Generation of sustained field potentials by gradients of polarization within single neurons: a macroscopic model of spreading depression

Abstract

Spreading depression (SD) is a pathological wave of depolarization of the neural tissue producing a negative macroscopic field potential (V(o)), used as a marker for diagnostic purposes. The cellular basis of SD and neuronal mechanisms of generation of V(o) at the microscopic level are poorly understood. Using a CA1 mathematical model and experimental verification, we examined how transmembrane currents in single cells scale up in the extracellular space shaping V(o). The model includes an array of 17,000 realistically modeled neurons (responsible for generating transmembrane currents) dynamically coupled to a virtual aggregate/extracellular space (responsible for V(o)). The SD wave in different tissue bands is simulated by imposing membrane shunts in the corresponding dendritic elements as suggested by experimentally assessed drop in membrane resistance. We show that strong isopotential depolarization of wide domains (as in the main SD phase) produce broad central cancellation of axial and transmembrane currents in single cells. When depolarization is restricted to narrow dendritic domains (as in the late SD phase), the internal cancellation shrinks and the transmembrane current increases. This explains why in the laminated CA1 the V(o) is smaller in the main phase of SD, when both dendritic layers are seized, than in the SD tail restricted to an apical band. Moreover, scattering of the neuronal somatas (as in cortical regions) further decreases the aggregate V(o) due to the volume averaging. Although mechanistically the V(o) associated to SD is similar to customary transient fields, its changes maybe related to spatial factors in single cells rather than cell number or depolarization strength.