Lecture 8

This week we moved on to some new material, taking a look at how we can write accurate mathematical descriptions of the electrical properties of neurons. In particular, what goes into modeling membrane dynamics? What can we infer about membrane structure from the models? And can those models be simplified without sacrificing too much accuracy?

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.

Lecture 7

This week we really swung for the fences! We read Sections 4.2 and 4.3 from Spikes (by Rieke) which cover neural coding of hyper-acuity in the bat and the fly. The fly visual system is pretty amazing - the fly can detect very small changes in its visual field far faster than can be explained by the raw speed of the visual system. It does this by integrating over a large number of broad receptive fields, thereby obviating the need for spatial oversampling. Pretty neat stuff!

The experiment described in the book goes like this: a fly is shown a random pattern and then that pattern is shifted by some small amount. The fly's H1 neuron is then monitored by dividing time from t=15-40ms post stimulus into 2ms bins and assigning a "one" (spike) or "zero" (no spike) to each of the 13 bins. (it takes 15ms for the signal to reach H1, and after 40ms, the fly has already reacted to the stimulus, meaning the signal has already been interpreted). There are therefore 2^13 possible outcomes of this experiment. The trick is to examine the contents of those 13 bits and determine whether the fly observed a pattern shift of x degrees or y degrees.

Spiking is, of course, a stochastic event - spike trains are probabilistic, not deterministic. We learned how to use signal-to-noise ratio to quantify the separability between two populations of spiking patterns, spiking patterns contributed to signal to noise ratio, and, most interestingly, that most of the information separating two populations comes in the timing of the first spike.

In general, this was a good conversation and a very tough piece of reading. I think next year this lecture could stand to be better developed, perhaps with some external readings and some simulated Matlab code.

Lecture 6

In Week 6, we focussed on specific methods of spike decoding, spending most of our time on linear decoding methods as spelled out in Kim 2006. We started by discussing the general concept of linear decoding, specifically that the firing rate of each neuron (at a specific time lag) is linearly related to the kinematic parameter of interest. Mathematically speaking we might say:

x(t) = Sum{wij * nij(t)}

where x(t) is the kinematic parameter being predicted and nij(t) is the number of times neuron "i" fired at the "j"th time-lag. The "wij" terms are the linear coefficients; these weights can be any real number, positive or negative. In reality, no known neuron actually fires linearly with respect to a kinematic parameter, but if we include enough lags and enough neurons in the model, we should be able to approximate reasonable kinematic behavior.

The trouble becomes finding acceptable combinations of weights, "wij". If our experiment includes 300 neurons at ten lags each, then there are 3000 weights altogether that must be approximated. This problem is poorly formed numerically and lends itself to non-singular matrices and non-optimal solutions.

The Kim paper essentially discusses methods of solving for the filter weights. The most basic is the optimal Wiener filter, and its closely related cousin the normalized least mean squares filter (which converges to the Wiener solution, at least in theory). The Kim paper also discussed the Kalman filter (which models both filter weights and their uncertainty), as well as the gamma filter (which condenses the neural signal in time) and the principal component filter (which condenses the neural signal in channel-space, with respect to maximal variance).

We also looked at some Matlab code I wrote that duplicated much of the math in the paper. One lesson that we observed off the bat is that the models all work reasonably well provided that the kinematic parameter always stays in the same range of values used during the training phase.

We also set out to look at Li 2009, which uses a modified unscented kalman filter to track neurons. Their UKF system uses a non-linear (quadratic) neural firing model and also takes temporal correlations into account. Unfortunately, we didn't get to spend as much time on this paper as I would have hoped, but at least everyone read it ;)

I didn't get as far as I would have liked with my neural decoding simulator - I would still like to code up the gamma filter and the extended kalman filter, but those will have to wait for a rainy day.

Blind Spots

I'm reading On Intelligence, by Hawkins. He argues that our brains are always making predictions about what our senses are going to tell us, and that this in part explains why we don't notice our blind spots. We don't notice them because our brain "fills in" whatever it predicts to see. So that got me wondering: what about babies? Without a lifetime of experience to tell them what to fill in to those blind spots, do they have a big gapin hole in their visual field? How would you even test this? How long after birth does the blind spot persist?

Any thoughts?

Spring Break Reading List

Its going to be a busy nine days! In addition to my many domestic responsibilities, I hope to tackle/complete:

• Fundamentals of Computational Neuroscience, by Trappenberg
• Adaptive Filter Theory, by Haykin
• On Intelligence, by Hawkins
• Theoretical Neuroscience, by Dayan and Abbott

Should be fun!

Chronic Traumatic Encephalopathy, Ctd.

Here's an NYTimes article about hockey player Bob Probert who died at 45 and was posthumously diagnosed with CTE. Another big win for the Boston University center studying all these brains. Are we heading (no pun intended) towards a gentler era of sport?

Brain Games

I came across this blog entry from IEEE Spectrum about a video game based on the $100 Mindwave headset from Neurosky. The reviewer is clearly impressed!

We are starting to investigate new techniques for creating wireless EEG headsets. The two leading companies in this area (Emotiv and Neurosky) have a reputation in the community for being insufficiently high-fidelity to suppor research grade recordings. The Emotiv only has a handful of channels and none of them are over brain regions correlated to motor planning or execution. The Neurosky (at least as of this writing) only has a single electrode over the forehead (FP1). Its not even clear that these devices are recording pure EEG - its more likely they record a combination of EEG and muscle artifacts.

In our lab, we've been trying to develop our own EEG-based brain computer interface system. For our first attempt, we used the Clevemed Bioradio to acquire EEG signals using an old EEG-cap we had lying around. The signal to noise ratio was a mess and we could barely get enough signal fidelity to move a cursor in one dimension. Since then we've upgraded to a higher quality EEG amplifier (a mint-condition 20-year old Grass Model 12 Amp with 22 channels that was donated to us by a very kind emeritus professor in Psych) as well as a snugger-fitting EEG cap. These two upgrades have improved the signal to noise ratio but we have persistent problems with the impedance between the electrodes and the scalp (the Model 12 allows us to measure the impedance). We are learning that even the world's nicest EEG amp won't do you much good if your electrode impedance is too high (say, greater than 10k Ohm).

Ultimately we'd like to design a research-grade wireless EEG system. Our biggest challenge (and one we feel hasn't been solved by either Emotiv of Neurosky) is to reduce the electrode/scalp impedance down to a more manageable level.

Happy gaming!