Evaluation of Various Drugs' Influence on Alzheimer's Disease Progress Using a New Analytical Model Based on Cellular Automata

Abstract

This article aims to introduce and propose a novel mathematical model for the study of Alzheimers disease (AD) progress. The presented model is based on Cellular Automata for better representation of AD progression. The differential equations of the Puri-Li model are utilized to calculate the number of Amyloid-{beta} molecules. Also, a new definition for AD rate 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-neuron communications, the model is obtained for a 3x3 neuron system to investigate the influence of drug injection on the reduction of AR, CR, and WR factors. It is shown that using drugs can decrease AR and CR factors and also enhance the WR. The presented study can be utilized for the investigation of various factors in the control and treatment of AD progression.