Modelo computacional de esferoides tumorales multicelulares

Resumo

Purpose: The objective of this work is to develop and validate an agent-based network model that describes the growth of multicellular tumor spheroids using simple Monte Carlo tools, that also simulates the evolution of these spheroids when they are irradiated, and that allows us to analyze the difference. between different radiotherapy fractionation schemes in different situations, in addition to being able to compare the predictive capacities of different classical mathematical growth models. Methods: The computational model consists of cells located at the vertices of a cubic grid. Different cell states (proliferative, hypoxic and cell death), cell evolution rules governed by 14 parameters and the influence of the culture medium are included. About 200 spheroids of the human breast cancer cell line MCF-7 were cultured, some of them being irradiated at different doses and others were used as control data. The experimental data were used to adjust the parameters in the model tuning process, and for its validation. As an application, we have reproduced breast cancer micro-metastases from a microscope image, and simulations of their evolution have allowed us to compare their growth with that of tumor aggregates of the same number of initial cells. These metastases and aggregates have been subjected to different fractionation schemes. In addition, we have used the simulated spheroids as pseudo-data to study both the predictive and retrospective capacity (adjusting to the totality of the growth curves and also to part of them) of the classic models of exponential growth, Gompertz, logistic, potential and Bertalanffy. Results: The simulated spheroids showed growth and structural characteristics, such as the size of the different regions in which they divide (proliferative, hypoxic and necrotic nucleus), which correspond to the experimental spheroids. Furthermore, the relationship between the radius of the necrotic nucleus and the total radius of the spheroid, as well as the number of cells, proliferative and hypoxic, as a function of volume, coincide for the experimental and simulated spheroids. The statistical variability of the Monte Carlo model did not describe the entire range of volumes observed for the experimental spheroids. Assuming that the model parameters vary within Gaussian distributions, a sample of spheroids was obtained that did reproduce the experimental findings. The simulated irradiated spheroids also showed adequate growth from the day of irradiation, reasonably mimicking the growth of the experimental spheroids. The calculated survival fraction of the simulated spheroids shows very good agreement with the experimental data. In the simulations of real micrometastasis patterns, we have observed differences in their evolution after undergoing different fractionation schemes, with respect to single aggregates of the same number of cells. Regarding the classical models, the Gompertz model provided the best fits for all growth curves, that is, it turned out to be the one with the best capabilities to describe the simulated growth data, yielding a better average value of 2 per degree of freedom, an order of magnitude less than those found for the other models. The Gompertz and Bertalanffy models gave a similar retrospective predictive ability. In terms of forward-looking predictive power, the Gompertz model showed by far the best performance. Conclusions: The developed model makes it possible to describe the growth of multicellular tumor spheroids in vitro, even if they are subjected to irradiation. It reproduces experimental variability very well and allows the follow-up period to be increased with respect to the usual periods in experiments. The flexibility of the model makes it possible to vary both the agents involved (cell types, characteristics of the environment, etc.) and the rules governing the growth of the spheroid. More general situations can be studied, for example, tumor vascularization, effects of radiotherapy on solid tumors or the validity of mathematical models of tumor growth. Of all the models analyzed, the Gompertz model shows the best predictive power. The flexibility of the model also allows different patterns of micro-metastases and localized tumors to be reproduced and subjected to different radiotherapy fractions. Differences have been found in the behavior of metastases and irradiated aggregates.