A Spatial Multi-Cellular Model of the Pancreatic Islet including 𝛼-, β -, and 𝛿-cells

Abstract

Our goal is to create a computational model of an islet of Langerhans, consisting of 𝛼-, β -, and 𝛿-cells. We will focus on varying the geometries and proportions of the cells in this islet, and study the hormonal secretion and reception of each cell at any point in time. We are currently considering basic cubic and spherical models, among others. Besides changing the physical shape of our islet, we will change the sequential ordering of the cell types in our model. We will have three different models (one for each cell type). While β -cells are already electronically wired, 𝛼-cell and 𝛿-cell paracrine interactions depend on a spatial-temporal model. We will use ODEs to model the behavior of these cells. We will use a diffusive PDE equation to model the propagation of the secretions . Out of computational concerns, we will hope to find and assume parameters that would allow us to use an analytical solution to the diffusive PDE. Currently, we are contemplating using the heat kernel to approximate a solution to. However, if such an approximation cannot be realized, we may just end up numerically solving the PDE's despite of the increase in computational complexity. (𝜕u/𝜕t) - Dƍ²u = f(u,t) K(t, x, y) = (1/(4ΠDt)³/²)e⁻⁽ˣ⁻ʸ⁾^²/⁴ᴰᵗ Upon creating a modeling tool, we will be able to model experimental scenarios with similar geometries and proportions to human and mouse islets given in your presentation. We hope to simulate a core and mantle geometry for the mouse model by creating a core of β-cells with an 𝛼 and 𝛿 mantle. We will see which geometries work best for such a simulation. Afterward, we will be prepared to compare our results to experimental data (already done by the NIH). We will also be able to use these models to isolate specif c cell types and compare them to each other at different points in the model, while toggling certain secretions or any system parameter to test if any paracrine interactions tame heterogeneity.