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I am reading Dennis M. Brown “Drug Delivery Systems in Cancer”. On Page 29 when referring to monotonic increase or decrease of n (being the number of cells n(t) I believe) then how are they getting

AUC50 = T(1-1/n)

I get how it equal k(1/n) because we just raise each side of equation IC50n * T = k to the 1/n power but not getting the the double equality here.

The relationship between IC50 and AUC50 occurs when n = 1 in (IC50)n * T = k which reduces to AUC50 = k, meaning effect only depends on AUC.

screenshot of book

  • what is the relationship between AUC and IC? – Kate Gregory Aug 24 '19 at 15:54
  • When n=1 $ (IC_{50})^{n}T = k reduces to (AUC_{50}) = k $ meaning effect only depends on AUC. Not sure why the latex is not working here. – Brian Wiley Aug 24 '19 at 19:24
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    latex doesn't work in comments, you can edit the question with this info – Kate Gregory Aug 24 '19 at 19:33
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Let's take the general equation they mentioned, (IC50)nT = k, and rearrange it to IC50 = (k/T)1/n = k1/nT-1/n. (IC50)nT = k reducing to AUC50 = k if n=1 implies that AUC50 = IC50T if n=1. If this equation holds for other n, then AUC50 = k1/nT1-1/n. That looks a LOT like the text if the author accidentally inserted a =.

This next bit is more speculative because the exact descriptions of these terms in the source are not available online, but AUC generally stands for "area under curve," aka integration. I have doubts AUC50 is some definite integral of IC50 because when n=1, IC50 = k/T, which has an indefinite integral F(T) = k*ln(T) + constant.

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  • Yes they must have inserted another = by accident! Thanks so much! – Brian Wiley Aug 25 '19 at 0:03

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