Next Article in Journal
A Collocation Method Based on Discrete Spline Quasi-Interpolatory Operators for the Solution of Time Fractional Differential Equations
Next Article in Special Issue
Numerical Analysis of Viscoelastic Rotating Beam with Variable Fractional Order Model Using Shifted Bernstein–Legendre Polynomial Collocation Algorithm
Previous Article in Journal
Optimal V-Plane Robust Stabilization Method for Interval Uncertain Fractional Order PID Control Systems
Previous Article in Special Issue
Boundary Value Problem for Fractional Order Generalized Hilfer-Type Fractional Derivative with Non-Instantaneous Impulses
Due to scheduled maintenance work on our core network, there may be short service disruptions on this website between 16:00 and 16:30 CEST on September 25th.
Article

The Impact of Anomalous Diffusion on Action Potentials in Myelinated Neurons

Department of Engineering Science and Mechanics, Pennsylvania State University, University Park, PA 16802, USA
Received: 18 November 2020 / Revised: 15 December 2020 / Accepted: 29 December 2020 / Published: 5 January 2021
(This article belongs to the Special Issue 2020 Selected Papers from Fractal Fract’s Editorial Board Members)
Action potentials in myelinated neurons happen only at specialized locations of the axons known as the nodes of Ranvier. The shapes, timings, and propagation speeds of these action potentials are controlled by biochemical interactions among neurons, glial cells, and the extracellular space. The complexity of brain structure and processes suggests that anomalous diffusion could affect the propagation of action potentials. In this paper, a spatio-temporal fractional cable equation for action potentials propagation in myelinated neurons is proposed. The impact of the ionic anomalous diffusion on the distribution of the membrane potential is investigated using numerical simulations. The results show spatially narrower action potentials at the nodes of Ranvier when using spatial derivatives of the fractional order only and delayed or lack of action potentials when adding a temporal derivative of the fractional order. These findings could reveal the pathological patterns of brain diseases such as epilepsy, multiple sclerosis, and Alzheimer’s disease, which have become more prevalent in the latest years. View Full-Text
Keywords: anomalous diffusion; fractional calculus; action potentials; fractional Hodgkin–Huxley model anomalous diffusion; fractional calculus; action potentials; fractional Hodgkin–Huxley model
Show Figures

Figure 1

MDPI and ACS Style

Drapaca, C.S. The Impact of Anomalous Diffusion on Action Potentials in Myelinated Neurons. Fractal Fract. 2021, 5, 4. https://0-doi-org.brum.beds.ac.uk/10.3390/fractalfract5010004

AMA Style

Drapaca CS. The Impact of Anomalous Diffusion on Action Potentials in Myelinated Neurons. Fractal and Fractional. 2021; 5(1):4. https://0-doi-org.brum.beds.ac.uk/10.3390/fractalfract5010004

Chicago/Turabian Style

Drapaca, Corina S. 2021. "The Impact of Anomalous Diffusion on Action Potentials in Myelinated Neurons" Fractal and Fractional 5, no. 1: 4. https://0-doi-org.brum.beds.ac.uk/10.3390/fractalfract5010004

Find Other Styles
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Access Map by Country/Region

1
Back to TopTop