Examining the histogram of one reconstructed slice (b), one observes that only four of the five Gaussians can be clearly related to known morphological structures of the human cerebellum. The fifth Gaussian with the largest half width describes the Δδ-values lying between the formalin and stratum moleculare related peaks. Therefore, this Gaussian basically corresponds to the partial volume between these two components. Aside from the partial volume one finds an additional peak at Δδ = 1.3 × 10−8, which appears rather as a shoulder. This shoulder becomes more obvious in the histogram of the entire three-dimensional dataset (c). The quantitative analysis of the shoulder reveals that the related Δδ-values are located in areas of the cerebellum that were in direct contact with the formalin solution during the whole fixation period. Obviously, the formalin treatment of the human cerebellum changes the electron density at the tissue periphery.
The usefulness of the absorption-contrast data of the second-generation synchrotron radiation source is restricted because intensity-based segmentation is in fact fairly complicated. The histogram of f
illustrates the crucial overlap of the absorption values of the three components. Note that the formalin solution yields absorption values just between those of white and grey matter. Hence, another solution with higher or lower absorption should be applied. Phosphate buffer, for example, leads to higher absorption values (Germann et al. 2008
) and is, therefore, better suited. The intensity-based segmentation of white and grey matter, however, remains difficult, since the green-coloured and blue-coloured peaks overlap in a significant manner.
The detailed comparison between the absorption-contrast data obtained from grating interferometry (b
) and the conventional ones (d
), both grey-scaled to three times the standard deviations σform
of the formalin peak, shows that the grating interferometry results yield less contrast between the internal features. This behaviour is expected because the selected photon energy is too high for optimal image acquisition. The optimal energy of 14 keV for aqueous specimen with diameter D
= 1 cm can be calculated from the equation µ
). The sharp features present in the ID19 absorption data concern internal interfaces as the results of edge enhancement and are not seen in the optimized absorption-contrast tomogram from the second-generation source.
The measurement sensitivity for the real part of the refractive index of the presented phase-contrast measurement (perhaps better termed as the resolution power) is enormously high and corresponds to an angular resolution of 1.7 × 10−8
rad. This corresponds to the size a small lorry parked on the Moon would appear from Earth. This value, however, is a factor of three lower than that found in a previous study (Pfeiffer et al. 2009
). The difference is predominantly due to data binning, which resulted in 15 µm voxel size compared with the 5 µm in the present study (Thurner et al. 2004
). Further influencing parameters are the operation mode of the insertion device, the photon energy that was around 10 per cent lower in the present study, the modified exposure time and the higher resolving FReLoN unit.
Comparing the histograms of a single phase-contrast slice () with the entire dataset (), one recognizes significant differences. The slice-wise cross-check of the histograms allows us to conclude that the broader peaks in are the consequence of relatively small displacements of the peak positions from slice to slice. It leads to rather higher uncertainties of the Δδ-values given in §3.1.
The sensitivity of the grating interferometry, however, is so high that individual Purkinje cells become visible without the application of any contrast agent. This is the most important result of the study, and to the best of our knowledge the first time that X-ray tomography permitted the identification of unstained cells in human soft tissue. So far, only osmium-stained ganglion cells have been made visible in absorption-contrast mode (Lareida et al. 2009
The three-dimensional images of the Purkinje cells can be weighted against histological results. First, the grating-based SRµCT data only show the larger features, namely the perikaryon and not the detailed dendritic tree, which propagates outwards in the direction of the stratum moleculare. Besides the limited spatial resolution, the reason behind this could be similar electron density values of the dendritic tree and the stratum moleculare. Second, according to the present tomographic study, the maximum diameter of an individual Purkinje cell corresponds to about 40 µm and the cell area to around 700 µm2
. There is no doubt that the visualization of the Purkinje cells is close to the limit of the experimental set-up. A true measurement of the cell size is therefore impossible. Nevertheless, the spatial resolution of 20 µm, together with the pixel size of 5.1 µm, allows a rough estimate of the diameters of the features detected, which correspond in location and size to the Purkinje cells often visualized in two-dimensional histological slices shown, for instance, in Fatemi et al. (2002
). Our results agree well with the data of Fatemi et al
., who obtained for the cell area (661 ± 85) µm2
from unfixed cerebellar sections but less with the result of stained histological slices by Tran et al. (1998
), who found (374 ± 34) µm2
. The alcohol fixation process apparently induces a significant shrinkage of the cells. Third, the two-dimensional Purkinje cell density of normal brain was determined at (16 ± 4) cells per mm2
(Jeste et al. 1984
), a value also obtained from our tomographic data. Note, the density of Purkinje cells is reduced by diseases such as schizophrenia, autism, Huntington's disease and other movement disorders (Jeste et al. 1984
; Tran et al. 1998
; Fatemi et al. 2002
). In summary, there remains no doubt that the micro-features shown in are the Purkinje cells, since the location, size, shape and density are very well comparable with the histological results.