## Saturday, 20 October 2007

### Why is the surface of the brain so strangely structured, with its sulci and gyri?

The question refers to the crazy grooves-and-bulges look of the grey matter of the cerebral cortex. The grooves are called sulci (singluar: sulcus) and the bulges are called gyri (singular: gyrus).

But why, we want to know, is the grey matter shaped in this mad spaghetti-like way?

This is actually a really clever trick that the human body uses in several places, and it's function is ingenious:- it increases the surface area available to the cerebral cortex within the narrow confines of the skull.

To see why, have a look at these (very lousily created) diagrams, meant to represent two possible versions of epithelial cells in the small intestine, which is another place where this technique is used.

Imagine that the cell is a perfect square and this is a (saggital) section through it - the part facing the intestine's lumen and needing to do the absorbing is the top. Let's do some maths to compare the two cells.

First the cell on the left. Call the dimensions of the cell 7 micrometres long. Therefore the surface area of the top is 7 x 7 = 49 micrometres2

Now for the cell on the right. This one appears to have an odd design - every 1 micrometre, a little piece, with sides of 1 micrometre each, is cut into the cell. What is the effect on the surface area? The surface area suddenly becomes 13 x 7 = 91 micrometres2 - an 85% increase! (If you're unsure why, leave a comment to that effect, and I'll see if I can explain it a bit better.)

In actual fact, such cells do a far less clumsy job of it, and can increase their surface area by hundreds and even thousands of times. It's really rather clever.

We could stop there, but I've got some nerdy time on my hands, so let's try to make a rough estimate of how much the brain benefits from this design.

Unfortunately, the brain is roughly an elipsoid shape, and so our calculations become difficult. But not impossible. Not being a mathematician by any stretch of the imagination, I had to look it up, but Professor Wikipedia says that an approximate equation for the surface area of such a body is:

$\approx 4\pi\!\left(\frac{ a^p b^p+a^p c^p+b^p c^p }{3}\right)^{1/p}.\,\!$

p can apparently be taken as about 1.6. Armed with this, we can plug some figures in. The average brain is apparently about 167 mm long, 140 mm wide and 93 mm high.

Now, if I'm right, the surface area comes out at about 220 000 mm2 (someone tell me if I've messed up!).

And how much surface area does the brain actually manage to achieve?

Around 2 m2, or 2 000 000 mm2. In other words, crazy as the sulci and gyri may look, the surface area is thereby increased by a factor of almost 10 times!

Told you I was a nerd.