Modeling two-dimensional spatial neurodynamics in neuronal calcium disorders using a fuzzy differential approach

Abstract The unbound calcium cations in the cytoplasmic matrix are imperative for numerous visceral and cellular functions. Changes in calcium concentration result in neuronal death, initiating the primary symptoms of the neuronal disease. Considering the above-mentioned points, the main objective of this research is to create a two-dimensional model in order to examine the spatial distribution patterns of calcium in neuronal cells. This model includes key parameters including buffer concentration, diffusion coefficient, and endoplasmic reticulum (ER). The proposed model is classified as an imprecise boundary value problem, with boundary conditions represented by triangular fuzzy functions. Additionally, research suggests that establishing a single solution for a specific issue effectively eliminates inherent ambiguity within the problem by employing a strategy based on linear transformation principles. We derived an estimated calcium profile using the fuzzy undetermined coefficient approach and compared the solutions with linear transformation principles. The significant impact of the buffer and ER has been obtained using a two-dimensional fuzzy boundary value problem. The solution was executed using MATLAB, and numerical results were obtained using simulation. The proposed model provides novel insights into the effect of dysregulation of calcium profile in the fuzzy environment, leading to the neurological disorder Alzheimer’s disease.