The development of predictive computational models of tumor initiation, growth, and decline is faced with many formidable challenges. The multiscale behavior of cancer evolution that encompasses a huge range of physical and biological events, the presence of uncertainties and the need of new algorithms to cope of these features, among others, are grand-challenges interdisciplinary research areas in which I have been focused most of my research strengths. I have been working with hybrid multiscale models (partial differential equations, phase-field models, agent-based models), numerical approximation of PDEs (finite elements and finite differences methods), stochastic methods (Monte Carlo, generalized polynomial chaos, collocation methods) and parallel computing, all applied on tumor growth models. We developed a hybrid ten-species vascular model for the tumor growth which falls within the framework of phase-field (or diffuse-interface) models suggested by continuum mixture theory. I co-advised three M.Sc. researches on vascular and avascular tumor growth modeling, encompassing hierarchical modeling development through sensitivity analysis tools and three scales (tissue-cell-intracell) hybrid modeling. The results of tumor growth models could have a significant impact on various treatments. The pursuit of affordable and reliable predictions of such complex biological systems requires advanced computational methods and a comprehensive and systematic approach for the treatment of the calibration and validation of the models, as well as the quantification of the uncertainties inherent in such models. Recently, the focus of my work is on the development of algorithms and computational tools for verification, calibration, validation, and uncertainty quantification of tumor growth models.
Multi-scale tumor growth model. Left: Agent-based model to capture the dynamics of the healthy cells (light blue cell nucleus) and tumor cells (dark blue cell nucleus). The tumor cells can be divided into quiescent (light blue cytoplasm), proliferative (green), apoptotic (red) and necrotic (they go through swelling and lose the cytoplasm, transitioning the color of the nucleus from dark blue to red depending on the calcification degree). Center: Nutrient concentration modeled by a reaction diffusion equation. Right: The Egf concentration (also modeled by a reaction diffusion equation) that will trigger the signalling pathway model responsible to drive the tumor cells proliferation (H. L. Rocha (2016)).