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