Tissue sampling
A series of 28 adult bovine brains (10 males, 10 females and 8 freemartins, all 24 months old), were obtained from local abattoirs in the Veneto region. Animals were treated according to the present European Community Council directive concerning animal welfare during the commercial slaughtering process and were constantly monitored under mandatory official veterinary medical care. The cerebella were collected under sterile conditions and fixed by immersion in phosphate-buffered formaldehyde 4% for 1 month. From each cerebellum, the lobules VIII and IX, classical paleocerebellar lobules located at the postero-inferior part of the vermis, were sampled, re-immersed in buffered formalin, then washed in phosphate saline buffer (PBS) 0.1 M, pH 7.4 and processed for paraffin embedding.
Nissl staining
The lobules VIII and IX of each specimen were cut into 8-µm-thick parasagittal sections. For each cerebellar sample, one section every five was stained (a total of 10 slides per individual per sex). Sections were stained following a standard Nissl protocol: sections were deparaffinized in xylene for 3 × 5 min, followed by a hydration series in graded alcohols for 3 min each. After 3 min in distilled water, sections were stained in 0.1% cresyl violet solution for 10 min at 57 °C. Sections were then differentiated in 95% alcohol for 20 min. After rinsing in distilled water, sections followed an ascending series of dehydration in graded alcohols for 3 min each, and finally 3 × 5 min in xylene. The sections were then covered with mounting medium and coverslip glass.
The most recent anatomical description of the bovine brain (Okamura
2002) contains illustrations of coronal sections including the main features of the subcortex. Additional details can be found in Yoshikawa (
1968). The gross anatomy of the cerebellum was assessed using these references and from Voogd (
1998) and Voogd and Glickstein (
1998).
All the brains used in the present study were extracted with a post-mortem interval no longer than 4 h, and subsequently spent the same amount of time in formalin. The brains were then processed following the same paraffin-embedding, cutting and staining protocol, to obtain remarkably constant results. Moreover, each staining run contained female, male and freemartin sections.
Image acquisition and automatic cell identification
Ten stained sections per subject were scanned with a semi-automated microscope equipment (D-Sight v2, Menarini Diagnostics, Italy) at a magnification of 40×, using constant lighting profiles.
Based on these digital images, the limits between layers were drawn independently by 3 neuroanatomists (AP, JMG, BC), each working autonomously using a raster image software (GNU Image Manipulation Program, Free Software Foundation, Inc.), and then compared until consensus was reached.
The complete analysis of the acquired images of cerebellar slices involves the detection and outline of tens of thousands of cells. This is not feasible by human annotation of the images, unless the procedure is carried out in small region of interest, potentially introducing bias in the procedure. To tackle the problem, we developed an automatic procedure (Grisan et al.
2018) that can process the images identifying the position and outline of most of the visible cells, taking care of the different sizes among the different cell populations, and at the same time addressing the packed and clustered appearance of cells in the different layers of the cerebellum, particularly in the granule cells layer.
The images were exported as Jpeg2000, resulting in a mean dimension of 42,000 × 42,000 pixels with a resolution of 0.5 μm per pixel. Each image was downsampled, to keep the computational burden low, to an equivalent resolution of 1 μm per pixel. The average target intensity was locked at 71% to ensure that the exposure was kept uniform while sampling.
The analyzed data consisted of information on tens of thousands individual neural cells. In a preliminary test, cells were localized within the three layers identified by the independent observers, and compared to the algorithm’s results.
Table
1 reports the performance of the proposed and competing algorithms in absolute numbers of detected cells (first column), wrong detections (second rows), and detected areas corresponding to multiple cells that were not separated (for details see Grisan et al.
2018).
Table 1
Algorithm comparison
| 1837 | 2178 | 14 |
| 2280 | 9226 | 94 |
| 3561 | 7233 | 56 |
Proposed | 3294 | 488 | 20 |
The quality of the detection performance of the algorithm was assessed based on its ability to correctly identify a cell (true positive, TP), to minimize the number of background. Please provide the subjects erroneously identified as cells (false positives, FP), and to correctly separate clusters of cells (remaining clusters). The proposed algorithm performed well both in terms of precision and recall, obtaining a F1-score of 0.87 on cerebellum Nissl-stained images.
Shortly (for additional details we refer to Grisan et al.
2018), a local space-varying threshold (Poletti et al.
2012) is applied to the image to separate the stained objects from the background, and from the local density of the foreground objects (mainly cells), a rough separation of the most densely (possibly with clustered and cluttered cells) and sparsest regions is obtained. Then, a small set of thresholds on the values of eccentricity, areas and solidity of the identified objects allows the identification of single small cells (limited area, high circularity and solidity), Purkinje cells (large area, high circularity, decreasing solidity with area), from possible clusters of cells.
All the objects that were appraised as a possible cluster undergo further analyses to disaggregate the individual cells that compose it. This is performed by modeling the intensity appearance of a cell as with 2-dimensional Gaussian shape. In case of clustered cells, this leads to a representation of the cluster as a mixture of Gaussian, with a number of modes corresponding to the number of cells composing the cluster. Hence, from the original image
\(I\), around each identified cluster, a sub-image
\({I}_{\mathrm{clu}}\)(
x,
y) is extracted. The sub-image intensities are assumed to be described by a bi-dimensional Gaussian mixture model (GMM) containing several modes
\(N\) equal to the number of the local maxima:
$$G\left(x,y;{c}_{i},{\Sigma }_{i}\right)={e}^{-0.5{(\left(x,y\right)-{c}_{i})}^{T}{{\Sigma }_{i}}^{-1}(\left(x,y\right)-{c}_{i})}$$
$$\mathrm{GMM}\left(x,y\right)=\sum_{i=1}^{N}{\alpha }_{i}G(x,y;{c}_{i},{\Sigma }_{i})$$
The parameters of the mixture of Gaussians are estimated by a non-linear least square fit to the sub-image data, and they provide both the center and dimension of the cells forming the cluster.
Cell morphometric descriptors definition
Each identified cell is then described by a set of morphometric measures characterizing its shape and local relationship with surrounding cells. These measures can be broadly assigned to three domains: size, regularity and density. Size and regularity domain address cell morphology and are composed by classical measures on shapes. The density domain characterizes the context around each cell by counting the number of cells that are present within a radius of 50 µm or within 100 µm. See Table
2.
Table 2
Morphological domains and morphometric descriptors, along with their description and/or mathematical formula
Size | Area | Area of the cell body expressed in μm2 |
Perimeter | Total length of neural cell boundary expressed in μm |
Major axis length | Measure of the length of the major axis of the cell body expressed in μm |
Minor axis length | Measure of the length of the minor axis of the cell body expressed in μm |
Regularity | Solidity | Proportion of pixels in the convex hull that are also in the region of the cell |
Extent | Area/(area of the bounding box) |
Inv.AR (1/AR) | Inverse of the aspect ratio, defined as (major axis length)/(minor axis length) |
Convex circularity | (4 × π × convex area)/(convex perimeter2) |
Density | Ngb_50 | No. of neighbor cells counted within a radius of 50 μm around a given cell |
Ngb_100 | No. of neighbor cells counted within a radius of 100 μm around a given cell |
It is worth noting that for size-related morphometric measures, a natural positive correlation exists with the neuron’s soma size. For regularity-based descriptors, the larger they are, the more regular is the neuron. Notably, all regularity descriptors are dimensionless ratios bounded in the closed interval [0;1]. Finally, both density-related descriptors refer to the amount of neighbor cells present around a given cell.
We analyzed separately in each cortical layer the morphometric data (inference on location), and the related anatomical variation (inference on scatter) for each domain (size, regularity and density). During the data collection process, two groups of cells emerged in the molecular layer, based on the measured parameters, and two groups in the granular layer. Since it is well established that in the molecular layer, two types of interneurons exist, the basket cells and the stellate cells, we performed data analysis dividing the cells in these groups: cells with a mean length of the major axis of 11 µm (that we define stellate-like cells), and cells with a mean length of the major axis of 19.5 µm (that we define basket-like cells). Similarly, the granular layer contains at least two main groups: Golgi cells and granule cells, we hence labeled our two cell groups for analysis as (i) granule cells, with a major axis length up to 15 µm (most of the detected cells, with a very round and regular aspect); and (ii) Golgi-like cells, over 15 µm of major axis length (larger, more irregular cells).
Multi-aspect testing and ranking inference
Separately for each type of cell (Basket = B, Stellate = S, Purkinje = P, Granules = Gr, Golgi = Go), the comparison of the morphometric descriptors (
Y) among the three populations (M = male, F = female and FM = freemartin) has been formalized by the following statistical linear model:
$${\mathbf{Y}}_{ilj} = {{\varvec{\upmu}}} + {{\varvec{\uptau}}}_{lj} + {\varvec{\varepsilon}}_{ilj} ,$$
(1)
where specific location (
τlj) and scale effects
σ2(
τlj) =
σ2lj,
i = B, S, P, Gr, Go,
j = M, F, FM, are both allowed to differ across populations, while the random components
ε are not specified in their distributional form according to a non-parametric permutation-oriented approach (Bonnini et al.
2014).
The inferential analysis to compare the sex-related groups has been formalized by the following null and alternative hypotheses:
$$\left\{ {\begin{array}{*{20}c} {H_{{0\left( {ljh} \right)}}^{{{\text{loc}}}} : \cap_{k} Y_{ljk} \mathop = \limits^{{{\text{loc}}}} Y_{lhk} \equiv \cap_{k} \left[ {\tau_{ljk } = \tau_{lhk } } \right]} \\ {\begin{array}{*{20}c} {H_{{1\left( {ljh} \right)}}^{{{\text{loc}}}} : \cup_{k} \left[ {\left( {Y_{ljk} \mathop < \limits^{{{\text{loc}}}} Y_{lhk} } \right) \cup \left( {Y_{ljk} \mathop > \limits^{{{\text{loc}}}} Y_{lhk} } \right)} \right]} \\ \end{array} } \\ { \equiv \cup_{k} \left[ {\left( {\tau_{ljk } < \tau_{lsk } } \right) \cup \left( {\tau_{ljk } > \tau_{lhk } } \right)} \right]} \\ \end{array} } \right.\quad \left\{ {\begin{array}{*{20}c} {H_{{0\left( {ljh} \right)}}^{{{\text{sca}}}} : \cap_{k} Y_{ljk} \mathop = \limits^{{{\text{sca}}}} Y_{lhk} \equiv \cap_{k} \left[ {\sigma_{ljk}^{2} = \sigma_{lhk}^{2} } \right]} \\ {\begin{array}{*{20}c} {H_{{1\left( {ljh} \right)}}^{{{\text{sca}}}} : \cup_{k} \left[ {\left( {Y_{ljk} \mathop < \limits^{{{\text{sca}}}} Y_{lhk} } \right) \cup \left( {Y_{ljk} \mathop > \limits^{{{\text{sca}}}} Y_{lhk} } \right)} \right]} \\ \end{array} } \\ { \equiv \cup_{k} \left[ {\left( {\sigma_{ljk}^{2} < \sigma_{lhk}^{2} } \right) \cup \left( {\sigma_{ljk}^{2} > \sigma_{lhk}^{2} } \right)} \right]} \\ \end{array} } \right.$$
(2)
where
l = B, S, P, Gr, Go,
j,h = M, F, FM, and
k = 1,⋯,
p, is the reference index for each univariate morphometric feature (see Table
2).
Permutation-based
p-values (Corain and Salmaso
2015) have been calculated under the null hypothesis of approximated exchangeability. For details, see the supplemental materials.
To calculate the location and scatter ranking, respectively, we used the ranking methodology proposed by Arboretti et al. (
2014).