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Volume of a Tumor

Don Wood

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A friend of mine who has lost two wives to cancer in his lifetime pointed out to me the other day that we think linearly when we talk about tumor shirinkage and that is the most pessimistic view.

When we say a tumor has shrunk say from 4cm to 3 cm, we say there is 25% shrinkage. Well, actually it is more than that. When we are talking about dimensions, we are talking about diameters of tumors.

So, if we consider the tumor approaches a circle (very flat), then the area of that tumor is 1/4 Pi times the square of the diameter. Don't worry about the math -- when you are comparing tumor sizes, only the diameter matters. So, if a tumor goes from 4cm to 3cm, you compare the squares of those two numbers; that is, 16 down to 9, a shrinkage of 7, or 44% shrinkage!

Now, if you consider a tumor is 3-dimensional and may approach a sphere shape, then the volume of the tumor is 1/6 Pi times the cube of the diameter. Again, only the cube of the diameter matters. So a tumor going from a diameter of 4cm to 3 cm -- comparing the volume gives the cubes, 64 down to 27, or a shrinkage of 37, 58% shrinkage!

I realize that no tumor is exactly a sphere, but what I am saying is, that if it shrinks from 4cm to 3 cm, it is not 25% shrinkage, but more like 44-58%! We need not think linearly when we are comparing volumes. You might try that one out on your onc!

I know some of you may be confused by the math, and I apologize, but I just want us to feel the full benefit of shrinkage of tumors. It is too important not to get closer to the truth. Cheers. Don

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Guest bean_si (Not Active)

Gee thanks. That makes sense. I can now see why they said my 8.5 tumor going to 5.6cm was a 70-80% shrinkage. After I'd done the math, I thought they'd gone mad.


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Those statistics made it about 1/32" into my brain and then my brain started laughing and quickly rejected even the remotest possibility that I was going to comprehend it. :lol: However, my brain did understand the bottom line - and it likes your numbers a whole lot more than the onc's numbers. Thanks for sharing!


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Thanks for sharing. It's even more encouraging for shrinkage than we thought. This is good news. I wonder why the oncs don't know more than they do about the %'s or maybe they do and just don't bother sharing or give us encouragement. How sad for some of us, that is why so many give up. For doctors not sharing and not wanting to give people a positive attitude and outlook is not in my opinion very compassionate....

Blessings and prayers,


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