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

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.

Hypofractionated Radiation Induced the Immunogenic Death of Bladder Cancer Cells Leading to the Immune Sensitization of Dendritic Cells

“…In our study, the expression of CD80, CD86 and CCR7 on imDCs was signi cantly increased after co-culture with BT-B cells after hypofractionated radiation. This is consistent with the ndings of Kulzer L et al in colorectal cancer after 5 Gy radiation (Kulzer et al 2014, Rodríguez-Barbeito et al 2019. At the same time, radiation increased the secretion of CCL21 in BC cells, which reached the highest at 10 Gy radiation.…”

Evaluation of indirect damage and damage saturation effects in dose–response curves of hypofractionated radiotherapy of early-stage NSCLC and brain metastases

“…There have been attempts at modelling the contribution of indirect damage [35][36][37], but there is no simple closed-form expression. As suggested in [37], we have investigated ad hoc modifications of the LQ-model with dose-dependent alpha-beta terms of the following form:…”

Evaluation of indirect damage and damage saturation effects in dose-response curves of hypofractionated radiotherapy of early-stage NSCLC and brain metastases

“…There have been attempts at modelling the contribution of indirect damage [35-37] , but there is no simple closed-form expression to model such effect. In order to study whether indirect damage contributes to observed clinical control rates, we hypothesize that an ad hoc modification of the LQ-model with dose-dependent alpha and beta terms, α(d ) and β(d ), may provide better fits to experimental dose-response curves.…”

“…For example, if indirect damage is more important for large doses, α(d ) and/or β(d ) should have the form of monotonically-increasing functions. As there is no functional form for the functions α(d ) and β(d ), even though phenomenological forms could be derived from studies like [35-37] , we have investigated simple functional dependencies with the following form:…”