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Math and Medicine

Sophomore year, third term, I took my first medically-relevant class at Caltech. It’s a course taught by Dr. Petrasek, who has a degree in medicine and later got a PhD in applied math at Tech, so it’s a class that deviates from the basic sciences to look at clinical research and medical advances. Since I loved the class last year, this year I decided to be a TA (teaching assistant) for it.

The class, titled BE153:Case Studies in Systems Physiology, approaches medicine with quantitative, engineering strategies. Basically, we look at different recent cases in clinical medicine (topics include sleep regulation, HIV, and cardiovascular physiology), try to come up with a mathematical model to explain the phenomenon, and see if our model matches up with experimental data in the scientific literature. The class has three sets and a final project– for the final project, students have to choose a biological/ medical phenomenon and then come up with a math model to simulate that phenomenon.

For example, this year, two students decided to model scar formation. Here’s how they did it:
Step 1: Model happy, healthy collagen matrix

Step 2: Make sure the model is biologically accurate. Does the collagen matrix generated look kinda like collagen matrix in vivo?


Step 3: Model a wound

Step 4: Model scar tissue formation

[c4 refers to how quickly scar tissue
compensates for missing skin tissue; c5 describes
the inhibiting effect of the kinetic energy of the normal skin tissue; c6 refers to the contact inhibition caused
by a closed matrix (this coefficient should be large)]

Ok, so they modelled scar tissue formation.. so what?
Well, if the model actually matches up with experimental data and is pretty accurate, it can be potentially predict how scars will form. So, surgeons can make carefully planned cuts and punctures to reduce scarring, making the scars less noticeable and more aesthetic!
Pretty cool, right?

Ketaki Panse