Brain Dynamics:

Challenges of the Spike

If someone could poke special cells in your head called neurons they would most certainly see an action potential, or more commonly termed a spike. What's a spike? Like all cells, neurons have membranes that separate their insides from their outsides. Current can flow across the membrane creating the pattern of electrical activity shown here:

What's the mathematical challenge in explaining spikes? There are three fundamental features of spikes that create the challenge. We'll explore them in turn, and then see how math meets them head-on.

Brain visualizations courtesy of Chris Johnson and Nathan Galli, Scientific Computing and Imaging Institute, University of Utah