Modeling neural activity in neurodegenerative diseases through a neural field model with variable density of neurons.

In recent years, a vertiginous advance has occurred within the Neural Field Theory with the development of the so-called Next Generation Neural Field models. Unlike the phenomenological models, these models manage to describe neuronal activity, macroscopically, from the thermodynamic limit of microscopic laws under the assumption of a homogeneous density of neurons. The study of neural activity during neurodegenerative processes associated to Alzheimer's, Parkinson's or Glioblastomas, should include a variable density of neurons. In this work, we propose an update of the Next Generation Neural Field model, extracted from the thermodynamic limit of the quadratic integration-and-fire model with realistic synaptic coupling and a variable density of neurons at the microscopic level. The thermodynamic limit of the system will allow us to study the patterns of synchronized neural activity that appear as the result of different spatial distribution of neurodegeneration. In particular, we demonstrate that during neurodegenerative processes, the relationship established between the thermodynamic states of the Neural Field and the Kuramoto order parameter (Measure of Neural Synchronization) differs from the classic results of the Next Generation Neural Field literature. Instead, the variation in neuron density directly modifies the Kuramoto order parameter. This might help us explain the diverse patterns of activity that can be found in different neurodegenerative processes and that could become experimental biomarkers of such pathologies.