Related Experiment Video
Updated: Mar 19, 2026

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach
Published on: July 3, 2020
[The enigma of the biological interpretation of the linear-quadratic model finally resolved? A summary for
L Bodgi1, A Canet2, A Granzotto1
1Inserm, UMR1052, centre de recherche en cancérologie de Lyon, bâtiment Cheney A, rue Laennec, 69008 Lyon, France.
Abstract:
The linear-quadratic (LQ) model is the only mathematical formula linking cellular survival and radiation dose that is sufficiently consensual to help radiation oncologists and radiobiologists in describing the radiation-induced events. However, this formula proposed in the 1970s and α and β parameters on which it is based remained without relevant biological meaning. From a collection of cutaneous fibroblasts with different radiosensitivity, built over 12 years by more than 50 French radiation oncologists, we recently pointed out that the ATM protein, major actor of the radiation response, diffuses from the cytoplasm to the nucleus after irradiation. The evidence of this nuclear shuttling of ATM allowed us to provide a biological interpretation of the LQ model in its mathematical features, validated by a hundred of radiosensitive cases. A mechanistic explanation of the radiosensitivity of syndromes caused by the mutation of cytoplasmic proteins and of the hypersensitivity to low-dose phenomenon has been proposed, as well. In this review, we present our resolution of the LQ model in the most didactic way.
Related Concept Videos
Quadratic Models
Pharmacodynamic Models: Linear Concentration–Effect Model
Pharmacodynamic Models: Logarithmic Concentration–Effect Model
Mechanistic Models: Compartment Models in Individual and Population Analysis
Parameters Affecting Nonlinear Elimination: Zero-Order Input, First-Order Absorption and Two-Compartment Model
When a drug is administered through a constant intravenous infusion and eliminated via nonlinear pharmacokinetics, it follows zero-order input. For example, oral drugs undergo first-order absorption upon administration and are eliminated through nonlinear pharmacokinetics.
In the case of subcutaneously administered drugs,...
Modeling with Differential Equations

