No abstract

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 reactiondiffusion 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.

The accretive operators theory is employed for proving an existence theorem for the evolutive energy equations involving simultaneously conduction, stationary convection (in the sense that the velocity field is assumed to be time independent), and radiation. In doing that we need to use new existence results for elliptic linear problems with mixed boundary conditions and irregular data.

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.