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Fundamental form of a population TCP model in the limit of large heterogeneity
Author(s) -
Carlone Marco C.,
Warkentin Brad,
Stavrev Pavel,
Fallone B. Gino
Publication year - 2006
Publication title -
medical physics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.473
H-Index - 180
eISSN - 2473-4209
pISSN - 0094-2405
DOI - 10.1118/1.2193690
Subject(s) - limit (mathematics) , population , statistical physics , mathematics , physics , medicine , mathematical analysis , environmental health
A population tumor control probability (TCP) model for fractionated external beam radiotherapy, based on Poisson statistics and in the limit of large parameter heterogeneity, is studied. A reduction of a general eight‐parameter TCP equation, which incorporates heterogeneity in parameters characterizing linear‐quadratic radiosensitivity, repopulation, and clonogen number, to an equation with four parameters is obtained. The four parameters represent the mean and standard deviation for both clonogen number and a generalized radiosensitivity that includes linear‐quadratic and repopulation descriptors. Further, owing to parameter inter‐relationship, it is possible to express these four parameters as three ratios of parameters in the large heterogeneity limit. These ratios can be directly linked to two defining features of the TCP dose response: D 50 and γ 50 . In the general case, the TCP model can be written in terms of D 50 , γ 50 and a third parameter indicating the ratio of the levels of heterogeneity in clonogen number and generalized radiosensitivity; however, the third parameter is unnecessary when either of these two sources of heterogeneity is dominant. It is shown that heterogeneity in clonogen number will have little impact on the TCP formula for clinical scenarios, and thus it will generally be the case that the fundamental form of the Poisson‐based population TCP model can be specified completely in terms of D 50 and γ 50 : TCP = 1 2erfc [ π γ 50 ( D 50 ∕ D − 1 ) ] . This implies that limited radiobiological information can be determined by the analysis of dose response data: information about parameter ratios can be ascertained, but knowledge of absolute values for the fundamental radiobiological parameters will require independent auxiliary measurements.

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