Modelagem matemática e simulação computacional do crescimento tumoral sob a inserção da quimioterapia e imunoterapia
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Data
2022-02-24
Autores
Toro, Paulo Felipe
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Universidade Estadual Paulista (Unesp)
Resumo
Câncer é um problema de saúde pública que afeta a população mundial, cuja incidência vem aumentando a cada ano. Uma das formas de tratamento comumente utilizada é a quimioterapia. Outro tipo de tratamento que tem ganhado espaço na ciência é a imunoterapia. Este trabalho busca entender a dinâmica do crescimento tumoral dada uma combinação destes tratamentos. O modelo proposto é composto por um sistema não-linear de Equações Diferenciais Ordinárias acopladas. Os pontos de equilíbrio do modelo foram obtidos e analisados via teoria de estabilidade local. O problema do tratamento ótimo associado ao problema direto foi estabelecido e resolvido por uma estratégia de otimização não-linear. Simulações computacionais da dinâmica tumoral foram realizadas, considerando diferentes cenários estabelecidos em relação aos tratamentos, variando-se os tipos, as doses aplicadas e as combinações possíveis entre si. Os resultados numéricos das simulações foram obtidos pelo método numérico de Runge-Kutta de quarta-ordem. A análise matemática e os resultados numéricos possibilitaram a compreensão dos cenários e aquele com a combinação dos tratamentos foi indicado como o mais promissor. Neste estudo, o problema do tratamento ideal foi também estabelecido e resolvido, possibilitando melhores resultados para o tratamento contínuo no tempo observado.
Cancer is a public health problem that affects the world population and its incidence is increasing every year. One of the commonly used forms of treatment is chemotherapy. Another type of treatment that has gained space in science is immunotherapy. This work seeks to understand the tumor growth dynamics, considering a combination of treatments. The proposed model is composedofanonlinearsystemofcoupledOrdinaryDifferentialEquations. Equilibrium points of the model were obtained via local stability theory. The optimal treatment problem associated with the direct problem was established and solved by a nonlinear optimization strategy. Computational simulations of tumor dynamics were performed, considering different scenarios established in relation to treatments, varying the types, the doses applied and the possible combinations between them. The results of the simulations were obtained by the fourth-order Runge-Kutta numerical method. Mathematical analysis and numerical results made it possible to understand the scenarios and the one with the combination of treatments was indicated as the most promising. In this study, the problem of the optimal treatment was also established and solved, making it possible to indicate better results for the continuous treatment in the observed time.
Cancer is a public health problem that affects the world population and its incidence is increasing every year. One of the commonly used forms of treatment is chemotherapy. Another type of treatment that has gained space in science is immunotherapy. This work seeks to understand the tumor growth dynamics, considering a combination of treatments. The proposed model is composedofanonlinearsystemofcoupledOrdinaryDifferentialEquations. Equilibrium points of the model were obtained via local stability theory. The optimal treatment problem associated with the direct problem was established and solved by a nonlinear optimization strategy. Computational simulations of tumor dynamics were performed, considering different scenarios established in relation to treatments, varying the types, the doses applied and the possible combinations between them. The results of the simulations were obtained by the fourth-order Runge-Kutta numerical method. Mathematical analysis and numerical results made it possible to understand the scenarios and the one with the combination of treatments was indicated as the most promising. In this study, the problem of the optimal treatment was also established and solved, making it possible to indicate better results for the continuous treatment in the observed time.
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Palavras-chave
Anticorpos monoclonais, Câncer, Otimização, Análise matemática, Sistemas de equações diferenciais ordinárias, Runge-Kutta, Soluções numéricas, Cancer, Mathematical analysis, Monoclonal antibodies, Numerical solutions, Optimization, Ordinary differential equation systems