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

Abstract

In recent years, extensive research has been done on the prediction, treatment, and recognition of Alzheimer’s disease (AD). The study of AD emerging and progression in the first years is valuable due to the nature of AD. Among scientific works, mathematical modeling of AD is an efficient way of studying the influence of various parameters on AD emerging. This paper proposes a novel model based on Cellular Automata (CA) for the study of AD's progress. In our model, the synapses of each neuron have been considered as square cells located around the central cell. The key parameter for AD progression in our model is 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 an M × L-neuron network, which can expand to the whole hippocampus space. 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 sensitive to astroglia variations compared to microglia variations. The presented model can improve the scientist's insight into the prediction of AD, which will assist them in effectively considering the influence of various parameters on AD.

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Correspondence to Yashar Sarbaz or Faegheh Golabi.

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The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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This work is partially supported by the Vice-Chancellor in Research Affair-Tabriz University of Medical Sciences under Ethical Code No. IR.TBZMED.VCR. REC.1399.377. The funders had no role in the study design, analysis, numerical simulations, the decision to publish, or the preparation of the manuscript.

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Jafari, N., Sarbaz, Y., Ebrahimi-kalan, A. et al. Novel mathematical model based on cellular automata for study of Alzheimer’s disease progress. Netw Model Anal Health Inform Bioinforma 11, 26 (2022). https://doi.org/10.1007/s13721-022-00366-2

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  • DOI: https://doi.org/10.1007/s13721-022-00366-2

Keywords

  • Alzheimer’s disease
  • Cellular Automata
  • Model
  • Progress
  • Amyloid-β