A model for axonal propagation incorporating both radial and axial ionic transport

Abstract

We present an axonal model that explicitly includes ionic diffusion in the intracellular, periaxonal, and extracellular spaces and that incorporates a Hodgkin-Huxley membrane, extended with potassium channel inactivation and active ion transport. Although ionic concentration changes may not be significant in the time course of one action potential, they are important when considering the long-term behavior (seconds to minutes) of an axon. We demonstrate this point with simulations of transected axons where ions are moving between the intra- and extracellular spaces through an opening that is sealing with time. The model predicts that sealing must occur within a critical time interval after the initial injury to prevent the entire axon from becoming permanently depolarized. This critical time interval becomes considerably shorter when active ion transport is disabled. Furthermore, the model can be used to study the effects of sodium and potassium channel inactivation; e.g., sodium inactivation must be almost complete (within 0.02%) to obtain simulation results that are realistic.

Effect of Ionic Diffusion on Extracellular Potentials in Neural Tissue

“…Diffusive currents along these gradients gave rise to a diffusion potential, which at t =42 s peaked in the soma subvolume where V was about -0.17 mV (Fig 9B2). Diffusion-evoked voltage gradients like this are well understood, and have been observed in many systems with spatial variation in ion composition [3, 20–22]. …”

“…Often they are referred to as liquid junction potentials , since they are most pronounced at the boundary between two solutions of different ion composition [20–22, 72]. …”

“…Commonly, it is assumed that extracellular potentials predominantly reflect transmembrane cellular current sources, including synaptic currents and currents through active and passive membrane mechanisms in neurons and glial cells [16–19]. However, in scenarios where ECS concentration gradients become sufficiently large, electrical currents carried by diffusing ions in the ECS could in principle also give measurable effects on the extracellular electrical potentials (cf., liquid junction potentials [20–22]). In support of this, local ion-concentration changes in the ECS are indeed often accompanied by slow local negative potential shifts, which can be on the order of a few millivolts [1, 3, 13, 23–27].…”

A General Approach to Modeling Conduction and Concentration Dynamics in Excitable Cells of Concentric Cylindrical Geometry

“…In many cases, in particular for simulation durations covering only a few action potentials, this assumption is well justi"ed. However, ion concentration dynamics can be of considerable importance for simulations that deal with repetitive activity and rate dependence, or in studies that deal speci"cally with long-term changes in concentrations as in the study of a transected nerve axon (van Egeraat & Wikswo, 1993). Changes in ion concentrations can a!ect the behavior of an excitable cell through several mechanisms, including the following: (1) changes in the concentration gradient across the cell membrane change the reversal (Nernst) potential of ionic currents and, thus, the resting potential of the cell; (2) the conductance of some ionic currents, notably the inward recti"er (I ) ) in cardiac cells, are modulated by ion concentrations (extracellular [K>] in the case of I ) ); and (3) the conductivities of the intra-and extracellular solutions depend on the concentration of the charge-carrying ions (and their mobilities).…”

Biomagnetic Detection of Injury Currents in Rabbit Ischemic Intestine

“…In the AC-coupled ECG, the electric signal from the diastolic injury currents is lost and ischemia is manifest as either an ST-segment elevation or depression. The signatures of injury currents from severed axons have been measured magnetically and are well described by an ionic diffusion model (11,12).…”