Model‐Based Evaluation of Radiation and Radiosensitizing Agents in Oncology

Abstract

Radiotherapy is one of the major therapy forms in oncology, and combination therapies involving radiation and chemical compounds can yield highly effective tumor eradication. In this paper, we develop a tumor growth inhibition model for combination therapy with radiation and radiosensitizing agents. Moreover, we extend previous analyses of drug combinations by introducing the tumor static exposure (TSE) curve. The TSE curve for radiation and radiosensitizer visualizes exposure combinations sufficient for tumor regression. The model and TSE analysis are then tested on xenograft data. The calibrated model indicates that the highest dose of combination therapy increases the time until tumor regrowth 10‐fold. The TSE curve shows that with an average radiosensitizer concentration of 1.0 normalμboldg/boldmboldL the radiation dose can be decreased from 2.2 boldGboldy to 0.7 boldGboldy. Finally, we successfully predict the effect of a clinically relevant treatment schedule, which contributes to validating both the model and the TSE concept.

Modeling long-term tumor growth and kill after combinations of radiation and radiosensitizing agents

“…Immediate cell killing sends a fraction of the proliferating cells to the compartment after which the cells are allowed up to one more cell division (and in the process transferring the daughter cells to the compartment ) before dying via the transit compartments , , and . Such an effect was used in an earlier analysis (see [ 15 ]) and is supported by experiments, showing that irradiated cells can survive one or multiple cell cycles before dying through mitotic catastrophe [ 17 , 18 ]. The second radiation effect describes an inhibition of the growth rate of the surviving cells.…”

“…Two simple models featured by Sachs et al and Schättler and Ledzewics shared the common feature of capturing the LQ prediction of the surviving cell fraction [ 13 , 14 ]. In a previous analysis, Cardilin et al proposed a semi-mechanistic model for combinations of ionizing radiation and radiosensitizing treatment that agrees with the LQ prediction [ 15 ]. However, the model does not account for long-term effects such as tumor eradication and regrowth dynamics.…”

“…A tumor model was developed to describe treatment effects of ionizing radiation (IR) and radiosensitizing agents on tumor volume. The model is an extension of an existing model (see [ 15 ]) to account for long-term growth dynamics. A schematic illustration of the model is shown in Fig.…”

“…In particular, a synergistic drug effect leads to a more convex (curving inward) TSC curve, whereas an antagonistic effect results in a more concave (curving outward) TSC curve [ 16 ]. A subsequent analysis presented a tumor model for combinations of radiation and chemical provocation that complied with the LQ prediction in radiobiology [ 15 ]. Radiation-induced cell killing was described as triggering apoptosis (possibly lumped with other death mechanisms) in lethally irradiated cells.…”

Crosstalk between HER2 and PD-1/PD-L1 in Breast Cancer: From Clinical Applications to Mathematical Models

“…Thus, such models can be used to investigate the efficacy of novel treatment strategies, and to find the optimal drug dose required for achieving certain desired drug response without actually testing on patients. Specific mathematical models of tumor-immune interaction with respect to the adopted mode of treatment such as chemotherapy [158], radiotherapy [159], immunotherapy [160], hormone therapy [161], anti-angiogenesis [162], nanomedicine-based cancer therapy [33], gene therapy and/or oncovirotherapy [163], and combination therapies [164] have been widely discussed recently. Many recent reviews summarize the history of mathematical models in various treatment areas related to cancer [33,40,156,[165][166][167][168].…”