AbstractID: 8931 Title: Inconsistency between the Generalized Equivalent Uniform Dose
Formulation and the Current Tumor Control Probability Model
Niemierko1 has proposed a generalized equivalent uniform dose (GEUD) formulation, applicable to tumor and normal tissues. The
GEUD model uses a power–law, wherein dose is raised to an exponent, a , that is determined from numerical fits to clinical trial
outcomes. Tumor and normal tissue EUDs are intended to reflect local control and biological iso-effect, respectively. In this work we
investigate the mathematical compatibility between the GEUD model and the tumor control probability (TCP) model based on
Poisson statistics. In order to do so, we have combined the GEUD and TCP formulations, and subjected them to a compatibility
constraint equation. The constraint equates tumor control probability from the original heterogeneous target distribution to that from
the GEUD formulation. The equation does not account for repopulation dynamics, but does allow for a heterogeneous distribution of
clonogenic cells. It is shown that this constraint equation can be solved to yield a unique closed-form relationship between the
()
a
radiation dose (D) and tumor cell survival fraction (SF), SF D = c 0 − c1 D . However, this relationship has a shortcoming in that it
is not bounded within the realistic cell survival limits of 0% and 100%, for any non-zero dose multiplier coefficient c1 . A logical
conclusion is that the GEUD and TCP formulations are inconsistent, if we insist that GEUD has an equivalent radiobiological effect
(TCP in this case) to the original 3D non-uniform physical dose delivered to the tumor volume.
1
A. Niemierko , A generalized concept of equivalent uniform dose (EUD) (Abstract) . Med Phys 26 (1999), p. 1100.