5. Models of point neuronal dynamic
Chapter 5
Ada Augusta, Countess of Lovelace, the daughter of poet Lord Byron, was a visionary English mathematician, considered by many as “the first computer programmer” for writing an algorithm for a mechanical computer (”analytical engine”) designed by Charles Babbage in the mid- 1800s. Ada was quoted back in 1815, saying:
"I have my hopes, and very distinct ones too, of one day, getting cerebral phenomena such that I can put them into mathematical equations. In short, a law or laws for the mutual actions of the molecules of brain... I hope to bequeath to the generations a calculus of the nervous system."
Learn more about the story of Ada Lovelace:
About 100 years later, Louis Lapicque provided one of the most widely utilized differential models for neural activity: the passive membrane model, later extended to the Leaky Integrated-and-Fire (LIF) model. Another important development is the Izhikevich neuron model, proposed by Eugene Izhikevich in 2003, offering a quadratic LIF with a recovery variable. A bio-plausible model was suggested by Alan Hodgkin and Andrew Huxley in 1952: The HH model, for which the authors were awarded the Nobel Prize in Physiology in 1963. The HH model provides a detailed differential description of neuronal dynamics and it is the principal mathematical description used for biologically plausible neuronal simulations. This chapter will discuss some of the mathematical formulations of these models to the level appropriate for this book’s scope. Due to the importance of the LIF model, it will be more profoundly discussed.
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