Considerations of Survival Curves and Target Theory

Powers, E. L.

doi:10.1088/0031-9155/7/1/301

Cited by 70 publications

(18 citation statements)

References 20 publications

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“…As has been shown in the development of several models (23)(24)(25) and as recently reviewed by Goodhead (26), repair saturation can also explain very effectively the shoulder on survival curves. Evidence exists at high doses that repair of double strand breaks shows the characteristics of saturation (27).…”

mentioning

confidence: 75%

Lethal and Potentially Lethal Lesions Induced by Radiation --- A Unified Repair Model

Curtis¹

1986

Radiation Research

438

214

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mentioning

confidence: 75%

Lethal and Potentially Lethal Lesions Induced by Radiation --- A Unified Repair Model

Curtis¹

1986

Radiation Research

438

214

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“…A lot of other models ranging from the inactivation of bacterial to mammalian cells describe the zero initial destruction rate with the same mathematical approach (Alper, Gillies, & Elkind, 1960;Bender & Gooch, 1962;Powers, 1962;Tyler & Dipert, 1962). Fig.…”

Section: Introductionmentioning

confidence: 99%

Impact of agglomeration on the quantitative assessment of Bacillus stearothermophilus heat inactivation

Mathys¹,

Heinz²,

Schwartz³

et al. 2007

Journal of Food Engineering

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“…Staying still within chemical kinetics, one of the alternatives to the IMM model is to conceive the damage repair as being mediated by the so-called pool repair molecules from the cell environment [56,[115][116][117][118][119][120]. To proceed, let the set of quan- Pool substances p can be both repair molecules and lesions.…”

Section: Cell Repair By Pool Repair Molecules From the Cell Environmentmentioning

confidence: 99%

The Euler T and Lambert W functions in mechanistic radiobiological models with chemical kinetics for repair of irradiated cells

Belkić

2018

J Math Chem

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Recently, the Euler T and Lambert W transcendental functions found useful applications in cellular radiobiology. Specifically, these functions appeared in mathematical modeling of cell survival after irradiation using the formalism of chemical kinetics. An example is a mechanistic inclusion of cell repair through enzyme catalysis in the Michaelis-Menten formalism, where the concentration of radiation lesions is given by the Lambert function. This function also appears in cell surviving fractions in an alternative aspect of chemical kinetics when lesion repair is carried out by the so-called pool repair molecules without passing through enzyme catalysis. Moreover, even with no reference to chemical kinetics at all, both the Lambert and Euler functions emerge in the framework of the cell repair dynamics described by delayed differential equations. The Euler function is also encountered within the cell blocking mechanism of damage repair in analogy with the counting coincidence correction for the dead time of the radiation detecting instruments. Presently, we analyze the overall usefulness of the Lambert and Euler functions in radiotherapy with a goal of motivating a further exploration of this analytical methodology in mechanistic radiobiological models for cell survival. The main reason for pursuing this pathway is in its unified mechanistic concept of cell surviving fractions valid at all doses from low through intermediate to high radiation exposures. With this advance, no artificial cut-off doses are needed any longer for empirical connections of the intermediate and high dose regimens in mathematical modelings. This is particularly important in radiotherapy because the clinically most frequently used linear-quadratic model is inadequate at high doses. High doses are of main relevance to stereotactic radiotherapy for treatment of localized tumors by efficaciously administering relatively large doses per fraction in a small number of fractions within only a few days. Such a non-conventional treatment schedule is advantageous both for the patient and hospitals' cost effectiveness, especially relative to conventional radiotherapy, which uses small doses (2 Gy) per fraction within a month long period.

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Considerations of Survival Curves and Target Theory

Cited by 70 publications

References 20 publications

Lethal and Potentially Lethal Lesions Induced by Radiation --- A Unified Repair Model

Lethal and Potentially Lethal Lesions Induced by Radiation --- A Unified Repair Model

Impact of agglomeration on the quantitative assessment of Bacillus stearothermophilus heat inactivation

The Euler T and Lambert W functions in mechanistic radiobiological models with chemical kinetics for repair of irradiated cells

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