designed for testing the sensitivity and resolution of the method for very small particles. It consisted of an 18 mm thick polymethyl methacrylate (PMMA) plate and pairwise test objects of aluminium and wood with diameters of 0.5, 0.7, 0.9, and 1.1 mm fixed on the PMMA plate with tape (configuration 1, see Fig. 2), pairwise horizontally and vertically aligned relative to the grating orientation. The PMMA plate was chosen to mimic the attenuation characteristics of soft tissue.
In the second step, the configuration of the above described phantom was extended by an aluminium-oxide plate of 1 cm (configuration 2), which mimics the attenuation of bone [20,21,22]. Images were acquired in both phantom configurations to verify the signal intensity in the intercarpal space as well as directly behind a bone.
Two images were acquired for configuration 1 with exposure times of 1 and 5 s per step. The exposure time for configuration 2 was 2 s per step.
Specimen preparation
The study was approved by the local institutional review board. The donor of the hand used in this study had given his body for educational and research purposes and provided written informed consent before death, in compliance with local institutional and legal requirements. The hand was fixed with formaldehyde solution before the experiments.
We inserted different typical wooden and metallic foreign objects in the human hand (Fig. 1c). For the measurement, the specimen was placed into a planar plastic container and the formalin level was reduced. The human hand was imaged with an exposure time of 5 s per step.
Visual foreign-body detection
All images were acquired using the above described preclinical setup with the same technical parameters. No specific post-processing has been applied. The stitched radiographic images were analysed by two trained radiologists (DM, AF), both of them with more than ten years of experience.
Signal-to-noise analysis
The signal-to-noise ratio (SNR) was calculated (NumPy package, Python 2.7) for all foreign-body objects in the specimen and the phantom for a region of interest \( \overline{\mathrm{s}} \) inside the object compared to the mean of a region of interest in the background \( \overline{\mathrm{b}} \) and the standard deviation of this background region σb according to the following formula:
$$ SNR=\frac{\left|\overline{\mathrm{s}}-\overline{\mathrm{b}}\right|}{\sigma_{\mathrm{b}}}. $$
An SNR value < 1 means that an object cannot be distinguished from the background. Thus, all values < 1 were set to zero.