Coupled Spatio-Temporal Dynamics and Nonlocality in Advanced Mathematical Models for the Analysis of Complex Neurodegenerative Disease Pathologies

  • Pal, Swadesh (MS2Dicovery IRI, WLU, Waterloo)
  • Melnik, Roderick (MS2Dicovery IRI, WLU, Waterloo)

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One in six of the world’s population has to deal with neurodegenerative disorders, and while medical devices exist to detect, prevent, and treat such disorders, some fundamentals of the progression of associated diseases remain ambiguous [1]. In this presentation, we focus on Alzheimer’s disease (AD), where amyloid-beta (Aβ) and tau proteins are among the main contributors to the development or propagation of AD. The Aβ proteins clump together to form plaques and disrupt cell functions. Moreover, the abnormal chemical change in the brain helps to build sticky tau tangles that block the neuron’s transport system. Astrocytes generally maintain a healthy balance in the brain by clearing the Aβ toxic plaques. Even so, over-activated astrocytes release chemokines and cytokines and also react to pro-inflammatory cytokines, further increasing the production of Aβ. We construct a novel mathematical model that can capture astrocytes’ dual behaviour, emphasizing the importance of spatio-temporal coupling and nonlocality. We reveal that the disease propagation depends on the disease’s earlier status, called the “memory effect” which involves non-Markovian processes [2]. We explain how to integrate brain connectome data in the network model and study this effect, as well as the dual role of astrocytes as a coupled phenomenon. Depending on toxic loads in the brain, we also provide details of the analysis of the neuronal damage in the brain. Examples will be given for different pathologies, subject to primary, secondary, and mixed tauopathies parameters of the model. Due to the mixed tauopathy, different brain nodes or regions in the brain connectome accumulate different toxic concentrations of toxic Aβ and toxic tau proteins. In the last part of this presentation, we explain how the memory effect can slow down the propagation of such toxic proteins in the brain and hence decreases the rate of neuronal damage. REFERENCES [1] S. Pal and R. Melnik, “Nonlocal models in the analysis of brain neurodegenerative protein dynamics with application to Alzheimer’s disease”, Scientific Reports, 12, Art. 7328 (2022).  [2] S. Pal and R. Melnik, “Non-Markovian behaviour and the dual role of astrocytes in Alzheimer's disease development and propagation”, arXiv: 2208.03540, submitted (2023).