Slow-gamma frequencies are optimally guarded against effects of neurodegenerative diseases and traumatic brain injuries.

We introduce a computational model for the cellular level effects of firing rate filtering due to the major forms of neuronal injury, including demyelination and axonal swellings. Based upon experimental and computational observations, we posit simple phenomenological input/output rules describing spike train distortions and demonstrate that slow-gamma frequencies in the 38-41 Hz range emerge as the most robust to injury. Our signal-processing model allows us to derive firing rate filters at the cellular level for impaired neural activity with minimal assumptions. Specifically, we model eight experimentally observed spike train transformations by discrete-time filters, including those associated with increasing refractoriness and intermittent blockage. Continuous counterparts for the filters are also obtained by approximating neuronal firing rates from spike trains convolved with causal and Gaussian kernels. The proposed signal processing framework, which is robust to model parameter calibration, is an abstraction of the major cellular-level pathologies associated with neurodegenerative diseases and traumatic brain injuries that affect spike train propagation and impair neuronal network functionality. Our filters are well aligned with the spectrum of dynamic memory fields including working memory, visual consciousness, and other higher cognitive functions that operate in a frequency band that is - at a single cell level - optimally guarded against common types of pathological effects. In contrast, higher-frequency neural encoding, such as is observed with short-term memory, are susceptible to neurodegeneration and injury.