Dark field of lung microstructures from synchrotron micro CT to a table top setup

From monochromatic beam and single sizes to a lung model

\(B = v / v_0 = \exp (-\mu_B t)\)

Sample made of identical spheres of the same material \(\mu_B(r, E; n, f)\) studied in recent literature:

• \(r\) radius of the spheres
• \(E\) beam energy
• \(n\) refractive index
• \(f\) volume fraction occupied by the spheres

Literature links

• Yashiro et al. (2010) On the origin of visibility contrast in x-ray Talbot interferometry
• Lynch et al. (2011) Interpretation of dark-field contrast and particle-size selectivity in grating interferometers
• Gkoumas et al. (2016) A generalized quantitative interpretation of dark-field contrast for highly concentrated microsphere suspensions

we used the latest for which we have the code

Polychromatic extension

\[ \mu_B = \int_{\text{radii}}\int_{\text{energies}} \mu(r, E; n, f)\rho(r)s(E)\mathop{dr}\mathop{dE} \]

Consistency check: integrating over energies only

Estimating \(n\) and \(f\)

• \(n\): NIST database with density matching beamline absorption at 12 keV
• \(f\): pixel counting in the segmented image

From lung microstructures to sphere distributions

Technical challenges

• datasets with 2540x2160x6000 pixels
• fiji implementation has excessive requirements on both memory and processing time

Complete rewrite

• C and C++ with python bindings
• code (with Goran and Arttu)
• eliminate empty spaces outside of the sample
• ignore airways larger than 100 μm
• process spheres from the largest to the smallest, drastically reducing cpu cycles
• split volume into several subvolumes for a smaller memory footprint
• used all hardware resources: gws-3, gws-4 and RA cluster

Polychromatic extension

\[ \mu_B = \int_{\text{radii}}\int_{\text{energies}} \mu(r, E; n, f)\rho(r)s(E)\mathop{dr}\mathop{dE} \]

Results

Thank you for your attention

Backup

Previous progress report

Microtomography and postprocessing

• synchrotron microtomography
• segmentation

Alveoli as spheres

• fit spheres in the lung microstructures
• plot diameter distribution

The final model

sum over the sphere size distribution times the dark field response for each spere size

ground truth

dark-field response