Progress has continued smoothly on my class project. I’ve done one of the key validation steps in the project, and am just about ready to move on to the meat of the study.

What I did was to current-clamp the two different models, and compare this with the results of the exact same experiment in the paper that the models are taken from. Below, you can see the results:

The top row contains snapshots of both types of model from the original paper. The bottom row shows my results for the same conditions. They’re essentially identical, although it’s hard to tell from the pictures in the original paper.

I still have a little more validation to do, but this is a pretty good sign.

At the moment I’m working on my Models of the Neuron Project #2. In particular, I’m coding a model of ventral cochlear neuron bushy cells, using Octave rather than Matlab.

I’ve also just had another shot of espresso from our new X6, and I’m listening to an all-string-instrument tribute to Radiohead’s OK Computer. It’s so beautiful it’s giving me chills.

This is what I love to do. I feel good. I’m coding something. When it’s done, it will be a useful, functional, scientific model of a biological system. I’m going to use it to examine the effects of input regularity on its output. There are some technical obstacles I need to figure out, but I love doing that. It’s nice to feel like I’m getting somewhere and doing something useful again.

Here’s a bonus plot of excitatory post-synaptic potentials from two different types of bushy cell models! These aren’t anything complicated, they’re just inputs for the cell, but they look like they’re supposed to, so I’m quite happy.

Practical mathematical ability, like other parts of the body (since it is encoded somewhere in the brain), atrophies over time. By the end of high school, I was able to score a 5 on the AP calculus BC exam, which allowed me to skip Calc I & II at Tulane. Freshman year, I learned more math, although I didn’t really like it and was going through a major adjustment to college life, and I didn’t pick it up very well. By sophomore year, I’d forgotten most of the integration tricks I knew, and some of the derivatives.

From time to time, I’ve re-learned this stuff. Experience (and scientific studies) have shown that it’s normal to re-learn things much more quickly that the initial learning time, which is nice. My research places me in kind of an odd spot though.

If I were doing purely theoretical work, I’d have pencil to paper all of the time, integrating, derivatizing (as we said in HS), solving differential equations, substituting variables, etc, etc. But I don’t do purely theoretical work.

On the other hand, were I an experimentalist or a clinician, my work would be much more hands-on, so my math skill would atrophy a great deal, but it wouldn’t matter as much.

I work somewhere in the middle. Our software is sufficiently advanced that my work is a lot like hands-on experimental work. It’s important for me to understand the underlying theory, and I do, but understanding it and sitting down to work out math problems (especially if you’ve gained the understanding by doing so already in the past) is a different story. I go through long periods without serious math work, punctuated by short bursts where I have to dig all the way back in. Lately it’s been for a class.

I used to feel guilty about this — I probably wouldn’t have even posted it on this blog a couple of years ago. However, after hearing many other academics — several of whom are much more advanced in their careers than me, and well respected — lament a similar problem, I no longer feel guilt. It’s a common problem. For professors that teach university classes, the problem is somewhat alleviated, as they have to teach classes on this stuff and it keeps them fresh.

Not to say that I want to have to teach any classes right now, mind you.

I’d be interested to hear if you have any suggestions for staying sharp when I’m in a mathematical lull.

I have a Perl script that goes through time data from my simulations and develops what are commonly known as isochronal maps or activation maps. They show a color-coded snapshot of which parts of the model were activated by time, usually in “bins” of several milliseconds. Here’s a sample isochronal map from one of our papers:

Anyway, these maps take about 10-30 seconds of processing for my 2D regional ischemia model. For my new, larger model, it takes about 28 minutes.