Effects of Focal Axonal Swelling Level on the Action Potential Signal Transmission.

Focal axon swelling refers to localized swelling in axons that may occur because of trauma (e.g., traumatic brain injury) or neurodegenerative diseases (e.g., Alzheimer's disease). Since the swelling region can be many times larger than its original axon size, many researchers hypothesize that the swelling can alter the action potential (AP) signal. This article discusses the results of a series of newly developed computational studies to elucidate the possible intervention or blockage of AP signals due to swelling in the brain. We argue that the spherical geometry of the swelling site with its enlarged conducting interior causes the entering electric currents to spread evenly over the entire swelled membrane. As such, when the swelled surface becomes larger than the threshold size, the electric current will spread too thin to trigger the AP to spike. In this study, we have used a hybrid membrane model to simulate AP propagation across axons of different radii and swelling radii. We used an integrated model where a cylindrical symmetric 2D model is used to examine the electric current inside a spherical swelling site. In addition, two 1D models are used to capture the current flows along the upstream and downstream stretch before and after the swelling site. The parameters for this model are obtained from literature dedicated to modeling the experimental outcomes of mammal neurons. We observed two factors, which simultaneously affect AP transmission across a swelled axon: a) the axon radius and b) the ratio of the swelled and unswelled axon radii. In general, a thicker axon needs a smaller swelling size and axon ratio to block AP transmission. On the other hand, a thinner axon will reach the threshold at a larger swelling size and axon ratio. When only swelling size is considered, then thinner axons will block AP transmission at a smaller swelling radius. The AP transmission delay inside the swelled region determines whether the AP transmits forward or not. Notably, the blockage is worse if the AP fires at a high frequency. An increase in the charging and reset time due to swelling appears to be the main reason for the variation in axonal response.