Multi-resolution X-ray phase-contrast and dark-field tomography of human cerebellum with near-field speckles

Sara Savatović; Sara Savatović; Marie-Christine Zdora; Marie-Christine Zdora; Fabio De Marco; Fabio De Marco; Christos Bikis; Christos Bikis; Margie Olbinado; Alexander Rack; Bert Müller; Pierre Thibault; Pierre Thibault; Irene Zanette

doi:10.1364/BOE.502664

Biomedical Optics Express
Vol. 15,
Issue 1,
pp. 142-161
(2024)
•https://doi.org/10.1364/BOE.502664

Multi-resolution X-ray phase-contrast and dark-field tomography of human cerebellum with near-field speckles

Sara Savatović, Marie-Christine Zdora, Fabio De Marco, Christos Bikis, Margie Olbinado, Alexander Rack, Bert Müller, Pierre Thibault, and Irene Zanette

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Sara Savatović, Marie-Christine Zdora, Fabio De Marco, Christos Bikis, Margie Olbinado, Alexander Rack, Bert Müller, Pierre Thibault, and Irene Zanette, "Multi-resolution X-ray phase-contrast and dark-field tomography of human cerebellum with near-field speckles," Biomed. Opt. Express 15, 142-161 (2024)

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- X-ray Microscopy and Imaging
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About this Article
History
- Original Manuscript: September 1, 2023
- Revised Manuscript: October 30, 2023
- Manuscript Accepted: November 9, 2023
- Published: December 7, 2023
Virtual Issues
Biomedical Optics Express Optics and the Brain (2023)

Abstract

In this study, we use synchrotron-based multi-modal X-ray tomography to examine human cerebellar tissue in three dimensions at two levels of spatial resolution (2.3 µm and 11.9 µm). We show that speckle-based imaging (SBI) produces results that are comparable to propagation-based imaging (PBI), a well-established phase-sensitive imaging method. The different SBI signals provide complementary information, which improves tissue differentiation. In particular, the dark-field signal aids in distinguishing tissues with similar average electron density but different microstructural variations. The setup’s high resolution and the imaging technique’s excellent phase sensitivity enabled the identification of different cellular layers and additionally, different cell types within these layers. We also correlated this high-resolution phase-contrast information with measured dark-field signal levels. These findings demonstrate the viability of SBI and the potential benefit of the dark-field modality for virtual histology of brain tissue.

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Data availability

Data underlying the results presented in this paper may be obtained from the authors upon request.

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Fig. 1. Experimental setup at the imaging beamline ID19, ESRF (Grenoble, France). Synchrotron radiation from an undulator insertion device is modulated by a diffuser before traversing the sample and finally reaching the detector. The diffuser is used to mark the wavefront, and distortions of the reference speckle pattern introduced by the sample are used to disentangle the different signals—attenuation, diffraction, and small-angle scattering.

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Fig. 2. Signals retrieved with UMPA for one example projection of the MR dataset. (a) Transmittance

$T$

, (b) dark-field

$D$

, and the differential-phase signals in the (c) horizontal (

$u_x$

) and (d) vertical direction (

$u_y$

);

$u_x$

and

$u_y$

are given in pixels.

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Fig. 3. Speckle characterization and visibility analysis. (a), (b) Speckle pattern for the MR and HR setups, with insets of a

$166 \times 166$

px and

$300 \times 300$

px region of interest, respectively. (c) Normalized intensity distributions of (a) and (b). (d), (e) show maps of visibility

$V$

and 3D representation of the speckle pattern autocorrelation (FWHM

$_{\text {MR}}$

= 3.3 px vs. FWHM

$_{\text {HR}}$

= 10.1 px). (f) Visibility distribution for the two setups.

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Fig. 4. Example projection of horizontal (

$\alpha _{x}$

) and vertical (

$\alpha _{y}$

) refraction angles from the MR dataset (a), (b) and the HR dataset (c), (d). The differential-phase signal from UMPA has been bias-corrected before the analysis, in order to reduce the amount of estimation bias-induced noise. The refraction angles were calculated for propagation distances of

$d_{2,\text {MR}}=45.0\,\mathrm {cm}$

and

$d_{2,\text {HR}}=8.5\,\mathrm {cm}$

. Insets show the

$50 \times 50\,\mathrm {px}$

ROIs used for the calculation of angular sensitivity.

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Fig. 5. Tomographic reconstruction of the four modalities retrieved in the MR scan: (a) linear attenuation coefficient

$\mu$

, retrieved from UMPA transmittance projections, (b) index of refraction decrement

$\delta$

from the PBI scan (projections with no diffuser), (c)

$\delta$

retrieved from UMPA differential-phase data, and (d) linear diffusion coefficient

$\varepsilon$

retrieved from UMPA dark-field data. Insets show a region highlighting contrast differences between paraffin wax, molecular layer (ml), and granular cell layer (gcl).

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Fig. 6. Phase tomogram of the human cerebellum at higher spatial resolution. (a) 3D rendering of the volume with some segmented features. (b) Transverse slice. Gray and white matter, as well as the molecular layer (ml), granular cell layer (gcl) and Purkinje cell layer (Pcl) can be distinguished. Large blood vessels (v) are also visible. Panels (c) and (d) show the same highlighted detail in (a) for the phase and the attenuation volumes. Purkinje cells (Pc) and stellate cells (sc) in the molecular layer and the granule cells (gc) in the granular cell layer can be easily distinguished. Synapses joining Pc and sc are better visualized in the attenuation volume, whereas cell bodies have higher contrast in the phase volume. (e) ROI of the slice in panel (b) at the transition zones of the gcl, Pcl and ml. The nuclei (white dots) of the Purkinje cells can be seen.

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Fig. 7. Phase and dark-field volumes of the human cerebellum acquired at the MR setup. (a),(b) Transverse phase and dark-field slice at the same height in the volumes. Different layers in the cerebellar tissue can be distinguished in both. Dark-field shows an increased contrast between the granular cell layer (gcl) and white matter (wm). (c) Sagittal slice with a zoomed inset with arrows pointing at a blood vessel (v) and some Purkinje cells (Pc), which appear as bright spots between the molecular layer and the gcl in the phase volume. (d),(e) Coronal slices in the phase volume show paraffin infiltration between the cerebellar folds, emphasizing the pia mater (pm), which is the inner membrane enclosing the brain. (f)-(h) show matching slices through the dark-field volume. The scale bar in (c)-(h) is 500 µm.

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Fig. 8. Cell size distribution and autocorrelation analysis. (a)-(c) show slices in the

$300 \times 300 \times 300$

px ROIs in the HR phase volume for different cerebellar layers. (d) shows

$G(\xi )$

, the radial average of the projection of the 3D autocorrelation for the different ROIs. The inset in (d) shows [

$1-G(\xi )$

], the relevant quantity for calculating

$\varepsilon$

, near the system autocorrelation length. (e) Segmentation of the granule cells and stellate cells in the molecular layer is color-coded according to cell size and shown in 3D along with some Purkinje cells (orange) and blood vessels (red). Granule and stellate cell size distributions and colormaps are reported under the segmentation. The locations of the three ROIs in panels (a)-(c) are highlighted in the 3D representation.

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Fig. 9. Spatial resolution estimation in phase tomograms. (a) MR phase tomogram slice. Reconstruction sensitivity can be estimated by measuring standard deviation

$\sigma$

in a homogeneous region. Assuming uniformity of the paraffin (dark region in (a)), we use the standard deviation inside the yellow regions as a noise estimate. (b) Array of same size as white region in (a), containing Gaussian noise with zero mean and standard deviation

$\sigma$

taken from yellow regions in (a). (c) Fourier Power Spectum (FPS) of the region highlighted by the white region in (a) and that of (b). We define the location

$f$

of their intersection as the resolution limit. Given the 3.1 µm pixel size,

$f=0.26/\mathrm {px}$

gives a spatial resolution of

$1/f=11.9$

µm. Spatial frequencies under the noise baseline are considered unresolved.

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Tables (4)

Table 1. Experimental parameters for the two tomographic SBI acquisitions.

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Table 2. Angular sensitivity of horizontal ( $α_{x}$ ) and vertical ( $α_{y}$ ) differential-phase data from the MR and HR scans.^a

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Table 3. Cell segmentation parameters for estimating the dark-field signal.^a

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Table 4. Spatial resolution of the phase-contrast reconstructions obtained from the PBI scan without diffuser (TIE-Hom filter proposed in [14]), from the differential phase retrieved in SBI with UMPA, and by filtering the transmittance from UMPA with the TIE-Hom filter.^a

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Equations (6)

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α_{x} = \frac{u_{x}}{d_{2}} = \frac{\partial}{\partial x} \int δ (z) d z, α_{y} = \frac{u_{y}}{d_{2}} = \frac{\partial}{\partial y} \int δ (z) d z,

δ = \frac{2 π ρ_{e} r_{0}}{k^{2}},

T = \frac{I}{I_{0}} = e^{- \int μ (z) d z} = e^{\int 2 k β (z) d z} .

D = \frac{V}{V_{0}} = e^{- \int ε (z) d z} .

V = \frac{\sqrt{\frac{1}{N} \sum σ_{n} {(I)}^{2}}}{\bar{I}} = \frac{\sqrt{\frac{1}{N} \sum ({\bar{I}}_{n}^{2} - {\bar{I}}_{n}^{2})}}{\bar{I}}, V_{x} = \frac{\sqrt{\frac{1}{N} \sum {| \frac{\partial I_{n}}{\partial x} |}^{2}}}{\bar{I}}, V_{y} = \frac{\sqrt{\frac{1}{N} \sum {| \frac{\partial I_{n}}{\partial y} |}^{2}}}{\bar{I}},

Σ = λ^{2} (Δ ρ_{e})^{2} r_{0}^{2} Φ (1 - Φ) ζ,

	MR	HR
Photon energy	26.5 keV	18 keV
Effective pixel size $p_{e f f}$	3.1 µm	0.65 µm
Diffuser-sample distance $d_{1}$	72.5 cm	52.5 cm
Sample-detector distance $d_{2}$	45.0 cm	8.5 cm
Diffuser	$2 \times$ P800	$5 \times$ P5000
Number of diffuser steps $N$	20	20
Number of projections per step	1801	2401
Acquisition time	46 min	60 min

	$σ_{α_{x}}$ [nrad]	$σ_{α_{y}}$ [nrad]
MR	147	127
HR	336	328

	R [µm]	$Φ$ [%]	$Δ ρ_{e}$ [#el./Å³]	$Σ$ [1/m]	$ε_{e s t}$ [1/m]	$ε_{m e a s}$ [1/m]
Granule cell layer	2.7	21	0.44	41.3	11.7	9.8
Molecular layer	3.7	1	0.13	0.3	0.06	1.0
White matter	n.a.	n.a.	0.25	n.a.	n.a.	5.7

	HR	MR
PBI: TIE-Hom phase [µm]	2.9	10.6
Analysis window size [px]	3 $\times$ 3	3 $\times$ 3	5 $\times$ 5	7 $\times$ 7	9 $\times$ 9	11 $\times$ 11	41 $\times$ 41
SBI: UMPA phase [µm]	2.3	11.9	18.6	21.3	25.1	27.9	76.9
SBI: TIE-Hom phase from UMPA transmittance [µm]	3.9	16.7	18.6	24.8	30.6	35.4	111.6

	MR	HR
Photon energy	26.5 keV	18 keV
Effective pixel size $p_{e f f}$	3.1 µm	0.65 µm
Diffuser-sample distance $d_{1}$	72.5 cm	52.5 cm
Sample-detector distance $d_{2}$	45.0 cm	8.5 cm
Diffuser	$2 \times$ P800	$5 \times$ P5000
Number of diffuser steps $N$	20	20
Number of projections per step	1801	2401
Acquisition time	46 min	60 min

Abstract

Data availability

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Figures (9)

Tables (4)

Equations (6)

Biomedical Optics Express