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

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.

A Model of Indirect Cell Death Caused by Tumor Vascular Damage after High-Dose Radiotherapy.

There is increasing evidence that high doses of radiotherapy, like those delivered in stereotactic body radiotherapy (SBRT), trigger indirect mechanisms of cell death. Such effect seems to be two-fold. High doses may trigger an immune response and may cause vascular damage, leading to cell starvation and death. Development of mathematical response models, including indirect death, may help clinicians to design SBRT optimal schedules. Despite increasing experimental literature on indirect tumor cell death caused by vascular damage, efforts on modeling this effect have been limited. In this work, we present a biomathematical model of this effect. In our model, tumor oxygenation is obtained by solving the reaction-diffusion equation; radiotherapy kills tumor cells according to the linear-quadratic model, and also endothelial cells (EC), which can trigger loss of functionality of capillaries. Capillary death will affect tumor oxygenation, driving nearby tumor cells into severe hypoxia. Capillaries can recover functionality due to EC proliferation. Tumor cells entering a predetermined severe hypoxia status die according to a hypoxia-death model. This model fits recently published experimental data showing the effect of vascular damage on surviving fractions. It fits surviving fraction curves and qualitatively reproduces experimental values of percentages of functional capillaries 48 hours postirradiation, and hypoxic cells pre- and 48 hours postirradiation. This model is useful for exploring aspects of tumor and EC response to radiotherapy and constitutes a stepping stone toward modeling indirect tumor cell death caused by vascular damage and accounting for this effect during SBRT planning. SIGNIFICANCE: A novel biomathematical model of indirect tumor cell death caused by vascular radiation damage could potentially help clinicians interpret experimental data and design better radiotherapy schedules.

Adaptive biokinetic modelling of iodine-131 in thyroid cancer treatments: implications on individualised internal dosimetry.

Nowadays therapies involving radioiodine (I-131) represent 84% of the total metabolic treatments in Europe, according to the last report of the European Association of Nuclear Medicine in relation to treatment planning for molecular radiotherapy. Last recommendations of the European Council, i.e. 2013/59/Euroatom, mandates that metabolic treatments should be planned according to the radiation doses delivered to individual patients, analogous to external beam radiotherapy. In this work, we present a novel biokinetic model for I-131 that allows on to obtain realistic activity distributions for particular patients with thyroid cancer in absence of metastasis. Other models existing in the literature present either a too simple metabolic description to obtain realistic results or a too complex one for adapting the model to individual patients, and many of these models are not indicated for metabolic treatments. The individualisation of activity distribution is obtained by an optimisation method that adjusts our model to a set of experimental measurements. Significant differences in terms of absorbed doses are observed between our model and the standard generalist models, especially in terms of red marrow absorbed dose.