A computer model of neuronal pathways in the basal ganglia.

Disorders of the basal ganglia and the extrapyramidal motor system exhibit an imbalance of neurotransmitter concentrations in affected neurons. For three synapses with dopamine, acetylcholine, and gamma-amino butyric acid (GABA), mathematical models of synaptic transmission are developed. To describe the kinetics of transmitter substances, compartment analysis is used. Membrane potential behaviour is described by the Hodgkin-Huxley equations with an additional equation accounting for a presynaptic calcium current mediating transmitter release. At the postsynaptic site, activated receptor molecules control the activity of ion channels, eliciting either inhibitory or excitatory postsynaptic potentials. A simple model of the feedback loop connecting the caudate nucleus and the substantia nigra is simulated on a digital computer using the simulation language ACSL. A comparison of the control case with a model of Parkinson's disease shows a shift of eigenvalues towards zero in the diseased state.