Brian L. Frost | Searcharxiv

arXiv2024

Foundations of the WKB Approximation for Models of Cochlear Mechanics in 1- and 2-D

The Wentzel-Kramers-Brillouin (WKB) approximation is frequently used to explore the mechanics of the cochlea. As opposed to numerical strategies, the WKB approximation facilitates analysis of model results through interpretable closed-form equations, and can be implemented with relative ease. As a result, it has maintained relevance in the study of cochlear mechanics for half of a century. Over this time, it has been used to study a variety of phenomena including the limits of frequency tuning, active displacement amplification within the organ of Corti, feedforward mechanisms in the cochlea, and otoacoustic emissions. Despite this ubiquity, it is challenging to find rigorous exposition of the WKB approximation's formulation, derivation and implementation in cochlear mechanics literature. In this tutorial, I discuss the foundations of the WKB approximation in application to models of cochlear macromechanics in 1-D and 2-D. This includes mathematical background, rigorous derivation and details of its implementation in software.

physics.bio-ph↗

arXiv2023

A high-efficiency model indicating the role of inhibition in the resilience of neuronal networks to damage resulting from traumatic injury

Recent investigations of traumatic brain injuries have shown that these injuries can result in conformational changes at the level of individual neurons in the cerebral cortex. Focal axonal swelling is one consequence of such injuries and leads to a variable width along the cell axon. Simulations of the electrical properties of axons impacted in such a way show that this damage may have a nonlinear deleterious effect on spike-encoded signal transmission. The computational cost of these simulations complicates the investigation of the effects of such damage at a network level. We have developed an efficient algorithm that faithfully reproduces the spike train filtering properties seen in physical simulations. We use this algorithm to explore the impact of focal axonal swelling on small networks of integrate and fire neurons. We explore also the effects of architecture modifications to networks impacted in this manner. In all tested networks, our results indicate that the addition of presynaptic inhibitory neurons either increases or leaves unchanged the fidelity of the network's processing properties with respect to this damage.

q-bio.NC↗