A mathematical model of dynamics of cell populations in squamous epithelium after irradiation

Abstract

Purpose

To develop multi-compartment mechanistic models of dynamics of stem and functional cell populations in epithelium after irradiation.

Methods and materials: We present two models, with three (3C) and four (4C) compartments respectively. We use delay differential equations, and include accelerated proliferation, loss of division asymmetry, progressive death of abortive stem cells, and turnover of functional cells. The models are used to fit experimental data on the variations of the number of cells in mice mucosa after irradiation with 13 Gy and 20 Gy. Akaike information criteria (AIC) was used to evaluate the performance of each model.

Results

Both 3C and 4C models provide good fits to experimental data for 13 Gy. Fits for 20 Gy are slightly poorer and may be affected by larger uncertainties and fluctuations of experimental data. Best fits are obtained by imposing constraints on the fitting parameters, so to have values that are within experimental ranges. There is some degeneration in the fits, as different sets of parameters provide similarly good fits.

Conclusions

The models provide good fits to experimental data. Mechanistic approaches like this can facilitate the development of mucositis response models to nonstandard schedules/treatment combinations not covered by datasets to which phenomenological models have been fitted. Studying the dynamics of cell populations in multifraction treatments, and finding links with induced toxicity, is the next step of this work.

Keywords:

• Biomathematical model
• radiotherapy
• mucositis
• radiobiology

Disclosure statement

The authors report no conflict of interest.

Additional information

Funding

This project was funded by Instituto de Salud Carlos III (ISCIII) through research grants PI17/01428 and DTS17/00123 (FEDER co-funding). J.P-M. is supported by ISCIII through a Miguel Servet II grant [CPII17/00028, FEDER co-funding]. O.L.P. is partially supported by FEDER and Xunta de Galicia [GRC2013-014], and by the Spanish Ministry of Science, Innovation and Universities [MTM2017-86459-R]

Notes on contributors

Martín Parga-Pazos

Martín Parga-Pazos carried on his MSc thesis in the Group of Medical Physics and Biomathematics at the Health Research Institute of Santiago, working on dynamics of cell populations in squamous epithelium after radiotherapy. He is currently a PhD student at CIC bioGUNE.

Óscar López Pouso

Óscar López Pouso is a faculty member in the Department of Applied Mathematics at the University of Santiago de Compostela. His areas of interest are the analysis and numerical resolution of mathematical models for applied sciences and biomedicine.

John D. Fenwick

John D. Fenwick is a senior lecturer in the Institute of Translational Medicine at the University of Liverpool, and honorary consultant clinical scientist at Clatterbridge Cancer Center, with research interests in radiotherapy and imaging physics.

Juan Pardo-Montero

Juan Pardo-Montero is a ‘Miguel Servet’ scientist at the Health Research Institute of Santiago (Group of Medical Physics and Biomathematics). His current research is focused on biomathematical models in radiotherapy and oncology, and radiation dosimetry.