A New Analytical Model Based on Cellular Automata to Study the Influence of Various Drugs on Alzheimer’s disease Progress

In recent years, extensive research has been done to predict, treat, and recognition of Alzheimer’s disease(AD). Among these scientific works, mathematical modeling of AD is an efficient way to study the influenceof various parameters such as drugs on AD progression. This article aims to introduce and propose a novelmathematical model for the study of Alzheimer’s disease (AD) progress. The presented model is based onCellular Automata for better representation of AD progression. The differential equations of the Puri-Limodel are utilized in this paper to calculate the number of Amyloid-β molecules. A new definition for ADrate is presented in this study. Moreover, other useful factors such as Critical Rate (CR) and Warning Rate(WR) are defined to determine the status of AD progression. To get exact insight into the neuron-to-neuroncommunications, the model is obtained for a ۳×۳ neuron system to investigate the influence of drug injectionon the reduction of AR, CR, and WR factors. It will be shown that the usage of the strong and suitable drugcan decrease AR and CR factors and also enhance the WR. The presented study can be utilized for theinvestigation of various factors in the control and treatment of AD progression.

Keywords:

Alzheimer disease , cellular automata , modelling , disease progress , Amyloid Beta