A Non-local Model of the Propagation of Action Potentials in Myelinated Neurons

Corina Stefania Drapaca (Associate Professor, Department of Engineering Science and Mechanics, Pennsylvania State University, University Park PA 16802,)
Sahin Ozdemir (Department of Engineering Science and Mechanics, Pennsylvania State University, University Park PA 16802,)
Elizabeth Proctor (1) Departments of Neurosurgery and Pharmacology, Pennsylvania State College of Medicine, Hershey PA 17033, USA 2) Department of Biomedical Engineering, Pennsylvania State University, University Park PA 16802,)

Emerging Science Journal
Vol 4, No 3 (2020): June

Myelinated neurons are characterized by the presence of myelin, a multilaminated wrapping around the axons formed by specialized neuroglial cells. Myelin acts as an electrical insulator and therefore, in myelinated neurons, the action potentials do not propagate within the axons but happen only at the nodes of Ranvier which are gaps in the axonal myelination. Recent advancements in brain science have shown that the shapes, timings, and propagation speeds of these so-called saltatory action potentials are controlled by various biochemical interactions among neurons, glial cells and the extracellular space. Given the complexity of brain’s structure and processes, the work hypothesis made in this paper is that non-local effects are involved in the optimal propagation of action potentials. A non- local model of the action potentials propagation in myelinated neurons is proposed that involves spatial derivatives of fractional order. The effects of non- locality on the distribution of the membrane potential are investigated using numerical simulations.