Novel mathematical model based on cellular automata for study of Alzheimer’s disease progress

Abstract

In recent years, extensive research has been done for the prediction, treatment, and recognition of Alzheimer's disease (AD). Among these scientific works, mathematical modeling of AD is an efficient way to study the influence of various parameters such as drugs on AD progression. This paper proposes a novel model based on Cellular Automata (CA), a powerful collection of colored cells, for the investigation of AD progress. In our model, the synapses of each neuron have been considered as square cells located around the central cell. The key parameter for the progression of AD in our model is the amount of amyloid-β (Aβ), which is calculated by differential rate equations of the Puri-Li model. Based on the proposed model in this article, we introduce a new definition of AD Rate for a 𝑀 × 𝐿-neuron network, which can be expanded for the whole space of the hippocampus. To better illustrate the mechanism of this model, we simulate a 33 neuron network and discuss the obtained results. Our numerical results show that the variations of some parameters have a great effect on AD progress. For instance, it is obtained that AD Rate is more sensitive to astroglia variations, in comparison to microglia variations. The presented model can improve the scientist's insight into the progress of AD, which will assist them to effectively consider the influence of various parameters on AD.