The equation of the Zaider-Minerbo model:

equation=8810

The solution of this equation will allow us to calculate the TCP(t) since

TCP(t)=A(s=0,t)

Because we are looking for a solution for which

A(s,0)=s^n

it can be shown that this is of the form

A(s,t)=\left[1-\displaystyle\frac{1}{\left(\displaystyle\frac{\Lambda(t)}{1-s}+b\displaystyle\int_0^t\Lambda(t')dt'\right)}\right]

with

equation=8808

With this it can be shown that the TCP function is of the form:

equation

The h function can be modeled with the L-Q model for the applicable dose history.

The following in a simulator that allows to calculate the TCP both under Poisson and Zaider Minerbo assuming two types of cells (birth rate, death, factors \alpha and \beta) dose and number of treatments:

The Zerider Minerbo model is based on the population equation

\displaystyle\frac{d}{dt}N=(b-d+h(t))N

however the births can be conditioned by what the generalization of the model can be based on the more general equation:

equation

Where the f function must be modeled separately.