Modelos fracionários de terapia gênica para o tratamento do câncer
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Data
2019-02-25
Autores
Tavoni, Robinson
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Universidade Estadual Paulista (Unesp)
Resumo
Câncer é umas das maiores causas de mortalidade mundial. Os tratamentos mais convencionais, tais como quimioterapia e radioterapia, além de debilitarem muito o paciente também matam as células normais. Em contrapartida, e em fase de tratamento experimental e ensaios clínicos, a terapia gênica tem poucos efeitos colaterais e provoca a morte seletiva das células tumorais. Este trabalho apresenta alguns conceitos do Cálculo Fracionário e o Método de Grünwald-Letnikov para simulação numérica de Equações Diferenciais Fracionárias, também estuda alguns modelos matemáticos de ordem inteira e não inteira, com derivada temporal de Caputo, que visam descrever o tratamento por terapia gênica. A análise de estabilidade e as simulações numéricas exibiram que mudanças no cenário da dinâmica tumoral estão relacionadas com a ordem da derivada fracionária, no qual observou-se uma atuação mais eficiente do tratamento quando o modelo está associado com ordens menores da derivada fracionária.
Cancer is one of the biggest causes of worldwide mortality. Conventional treatments, such as chemotherapy and radiotherapy, in addition to weakening the patient also kill normal cells. On the other hand, in experimental treatments and clinical trials, gene therapy has few side effects and causes selective killing of tumor cells. This work presents some concepts of the Fractional Calculus and the Grünwald-Letnikov Method for numerical simulation of Fractional Differential Equations, also studies some mathematical models of integer order and non-integer order, with temporal derivative of Caputo, that aim describe the treatment by gene therapy. Stability analysis and numerical simulations have shown that changes in the scenery of the tumor dynamics are related to the order of the fractional derivative, in which a more efficient treatment performance was observed when the model is associated with smaller orders of the fractional derivative.
Cancer is one of the biggest causes of worldwide mortality. Conventional treatments, such as chemotherapy and radiotherapy, in addition to weakening the patient also kill normal cells. On the other hand, in experimental treatments and clinical trials, gene therapy has few side effects and causes selective killing of tumor cells. This work presents some concepts of the Fractional Calculus and the Grünwald-Letnikov Method for numerical simulation of Fractional Differential Equations, also studies some mathematical models of integer order and non-integer order, with temporal derivative of Caputo, that aim describe the treatment by gene therapy. Stability analysis and numerical simulations have shown that changes in the scenery of the tumor dynamics are related to the order of the fractional derivative, in which a more efficient treatment performance was observed when the model is associated with smaller orders of the fractional derivative.
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Palavras-chave
Terapia gênica, Modelagem fracionária, Estabilidade fracionária, Vírus oncolítico, Biomatemática, Gene therapy, Fractional modeling, Fractional stability, Oncolytic virus, Biomathematics