01.12.2015 | Methodology | Ausgabe 1/2015 Open Access

# On the representation of cells in bone marrow pathology by a scalar field: propagation through serial sections, co-localization and spatial interaction analysis

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- Diagnostic Pathology > Ausgabe 1/2015

## Electronic supplementary material

## Competing interests

## Authors’ contributions

## Background

## Methods

### Patient collective

### Immunohistochemistry staining

### Comment on image ethics

### Image acquisition and pre-processing (Additional file 1: Figure S1)

### Definition and segmentation of spaces and niches

### Image processing in MATLAB to detect cells (Additional file 1: Figure S1)

### Introduction of a field (Additional file 1: Figure S1)

_{P}and y

_{P}as coordinates of the centroid. The invers multiquadric RBF was chosen among the many other RBF due to its feasible shape for this project and due to its many changeable parameters. However, many other RBF would be likewise applicable. The parameter α is chosen to have an arbitrary maximum of 100 [arbitrary unit] at the coordinates of the centroid. Hereby, the shape of the RBF, which is defined by the parameters \( \upbeta \) and \( \upgamma \), could be adapted to different cell interaction models [33]: Hypothesis 1) Direct spatial cell-cell- and cell-niche-interaction (henceforth called ‘direct interaction’) is represented by a RBF (henceforth denoted by ’RBF

_{direct}’) with high values in the area of the nucleus (>90), mediate values in the area of the cell (>80) and with a step, asymptotic decrease towards 0 (black solid line Fig. 1). Hypothesis 2) Indirect spatial interactions via proposed secretory factors (henceforth called ‘indirect interaction’) are represented by a RBF (henceforth denoted by ‘RBF

_{indirect}’) with, again, high values at the centroid position (>90) but a broad shape and medium values within the proposed 250 μm range for paracrine interaction [33, 34] (solid red line Fig. 1).

### Normalization of field values

_{min}as the absolute minimum and with C

_{max}as the absolute maximum of the scalar field is applied.

### Calculation of the gradient and the divergence

### Statistical evaluation (Additional file 1: Figure S1)

_{1}and M

_{2}[37, 38]) and graphical presentation were performed with R [39], in particular with the ggplot2 package [40].

## Results

### Proof of principle for the description of colocalization and possible spatial interaction via a scalar field

_{direct}(hypothesis 1 in the method section that a sharp function could map direct cellular contact) and further processed. The matrices containing the scalar values could be linearized and plotted against each other as routinely performed in co-localization analysis: For a single point versus another single point (Fig. 2a-c) and for a single point versus a cluster (Fig. 2d-f) the width of the point cloud depends on the distance. Furthermore, the shape of the point cloud also depends on the number of points per matrix. Of note, the absolute number of pairs of variants in this case depends on the image size (e.g. for a 10×10 pixel image 100 pairs of variants and not on the number of points.

_{1}and M

_{2}[37, 38] could be obtained after setting a threshold (e.g. 50 to get the overlap of 50-perzentile). These values also correlated with the distance and showed a relation with both the number of points and the distance of points within a cluster: E.g. one cluster and one point at a distance of 50 pixel show Manders coefficients of M

_{Cluster}= 0.83 and M

_{Point}= 0.59, while the values were M

_{cluster}= 0.03 and M

_{Point}= 0.02 at a distance of 200 pixel.

### Comparison to colocalization via colour channel analysis

### Proof of principle for valid distance measurements through histogram intersection

_{direct}approximately 200 pixel/100 μm), the intersection function shows an asymptotic behaviour. Therefore, the distance and the histogram intersection cease correlating beyond a certain value (in this example beyond 0.4).

### Proof of principle for description and detection of object clusters via calculation of the gradient and the divergence

### Application on histological images

### Example 1: Spatial interaction of B-cell markers in a focal, dense infiltration

_{direct}(Fig. 4f for CD20 and G for Bcl2). Theoretically, the two fields could be combined by addition to one field describing the density of the infiltration by CD20+ Bcl2+ B-cells (data not shown); as delineated in the method section (equation 4).

### Example 2: Allocation and spatial interaction of B- and T-cells in a focal, dense infiltration

_{T-cell}= 0.34 and M

_{T-cell}= 0.67.

### Example 3: Co-localization of T-cell markers in a lose infiltration

Direct interaction/RBF _{direct}
| Indirect interaction/RBF _{indirect}
| |||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

CD3 | CD3 Bone | CD4 | CD4 Bone | CD8 | CD8 Bone | CD20 | CD20 Bone | CD3 | CD3 Bone | CD4 | CD4 Bone | CD8 | CD8 Bone | CD20 | CD20 Bone | |

CD3 | M _{CD3} = 0.00 | M _{CD3} = 0.00^{b}
| M _{CD3} = 0.02 | M _{CD3} = 0.00^{b}
| M _{CD3} = 0.02 | M _{CD3} = 0.10^{a}
| M _{CD3} = 0.00 | M _{CD3} = 0.60 | M _{CD3} = 0.54 | M _{CD3} = 0.36 | M _{CD3} = 0.54 | M _{CD3} = 0.36 | M _{CD3} = 0.69^{a}
| M _{CD3} = 0.60 | ||

CD3 Bone | M _{CD3Bone} = 0.00 | M _{CD3Bone} = 0.03 | M _{CD3Bone} = 0.43^{a}
| M _{CD3Bone} = 0.00 | M _{CD3Bone} = 0.43^{b}
| M _{CD3Bone}=0.00 | M _{CD3Bone}=0.88 | M _{CD3Bone} = 0.89 | M _{CD3Bone} = 0.71 | M _{CD3Bone} = 0.50 | M _{CD3Bone} = 0.71 | M _{CD3Bone} = 0.50 | M _{CD3Bone}=0.59 | M _{CD3Bone}=0.98 | ||

CD4 | M _{CD4} = 0.00^{b}
| M _{CD4} = 0.61 | M _{CD4} = 0.00 | M _{CD4} = 0.00 | M _{CD4} = 0.00 | M _{CD4} = 0.00 | M _{CD4} = 0.39 | M _{CD4} = 0.91 | M _{CD4} = 0.80 | M _{CD4} = 0.24 | M _{CD4} = 0.72 | M _{CD4} = 0.21 | M _{CD4} = 0.69 | M _{CD4} = 0.24 | ||

CD4 Bone | M _{CD4Bone} = 0.00 | M _{CD4Bone} = 0.79^{a}
| M _{CD4Bone} = 0.00 | M _{CD4Bone} = 0.00 | M _{CD4Bone}=0.84 | M _{CD4Bone}=0.01 | M _{CD4Bone}=0.31 | M _{CD4Bone} = 0.88 | M _{CD4Bone} = 0.83 | M _{CD4Bone} = 0.36 | M _{CD4Bone} = 0.66 | M _{CD4Bone}=0.92 | M _{CD4Bone}=0.54 | M _{CD4Bone}=0.82 | ||

CD8 | M _{CD8} = 0.00^{b}
| M _{CD8} = 0.00 | M _{CD8 =}0.00 | M _{CD8} = 0.00 | M _{CD8} = 0.00 | M _{CD8} = 0.00 | M _{CD8} = 0.00 | M _{CD8} = 0.91 | M _{CD8} = 0.80 | M _{CD8 =} 0.50 | M _{CD8} = 0.31 | M _{CD8} = 0.27 | M _{CD8} = 0.80 | M _{CD8} = 0.51 | ||

CD8 Bone | M _{CD8Bone} = 0.00 | M _{CD8Bone} = 0.71^{b}
| M _{CD8Bone} = 0.00 | M _{CD8Bone} = 0.96 | M _{CD8Bone} = 0.00 | M _{CD8Bone}=0.01 | M _{CD8Bone}=0.25 | M _{CD8Bone} = 0.89 | M _{CD8Bone} = 0.83 | M _{CD8Bone} = 0.21 | M _{CD8Bone} = 1.00 | M _{CD8Bone} = 0.64 | M _{CD8Bone}=0.51 | M _{CD8Bone}=0.83 | ||

CD20 | M _{CD20=0.15}
^{a}
| M _{CD20=0.00}
| M _{CD20} = 0.00 | M _{CD20} = 0.06 | M _{CD20} = 0.00 | M _{CD20} = 0.07 | M _{CD20} = 0.00 | M _{CD20=0.99}
^{a}
| M _{CD20=0.57}
| M _{CD20} = 0.59 | M _{CD20} = 0.31 | M _{CD20} = 0.99 | M _{CD20} = 0.27 | M _{CD20} = 0.58 | ||

CD20 Bone | M _{CD20Bone=0.00}
| M _{CD20Bone=0.91}
| M _{CD20Bone}=0.03 | M _{CD20Bone}=0.46 | M _{CD20Bone}=0.00 | M _{CD20Bone}=0.44 | M _{CD20Bone}=0.00 | M _{CD20Bone=0.90}
| M _{CD20Bone=0.99}
| M _{CD20Bone}=0.36 | M _{CD20Bone}=0.50 | M _{CD20Bone}=0.68 | M _{CD20Bone}=0.46 | M _{CD20Bone}=0.60 |

_{CD3}= 0.10 versus M

_{CD20}= 0.15). Due to morphological changes (the changes are highlighted by arrows in Additional file 3: Figure S3), there is also no spatial interaction between CD3, CD4 and CD8 (Manders coefficients each 0.00). For the indirect interaction, the Manders coefficients are each higher but still less than for CD3 and CD20. This finding will be picked up in the Discussion.

### Example 4: Localization of cellular infiltrates in relation to bone trabeculae

_{indirect}. By doing so, for the dense lymphoid infiltration in example 1 (follicular lymphoma) there is more indirect spatial interaction (k

_{CD20+}= 0.91) than for the “loose” infiltrate in example 2 (k

_{CD20+}= 0.73) between CD20+ cells and the bone trabeculae.

## Discussion

### 1) Is co-localization analysis on basis of scalar fields in serial sections possible?

_{1}and M

_{2}[38]. However, since these methods are initially defined for scatter plots of intensity values of different channels (e.g. green and red) and not for scalar field values, the interpretation of the resulting graphs and values need to be adapted: There is no relation between the number of particles and the points in the scatter plot similar to a scatterplot of two colour channels of one immunofluorescence image. The shape and position of the point cloud encodes the co-localization and also the clustering (see Fig. 2). In this context, especially the overlap coefficients M

_{1}and M

_{2}seem to fit best for the spatial interaction/co-localization analysis; by setting a threshold, one obtains the overlap of the corresponding percentiles (e.g. 50 %-percentile in Fig. 3 and Additional file 3: Figure S3).

_{1}and M

_{2}) or as histogram intersection. These measurements may be more significant in regard to biology as pure metric measurements, since they already incorporate interaction models depending on distances for direct and indirect cellular interaction [33].

### 2) Is there are difference between co-localization and spatial interaction?

_{direct}for spatial object-object interaction (maximum value at the centroid, medium values at the cell edge and then a step slope; compare black solid line in Fig. 1b) and (hypothesis 2) RBF

_{indirect}for indirect interaction (medium values within the proposed 250 μm range for paracrine interaction [33, 34] and a slight slope; compare red solid line in Fig. 1b); these fields could overlap and, therefore, could describe co-localization on basis of overlap. Thus, an huge overlap of RBF

_{direct}points to spatial co-localization of two objects whereas an intermediate (e.g. histogram intersection of >0.95 for direct spatial contact and of 0.81 for 20 μm distance) overlap rather points to a close neighbourhood of them. Whether two objects are co-localized or occur as neighbours mainly depends on the chosen shape of the radial basis function; a broad radial basis function is less prone to registration errors whereas a narrow function is more specific for real overlap of objects. This trade off comes to effect in example 3 and in the linked sketch in Additional file 4: Figure S4: On the one hand, the narrow RBF results in very specific co-localization of markers; on the other hand this function is very prone to morphological changes throughout serial sections. This limitation can almost certainly be overcome by applying repetitive cycles of staining/de-staining using a spectrum of different antibodies on one given section [17, 45–47].