Modeling Alzheimer's Disease: From Memory Loss to Plaque & Tangles Formation

Abstract: We employ the Hopfield model as a simplified framework to explore both the memory deficits and the biochemical processes characteristic of Alzheimer's disease. By simulating neuronal death and synaptic degradation through increasing the number of stored patterns and introducing noise into the synaptic weights, we demonstrate hallmark symptoms of dementia, including memory loss, confusion, and delayed retrieval times. As the network's capacity is exceeded, retrieval errors increase, mirroring the cognitive confusion observed in Alzheimer's patients. Additionally, we simulate the impact of synaptic degradation by varying the sparsity of the weight matrix, showing impaired memory recall and reduced retrieval success as noise levels increase. Furthermore, we extend our model to connect memory loss with biochemical processes linked to Alzheimer's. By simulating the role of reduced insulin sensitivity over time, we show how it can trigger increased calcium influx into mitochondria, leading to misfolded proteins and the formation of amyloid plaques. These findings, modeled over time, suggest that both neuronal degradation and metabolic factors contribute to the progressive decline seen in Alzheimer's disease. Our work offers a computational framework for understanding the dual impact of synaptic and metabolic dysfunction in neurodegenerative diseases.