Modelos matemáticos de dinâmica tumoral com EDO de ordem inteira e não inteira
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Data
2020-06-15
Autores
Silva, Jairo Gomes da
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Editor
Universidade Estadual Paulista (Unesp)
Resumo
Modelos matemáticos são estratégias cada vez mais comuns no estudo de processos biológicos, e aqueles envolvendo equações diferenciais, sejam do tipo ordinárias, parciais ou fracionárias, estão entre os mais usados. O câncer é um nome usado para designar um conjunto com mais de 200 doenças, tendo em comum o crescimento desordenado de células, com a capacidade de invadir e proliferar em diferentes tecidos e órgãos. À medida que tais células se aglomeram e se multiplicam há a formação de tumores malignos. Tais agrupamentos, devido a diversos fatores, também podem permanecer indetectáveis, e apresentarem um lento crescimento durante certos períodos de tempo, a dormência tumoral. O câncer de tireoide é a malignidade mais prevalente do sistema endócrino, sendo que o tipo diferenciado, em que as células malignas preservam algumas características das células normais, é o observado em 9 a cada 10 pessoas com esse tipo de câncer. Neste trabalho, desenvolvemos diversos estudos com o uso de modelos matemáticos aplicados ao câncer, sendo: um estudo com dois modelos matemáticos voltados à dormência tumoral, com o uso de derivadas fracionárias de Caputo; uma revisão sistemática de modelos matemáticos aplicados ao câncer de tireoide; e dois estudos com o desenvolvimento de três modelos matemáticos usando equações diferenciais ordinárias, o primeiro para estudo do carcinoma papilífero da tireoide, submetido a tratamento com tireoidectomia e radiofármaco 131I, e os demais sobre tratamentos ao carcinoma diferenciado da tireoide refratário a iodo, usando terapia-alvo, apenas, e considerando a combinação com imunoterápico. Os estudos realizados permitem: observar que o uso de derivada de ordem não inteira pode alterar a estabilidade de pontos de equilíbrio, e no caso da dormência tumoral, representar uma maior eficácia do sistema imune em controlar o tumor; notar a ausência de estudos que consideram o sistema imune como variável em modelos sobre o câncer de tireoide, até 2018; compreender a eficácia do RAI em eliminar células tumorais da tireoide sob influência positiva da interleucina-6, com dinâmica populacional segundo o efeito Allee; e analisar resultados via modelos matemáticos que sugerem a combinação de terapia-alvo com imunoterápico como melhor opção de tratamento a pacientes com câncer diferenciado da tireoide refratário a RAI, quando comparado apenas ao uso de terapia-alvo.
Mathematical models are increasingly common strategies in the study of biological processes, and those that involve differential equations, whether the ordinary, partial or fractional type, are among the most used. Cancer is a common name for a group with more than 200 diseases, having in common the disorderly growth of cells, with the ability to invade and proliferate in different tissues and organs. As these cells clump and multiply, the formation of malignant tumors is observed. Some colonies of tumor cells, due to multiple factors, can remain undetectable and show a slow growth during certain periods of time, this phase is known as tumor dormancy. Thyroid cancer is the most prevalent malignancy in the endocrine system, and differentiated carcinoma is seen in nine out of ten people with this type of cancer. In this work we present some studies with the use of mathematical models applied to cancer: two investigations related to tumor dormancy, in which we consider fractional derivatives of Caputo; a systematic review of mathematical models applied to thyroid cancer; and the development of three models of ordinary differential equations on different treatments for thyroid cancer. In the latter case, with the first model we addressed the treatment of papillary thyroid cancer performed with radioiodine 131I, while in the others we evaluated two types of treatments for differentiated carcinoma of the thyroid refractory to iodine, which are considered target therapy and its combination with immunotherapy. The studies carried out allow us to observe that the use of the non-integer derivative can change the stability of the equilibrium points, and in the case of tumor dormancy, represent a greater effectiveness of the immune system in controlling the tumor; observe the absence of studies that consider the immune system as a variable in models on thyroid cancer, until 2018; understand the effectiveness of RAI in eliminating thyroid tumor cells under the positive influence of interleukin 6 and population dynamics according to the Allee effect; and to analyze results through mathematical models that suggest the combination of target therapies with immunotherapy as the best treatment option for patients with differentiated thyroid cancer refractory to RAI, when compared only to the use of target therapy.
Mathematical models are increasingly common strategies in the study of biological processes, and those that involve differential equations, whether the ordinary, partial or fractional type, are among the most used. Cancer is a common name for a group with more than 200 diseases, having in common the disorderly growth of cells, with the ability to invade and proliferate in different tissues and organs. As these cells clump and multiply, the formation of malignant tumors is observed. Some colonies of tumor cells, due to multiple factors, can remain undetectable and show a slow growth during certain periods of time, this phase is known as tumor dormancy. Thyroid cancer is the most prevalent malignancy in the endocrine system, and differentiated carcinoma is seen in nine out of ten people with this type of cancer. In this work we present some studies with the use of mathematical models applied to cancer: two investigations related to tumor dormancy, in which we consider fractional derivatives of Caputo; a systematic review of mathematical models applied to thyroid cancer; and the development of three models of ordinary differential equations on different treatments for thyroid cancer. In the latter case, with the first model we addressed the treatment of papillary thyroid cancer performed with radioiodine 131I, while in the others we evaluated two types of treatments for differentiated carcinoma of the thyroid refractory to iodine, which are considered target therapy and its combination with immunotherapy. The studies carried out allow us to observe that the use of the non-integer derivative can change the stability of the equilibrium points, and in the case of tumor dormancy, represent a greater effectiveness of the immune system in controlling the tumor; observe the absence of studies that consider the immune system as a variable in models on thyroid cancer, until 2018; understand the effectiveness of RAI in eliminating thyroid tumor cells under the positive influence of interleukin 6 and population dynamics according to the Allee effect; and to analyze results through mathematical models that suggest the combination of target therapies with immunotherapy as the best treatment option for patients with differentiated thyroid cancer refractory to RAI, when compared only to the use of target therapy.
Descrição
Palavras-chave
Câncer de tireoide, Dormência tumoral, Crescimento tumoral, Efeito Allee, Estabilidade, Radiofármaco 131I, Thyroid cancer, Tumor dormancy, Tumor growth, Allee effect, Stability, Radioiodine 131I