Oscillatory electrographic activity in the hippocampus: a mathematical model.

This model of hippocampal function describes the bilaterally symmetrical interactions of the various intrahippocampal populations of neurons that are functionally homogeneous (septal and entorhinal sources of input, granule cells, CA field pyramids cells, and basket cells). Activity of each homogeneous population is described as a first order nonlinear differential equation. Parameters are simulated, with activity defined in relative units ranging from 0 to 1.0. The first 26 equations (13 identified pools in each hemisphere) were solved simultaneously by computer to produce plots of the time course of activity changes in each of the populations. The simulations performed thus far show that the model parallels certain known properties of the system: (1) there is the expected reciprocal relationship between pyramidal cells and basket cells; (2) activity can be made to oscillate or achieve steady-state, simulating EEG "theta" rhythm or low voltage, fast activity; (3) oscillation occurs where it is known to occur (CA pyramidal cells and the dentate region), where it is presumed to occur (in basket cells), and does not occur where it is known not to occur (CA pyramidal cells); (4) there is a narrow range of frequency, and attempts to increase frequency readily terminate oscillation to cause steady-state activity; (5) oscillation requires excitatory drive from the medial septum, whereas entorhinal input is relatively less important; and (6) increases in medial septal activity can increase oscillation frequency. The results also predict certain undiscovered phenomena: (1) there is a major influence of variations in decay rate of activity in various neuronal pools; (2) there is probably an ultra-slow oscillation in the CA area; and (3) the CA projection ot the entorhinal cortex seems to be important in modulating frequency and amplitude of theta rhythm.