Estimations of lung structural properties from a single propagation-based dark-field X-ray image

In this investigation, we applied a single-projection dark-field imaging technique to gain statistical information on the smallest airway structures within the lung$\unicode{x2014}$the alveoli$\unicode{x2014}$focusing on their size and number as key indicators of lung health. The algorithm employed here retrieves the projected thickness of the sample from a propagation-based phase contrast image using the transport-of-intensity equation. The first Born approximation is then used to isolate the dark-field signal associated with edge scattering, which increases the visibility of microstructure boundaries. PMMA spheres of known sizes were imaged first as an idealised alveolar model. The dark-field signal was then recovered from propagation-based phase-contrast X-ray images of the lungs of small mammals using this method. The retrieved dark-field signal was found to be proportional to both the alveolar size ($R^2 = 0.85$) and the number in projection ($R^2 = 0.69$), and these measurements could be combined to provide an estimate of the total surface area of the alveolar interfaces ($R^2 = 0.78$). This demonstrates the approach's ability to indicate lung health using the dark-field signal retrieved from a single-phase-contrast X-ray image.