Geometrical modelling of neuronal clustering and development

Approaches to Embryonic Neurodevelopment: From Neural Cell to Neural Tube Formation through Mathematical Models

“…Further, the electrical activity (E) of the cells is regarded as another independent factor that contributes to the morphological change of the cells (assuming the change in the manifolds shown in Figure 8 as Functor E: Ef(M1)→Ef(M2)) and leads to cellular growth. The equation is called the Van der Pol equation 4 and is applied to generate the vector field in two-phase, which is 𝑥2 = −𝑥 1 − 𝑚(𝑥 1 2 − 1)𝑥 2 , m = 0.1 and m = 1, E= 𝑥2. .…”

“…In mathematical modelling of the neurodevelopmental processes, one of the biggest challenges is how to "approach", meaning where to begin, and how to look at this entity for inspiration for computation/neural networks, but more importantly, to understand the underlying mechanisms that drive neurodevelopment during embryonic development 2,3 . Our previous study addressed these questions at a preliminary level 4 . Eventually, we devised an equation that theoretically showed neuronal clustering in the cortex 5 by using the cellular characteristics, since such descriptions are limited 4 , this study addresses these fundamental questions using more complex equations and algorithms.…”

“…Our previous study addressed these questions at a preliminary level 4 . Eventually, we devised an equation that theoretically showed neuronal clustering in the cortex 5 by using the cellular characteristics, since such descriptions are limited 4 , this study addresses these fundamental questions using more complex equations and algorithms. We explore the possibilities and pitfalls to understand how neurodevelopmental processes during embryogenesis can be analyzed mathematically.…”

“…A. Schematic illustration shows how the neuronal progenitors change shape and directionduring neurodevelopment. This illustration is related to our previous study4 , in which we designed how cell shape, direction, and electrical activity are defined as independent elements for neurodevelopment. The 3D position of cells in beginning= {𝑖, 𝐽 ̂, 𝑘 ̂}, the G function and its parameters as The change in position of cells = {d𝑝 1 , d𝑝 2 , d𝑝 3 }, Shapes= Sphere, ellipsoid, pyramidal approximation, other convex bodies, Electrical activity= Excitatory {+}, Inhibitory {−}, Excitatory/Inhibitory {±}, X (𝑑𝑝 1 , s, 𝑒 1 ), Y (𝑑𝑝 2 , s, 𝑒 2 ), Z (𝑑𝑝 3 , s, 𝑒 3 ).…”