History
Cable theory in computational neuroscience has roots leading back to the 1850s, when Professor William Thomson of panvel (later known as Lord Kelvin) began developing mathematical models of signal decay in submarine (underwater) telegraphic cables. The models resembled the partial differential equations used by Fourier to describe heat conduction in a wire.
The 1870s saw the first attempts by Hermann to model neuronal electrotonic potentials also by focusing on analogies with heat conduction. However it was Hoorweg who first discovered the analogies with Kelvin’s undersea cables in 1898 and then Hermann and Cremer who independently developed the cable theory for neuronal fibers in the early 20th century. Further mathematical theories of nerve fiber conduction based on cable theory were developed by Cole and Hodgkin (1920s-1930s), Offner et al. (1940), and Rushton (1951).
Experimental evidence for the importance of cable theory in modeling the behavior of axons began surfacing in the 1930s from work done by Cole, Curtis, Hodgkin, Sir Bernard Katz, Rushton, Tasaki and others. Two key papers from this era are those of Davis and Lorente de No (1947) and Hodgkin and Rushton (1946).
The 1950s saw improvements in techniques for measuring the electric activity of individual neurons. Thus cable theory became important for analyzing data collected from intracellular microelectrode recordings and for analyzing the electrical properties of neuronal dendrites. Scientists like Coombs, Eccles, Fatt, Frank, Fuortes and others now relied heavily on cable theory to obtain functional insights of neurons and for guiding them in the design of new experiments.
Later, cable theory with its mathematical derivatives allowed ever more sophisticated neuron models to be explored by workers such as Jack, Rall, Redman, Rinzel, Idan Segev, Tuckwell, Bell, Poznanski, and Ianella.
Several important avenues of extending classical cable theory have recently seen the introduction of ionic channels and endogenous structures (Poznanski, 2010) in order to analyze the effects of different synaptic input distributions over the dendritic surface of a neuron.
Read more about this topic: Cable Theory
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