Figure 1.
Microscopic overview of the segmented nerve.
Light microscopic image of the small cutaneous nerve accompanying the rat sciatic nerve (A). Electron-microscopy of the area indicated by the arrowhead reveals umyelinated fibers as greyish matter between mylinated axons (B).
Figure 2.
Touching axons creating a false axon.
The fluorescent pictures are bicolored: the background is black and the structures are indicated with a specific color, e.g. red. In this figure, 3 axons (i) nearly touch, creating a semi-closed space (a), which might be interpreted as an additional axon using an automatic segmentation routine due to its color. The automatic segmentation of light microscopy images has therefore not only relies on color but also the shape features of the structure.
Figure 3.
Workflow for segmentation including the software.
Workflow from the nerve tissue to a virtual 3D model.
Figure 4.
We selected 120 axons in a geometrical arrangement to cover all locations and sizes of the axons for the statistical analysis.
Figure 5.
A: Distribution of the idealized diameters of axons with respect to the sum of all measured inner cross-sectional axonal areas in %. The classes A to E contain 24 axons each, within the following diameter intervals: (A) 1.14 µm to 1.65 µm, B) 1.66 µm to 1.83 µm, C) 1.84 µm to 2.55 µm, D) 2.56 µm to 3.54 µm, E) 3.55 to 6.04 µm. B: Median and quartiles for each group were calculated on the basis of the individual derivations from the mean area within the individual axons. The narrowest quartiles were observed in the largest axon classes. In the pooled approach, the five classes were significantly different from each other (Kruskal-Wallis test, p = 0.0006). Note that while all classes are significantly different, the larger axons have diameter variation through the tracing of 32 slices.
Table 1.
Results of the individual comparison of the normalized area fluctuation for grouped axons of given diameter intervals (Welch t-test).
Figure 6.
Absolute number of tracing abortions during segmentation in correlation to the inter-slice intervals.
Absolute number of aborted segmentations, as a function of the (idealized) axon diameter, for the three different inter-slice intervals (top: 0.8 µm, middle: 1.6 µm, bottom: 2.4 µm). The plots contain exponential fits (one phase decay). Due to heteroscedasticity in the scatter, we used Spearman’s rank correlation coefficient to quantify the slope of the correlation between tracing abortions and axon diameters. Note: The absolute number of tracing abortions correlates negatively with the axon diameter and the steepness of the slope of the non-linear correlation increases with the inter-slice interval. The increasing inter-slice interval greatly affects the abortion rate (see λ and τ of exponential fit) for axons with diameters below 4 µm (inner cross-sectional areas below 12.57 µm2).
Figure 7.
Number of abortions with respect to the axon position.
Using the radial distance of the axons from the center of the nerve as the abscissa against the abortions that occurred for each axon, the linear correlation shows a positive slope. Although the correlation coefficient is weak, the positive slope is significantly different from zero (p = 0.0195).
Figure 8.
Final smoothing of the model to reduce file size.
A to C Different stages of model processing in Meshlab showing the nerve in isometric view (A = unprocessed model from Reconstruct, B = smoothed model HC Laplacian smoothing, C = after smoothing and vertex reduction using “Quadratic based edge collapse strategy”). A to D to F The same processing steps, showing a horizontal zoomed view of only a few axons of the nerve model. The processing of D corresponds to A, E to B and F to C. Details regarding the filter algorithms are discussed in the text. Note that the smoothing only mildly reduced the thickness of the axon diameter and the reduction of vertices from 4,296,603 to 1,666,224 neither alters the smoothed surface nor the results in new artifacts. Left scale bar indicates 0.5 mm, right scale bar indicates 80 µm.
Table 2.
Commercial and OpenSource software for the segmentation of biological and medical datasets.