Sensitivity analysis as a tool for tumor growth modeling

• Ano de defesa: 2016
• Autor(a) principal: Resende, Anna Claudia Mello de
• Orientador(a): Almeida, Regina Célia Cerqueira de , Lima, Ernesto Augusto Bueno da Fonseca
• Banca de defesa: Costa, Michel Iskin da Silveira , Coutinho, Álvaro Luiz Gayoso de Azeredo, Mancera, Paulo Fernando de Arruma
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: eng
• Instituição de defesa: Laboratório Nacional de Computação Científica
• Programa de Pós-Graduação: Programa de Pós-Graduação em Modelagem Computacional
• Departamento: Serviço de Análise e Apoio a Formação de Recursos Humanos
• País: Brasil
• Palavras-chave em Português: Câncer; Modelos matemáticos
• Palavras-chave em Inglês: Mathematical models
• Área do conhecimento CNPq: CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA::MATEMATICA APLICADA; CNPQ::CIENCIAS DA SAUDE::MEDICINA::CLINICA MEDICA::CANCEROLOGIA
• Link de acesso: https://tede.lncc.br/handle/tede/237

Mathematical and computational modeling of tumor growth have become valuable tools for learning and understanding various aspects of tumor onset and development. They can also help to generate new hypotheses for experimental testing and to verify the efficiency or optimize clinical therapies. From the computational point of view, a huge challenge is to deal with highly nonlinear and multi-components mathematical models that aim to display multiple types of biological interactions across different biological, temporal and physical scales. Computational and numerical difficulties usually appear. Also, nonlinear interactions may give rise to interesting and unexpected dynamics which make it difficult to anticipate a model's outcome. Here we make a step towards developing a model-building framework to improve the understanding of the model itself and the key issues to drive model modifications and simplifications. We develop a family of deterministic tumor growth models based on a mathematical model built in the literature, which is a continuous model of seven coupled nonlinear partial differential equations that can capture both avascular and vascular phases of the disease. Although simple, this model provides considerable insight about important mechanisms related to tumor progression, as angiogenesis, for example, which is the fundamental strategy tumors acquire to keep and improve growth. Its main assumptions and mathematical formulation are discussed in details, and we propose some modifications to fix ambiguities in the original model. The extension to multidimensional problems is considered, for which we develop reliable approximate finite element solution. We propose in this work a simple framework to build a hierarchical family of tumor growth models by selecting a subset of the most important parameters of our base model with respect to the evolution of the tumor volume. The importance of each parameter is identified through two model-free sensitivity analysis techniques, the construction of scatterplots and the elementary effects, due to their simplicity and low computational costs. This model framework encompasses the essential hypotheses and the limited set of important parameters acquired from the sensitivity analysis. In this way, we are able to create a family of models described by at least the same essential conditions and parameters but with different complexities regarding the number of parameters used. Numerical experiments are conducted to provide a comprehensive understanding of the hierarchical developed family of tumor growth models. Finally, we emphasize that the modeling framework in this manner provides a powerful way for studying a model itself or either its simplification or extension. The framework can also be tailored to form the basis for future models, incorporating new processes and phenomena.