Multiscale x-ray phase-contrast tomography in a mouse model of transient focal cerebral ischemia

: Cerebral ischemia is associated with a lack of oxygen and high-energy phosphates within the brain tissue, leading to irreversible cell injury. Visualizing these cellular injuries has long been a focus of experimental stroke research with application of immunohistochemistry as one of the standard approaches. It is, however, a destructive imaging technique with non-isotropic resolution, as only the two-dimensional tissue structure of a thin brain section is visualized using optical microscopy and speciﬁc stainings. Herein, we extend the structural analysis of mouse brain tissue after cerebral ischemia to the third dimension via microfocus computed tomography (µ-CT). Contrast of the weakly absorbing unstained brain tissue is enhanced by phase contrast. We show that recordings at two diﬀerent magniﬁcations and ﬁelds of view can be combined as a single approach for visualization of the associated structural alterations at isotropic resolution, from the level of the whole organ down to single cells.

through an object, the contrast can be enhanced. This can be easily understood based on the optical constants governing the phase velocity of x-rays in matter, namely the real part δ(r) of the material-dependent complex index of refraction n(r) = 1 − δ(r) + i β(r). The latter is up to a factor of 1000 larger than the imaginary part β(r), which is associated with absorption. In order to convert the phase shifts into measurable intensity modulations, several methods have been developed, in particular Talbot interferometry [2][3][4], speckle-based imaging [5][6][7], or edge illumination [8,9]. In this work, free-space propagation between the object and the detector is used, which is based on self-interference of the beam, resulting in a conversion of the phase profile to measurable intensities, and in consequence enhanced contrast in the resulting images [10][11][12]. To reconstruct the phase map of the wave exiting the object and hence information about the sample's projected density, suitable phase-retrieval algorithms have to be employed [13,14]. Compared to Talbot interferometry and also to edge or structured illumination, propagation-based imaging enables higher spatial resolution, albeit at reduced phase sensitivity [15]. In order to resolve individual neurons in the tissue, the high resolution of propagation-based imaging is indispensable. Further, this method does not require any additional optical elements, as in speckle contrast. Finally, when implemented with suitable reconstruction techniques, it is robust with respect to the non-ideal conditions of low partial coherence typical for µ-CT sources [14]. For all x-ray phase contrast methods which have emerged in recent years, the translation from x-ray optical innovation to biomedical applications is now of central importance.
In this proof-of-principle work we show that propagation-based x-ray phase-contrast tomography is capable of imaging tissue alterations in a mouse model of cerebral ischemia. We show that by acquiring a tomogram at lower resolution, with a field of view large enough to cover the entire brain, the affected area can be identified within the reconstructed density distribution. Subsequently, biopsy punches from the left and right hemisphere are placed based on the information of the overview scan. Within this much smaller volumes, high-resolution µ-CT data is recorded, from which the 3D distribution of neurons can be quantified in affected and healthy tissue by comparison of corresponding regions in the two hemispheres. Fig. 1(a) shows a schematic of the setup, consisting of a liquid-metal jet microfocus x-ray source (JXS D2, Excillum, Sweden) with the metal alloy Galinstan (68.5 % Ga, 21.5 % In and 10 % Sn) as anode material, and a home-built tomography instrument. The object is positioned at a distance z 01 behind the source, on a fully motorized sample stage, including a rotation for tomographic measurements, two translational motors above the rotation to align the sample with respect to the rotation axis and three additional linear stages below for positioning and alignment of the rotation axis. The intensity distributions of the propagated x-ray beam behind the object are recorded by a detector at a distance z 12 behind the sample. The divergent beam emanating from the quasi-point source results in a geometrical magnification M = z 01 +z 12 z 01 , and an effective pixel size p eff = p M in the object plane, as well as an effective propagation distance z eff = z 12 M , based on the Fresnel scaling theorem [16]. Importantly, p eff and z eff can be adjusted by changing the source-to-sample or source-to-detector distance, respectively, to combine overview scans with higher resolved regions of interest. In recent work, we have detailed the choice of geometry, detection and reconstruction parameters, as optimized for different imaging requirements [17][18][19].

Experimental setup
In particular, it has turned out to be useful to operate the tomography setup in two main imaging geometries (cf. Fig. 1(a)). In the classical geometry, denoted by 'cone-beam geometry' in the following, the source-to-sample distance is chosen small compared to the distance between the sample and the detector (z 01 z 12 ), leading to a large magnification M 1. In this geometry, a flat panel CMOS detector equipped with a 150 µm thick gadox scintillator (PerkinElmer, USA), consisting of 1536 × 1944 pixels with a size of 75 µm, is used for imaging. In the 'inverse geometry', the sample is moved close to the detector, leading to a small geometrical magnification M 1 of the imaging system. In this case, images are acquired with the XSight Micron (Rigaku, Czech Republic), a 2504 × 3326 pixels CCD camera equipped with a 10-fold magnification objective, resulting in a pixel size of 540 nm, and a thin single crystal scintillator which is designed to reduce diffuse scatter of light.
The system resolution as a function of the source and detector standard deviation, denoted as σ src and σ det , respectively, is given by [20] In the cone-beam geometry (M 1) the resolution is hence limited by the source size and therefore restricted to ∼ 4 µm (FWHM), while in the inverse geometry (M 1), the resolution of the detector is the limiting factor, enabling half-period resolutions below 1 µm [19].
By combining both geometries, the sample can be imaged on multiple length scales. An At a distance z 01 behind the source, the sample is positioned on a fully motorized sample stage and the intensity distributions are recorded downstream by a detector, located at z 12 behind the sample. Depending on the desired resolution and field of view, the setup can be either operated in a cone-beam (z 01 z 12 ) or inverse geometry (z 01 z 12 ). (b) The entire mouse brain, in which a stroke was induced in the left hemisphere, was embedded in paraffin and a 1 mm biopsy punch was taken both from the affected area as well as the corresponding counterpart from the right hemisphere. For the mounting in the experimental setup, the punches were squeezed into a 1 mm Kapton tube which was glued to a sample holder. overview scan with a relatively large field of view in the range of several square millimeters can be obtained in the cone-beam geometry. By subsequently changing the setup to the inverse geometry, enabling fields of view of ∼ 1 × 1.5 mm 2 , specific regions of interest can be imaged at higher resolution, providing insights into the three-dimensional sample structure at the cellular level.

Induction of cerebral ischemia
Animal experiments were performed in compliance with institutional guidelines and were approved by local government authorities. These experiments were in compliance with the ARRIVE guidelines (Animal Research: Reporting in Vivo Experiments) for how to report animal experiments. Male C57BL6 mice (23-26 g) were exposed to 45 min of intraluminal middle cerebral artery occlusion (MCAO) [21] followed by 24 h of reperfusion. Briefly, mice were anesthetized with isoflurane (1.0-1.5%). A midline neck incision was performed and the common carotid artery (CCA) was isolated and incised. A silicon-coated nylon monofilament (Doccol, USA) was inserted into the left CCA and pushed forward through the internal carotid artery until the branching point of the left MCA, where it was kept in situ for 45 min under constant laser Doppler flow (LDF) control. Thereafter, the filament was removed. LDF was continuously recorded for an additional 15 min in order to ensure adequate reperfusion. Wounds were carefully sutured. Survival rates of animals submitted to 45 min of MCAO followed by 24 h reperfusion were 100% with a total number of animals undergoing surgery of four. Animals were sacrificed applying an overdose of chloral hydrate followed by transcardial perfusion with 4% paraformaldehyde in 0.1 M phosphate-buffered saline (PBS). The complete brains were removed and used for tissue processing via paraffin embedding.

Experimental parameters
For the experiments, excess paraffin was removed around the brain and the sample was mounted in the setup by fixing it on a flat sample holder with haematocrit sealing compound (Brand, Germany). To image the entire brain, the laboratory setup was used in cone-beam geometry with the flat panel detector located at a source-to-detector distance z 02 = 1.52 m. The setup was operated at an acceleration voltage of 70 kV, an electron spot size of 10 × 40 µm 2 and an electron beam power of 100 W. The electron beam was shifted laterally by 25 µm with respect to the center position to reduce self absorption within the metal, leading to an approximate projected source spot of ∼ 10 × 13 µm 2 . A filter consisting of a 25 µm nickel foil and a 35 µm silver foil was used for pre-hardening of the beam, leading to a main energy at the In-K α emission line at 24.2 keV [18,22]. The sample was located 110 mm behind the source spot, resulting in an effective pixel size of 5.44 µm and a corresponding field of view of 8.36 × 10.58 mm 2 . For the tomographic scan, 1000 projections were recorded with an exposure time of 1.8 s over an angular range of 183 • to account for the opening angle of the divergent beam. To increase the signal-to-noise ratio, three images were acquired at each angular position and averaged in the data analysis.
Subsequently, the affected area was identified in the reconstructed volume, and biopsy punches were taken from this area as well as the corresponding counterpart from the right hemisphere and transferred to a Kapton tube which was glued to a sample holder (cf. Fig. 1(b)). To control for the location of the punches, a second overview scan was recorded afterwards with the same parameters as described above. The biopsy punches were measured in the inverse geometry in order to obtain results at cellular detail. By imaging the small 1 mm punches instead of zooming into the corresponding regions of the intact paraffin-embedded mouse brain, absorption by sample parts outside the field of view can be reduced, resulting in a higher signal-to-noise ratio in the reconstructed volumes. Note, however, that this comes at the prize of a more complex tissue preparation as the punches have to be placed such that affected region and its counterpart are included. Moreover, tissue alterations as cracks through the paraffin might occur. The XSight Micron detector was placed at a source-to-detector distance of 0.183 m and the acceleration voltage was decreased to 40 kV, enabling a maximum power of 57 W. The source spot settings were chosen as in the cone-beam geometry and in this case no filter was used for pre-hardening of the beam. The sample was located at a source-to-sample distance of 158.75 mm, resulting in an effective pixel size of 0.47 µm with a field of view of 1.15 × 1.53 mm 2 . Tomographic measurements were carried out by acquiring 1000 projections over 180 • with an exposure time of 50 s. In order to image the entire biopsy punch, three tomograms at adjacent vertical positions along the sample were recorded with sufficient overlap both for the punch from the left and right hemisphere. All experimental parameters are summarized in Table 1.

Data analysis
Phase retrieval was carried out for each empty-beam corrected projection, using the Bronnikov-Aided Correction (BAC) [23]. In this scheme, the intensity distribution in the object plane is reconstructed from the recorded intensity in the detection plane I(r ⊥ , z) by To this end, the phase distribution φ † (r ⊥ ) has to be approximated in a first step. This can be accomplished by the Modified Bronnikov Algorithm (MBA) [24] with the dimensionless reciprocal variable k 0 ⊥ = p eff · (k x , k y ), and the (also dimensionless) Fresnel number F = p 2 eff z eff λ . F denotes the Fourier transform. Hence, the BAC is a two-step reconstruction algorithm comprising two regularization parameters, α and γ, which have to be chosen based on visual inspection, removing the edge-enhancement effects while providing a sharp representation of the intensity distribution in the object plane.
For the case of the cone-beam recordings of this work, phase retrieval was performed with the regularization parameters α = 0.03 and (γ · F) = 0.16. Next, a wavelet-based ring-removal algorithm [25] was applied on the sinograms. Finally, tomographic reconstruction was carried out using the FDK implementation of the ASTRA toolbox [26][27][28]. The signal-to-noise ratio in the reconstructed volume was increased by filtering each two-dimensional slice with a Gaussian function with a 1 pixel standard deviation. To compare the overview scans recorded before and after taking the biopsy punches, the scans were manually aligned to each other in Avizo (FEI Visualization Sciences Group, USA).
For the measurements in inverse geometry, phase retrieval was performed using the regularization parameters α = 0.01 and (γ · F) = 0.16. Prior to the phase-retrieval step, the projections were resampled by a factor of 2 to increase the signal-to-noise ratio. Ring artifacts were again reduced via the wavelet-based approach and the tomographic reconstruction was carried out via the FDK implementation of the ASTRA toolbox. Subsequently, the signal-to-noise ratio was further improved by filtering the reconstructed virtual slices with a Gaussian function with a standard deviation of 1 pixel. The single tomograms recorded at adjacent positions along the sample were aligned and merged in Avizo. Afterwards they were scaled to the size of the overview scans and manually aligned to these scans so that the position of the punches could be set in relation to the entire brain. This makes it possible to identify similar brain regions within the two punches using the results of the overview scan, which is necessary for a valid comparison.

Results
Figure 2(a) shows a volume rendering of the intact brain prior to taking the biopsy punches. The outer shape of the brain including the two hemispheres and the cerebellum is easily recognized. A slight swelling of the left hemisphere can be observed due to the ischemic stroke. The planes indicate the positions of the virtual coronal as well as sagittal slices through the brain, shown in (b) and (c), respectively. In the coronal slice, the affected area in the left hemisphere, which can be recognized as a region with slightly lower electron density compared to the corresponding part of the right hemisphere, is marked in red. Also in the two sagittal slices, chosen symmetrically with respect to the center line of the brain, the affected left hemisphere exhibits a lower density compared to the healthy right hemisphere. Additionally, a difference in ventricle size can be observed which is caused by the swelling of the left hemisphere, leading to a volume reduction of the corresponding ventricle (cf. Appendix, Fig. 5).
To verify the position of the two biopsy punches, a volume rendering of the second overview scan is depicted in (d). The location of the punches is clearly visible as two cylindrical holes through the left and right hemispheres, located symmetrically with respect to the center line of the brain. Hence, similar regions from the left and right hemisphere were measured in the high-resolution scans, facilitating an unbiased comparison between affected and healthy tissue. Note that in the center of the brain, a crack running approximately perpendicular to the center line can be recognized which occurred after taking the second punch. The planes again indicate the positions of the two sagittal slices in (e), coinciding with those shown in (c) for a better comparison.
The results of the high-resolution measurements are depicted in Fig. 3, showing sagittal slices through the 3D density distributions of the punches from the right and left hemispheres in (a) and (b), respectively. Note that the positions of these slices correspond to those in Fig. 2(c) and (e) of the overview scans. In this way, the high-resolution scans can be put in relation to the entire brain reconstruction, as further visualized in Visualization 1. The gain in resolution compared to the overview scan allows for the identification of single cells throughout the volume, visible as electron-dense round structures. Contrarily, the overview scan can only visualize the gross anatomy. Typical features as the cortex of the mouse brain, part of the pyramidal cell layer of the hippocampus, the ventricle as well as the striatum can be recognized. As already visible in the overview scan, the overall tissue density, especially in the striatum, seems to be lower in the left hemisphere as the corresponding gray values, which are proportional to electron density, Fig. 2. Overview scan of the paraffin-embedded mouse brain with an ischemic stroke induced in the left hemisphere, both before and after taking a 1 mm punch from each of the hemispheres. (a) Volume rendering of the intact brain. A slight swelling of the left hemisphere can be recognized in the 3D visualization (see Visualization 1). Three planes mark the positions of the coronal slice depicted in (b) and sagittal slices in (c), lying symmetrically around the center line of the brain. (b) Coronal slice through the brain, showing both the left and the right hemisphere. In the left hemisphere, the affected area (marked as red) exhibits slightly lower electron density. (c) Sagittal slices through the brain from both the right and left hemisphere. (d) Volume rendering of the brain after taking the two punches. A crack which occurred after the second punch can be recognized in the center of the brain. (e) Two sagittal slices at approximately the same position as in (c). The location of the punches can be clearly recognized, enabling a valid comparison between the two high-resolution measurements in Fig. 3. Scale bars: 1 mm are slightly lighter. At the same time, however, an increase in cell density is observed in the stroke affected region of the left hemisphere, as can be seen in the enlarged views of the regions indicated by the red rectangles, depicted in (c) and (d) for the right (healthy) and left (stroke affected) hemisphere, respectively.
To quantify this further, an automated cell segmentation workflow based on the Spherical Hough transform [29] was applied on 400 × 400 × 400 voxels 3 sub-volumes from similar regions in both hemispheres, as indicated in Fig. 4(a) and (b). The output of this algorithm is depicted in (c) and (d) in 3D and confirms the impression of a higher cell density in the left hemisphere. By determining an envelope around all segmented cells via the Matlab implemented function boundary, the cell densities were estimated as 4.9 × 10 4 mm −3 and 2.9 × 10 5 mm −3 in the right and left hemisphere, respectively, which quantifies the observation of a higher number of cells in the brain area affected by the stroke. At first sight, this finding seems to contradict the fact that an ischemic stroke leads to neuronal cell loss. However, as propagation-based imaging is sensitive to electron density differences only, the differentiation between cell types in unstained tissue is mainly limited to differences in shape, and cells of similar shape are not distinguishable. Hence, it seems plausible that the observed cells are not neurons but could be cells which have migrated into the affected region in the course of the inflammatory response following an ischemic stroke. As this is known to result in an activation of microglia and astrocytes as well as an infiltration of neutrophils [30,31], the inflammatory process could explain the observed increase in cell density in the affected regions. The overall tissue density can also be estimated by evaluating the averaged gray values within the two sub-volumes, as these are roughly proportional to the electron density. For the right and left hemisphere we obtain 2.78 × 10 −4 and 2.74 × 10 −4 , respectively, showing that the overall tissue density in the affected area is slightly lower compared to the healthy tissue, despite the significantly higher number of electron dense cells in the left hemisphere. Hence, especially in the areas surrounding the cells, the stroke seems to be accompanied by a density reduction, as was already visually observed in form of the lighter gray appearance.

Discussion and outlook
In this work, x-ray phase-contrast µ-CT at a laboratory source was used to image the effect of ischemic stroke induced in a mouse model by reconstructing the 3D density within the brain tissue. The setup was used in two different configurations in order to perform overview scans of the entire brain at relatively low resolution and to subsequently record two biopsy punches from the left and right hemisphere at a resolution high enough to observe individual cells. The overview scans allowed us to first identify regions of interest, enabling a precise positioning of the punches with respect to the affected area. At the same time, overview scans after the punch could validate and control the positioning a posteriori. Further, the reconstructed densities of the high-resolution scans could in this way be put in proper relation with respect to the entire brain, e.g., by manually aligning the datasets to each other. This has enabled the identification of similar regions within the two punches from the left and right hemisphere, which would not have been possible without the overview scan. Both in the overview scan as well as the high-resolution measurements of the biopsy punches, the affected area could be identified due to a lower overall tissue density visible as lighter gray values in the corresponding regions. Within the punch from the left hemisphere, a higher cell density was observed in the region of the striatum which at first sight seems to be in contradiction to the expected neuronal cell loss after an ischemic stroke. However, as x-ray phase-contrast µ-CT is only sensitive to changes in electron density, the additional cells are not necessarily neurons but could in fact be cells of the immune system which have migrated to the affected regions due to the inflammatory response of the brain to ischemia [30,31].
To unambiguously answer the question of cell types, the x-ray experiments could be combined with subsequent histological experiments on selected regions of interest with specific staining agents. Note that the 3D reconstruction can facilitate the proper positioning of histological sections, so that the total number of slices and microscopy recordings can be kept at manageable number, while warranting a high 'hit rate'.
In the future, it also seems very suitable to vary the time lapse between the initiation of the stroke and the dissection of the brain to monitor the time course of the suspected inflammatory response. The workflow could be further optimized by developing an instrument which can automatically place the biopsy needle based on the results from the overview scan, enabling a more robust method to ensure that the affected region as well as the corresponding healthy counterpart will in fact be within the punches and that similar brain regions can be measured throughout specimens. While this work was conceived as a proof-of-principle study, proving that µ-CT can be used to image the alterations in brain tissue due to ischemic stroke in a mouse model, such an envisioned automation would make it possible to carry out studies with a higher case number. In this way, statistical relevance required for biomedical conclusions can be achieved.
The possibility to perform the experiments on the laboratory scale, as opposed to studies in need of high brilliant synchrotron sources, is another significant factor as the high availability enables a frequent repetition of the experiments without the need to constantly apply for beamtime. In contrast to synchrotron, however, the spatial resolution in 3D does not reach the resolution of histology on individual 2D slices. Further, laboratory µ-CT still suffers from very long scanning times, so that 3D virtual histology is not yet faster than conventional 2D histology. At the same time the scans are carried out without intervention of an operator and are therefore less labor intensive. Finally, we stress the important advantage of the presented approach in providing fully digitalized data, which lends itself to quantification of the 3D structure. The cell segmentation and cell counting as well as the evaluation of average gray values are first examples of structural quantifications which can be signficantly extended in the future.

Funding
Deutsche Forschungsgemeinschaft Cluster of Excellence 171 and Collaborative Research Center 755.

Disclosures
The authors declare that there are no conflicts of interest related to this article. (a) Segmentation of the ventricles (blue) with respect to the entire mouse brain. (b) Gray value-based semi-automatic segmentation of the ventricles using a region-growing tool included in Avizo with a manually defined seeding point. The visual comparison of the right and left ventricle shows a decreased volume of the latter, which can be explained by a slight swelling of the left hemisphere due to the ischemic stroke.