Model of mammalian cell reproductive death I. Basic assumptions and general equations

Obaturov, G. M.; Moiseenko, Vitali; Filimonov, Alexander

doi:10.1007/bf01225916

Cited by 10 publications

(6 citation statements)

References 17 publications

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“…This result was demonstrated by several authors (17, 32–35) for the RMR (Repair-Misrepair) model (36), LPL (Lethal-Potentially Lethal) model (33), and more general binary misrepair models. In light of the conceptual similarities between the LQ model and other binary misrepair models, the fact that the corresponding formalisms make virtually equivalent predictions for dose-time relationships is not, in retrospect, particularly surprising.…”

Section: Is the Lq Model Correct?mentioning

confidence: 57%

The Linear-Quadratic Model Is an Appropriate Methodology for Determining Isoeffective Doses at Large Doses Per Fraction

Brenner

2008

Seminars in Radiation Oncology

468

336

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The tool most commonly used for quantitative predictions of dose / fractionation dependencies in radiotherapy is the mechanistically-based linear-quadratic (LQ) model. The LQ formalism is now almost universally used for calculating radiotherapeutic isoeffect doses for different fractionation/ protraction schemes. In summary, LQ has the following useful properties for predicting isoeffect doses: First, it is a mechanistic, biologically-based model; second, it has sufficiently few parameters to be practical; third, most other mechanistic models of cell killing predict the same fractionation dependencies as does LQ; fourth, it has well documented predictive properties for fractionation/doserate effects in the laboratory; fifth, it is reasonably well validated, experimentally and theoretically, up to about 10 Gy / fraction, and would be reasonable for use up to about 18 Gy per fraction. To date, there is no evidence of problems when LQ has been applied in the clinic.Let us start from the premise that we need some model for calculating iso-effect doses when alternate fractionation schemes are considered. In addition, apart from increasing interest in alternative fractionation/protraction schemes, it is essential that we know how to compensate appropriately for missed radiotherapy treatments.The tool most commonly used for quantitative predictions of dose / fractionation dependencies is the linear-quadratic (LQ) formalism (1-5). In radiotherapeutic applications, the LQ formalism is now almost universally used for calculating isoeffect doses for different fractionation/protraction schemes.In contrast to earlier methodologies, such as CRE, NSD and TDF (6,7), which were essentially empirical descriptions of past clinical data, the LQ formalism has become the preferred tool largely because it has a somewhat more biological basis, with tumor control and normal tissue complications specifically attributed to cell killing. By contrast, descriptive empirical models can go disastrously wrong if used outside the dose/fractionation range from which they were derived -as when NSD was applied to large doses per fraction (8,9).

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Section: Is the Lq Model Correct?mentioning

confidence: 57%

The Linear-Quadratic Model Is an Appropriate Methodology for Determining Isoeffective Doses at Large Doses Per Fraction

Brenner

2008

Seminars in Radiation Oncology

468

336

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“…14,15) also lead to the same generalized Lea-Catcheside time factor, G, in an appropriate approximation, and thus predict virtually the same time-dose relationships as does the LQ approach. This result was demonstrated by several authors (15)(16)(17)(18) for the repair-misrepair (RMR) model (14), the lethal-potentially lethal (LPL) model (15) and more general binary misrepair models. The conditions for equivalence are that the dose or dose rate not be too large, and that survival is determined after repair and misrepair have been completed.…”

Section: Introductionmentioning

confidence: 73%

The Linear-Quadratic Model and Most Other Common Radiobiological Models Result in Similar Predictions of Time-Dose Relationships

Brenner¹,

Hlatky²,

Hahnfeldt³

et al. 1998

Radiation Research

188

133

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One of the fundamental tools in radiation biology is a formalism describing time-dose relationships. For example, there is a need for reliable predictions of radiotherapeutic isoeffect doses when the temporal exposure pattern is changed. The most commonly used tool is now the linear-quadratic (LQ) formalism, which describes fractionation and dose-protraction effects through a particular functional form, the generalized Lea-Catcheside time factor, G. We investigate the relationship of the LQ formalism to those describing other commonly discussed radiobiological models in terms of their predicted time-dose relationships. We show that a broad range of radiobiological models are described by formalisms in which a perturbation calculation produces the standard LQ relationship for dose fractionation/protraction, including the same generalized time factor, G. This approximate equivalence holds not only for the formalisms describing binary misrepair models, which are conceptually similar to LQ, but also for formalisms describing models embodying a very different explanation for time-dose effects, namely saturation of repair capacity. In terms of applications to radiotherapy, we show that a typical saturable repair formalism predicts practically the same dependences for protraction effects as does the LQ formalism, at clinically relevant doses per fraction. For low-dose-rate exposure, the same equivalence between predictions holds for early-responding end points such as tumor control, but less so for late-responding end points. Overall, use of the LQ formalism to predict dose-time relationships is a notably robust procedure, depending less than previously thought on knowledge of detailed biophysical mechanisms, since various conceptually different biophysical models lead, in a reasonable approximation, to the LQ relationship including the standard form of the generalized time factor, G.

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“…The increase in blood perfusion, which has been recognized in some cases to be an important cause of reoxygenation (Sonveaux et al, 2002;Crokart et al, 2005), might be incorporated in the model by a modulation of the oxygen concentration in blood. Moreover, suitable modifications could account for more detailed mechanisms of lethal damage induction and death of damaged cells (Obaturov et al, 1993;Sachs et al, 1997). Finally, we note that our model takes into account the processes of repair, reoxygenation, repopulation and redistribution between proliferating and quiescent cells.…”

Section: Discussionmentioning

confidence: 98%

Reoxygenation and Split-Dose Response to Radiation in a Tumour Model with Krogh-Type Vascular Geometry

et al. 2008

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After a single dose of radiation, transient changes caused by cell death are likely to occur in the oxygenation of surviving cells. Since cell radiosensitivity increases with oxygen concentration, reoxygenation is expected to increase the sensitivity of the cell population to a successive irradiation. In previous papers we proposed a model of the response to treatment of tumour cords (cylindrical arrangements of tumour cells growing around a blood vessel of the tumour). The model included the motion of cells and oxygen diffusion and consumption. By assuming parallel and regularly spaced tumour vessels, as in the Krogh model of microcirculation, we extend our previous model to account for the action of irradiation and the damage repair process, and we study the time course of the oxygenation and the cellular response. By means of simulations of the response to a dose split in two equal fractions, we investigate the dependence of tumour response on the time interval between the fractions and on the main parameters of the system. The influence of reoxygenation on a therapeutic index that compares the effect of a split dose on the tumour and on the normal tissue is also investigated.

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Model of mammalian cell reproductive death I. Basic assumptions and general equations

Cited by 10 publications

References 17 publications

The Linear-Quadratic Model Is an Appropriate Methodology for Determining Isoeffective Doses at Large Doses Per Fraction

The Linear-Quadratic Model Is an Appropriate Methodology for Determining Isoeffective Doses at Large Doses Per Fraction

The Linear-Quadratic Model and Most Other Common Radiobiological Models Result in Similar Predictions of Time-Dose Relationships

Reoxygenation and Split-Dose Response to Radiation in a Tumour Model with Krogh-Type Vascular Geometry

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