Óscar López-Pouso

Objective. This work aims to investigate the iso-effectiveness of conventional and FLASH radiotherapy on tumors through in-silico mathematical models. We focused on the role of radiolytic oxygen depletion (ROD), which has been argued as a possible factor to explain the FLASH effect. Approach. We used a spatiotemporal reaction-diffusion model, including ROD, to simulate tumor oxygenation and response. From those oxygen distributions we obtained surviving fractions (SFs) using the linear-quadratic (LQ) model with the oxygen enhancement ratios (OERs). We then employed the calculated SFs to describe the evolution of preclinical tumor volumes through a mathematical model of tumor response, and we also extrapolated those results to calculate tumor control probabilities (TCPs) using the Poisson-LQ approach. Main results. Our study suggests that the ROD effect may cause differences in SF between FLASH and conventional radiotherapy, especially in low α/β and poorly oxygenated cells. However, a statistical analysis showed that these changes in SF generally do not result in significant differences in the evolution of preclinical tumor growth curves when the sample size is small, because such differences in SF may not be noticeable in the heterogeneity of the population of animals. Nonetheless, when extrapolating this effect to TCP curves, we observed important differences between both techniques (TCP is lower in FLASH radiotherapy). When analyzing the response of tumors with heterogeneous oxygenations, differences in TCP are more important for well oxygenated tumors. This apparent contradiction with the results obtained for homogeneously oxygenated cells is explained by the complex interplay between the heterogeneity of tumor oxygenation, the OER effect, and the ROD effect. Significance. This study supports the experimentally observed iso-effectiveness of FLASH and conventional radiotherapy when analyzing the volume evolution of preclinical tumors (that are far from control). However, this study also hints that tumor growth curves may be less sensitive to small variations in SF than tumor control probability: ROD may lead to increased SF in FLASH radiotherapy, which while not large enough to cause significant differences in tumor growth curves, could lead to important differences in clinical TCPs. Nonetheless, it cannot be discarded that other effects not modeled in this work, like radiation-induced immune effects, can contribute to tumor control and maintain the iso-effectiveness of FLASH radiotherapy. The study of tumor growth curves may not be the ideal experiment to test the iso-effectiveness of FLASH, and experiments reporting TCP or D ₅₀ may be preferred.

Extended presentation of the FEM solver, capillary model, pimo diffusion, and sensitivity analysis

Extended presentation of the FEM solver, capillary model, pimo diffusion, and sensitivity analysis

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.

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.

There is evidence of synergy between radiotherapy and immunotherapy. Radiotherapy can increase liberation of tumor antigens, causing activation of antitumor T-cells. This effect can be boosted with immunotherapy. Radioimmunotherapy has potential to increase tumor control rates. Biomathematical models of response to radioimmunotherapy may help on understanding of the mechanisms affecting response, and assist clinicians on the design of optimal treatment strategies. In this work we present a biomathematical model of tumor response to radioimmunotherapy. The model uses the linear-quadratic response of tumor cells to radiation (or variation of it), and builds on previous developments to include the radiation-induced immune effect. We have focused this study on the combined effect of radiotherapy and PDL1/CTLA4 therapies. The model can fit preclinical data of volume dynamics and control obtained with different dose fractionations and PDL1/CTLA4. A biomathematical study of optimal combination strategies suggests that a good understanding of the involved biological delays, the biokinetics of the immunotherapy drug, and the interplay between them, may be of paramount importance to design optimal radioimmunotherapy schedules. Biomathematical models like the one we present can help to interpret experimental data on the synergy between radiotherapy and immunotherapy, and to assist in the design of more effective treatments.

This paper is devoted to solve the steady monoenergetic Fokker-Planck equation in the 1D slab when the incoming fluxes and the source term are allowed to depend on the azimuth θ. The problem is split into a collection of θ-independent problems for the Fourier coefficients of the full solution. The main difficulty is that, except for the zeroth Fourier coefficient, each of these problems contains an artificial absorption coefficient which is singular at the poles. Two numerical schemes capable of dealing with the singularities are proposed: one that is considered as the main scheme, and a second ‘security’ scheme which is used to verify that the results obtained by means of the first one are reliable. Numerical experiments showing second order of convergence are conducted and discussed.

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.