Segmentation and geometric measurements of synapses

To analyze the geometric features of the synapses, I made use of the isotropy characteristics of the FIB-SEM datasets (voxel size, 5 × 5 × 10-nm), and performed

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a semi-automated synapse segmentation. The aligned FIB-SEM images in the TrakEM2 project were first exported as tiff images. The exported datasets also contained margin areas due to the transformation of the 2D images from alignment procedure. The margin areas all had initial pixel values of 0 on the RGB scale, and converted to 255 (changed from totally dark to totally bright) during export with a custom-made macro in Fiji software. Additionally, a subset of 200 consecutive images from the same dataset was exported to serve as a training set for subsequent synapse segmentation.

Figure 2. 8: Synapse segmentation from FIB-SEM dataset. (a) Aligned FIB-SEM images were imported into the ilastik software. This sample image from the stack serves as a reference for (b) – (d). (b) The true neurostructural identities of objects inside the images, as the ground truth of the synapse segmentation, were labeled manually. Key objects, such as synapses, membranes, vesicles, and mitochondria, are labeled in different colors. The synapses are labeled in red. (c) Computed prediction map of the pixel identities based on the ground truth. The pixels predicted to be synapses are in red.

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(d) Binary image of the synapse segmentation results. Only pixels segmented as synapses are shown with a red-pixel overlay on the original EM image.

The synapse segmentation was performed in ilastik, an interactive machine-learning toolkit for 3D image segmentation (Sommer et al. 2011). The training set and entire dataset were first imported together into ilastik as single 3D/4D volumes. A procedure of a pixel classification followed by an object classification was performed semi-automatically. This procedure was based on discussions with the ilastik developer who was familiar with synapse segmentation on FIB-SEM datasets (Kreshuk et al. 2011). For training, ilastik uses a random forest classifier (Breiman 2001) to classify pixels or objects into different neurostructural identities, based on selected graphic features (see Table 1 (Voxel features) in Kreshuk et al., 2011) and manual labeling of ground truth (defined as the true neurostructural identities of objects).

The manual labeling of the ground truth of the FIB-SEM datasets was performed by Houda Khaled (a student in the Neuroscience Program, Wellesley College, Wellesley, MA, USA). For each training-set, 5 categories of objects in the training-set were labeled: synapses, mitochondria, membrane compartments, vesicles, and areas containing none of these features (“remainder”) (Figure 2. 8, b).

Large black objects were observed to interfere with the synapse segmentation during the development of the segmentation procedure. Consequently, the margin area was artificially changed from black to white and then, together with myelin sheaths and extracellular space, categorized as the “remainder” of the data.

The initial labeling was performed on 20 slices that were evenly distributed across the training set. The training of the pixel classifier was supervised, and the pixel prediction map could be updated and visualized (Figure 2. 8, c) at any time during the manual labeling. The trained pixel prediction map after each iteration was evaluated and corrected until there was no major mistakes (i.e. no missing synapses).

Gaussian smoothing with a standard deviation (SD) of 10 voxels was performed on the pixel prediction map to remove noise, and the map was then subjected to the object classification. The object classifier only examined voxels with predicted synapse probabilities that were over 50%. It also excluded objects containing less than 1000 interconnected synapse-voxels that were too small to be synapses. The quality of the segmentation was again verified after the object classification.

After the training and verification, the classifier was applied to the larger dataset that contained all of the images with converted white margins. Once the synapse segmentation results were verified, they were exported as binary image stack in multipage tiff files. The segmentation stack had the same dimensions as the input larger dataset, and the pixel value indicated if the pixel belonged to a synapse (value of 1) or not (value of 0) (Figure 2. 8, d).

During the synapse segmentation process, the ilastik software created several intermediate datasets that were 4 times the size of the original FIB-SEM stacks.

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Therefore, adequate RAM and disk space are required. In this experiment, the FIB-SEM datasets were 2 - 4 GB. The synapse segmentation was done with ilastik on a 2.8-GHz 6-Core Intel^® Xeon^® work-station with 24 GB RAM running Windows 7.

I wrote a set of scripts in MATLAB to visualize, process, and analyze the segmentation results. With these scripts, the binary synapse segmentation stack was colored in red and superimposed on the original FIB-SEM stack. The superimposed image stack was visualized in MATLAB with a custom-made 3D image viewer (Figure 2. 9). Each segmented synapse was recognized as an object composed of connected synapse-pixels and assigned a numeric ID number. I made use of the previously identified synapses in TrakEM2 (from section 2.2.6), extracted their coordinates into MATLAB to guide synapse recognition and evaluation. False positive (nonsynapse) and partial segmentations (not fully contained in the dataset) were automatically discarded, while false negative (missing synapse) segmentations were verified. False split and merged segmentations were also automatically identified and corrected with my MATLAB scripts (See Supplementary Method and Data section S.2).

Figure 2. 9: Illustration of the segmentation results. The synapse segmentation results were colored red, superimposed onto the original FIB-SE images, and assigned numerical IDs in MATLAB. A 3D image viewer was written with a graphical user interface (GUI) to facilitate the evaluations and postprocessing of the synapse segmentation results. A scroll bar was added at the bottom of the viewer to enable quick

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browsing of different slices of the image stack. The left and right panels show two different Z-slices of the same image stack.

The corrected synapse segmentations were then subjected to volumetric and geometric measurements (Figure 2.10). The precise physical sizes of the voxels in the FIB-SEM datasets were obtained during the FIB-SEM imaging so that the physical volume of each segmented synapse could be easily calculated by summing all of the segmented voxels belonging to it. The size of the synapse, which was defined as the physical volume containing the pre- and post-synaptic membranes, their associated synaptic densities, and the synaptic cleft in between, was represented by the total volume of the complete synapse segmentation. The object Feret diameter, which is defined as the diameter of the minimum bounding sphere of a 3D object, was calculated from each synapse segmentation. A linear time randomized algorithm (Welzl 1991) was implemented in MATLAB to improve the efficiency of this calculation.

Figure 2.10: 3D reconstruction of postprocessed synapse segmentations in a FIB-SEM dataset. Left: The synapse in the original FIB-SEM dataset. Middle: 3D orthoslices intersected at the center of the same synapse. The segmented synapse voxels are shown

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in red or blue color. Right: 3D reconstruction of the same synapse based on the segmented voxels. The arrow indicates the presynaptic-to-postsynaptic of the synapse.

(a)-(d): Representative asymmetric and symmetric synapse reconstructions. The asymmetric synapse segmentations are shown in red, and the symmetric synapse segmentations are shown in blue. Volumetric and geometric measurements can be determined with these 3D-reconstructed synapses. Scale bar: 500 nm.

In each bird, approximately 300 synapses were fully segmented and pooled for the synapse size and Feret diameter measurements. The asymmetric and symmetric synapse subtypes were further classified using the same criterion and procedure described in section 2.2.6, and their sizes and diameters were measured. The group means were determined by averaging the values of all birds in the same group (see Table 2. 15 and Table 2. 21).

The distributions of the synapse size and Feret diameter data were investigated further. Histograms of the distributions of the logarithmic-transformed volumes and diameter data were plotted with a Gaussian fit (see Figure 2. 24 and Figure 2. 28). A goodness-of-fit check was performed with a Kolmogorov-Smirnov test (Merchán-Pérez et al. 2014) to determine how well these two anatomical parameters fit the log-normal distribution in each bird and each group and in all of the groups together (see Table 2. 14 and Table 2. 20). When the measurements fit to the log-normal distribution adequately in all the birds, parametric statistical tests were considered appropriate. Therefore, to investigate differences in synapse size and diameter between groups, two-sample t-tests were performed on the log-transformed data. Differences between groups were considered significant when the test resulted in p values less than 0.05.

Additionally, to better represent the log-normal distributed data in the results, the population mean and SE were both calculated from the log-transformed data. Let us consider the synapse volume data as an example. For a given synapses 𝒊 with a

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The term between the square brackets in Equation 2. 5 is therefore the arithmetic mean of the log-transformed data, 𝑾.

The SD of the log-transformed data 𝝈𝑾 can also be easily determined. The variance 𝒗𝒂𝒓 of a given log-normal distribution with an associated normal distribution that is defined by mean 𝛍 and SD 𝛔 is given as:

Equation 2. 6:

𝑣𝑎𝑟 = exp(2μ + σ

) ∗ (exp(σ

) − 1)

The above equation was taken from the Introduction to the Theory of Statistics [see Appendix B, Table 2 (Continuous Distributions) in Mood 1950], and calculated with the Statistics and Machine Learning Toolbox (lognstat function) in MATLAB (ver.

R2017a). After the variance 𝒗𝒂𝒓 was determined, the 𝑆𝐸 of the volume data from the total 𝑁 synapses in the given bird was easily calculated with the following fomula:

Equation 2. 7:

𝑆𝐸 =

√𝑁

These methods for computing the variance and SD of the log-normal-transformed data have been tested with clinical studies and simulation studies and considered valid (Quan and Zhang 2003). Data of the synapse volume and Feret diameter, including the data of asymmetric and symmetric subtypes, were treated in the same way.

The log-transformed data of synapse volume and synapse Feret diameter were also examined with a linear regression analysis, which will be described in detail in the next section.