Simulation of the effect of Na+ and Cl- on the velocity of a spreading depression wave using a simplified electrochemical model of synaptic terminals

A quantitative model of cortical spreading depression due to purinergic and gap-junction transmission in astrocyte networks

Spreading depression (SD), a propagating wave of electrical silence in the cortex and archicortex, involves depolarization of neurons and astrocytes for approximately 1 min, due principally to a large increase in extracellular K+. SD is accompanied by large increases in extracellular ATP and is blocked by glutamate N-methyl-D-aspartate receptor antagonists. As a principal means of transmission between astrocytes is through their release of ATP, we have investigated if a model in which SD is driven by the effects of astrocyte waves of ATP interacting with waves of glutamate release from neurons and astrocytes can give a quantitative account of experimental observations on SD. We show that the characteristics of SD and the accompanying extracellular ionic changes can be accommodated by such a model-whether astrocyte transmission is principally through the release of ATP, as in archicortex (hippocampus) and spinal cord, or via gap junctions, as in the neocortex. Furthermore, these models give quantitative accounts of the effects on the characteristics of SD of agents toxic for astrocytes and of gap-junction blockers. Finally, an additional series of critical tests of the model is suggested.

Modeling parkinsonian circuitry and the DBS electrode. I. Biophysical background and software

Deep brain stimulation (DBS) of the subthalamic nucleus (STN) for Parkinson's disease (PD) has become routine over the past decade, utilizing microelectrode recordings to ensure accurate placement of the stimulating electrodes. The clinical benefits of STN DBS for PD are well documented, but the mechanisms by which DBS achieves these results remain elusive. We have created a closed-form mathematical function of the potential field generated by a typical 4-contact DBS electrode and inserted this function into a computational model designed to simulate individual neurons and neural circuitry of significant portions of the basal ganglia. We present the mathematical function representing the potential field itself and the basis for the neural circuitry modeling in this paper.

A steady-state model of spreading depression predicts the importance of an unknown conductance in specific dendritic domains

Spreading depression (SD) is a pathological wave of transient neuronal inactivation. We recently reported that the characteristic sustained complete depolarization is restricted to specific cell domains where the input resistance (R(in)) first becomes negligible before achieving partial recovery, whereas in adjacent, more polarized membranes it drops by much less. The experimental study of the participating membrane channels is hindered by their mixed contribution and heterogeneous distribution. Therefore, we derived a biophysical model to analyze the conductances that replicate the subcellular profile of R(in) during SD. Systematic variation of conductance densities far beyond the ranges reported failed to fit the experimental values. Besides standard potassium, sodium, and Glu-mediated conductances, the initial opening and gradual closing of an as yet undetermined large conductance is required to account for the evolution of R(in). Potassium conductances follow in the relative contribution and their closing during the late phase is also predicted. Large intracellular potential gradients from zero to rest are readily sustained between shunted and adjacent SD-spared membranes, which remain electroregenerative. The gradients are achieved by a combination of high-conductance subcellular domains and transmembrane ion redistribution in extended but discrete dendritic domains. We conclude that the heterogeneous subcellular behavior is due to local membrane properties, some of which may be specifically activated under extreme SD conditions.