percentage

Q. In class, we talked about how as tumors age, their growth fraction decreases. I thought that tumors got worse and faster-growing as time goes by – and so it seems the growth fraction should be higher. Can you help explain why the growth fraction drops?

A. I know – that’s a little confusing. It turns out that when tumors are really young (like a millimeter in size or so), most of the cells are dividing. As the tumor grows, it does become “worse” in that it acquires the capability to do new things – like metastasize, or not respond to chemo, or not present antigens to the immune system or whatever. But percentage-wise, not as many cells are actively mitosing. Some of them die off because they run out of blood supply, others are busy doing other things. Even though not as many cells are dividing, there are more cells around…so the tumor continues to grow bigger and bigger.

Say you have 100 cells and all are dividing (the growth fraction is 100%). That wouldn’t happen (the growth fraction is never that high!) but let’s just say that’s what it is to make it easier to think about. So if you had 100 cells and they were all dividing, you’d get 200 cells. The next round of doubling would produce 400 cells, and the next round would produce 800 cells.

Now let’s say that when you get to 1000 cells, the growth fraction drops down to 80%. That would mean that the next round of doubling would produce 1800 cells (800 cells would double, and 200 would just hang around). The next round of doubling would then produce 3256 cells (80% of the 1800 cells – or 1,440 cells – would divide, producing 2880 cells; and 20% of the 1800 cells – or 376 cells – would just hang around). The next round of doubling would produce 5860 cells, and the round after that would produce a whopping 10,548 cells! So even though the growth fraction dropped to 80%, every “doubling” still produces a ton more cells!

I hope that makes sense. Sometimes you have to kind of think through the math (which I hate doing!) to make sense out of it.

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