Resumen
Apresenta-se um modelo matemático baseado na hipótese de que o crescimento de tumores tem sua origem nas células-tronco cancerígenas (CTCs). No entanto, o próprio conceito de célula-tronco cancerígena (CTC) tem sido alvo de controvérsias na literatura e uma das questões abertas à discussão se refere à proporção de CTCs em um tumor. O modelo apresentado, baseado no comportamento do sistema hematopoiético, tem uma estrutura hierárquica composta de dois compartimentos: o de células-tronco (CT) e o de células diferenciadas ou progenitoras (CPs). Admite-se que um tumor seja constituído por uma população de células que se tornaram anormais por adquirirem mutações durante o processo de mitose. Para o modelo matemático proposto, mostramos que as CTCs podem ser células anormais que residem no compartimento de células-tronco, mas também podem ser CPs que, através de mutação adquirida na mitose, se tornam capazes de se autorrenovarem. Mostramos, em concordância com resultados experimentais, que a proporção de CTCs em um tumor pode variar de acordo com a mutação que o originou. Nosso modelo sugere que os tumores mais agressivos são aqueles em que a proporção de CTCs é grande.
Palavras-chave: Modelo matemático. Célula-tronco cancerígena. Tumor.
Mathematical analysis of a model for the cancer stem cells growing in tumors
We present a mathematical model based on the hypothesis that the growing of a tumor is driven by the cancer stem cells (CSC). However, the concept of CSC and the proportion of this subpopulation in a tumor remain as topics of considerable controversy. Our model, based on the known behavior of the hematopoietic system, has a hierarchical structure with only two compartments: one for the stem-cells (SC) and another for the differentiated or progenitor cells (PC). We admit that a tumor is constituted by a population of abnormal cells, that is, cells that, during mitosis, acquired a mutation. Our mathematical model suggests that a CSC can either be a cell residing in the stem cell compartment or a differentiated cell that, due to the mutation, became able of self-renewal. In accordance to some experimental results, our model shows that any proportion of CSC is possible in a tumor. However, the bigger this proportion is, the more aggressive is the tumor.
Keywords: Mathematical model. Cancer stem cell. Tumor.
Citas
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