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Publicação
Stochastic graph-based models of tumor growth and celular interations
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Autores
Orientador(es)
Resumo(s)
The tumor microenvironment is a highly dynamic and complex system where cellular interactions evolve over time, influencing tumor growth, immune response, and treatment resistance. In this study, we develop a graph-theoretic framework to model the tumor microenvironment, where nodes represent different cell types, and edges denote their interactions. The temporal evolution of the tumor microenvironment is governed by fundamental biological processes, including proliferation, apoptosis, migration, and angiogenesis, which we model using differential equations with stochastic effects. Specifically, we describe tumor cell population dynamics using a logistic growth model incorporating both apoptosis and random fluctuations. Additionally, we construct a dynamic network to represent cellular interactions, allowing for an analysis of structural changes over time. Through numerical simulations, we investigate how key parameters such as proliferation rates, apoptosis thresholds, and stochastic fluctuations influence tumor progression and network topology. Our findings demonstrate that graph theory provides a powerful mathematical tool to analyze the spatiotemporal evolution of tumors, offering insights into potential therapeutic strategies. This approach has implications for optimizing cancer treatments by targeting critical network structures within the tumor microenvironment.
Descrição
This research was partially sponsored with national funds through the Fundação Nacional para a Ciência e Tecnologia, Portugal-FCT, under projects UIDB/04674/2020 (CIMA). DOI: https:
//doi.org/10.54499/UIDB/04674/2020.
Palavras-chave
Tumor microenvironment Graph theory Cellular interactions Tumor growth modeling Differential equations Stochastic processes Network dynamics Proliferation and apoptosis Mathematical oncology Topology and stability analysis Topological data analysis Algebraic connectivity Network robustness Systems biology 92-10 UIDB/04674/2020
Contexto Educativo
Citação
Rodrigues, J. A. (2025). Stochastic graph-based models of tumor growth and celular interations. AppliedMath, 5(2), 1-19. https://doi.org/10.3390/appliedmath5020062
Editora
MDPI