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Edited by: Idan Segev, The Hebrew University of Jerusalem, Israel

Reviewed by: Alino Martinez-Marcos, Universidad de Castilla-La Mancha, Spain; Yoshiyuki Kubota, National Institute for Physiological Sciences, Japan

*Correspondence: Angel Merchán-Pérez, Laboratorio Cajal de Circuitos Corticales, Centro de Tecnología Biomédica, Universidad Politécnica de Madrid, Campus Montegancedo S/N, Pozuelo de Alarcón, 28223 Madrid, Spain e-mail:

This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in other forums, provided the original authors and source are credited and subject to any copyright notices concerning any third-party graphics etc.

Geometrical features of chemical synapses are relevant to their function. Two critical components of the synaptic junction are the active zone (AZ) and the postsynaptic density (PSD), as they are related to the probability of synaptic release and the number of postsynaptic receptors, respectively. Morphological studies of these structures are greatly facilitated by the use of recent electron microscopy techniques, such as combined focused ion beam milling and scanning electron microscopy (FIB/SEM), and software tools that permit reconstruction of large numbers of synapses in three dimensions. Since the AZ and the PSD are in close apposition and have a similar surface area, they can be represented by a single surface—the synaptic apposition surface (SAS). We have developed an efficient computational technique to automatically extract this surface from synaptic junctions that have previously been three-dimensionally reconstructed from actual tissue samples imaged by automated FIB/SEM. Given its relationship with the release probability and the number of postsynaptic receptors, the surface area of the SAS is a functionally relevant measure of the size of a synapse that can complement other geometrical features like the volume of the reconstructed synaptic junction, the equivalent ellipsoid size and the Feret's diameter.

Chemical synapses play a pivotal role in the exchange of information between neurons. They are formed by a presynaptic axon terminal and a postsynaptic membrane, separated by the synaptic cleft. At the presynaptic membrane, the active zone (AZ) contains the molecular machinery necessary for the rapid docking of synaptic vesicles and subsequent release of the neurotransmitter that they contain (Sigrist and Schmitz,

Both the AZ and the PSD are electron-dense structures that can be readily identified under the electron microscope. Although they are separated by the synaptic cleft, this space is not always visible, and the pre- and postsynaptic membranes may give the impression of being fused together when the synaptic junction is sectioned obliquely or parallel to the cleft (

At present, it is possible to study the ultrastructure of large numbers of synapses within 3D samples of brain tissue. Indeed, using combined focused ion beam milling and scanning electron microscopy (FIB/SEM), it has been shown that virtually all synaptic junctions can be identified regardless of the plane of the section (Merchán-Pérez et al.,

The main difficulty when attempting to extract the SAS from actual 3D reconstructions of synaptic junctions resides in the large variability of their size and shape. For example, there are highly tortuous synaptic junctions, and others that have one or several holes (perforated synapses) that also vary in shape, size, and distribution. This variability precludes the use of the techniques currently available, so we have developed a new method to overcome the difficulties associated with SAS extraction. We propose a hybrid solution that obtains the desired result very efficiently by a combination of a deformable template surface and a distance transform method.

Several different approaches have been proposed to extract internal surfaces from 3D volumes. Skeletonization algorithms (Hisada et al.,

The application of a distance transform to a binary image produces a distance image where each pixel is assigned a distance label. In a 3D object, for each voxel the label stores a value indicating the shortest distance to the external contour. The set of voxels with their corresponding distance labels constitute the distance map (Borgefors,

The whole procedure for the extraction of the SAS is performed in the following steps:

It is necessary to first perform the segmentation of the synaptic junctions that are present in a stack of serial images obtained by FIB/SEM. In the present study this was achieved with ESPINA, a software tool designed for the segmentation of electron microscopy images that uses heuristics based on gray levels and connectivity (Morales et al.,

In order to obtain a spatial reference to locate the deformable template, we have to determine the predominant orientation of the reconstructed synaptic junction. For this purpose, we compute the Oriented Bounding Box (OBB). The OBB is the smallest rectangular box that encloses the segmented synaptic junction (Figure

We then obtain the distance map of the segmented synaptic junction by applying the distance transform (Maurer et al., _{i} representing the distance between each voxel _{s} is an adjustable value between 0 and probit (0.25) = 0.674489 (see below); probit is the quantile function of the Gaussian distribution; and max (

Although the value of _{s} can be chosen by the user, we have adjusted its default value to _{s} = 0.67. The rationale for this choice stems from the properties of the Gaussian smoothing transformation. As an example, we can illustrate the effect of applying the smooth transformation on the distance map of a sphere. In this case, max (_{s} = 0, no actual smoothing is performed. If we increase _{s} values, this results in progressively more intense smoothing until a negative value is obtained for the distance map at the center of the sphere when _{s} is larger than 0.674489. The center of the sphere would therefore be labeled as an external point, not belonging to the sphere itself, clearly indicating that the smoothing was too intense. Although higher _{s} values would be possible with objects that are flatter than a sphere, we have set _{s} = 0.67 as the upper bound, to obtain the maximum smoothing possible without causing undesired artifacts.

We then compute the best location to place the deformable template within the synaptic junction. To achieve this, we obtain the set of voxels with the highest _{i} values in the distance map, corresponding to the most interior points, and we compute the geometric center of this set of points (Figure

The deformable template is generated. It is a planar mesh that is oriented along the principal axes of the OBB and intersects the geometric center obtained in the previous step (Figure

The gradient of the distance map gives us a measure of the deformation required to adjust the planar template to the 3D shape of the synaptic junction. We obtain a gradient image (Figure

Taking into account the orientation of the synaptic junction, we project the gradient vectors along the normal direction _{i}·

The deformation is then applied to the template vertices according to the values of the normal vectors calculated in the previous step. The higher the vector value, the more the template mesh vertices must be displaced (Figure _{i} of the template vertices are transformed according to the following expression:

This is the only step where several iterations may occur. Since the sequential deformation drives the template vertices to a point of convergence, the stop condition will be reached ideally when the template no longer needs to be deformed. Occasionally the final state is not a unique position but a set of positions between which the template vertices oscillate indefinitely, so we keep a record of the last

The portions of the deformed mesh protruding outside the segmented synaptic junction are removed by a clipping operation (Figure

To test the performance of the algorithm described above, we applied it to two sets of 253 and 320 synaptic junctions. They were segmented with ESPINA from samples obtained by FIB/SEM from the rat somatosensory cortex (Figure

The present method has been implemented in C++. We have chosen a set of stable and widely tested free distribution tools to ensure the portability of the code: ITK vs. 3.16 as the image processing library and VTK vs. 5.6 as the mesh manipulation and visualization library. The results have been generated on a PC with Intel Pentium Core I7 920 2.67 GHz CPU and 12 GB RAM memory. Software is available for testing at

Several geometrical features of the synaptic junctions are already calculated by ESPINA (Morales et al.,

The SAS extracted from a given synaptic junction not only provides qualitative visual information about the shape of the synaptic junction, i.e., whether it is flat, curved or perforated. The SAS can also be quantitatively characterized, providing additional information over and above that which can be obtained from the 3D reconstructed synaptic junctions alone (Figure

While the surface area is related to the probability of neurotransmitter release and to the number of postsynaptic receptors, the SAS curvature is related to the shape of the synaptic junction, that is, the shape of the SAS shows whether the synaptic junction is flat, curved, or tortuous. Thus, a measure of the surface curvature allows us to further characterize the shape of the SAS. It is important to find global measures that ensure a robust shape analysis of the SAS features. A simple and intuitive measure involves comparing the surface area of the SAS with its projected area on the largest face of the OBB. This area ratio (Figure

Area ratio of the SAS: one minus the ratio between the projected area of the SAS on the largest face of the OBB and the area of the SAS. This measure would equal 0 in a perfectly flat SAS, and it would yield progressively higher values as the SAS curvature increases.

Other measures of curvature can be extracted locally at each vertex

Minimum normal curvature at each vertex _{1}(

Maximum normal curvature at each vertex _{2}(

Mean normal curvature at each vertex

Gaussian curvature at each vertex _{1}(_{2}(

In Euclidean space, κ_{1} and κ_{2} are the maximum and minimum curvatures of the set of curves crossing one vertex

Mean and standard deviation of the minimum and maximum normal curvatures:

Mean and standard deviation of the mean normal curvature of the SAS:

Mean and standard deviation of the Gaussian curvature of the SAS:

Where

_{1} and κ_{2}, respectively) are determined at each vertex of the surface

Although several geometric characteristics can be extracted from synaptic junctions reconstructed in 3D, they only represent rough estimates of the size and shape of synapses. The SAS, however, is approximately equivalent to the AZ and the PSD. The surface area of the SAS is therefore a biologically relevant measure of synapse geometry since it is related to vesicle release probability at the presynaptic side, and to the number of specific receptors present at the postsynaptic side. Additional information on the shape of the SAS can be obtained by measuring its perimeter, curvature, and tortuosity. We have implemented an algorithm that is capable of extracting the SAS from a 3D volume representing a previously segmented synaptic junction. This algorithm is a hybrid approach that combines a distance transform method and a deformable planar template. The algorithm is fast and does not require user intervention. From a computational point of view, one of its most relevant features is its efficiency and its simplicity, since no complex mathematical background is required. Thus, our algorithm can be applied to the large number of synapses that are currently segmented from stacks of images obtained by three-dimensional electron microscopy techniques such as FIB/SEM. There is considerable interest in determining the geometrical properties of synapses, since changes in the size of the AZ and/or PSD have been reported under a variety of normal, pathological, and experimental conditions and, in general, these changes have been associated with plastic responses and synaptic malfunction. Thus, the combination of FIB/SEM and the algorithm presented here will help to obtain relevant morphological information that will allow the functional characteristics of large numbers of synapses to be correlated with their geometric properties, which is particularly relevant for better understanding the synaptic organization of the brain in both health and disease. Indeed, FIB/SEM technology has already been shown to be useful in the study of alterations of cortical synapses in the brain of patients with Alzheimer's disease (Blazquez-Llorca et al.,

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

This work was supported by grants from the following entities: Center for Networked Biomedical Research in Neurodegenerative Diseases (CIBERNED, CB06/05/0066, Spain) and the Spanish Ministry of Economy and Competitiveness (Ministerio de Economía y Competitividad: SAF2009-09394, BFU2012-34963; TIN2010-21289 and the Cajal Blue Brain Project, the Spanish partner of the Blue Brain Project initiative from EPFL). Preliminary work on this subject has been presented as a conference communication (Morales et al.,

The Supplementary Material for this article can be found online at: