Abstract
A simplified model is presented of the dynamics of excitatory and inhibitory neurons in the cerebral cortex. A key feature of the model is that neurons may cease to fire when strongly depolarized (spike inactivation). Computer simulations for different parameters reveal five classes of solutons: a) steady states in which neither excitatory nor inhibitory cells are active, b) steady states in which one or both types of cells fire repetitively, c) states in which one type of cell fluctuates rapidly between bursts of action potentials and inactivity due to strong depolarization, d) rhythmic activity in which both types of cells fire in unison followed by a period of spike inactivation and e) states similar to d but in which the inhibitory cells never produce action potentials. Solutions b, c, d, and e qualitatively resemble the different firing patterns observed during experimental seizures. It is shown that changes in those parameters that are functions of potassium concentration can induce changes in the type of solution. It is therefore proposed that the increase in extracellular potassium concentration during seizures may be responsible for the progressive changes observed in firing patterns and particularly for the transition from tonic to clonic patterns. A method is also outlined for testing the predictions of the model.
Similar content being viewed by others
References
Ayala, G.F., Dichter, M., Gumnit, R.F., Matsumoto, H., Spencer, W.A.: Genesis of Epileptic Interictal Spikes. New Knowledge of cortical feedback systems suggests a neurophysiological explanation of brief paroxysms. Brain Res. 52, 1–17 (1973)
Calvin, W.H.: Synaptic potential summation and repetitive firing mechanisms: Input-output theory for the recuritment of neurons into epileptic bursting firing patterns. Brain Res. 39, 71–94 (1972)
Calvin, W.H.: Generation of spike trains in C.N.S. Neurons. Brain Res. 84, 1–22 (1975)
Calvin, W.H., Sypert, G.W.: Cerebral cortex neurons with extra spikes: a normal substrate for epileptic discharges? Brain Res. 83 498–503 (1975)
Cooke, J.D., Quastel, D.M.J.: The specific effect of potassium on transmitter release by motor nerve terminals and its inhibition by calcium. J. Physiol. (Lond.) 228, 435–458 (1973)
Dichter, M.A., Herman, C.J., Selzer, M.: Silent cells during interictal discharges and seizures in hippocampal penicillin foci. Evidence for the role of extracellular K + in the transition from the interictal state to seizures. Brain Res. 48, 173–183 (1972)
Eidelberg, E.: Extracellular potassium and steady potential. Neurosci. Res. Prog. Bull. 12, 126–127 (1974)
Ferguson, J.R.: Acetycholine-induced seizure activity. In: Dynamic patterns of brain cell assemblies. Neurosci. Res. Prog. Bull. 12, 145–147 (1974)
Freeman, W.J.: Linear analysis of the dynamics of neural masses. Ann. Rev. Biophys. Bioeng. 1, 225–256 (1972)
Granit, R., Kernell, D., Smith, R.S.: Delayed depolarization and the repetitive response to intracellular stimulation of mammalian motoneurons. J. Physiol. (Lond.) 168, 890–910 (1963)
Hotson, J.R., Sypert, G.W., Ward, A.A.: Extracellular potassium changes during propagated seizures in neocortex. Exp. Neurol. 38, 20–26 (1973)
Kaczmarek, L.K., Adey, W.R.: Some chemical and electrophysiological effects of glutamate in cerebral cortex. J. Neurobiol. 5, 231–241 (1974)
Kaczmarek, L.K., Adey, W.R.: Cortical release of labeled compounds during arousal in the cat: Correlations with carbon dioxide, brain temperature and EEG. Exp. Neurol. 46, 57–68 (1975a)
Kaczmarek, L.K., Adey, W.R.: Extracellular release of cerebral macromolecules during potassium and low calcium induced seizures. Epilepsia 16, 91–98 (1975b)
Katz, B.: Nerve muscle and synapse. New York-London: McGraw-Hill, 1966
Kling, V., Szekely, G.: Simulation of rhythmic nervous activities. I: Functions of networks with cyclic inhibitions. Kybenetik 3, 89–109 (1968)
Perkel, D.H., Mullony, B.: Motor pattern production in reciprocally inhibitory neurons exhibiting postinhibitory rebound. Science 185, 181–183 (1974)
Pintilie, C., Mison-Crighel, N., Tudor, I.: Correlations between some biochemical constituents of the blood and cerebrospinal fluid, the clinical forms and the electroencephalographic patterns in epileptics. Rev. Roum. Neurol. 8, 197–207 (1971)
Scheibel, M.E., Crandall, P.H., Scheibel, A.B.: The hippocampaldentate complex in temporal lobe epilepsy. Epilepsia 15, 55–80 (1974)
Stein, R.B., Leung, K.V., Oguztoreli, M.N., Williams, D.W.: Properties of small neural networks. Kybernetik 14, 223–230 (1974)
Sypert, G.W., Oakley, J., Ward, Jr. A.A.: Single unit analysis of propogated seizures in neocortex. Exp. Neurol. 28, 308–325 (1970)
Weight, F.F.: Physiological mechanisms of synaptic modulation. In: Schmitt, F.O., Worden, F.G., (eds.): The Neurosciences Third Study Program. pp. 929–941, Massachusetts-London: M.I.T. Press
Wilson, H.R., Cowan, J.D.: Excitatory and inhibitory interactions in localized populations of model neurons. Biophys. J. 12, 1–24 (1972)
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Kaczmarek, L.K. A model of cell firing patterns during epileptic seizures. Biol. Cybernetics 22, 229–234 (1976). https://doi.org/10.1007/BF00365088
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00365088