Abstract：
Cytosolic-free calcium ions play an important role in various physical and physiological processes. A vital component of neural signaling is the free calcium ion concentration often known as the second messenger. There are many parameters that effect the cytosolic free calcium concentration like buffer, voltage-gated ion channels, Endoplasmic reticulum, Mitochondria, etc. Mitochondria are small organelles located within the nervous system that are involved in processes within cells such as calcium homeostasis management, energy generation, response to stress, and cell demise pathways. In this work, a mathematical model with fuzzy boundary values has been developed to study the effect of Mitochondria and ER fluxes on free Calcium ions. The intended findings are displayed utilizing the physiological understanding that amyloid beta plaques and tangles of neurofibrillary fibers have been identified as the two main causes of AD. The key conclusion of the work is the investigation of [Formula: see text] for healthy cells and cells affected by Alzheimer\'s disease, which may aid in the study of such processes for computational scientists and medical practitioners. Also, it has been shown that when a unique solution is found for a specific precise problem, it also successfully deals with any underlying ambiguity within the problem by utilizing a technique based on the principles of linear transformation. Furthermore, the comparison between the analytical approach and the generalized hukuhara derivative approach is shown here, which illustrates the benefits of the analytical approach. The simulation is carried out in MATLAB.
摘要：
无胞质钙离子在各种物理和生理过程中起重要作用。神经信号的重要组成部分是游离钙离子浓度，通常被称为第二信使。有许多参数影响胞浆游离钙浓度，如缓冲液，电压门控离子通道，内质网,线粒体,等。线粒体是位于神经系统内的小细胞器，参与细胞内的过程，如钙稳态管理，能源生产，对压力的反应，和细胞死亡途径。在这项工作中,已经建立了具有模糊边界值的数学模型来研究线粒体和ER通量对游离钙离子的影响。利用生理学理解显示了预期的发现，即β淀粉样蛋白斑块和神经原纤维缠结已被确定为AD的两个主要原因。这项工作的关键结论是研究健康细胞和受阿尔茨海默病影响的细胞的[公式：见文字]，这可能有助于计算科学家和医疗从业者研究这些过程。此外，已经表明，当找到一个特定的精确问题的唯一解决方案时，它还通过利用基于线性变换原理的技术成功地处理了问题中的任何潜在歧义。此外，这里显示了分析方法和广义胡原导数方法之间的比较，这说明了分析方法的好处。在MATLAB中进行了仿真。
