Relatioship between the generalized equivalent uniform dose formulation and the Poisson statistics-based tumor control probability model

Su Min Zhou, Shiva Das, Zhiheng Wang, Lawrence B. Marks

Research output: Contribution to journalArticle

10 Scopus citations


The generalized equivalent uniform dose (GEUD) model uses a power-law formalism, where the outcome is related to the dose via a power law. We herein investigate the mathematical compatibility between this GEUD model and the Poisson statistics based tumor control probability (TCP) model. The GEUD and TCP formulations are combined and subjected to a compatibility constraint equation. This compatibility constraint equates tumor control probability from the original heterogeneous target dose distribution to that from the homogeneous dose from the GEUD formalism. It is shown that this constraint equation possesses a unique, analytical closed-form solution which relates radiation dose to the tumor cell survival fraction. It is further demonstrated that, when there is no positive threshold or finite critical dose in the tumor response to radiation, this relationship is not bounded within the realistic cell survival limits of 0%-100%. Thus, the GEUD and TCP formalisms are, in general, mathematically inconsistent. However, when a threshold dose or finite critical dose exists in the tumor response to radiation, there is a unique mathematical solution for the tumor cell survival fraction that allows the GEUD and TCP formalisms to coexist, provided that all portions of the tumor are confined within certain specific dose ranges.

Original languageEnglish (US)
Pages (from-to)2606-2609
Number of pages4
JournalMedical physics
Issue number9
StatePublished - Sep 2004



  • Cell survival fraction
  • EUD
  • TCP

ASJC Scopus subject areas

  • Biophysics
  • Radiology Nuclear Medicine and imaging

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