# An Algorithm for Creating a Synaptic Cleft Digital Suitable for Further Numerical Modeling
## 2 Materials and Methods
### Astrocytic Leaflets  
The astrocytic leaflet has a spongy structure and protrudes within the presynaptic and postsynaptic endings to the synaptic cleft. They have a very dynamic shape and their protrusion extent varies with synaptic plasticity, circadian rhythms, stress conditions, and neurodegenerative disorders [44; 45; 46]. According to an EM study, about 20% to 80% of rat hippocampus spines have glia cells opposed to them [47], and only 20% to 65% of synapses could be surrounded by astrocytes at the periphery [48]. The distance between astrocytic and neuronal membranes is no less than 7 nm for ISF diffusion feasibility, as is the case for all cells of the brain parenchyma [38]. Furthermore, the leaflet tip cannot be too thin, as it must have the capacity to contain cell structure elements inside it, and the curvature of the cell membrane is limited. We took the above criteria into consideration for 3D astrocytic leaflet modeling in detail, utilizing a combination of geometric and Boolean operations. As above, the surrounding synaptic cleft astrocytic geometric object was built by connecting the adjacent faces of \(\partial\Omega_{1-2}\) and \(\partial\Omega_{2-1}\) using the loft procedure (Standard Geometry \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multicolumn{2}{c}{\(\partial\Omega_{\text{AZ}}\)**Properties**} & \(\mathbf{R_{SP}}\) **= 50 nm** & \(\mathbf{R_{SP}}\) **= 130 nm** & \(\mathbf{R_{SP}}\) **= 200 nm** & \(\mathbf{R_{SP}}\) **= 300 nm** & \(\mathbf{R_{SP}}\) **= 450 nm** \\ \hline \multirow{2}{*}{\(\text{H}_{\text{SP}}\) = 15 nm} & \(\frac{\partial\Omega_{\text{AZ}}\), \(\upmu\)m\({}^{2}}{\partial\Omega_{\text{PSD}}\), \(\upmu\)m\({}^{2}}\) & 0.007 & 0.045 & 0.090 & 0.149 & 0.200 \\ \hline \multirow{2}{*}{\(\text{H}_{\text{SP}}\) = 20 nm} & \(\frac{\partial\Omega_{\text{AZ}}\), \(\upmu\)m\({}^{2}}{\partial\Omega_{\text{PSD}}\), \(\upmu\)m\({}^{2}}\) & 0.008 & 0.049 & 0.104 & 0.184 & 0.259 \\ \hline \multirow{2}{*}{\(\text{H}_{\text{SP}}\) = 25 nm} & \(\frac{\partial\Omega_{\text{AZ}}\), \(\upmu\)m\({}^{2}}{\partial\Omega_{\text{PSD}}\), \(\upmu\)m\({}^{2}}\) & 0.008 & 0.051 & 0.112 & 0.206 & 0.302 \\ \hline \multirow{2}{*}{\(\text{H}_{\text{SP}}\) = 30 nm} & \(\frac{\partial\Omega_{\text{AZ}}\), \(\upmu\)m\({}^{2}}{\partial\Omega_{\text{PSD}}\), \(\upmu\)m\({}^{2}}\) & 0.009 & 0.052 & 0.116 & 0.221 & 0.335 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The surface area of AZ and PSD for different chosen geometric parameters of the synapse phantom. The square of AZ is equal to the same as that for PSD. module, COMSOL Multiphysics Software). The number of adjacent faces was allowed to vary, in order to enfold the chosen synaptic periphery distance. In the current work, the surrounding synaptic cleft region leaflets presented 24%, 38%, 48%, and 62% cradle variation. An additional loft operation was used to link this leaflet part to several faces of \(\Omega_{3}\). Thus, the intermediate astrocytic leaflet structure, \(\Omega^{\prime}{}_{\text{leaflet}}\), was created. The Boolean subtraction operation was used on the differently scaled \(\Omega_{1}\) and \(\Omega_{2}\) objects for replication of the space between neuronal and astrocytic 3D objects. Similar to \(\Omega^{\prime}{}_{i}\), an isotropic scaling procedure was applied to each body separately, with their corresponding scaling center and an empirically chosen scale factor (\(\lambda=1.015\)), and the resulting bodies are denoted as \(\Omega^{\prime\prime}{}_{1}\) and \(\Omega^{\prime\prime}{}_{2}\). The object after subtraction will have the required extracellular distance to \(\Omega_{\text{pre}}\) and \(\Omega_{\text{post}}\). The tip of \(\Omega^{\prime}{}_{\text{leaflet}}\) is strikingly edge and is not suitable for further application in numerical calculations using FEM. Moreover, the leaflet tip is formed with the involvement of cell structure elements, so biologically reasonable restrictions should be applied on the stochastically created object.