Does a local bystander effect necessitate a revision of TCP models that are based on observed clinical data?

It is shown that in order to derive a general model for tumor control probability (TCP) the two assumptions that on the microscopic level (1) clonogens are non-interacting and (2) clonogen killings are uncorrelated events are not necessary. In fact, these two assumptions can be replaced with two weaker ones that only ask that (a) therapy fractions are independent and non-overlapping and (b) the probability of an event only depends on the number of incidents happening during a time interval and the length of this time interval but not on time itself. This change in assumptions implies that TCP models based on clinical data are flexible enough to include interaction of clonogens on the microscopic level and therefore also a possible bystander effect in cell killing. Based on this new set of assumptions the equation for TCP is derived, first for the homogenous case and then for the general case of a heterogeneous ensemble of tumors irradiated in-homogeneously.