Survival of radiation-damaged cells via mechanism of repair by pool molecules: the Lambert function as the exact analytical solution of coupled kinetic equations

DOI10.1007/s10910-014-0307-3zbMath1311.92085OpenAlexW2099562480MaRDI QIDQ2014805

Dževad Belkić

Publication date: 16 June 2014

Published in: Journal of Mathematical Chemistry (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10910-014-0307-3

zbMATH Keywords

chemical kineticsrate equationsLambert functionradiobiological modelsdose planning systemshypofractionated radiotherapyrepair pool molecules

Mathematics Subject Classification ID

Kinetics in biochemical problems (pharmacokinetics, enzyme kinetics, etc.) (92C45) Biochemistry, molecular biology (92C40)

Related Items (8)

The Euler \(T\) and Lambert \(W\) functions in mechanistic radiobiological models with chemical kinetics for repair of irradiated cells ⋮ Analytical solutions for the rate equations of irreversible two-step consecutive processes with mixed second order later steps ⋮ Quantification by the fast Padé transform of magnetic resonance spectroscopic data encoded at 1.5 T: implications for brain tumor diagnostics ⋮ All the trinomial roots, their powers and logarithms from the Lambert series, Bell polynomials and Fox-Wright function: illustration for genome multiplicity in survival of irradiated cells ⋮ Analytical solutions for the rate equations of irreversible two-step consecutive processes with second order later steps ⋮ Padé optimization of noise-corrupted magnetic resonance spectroscopic time signals from fibroadenoma of the breast ⋮ Repair of irradiated cells by Michaelis-Menten enzyme catalysis: the Lambert function for integrated rate equations in description of surviving fractions ⋮ Kinetics of irreversible consecutive processes with first order second steps: analytical solutions

Uses Software

• WAPR
• Algorithm 443

Cites Work

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• The potential for practical improvements in cancer diagnostics by mathematically-optimized magnetic resonance spectroscopy
• On the Lambert \(w\) function
• Repair of irradiated cells by Michaelis-Menten enzyme catalysis: the Lambert function for integrated rate equations in description of surviving fractions
• Mechanistic description of survival of irradiated cells: repair kinetics in Padé linear-quadratic or differential Michaelis-Menten model
• Real values of the W -function
• Algorithm 743: WAPR--a Fortran routine for calculating real values of the W -function

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