Our reading was Chapter 5 of Dayan and Abbott, which does an excellent job discussing the physical underpinnings of membrane capacitance and resistance. The chapter also discusses the Hodgkin-Huxley model of electrically excitable cells, which is perhaps one of the finest basic science experiments of the 20th century. Hodgkin and Huxley did a series of painstaking experiments from which they deduced the microscopic structure and function of the membranes of electrically excitable cells. They determined how ions such as sodium and potassium flow across cell membranes in order to effect flow of current, and how this leads to action potential formation. Although there are a number of details to keep track of, the essential mechanics of membrane behavior are not more sophisticated that first-order differential equations. The Hodgkin-Huxley membrane model simplifies to four interconnected first-order diff-eqs that can be easily solved by any number crunching software (we prefer Matlab, although C/C++ will work in a pinch ;). My Matlab implementation of the Hodgkin-Huxley code can be found here. Next week we'll discuss some of the simplified models in detail, such as Integrate and Fire, as well as the notorious Izhikevitch model.
There was an interesting question about whether alternative computing platforms can be used to accelerate neural modeling. It turns out some at Georgia Tech have been trying to use FPGAs for neural modeling. Interesting papers can be found here and here.
Someone brought up the really fun question of why even bother writing mathematical models of neural activation. Fair question! Answering this question led to a lively discussion on improving medical devices such as pacemakers by trying to predict how changes to the device (or its placement) would affect functionality. Cardiac pacemakers are a great example actually: high quality electrical models of cardiac tissue are routinely used to make predictions about how to optimize performance by changing either the properties of the electrical stimuli or perhaps the locations in the cardiac muscle where those stimuli are delivered. Along those same lines, we discussed deep brain stimulation, which is commonly used to treat movement disorders such as Parkinsons and Essential Tremor. I brought up the point that despite its efficacy, there is much debate on how exactly DBS works. Neural models are being used to study DBS and to make predictions about how stimulating various parts of the brain can curb the effects of these diseases. Some incredible before-and-after video of DBS patients can be found here.