Investigating Disruptions in Calcium Homeostasis in Neuron Cells Due to VOCC and NCX: Fuzzy Differential Approach

The concentration of calcium in the cytosol is influenced by many physiological processes, including calcium ion channel flow and buffering. Given the preceding, the main objective of this work is to create a model of the distribution of calcium in neural cells in the presence of an exchanger of sodium and calcium and a voltage-operated calcium channel. Reduced buffer levels and increased calcium activity in the voltage-operated calcium channel and exchanger of sodium and calcium are the root causes of neural diseases such as Alzheimer’s. Because of these changes, Alzheimer’s disease impacts and disrupts the calcium transport there. Furthermore, in situations where buffers are fully saturated or cannot bind calcium due to an anomaly or buffer damage, among other circumstances, the roles of voltage-operated calcium channels and exchanger of sodium and calcium in controlling the calcium concentration level become increasingly important. This study focuses on how calcium level changes in the presence of buffers, Endoplasmic Reticulum, voltage-operated calcium channels, and exchangers of sodium and calcium. Based on the physiological traits, appropriate boundary conditions have been developed in a fuzzy environment. The boundary conditions of this model are represented by triangular fuzzy functions, and it is addressed as a fuzzy boundary condition. Here, the approximated solution has been examined by using an undetermined fuzzy coefficient approach. An undetermined fuzzy coefficient approach is a technique for solving fuzzy differential equations that take uncertainty into account by predicting unknown coefficients as fuzzy numbers. To avoid cell loss in Alzheimer’s disease, the combined effect of all these parameters helps to maintain the calcium concentration.