Estimating Memory Deterioration Rates Following Neurodegeneration and Traumatic Brain Injuries in a Hopfield Network Model

Neurodegenerative diseases and traumatic brain injuries (TBI) are among the main causes of cognitive dysfunction in humans. At a neuronal network level, they both extensively exhibit focal axonal swellings (FAS), which in turn, compromise the information encoded in spike trains and lead to potentially severe functional deficits. There are currently no satisfactory quantitative predictors of decline in memory-encoding neuronal networks based on the impact and statistics of FAS. Some of the challenges of this translational approach include our inability to access small scale injuries with non-invasive methods, the overall complexity of neuronal pathologies, and our limited knowledge of how networks process biological signals. The purpose of this computational study is three-fold: (i) to extend Hopfield's model for associative memory to account for the effects of FAS, (ii) to calibrate FAS parameters from biophysical observations of their statistical distribution and size, and (iii) to systematically evaluate deterioration rates for different memory-recall tasks as a function of FAS injury. We calculate deterioration rates for a face-recognition task to account for highly correlated memories and also for a discrimination task of random, uncorrelated memories with a size at the capacity limit of the Hopfield network. While it is expected that the performance of any injured network should decrease with injury, our results link, for the first time, the memory recall ability to observed FAS statistics. This allows for plausible estimates of cognitive decline for different stages of brain disorders within neuronal networks, bridging experimental observations following neurodegeneration and TBI with compromised memory recall. The work lends new insights to help close the gap between theory and experiment on how biological signals are processed in damaged, high-dimensional functional networks, and towards positing new diagnostic tools to measure cognitive deficits.