Sister Cyster

In my ruminations about off-label drugging for weight-loss and headache, I mentioned an intra-cranial cyst. To be told that a fluid-filled lump the size of a golf-ball is the cause of your intermittent headaches must be knee-weakeningly worrying. Not lessened by having brain-surgery on the cards for much of your three day stay in hospital[s] getting diagnosed and, ultimately, sorted. But my young friend addressed the crisis with considerable courage, not to say gay insouciance. "I've got a cyst that makes up 25% of my brain", she quipped. No it doesn't, I replied, it just cannot be that big: it doesn't make biological or mathematical sense.

Later on I sent her my calculations to show that her lump was, at most, only 4% of the volume inside her skull.

Here’s a sphere (set inside a cube). What is its volume? The formula is 4/3πr³. Π = Pi = 3.14159 call it 3. 4/3 of 3 is 4. Diameter of cyst = 5cm, so radius = 2.5 cm and volume = 4 x 2.5 x 2.5 x 2.5 =  ~60 cc.

My head is about 14cm across and yours is similar; call it radius = 7cm. if we treat the brain as a sphere with that radius then the volume = 4 x 7 x 7 x 7 = 1372 cc.

Ratio of volumes = 60/1372 = 0.04 = 4%!

Funnily enough, the average human brain is given as 1,300 cc with an adult range of 1,000 cc = 1 litre to 2,000 cc. So my rough arm-waving guesstimate is quite good.

Q. What’s with putting the sphere in a cube in the picture?
A. It might make the math easier: volume of a cube 5cm across is
5 x 5 x 5 = 125cc. I’d guesstimate that the interior sphere fills about half the volume and the formula gives a similar answer. Actually the cube's volume is 1.9x that of the sphere.

There is a comforting amount of consistency in the numbers. It is so important to have the mental tools to make such calculations: it really helps in your crap-detecting reading of the newspapers.
But this elicited the repsonse: Amazing! 4% cyst doesn’t sound half as impressive though . . . I say, print the myth!