  It has been shown recently that changing the fluidic properties of a drug can
improve its efficacy in ablating solid tumors. We develop a modeling framework
for tumor ablation, and present the simplest possible model for drug diffusion
in a spherical tumor with leaky boundaries and assuming cell death eventually
leads to ablation of that cell effectively making the two quantities
numerically equivalent. The death of a cell after a given exposure time depends
on both the concentration of the drug and the amount of oxygen available to the
cell. Higher oxygen availability leads to cell death at lower drug
concentrations. It can be assumed that a minimum concentration is required for
a cell to die, effectively connecting diffusion with efficacy. The
concentration threshold decreases as exposure time increases, which allows us
to compute dose-response curves. Furthermore, these curves can be plotted at
much finer time intervals compared to that of experiments, which is used to
produce a dose-threshold-response surface giving an observer a complete picture
of the drug's efficacy for an individual. In addition, since the diffusion,
leak coefficients, and the availability of oxygen is different for different
individuals and tumors, we produce artificial replication data through
bootstrapping to simulate error. While the usual data-driven model with
Sigmoidal curves use 12 free parameters, our mechanistic model only has two
free parameters, allowing it to be open to scrutiny rather than forcing
agreement with data. Even so, the simplest model in our framework, derived
here, shows close agreement with the bootstrapped curves, and reproduces well
established relations, such as Haber's rule.
