# An Algorithm for Creating a Synaptic Cleft Digital Suitable for Further Numerical Modeling
## 4 Discussion  
Computational modeling of the diffusion of chemical species in synaptic and perisynaptic spaces, metabolic pathways, reaction compartmentalization in brain parenchyma, receptor activation reactions, or transmitter uptake implies specific geometric decisions. There are many ways to carry out synaptic modeling. The first and simplest is to use a two-dimensional geometry. Although planar models can provide insights on some valuable functional characteristics, more vivid three-dimensional geometry can also be used. Simple spherical 3D synaptic models have been based on quantitative EM observations of the cell membrane patterns in a planar section of the rat hippocampus. The superposition of several synaptic profiles allows for a reasonable approximation using two solid hemispheres, representing the presynaptic and postsynaptic parts of neurons as obstacles to diffusion. They are separated from each other by a cylindrical synaptic cleft area and surrounded with a spherical porous medium representative of brain parenchyma [39; 47]. These models have been amended with more elaborate geometric primitives; for example, a bowl-shaped presynaptic ending and spherical dendritic parts of neurons [56], reversed truncated hemispheres [57], or simply cylindrical nerve endings [58; 59]. They have also been improved through the addition of glial sheets which envelop the synaptic junction and contain transporters for matching neurotransmitters [56; 60; 61]. There are also compromising cases which approximate the synaptic space with two infinite planes [62; 63], or a combination of a plane and rectangular elements mimicking dendritic spines [64] for transmitter diffusion modeling. The results obtained with such models are of great importance, but more realistic structures can still be generated. Therefore, spherical objects have been used to mimic dendritic spines and axon boutons in association with cylindrical cell parts, including axons, spine necks, dendritic shafts, and astrocyte processes [65; 66]. The whole dendritic segments with multiple spines have been constructed using truncated spherical and cylindrical primitives for LTP plasticity modeling [67]. Most native structures are created through 3D reconstruction of ultra-resolution EM data [68]. This type of model is very precise for geometrical definition of brain parenchyma cellular parts--for example, in terms of surface-to-volume ratio (SVR) and spatial distribution or changes in metabolic concentration--yet cannot be used for diffusion modeling. A stochastic model of brain parenchyma with a cylindrical synaptic cleft in the center of a cube filled with randomly scattered, overlapping spheroids representing neuronal and astroglial cell parts with sizes obtained from EM data has been presented recently as more biologically relevant geometric environment for transmitter diffusion simulation [69]; however, it is still not a 3D reconstruction.  
In the present study, we produced a stochastic and biologically precise 3D model of a single synaptic cleft including contact with an astrocytic leaflet, which is suitable for use in transmitter reaction-diffusion modeling. It should be noted that, despite the specific type of considered synapse (i.e., glutamatergic synapse), the introduced algorithm will create a digital phantom reflecting any type of synapse in the CNS. The basic steps are the same for each synaptic contact, as the nature of neurotransmission between neurons is similar for various receptors and neuromediator systems. Moreover, the clear separation of the inside and outside areas allows the created phantoms to be used according to the H/H Classification of convectional reaction-diffusion boundary problems introduced earlier [70].