# An Algorithm for Creating a Synaptic Cleft Digital Suitable for Further Numerical Modeling
## 2 Materials and Methods
\begin{table}
\begin{tabular}{c c c} \hline
**The Object** & **Description** & **Comments** \\ \hline \hline \multicolumn{3}{c}{Input Voronoi diagram bodies} \\ \hline \(\Omega_{1}\) & The first Voronoi diagram body & This object can be chosen fluently \\ \hline \(\Omega_{2}\) & The second Voronoi diagram body & This object is selected as a close neighbor of \(\Omega_{1}\) \\ \hline \(\Omega_{3}\) & The third Voronoi diagram body & The third object lies near the contact area of \(\Omega_{1}\) and \(\Omega_{2}\) \\ \hline \multicolumn{3}{c}{Auxiliary objects, planes, and surfaces} \\ \hline \(\Omega^{\prime}_{1}\) and \(\Omega^{\prime}_{2}\) & The auxiliary scaled \(\Omega_{1}\) and \(\Omega_{2}\) for astrocytic & \(\Omega^{\prime}_{i}=\gamma\cdot\Omega_{i}\) \\  & leaflet tip cutting & \\ \hline \(\Omega^{\prime}_{1-2}\) & \(\Omega_{1-2}\) edge projection on auxiliary plane is used for & \(\Omega^{\prime}_{1-2}=\Omega^{\prime}_{1}\bigcap\Omega^{\prime}_{2}\) \\  & leaflet tip cutting & \\ \hline \(\partial\omega\) & An auxiliary plane & \(\partial\Omega_{\text{bp}}<\partial\omega;\partial\Omega^{\prime}_{\text{bp}} \subset\partial\omega\) \\ \hline \(\Omega^{\prime}_{\text{ leaflet}}\) & A combination of two loft objects for leaflet creation & An intermediate leaflet object (see in text) \\ \hline \(\Omega^{\prime\prime}_{1}\) and \(\Omega^{\prime\prime}_{2}\) & The auxiliary scaled \(\Omega_{1}\) and \(\Omega_{2}\) for astrocytic & \(\Omega^{\prime\prime}_{i}=\lambda\cdot\Omega_{i}\) \\  & leaflet cutting & \\ \hline \(\Omega_{\text{bp}}\) & A 3D template for leaflet cutting & \(\Omega_{\text{bp}}=\partial\text{h}\cdot\partial\Omega_{\text{bp}}\) \\ \hline \(\Omega^{\prime}_{\text{bp}}\) & A 3D template for leaflet cutting in the case of bigger & \(\Omega^{\prime}_{\text{bp}}=\partial\text{h}\cdot\partial\Omega^{\prime}_{\text {bp}}\) \\  & synaptic phantoms & \\ \hline \(\Omega_{\text{SP}}\) & Synapse phantom & Determined by the experimental data object composed of upper and lower hemispheres joined by a cylindrical linker \\ \hline \(\Omega_{\text{ellipsoid}}\) & An ellipsoid used for indication of considered & The geometric parameters of ellipsoid have a common restriction (see in text) \\  & ISF borders & \\ \hline \(\partial\Omega_{\text{bp}}\) & A solid type of interpolation curve of \(\Omega_{1-2}\) edge projection on auxiliary plane \(\partial\omega\) & \(\partial\Omega_{\text{bp}}\subset\partial\omega\) \\ \hline \(\partial\Omega^{\prime}_{\text{bp}}\) & A solid type of combined interpolation curve on auxiliary plane \(\partial\omega\) & \(\partial\Omega^{\prime}_{\text{bp}}\subset\partial\omega\) \\ \hline \(\partial\Omega_{1-2}\) & The presynaptic membrane & Enclosing first two Voronoi bodies contact area which faces \(\Omega_{1}\) \\ \hline \(\partial\Omega_{2-1}\) & The postsynaptic membrane & Enclosing first two Voronoi bodies contact area which faces \(\Omega_{2}\) \\ \hline \multicolumn{3}{c}{Digital domains corresponding to nervous tissue’s cells and ISF} \\ \hline \(\Omega_{\text{pre}}\) & The first body with embedded synapse phantom track for presynaptic modeling & \(\Omega_{\text{pre}}=\Omega_{1}\backslash\Omega_{\text{SP}}\) \\ \hline \(\Omega_{\text{post}}\) & The second body with embedded synapse phantom track for postsynaptic modeling & \(\Omega_{\text{post}}=\Omega_{2}\backslash\Omega_{\text{SP}}\) \\ \hline \(\Omega_{\text{ leaflet}}\) & A small protrusion of \(\Omega_{3}\) toward the synaptic cleft for astrocytic leaflet modeling & \(\Omega_{\text{leafnet}}=\Omega^{\prime}_{\text{leafnet}}\backslash(\Omega^{ \prime}_{1}\bigcup\Omega^{\prime}_{2}\bigcup\Omega_{\text{bp}}\bigcup\Omega^{ \prime}_{\text{synapse}})\) (see in the text) \\ \hline \(\Omega_{\text{AL}}\) & A complex body for astrocyte modeling & \(\Omega_{\text{AL}}=\Omega_{3}\bigcup\Omega_{\text{leafnet}}\) \\ \hline \(\Omega_{\text{ISF}}\) & The final complex body which limits neurotransmitter diffusion area includes synaptic cleft space and marked & \(\Omega_{\text{ISF}}=\Omega_{\text{ellipsoid}}\backslash(\Omega_{\text{pre}}\bigcup \Omega_{\text{post}}\bigcup\Omega_{\text{AL}})\) \\  & \(\partial\Omega_{\text{AL}Z}\), \(\partial\Omega^{\prime}_{\text{fusion}}\), and \(\partial\Omega_{\text{PSD}}\) & \\ \hline \multicolumn{3}{c}{Digital surfaces coinciding with essential biological areas} \\ \hline \(\partial\Omega_{\text{AL}Z}\) & The presynaptic membrane area on \(\Omega_{\text{pre}}\), which contains \(\text{Ca}^{2+}\)-channels and vesicular emitting protein machinery & The track after \(\Omega_{1}\backslash\Omega_{\text{SP}}\) Boolean operation \\ \hline \(\partial\Omega^{\prime}_{\text{fusion}}\) & The places of plausible vesicular fusion pores on \(\partial\Omega_{\text{AL}Z}\) & \(\partial\Omega^{\prime}_{\text{fusion}}\) diameter is approximately 9 nm and has consistent pattern on \(\partial\Omega_{\text{AL}Z}\) (see in the text) \\ \hline \(\partial\Omega_{\text{PSD}}\) & The PSD area on \(\Omega_{\text{post}}\) & The track after \(\Omega_{2}\backslash\Omega_{\text{SP}}\) Boolean operation \\ \hline \end{tabular}
\end{table}