2D Model for C a 2 + $Ca^{2+}$ Dynamics Regulating I P 3 $IP_3$ , ATP and Insulin in A Pancreatic β $\beta$ -Cell

The regulation of insulin in pancreatic $\beta$-cells is dependent on changes in the cytoplasmic calcium concentration $\left({\left[{Ca}^{2+}\right]}_i\right)$. The well-balanced influx and efflux routes are required for insulin secretion. Therefore, this research presents a simplified yet valuable model for investigating calcium dynamics in a $\beta$-cell under 2D unsteady state conditions. The model integrates diffusion, reactions involving sources, excess buffers, and fluxes, including efflux through leak and SERCA mechanisms. Boundary and initial conditions are tailored to $\beta$-cell physiology. Numerical solutions are computed using the finite element method with co-axial circular elements, chosen for their effectiveness in discretizing the cell domain and improving accuracy. This approach minimizes errors, enhancing predictive fidelity and capturing the intricate geometries and dynamics within $\beta$-cells. The model's findings highlight the influence of buffers and source influx on calcium regulation, and integrate temporal fluctuations in IP₃(Inositol 1,4,5-Trisphosphate) synthesis and degradation, Adenosine Triphosphate (ATP) generation, insulin release, and metabolic processes. Computational analysis suggests disruptions in cellular energy production and metabolite distribution may underlie conditions like metabolic syndrome and diabetes. This study contributes to a deeper understanding of $\beta$-cell biology, potentially informing therapeutic strategies for related disorders.