Mathematics of Cancer Treatment

Eugene Demidenko, Dartmouth College

Many biological studies confirmed that the growth of
unpertubated cancer tumor follows Gompertz curve, which can
be defined via a simple ODE. While there are several
complicated biomathematical models to describe cell
population, construction of parsimonious (specified by a
small number of parameters) tumor re-growth model is a long-
standing problem of mathematical cancer biology. I show how
to construct such curves based on the four compartment cell
cycle model. This model fits real life data incredible
well. An important application of the re-growth curve
theory is the ability (a) to recover cell kill in vivo (b)
determine the supra-additive effect when several treatments
are combined. The ideas are illustrated on real life cancer
data experiments.

This talk is about applied mathematics where emphasis is on
conceptual not technical matters.

This talk requires just basic calculus and some ordinary
differential equation theory. All needed biological terms
and notions will be introduced. Thus it is accessible even
for undergraduate students.