Kozusko F, Bourdeau M
Department of Mathematics, Hampton University, Hampton, VA 23668, USA.
Cell Prolif. 2007 Dec;40(6):824-34. doi: 10.1111/j.1365-2184.2007.00474.x.
A class of sigmoid functions designated generalized von Bertalanffy, Gompertzian and generalized Logistic has been used to fit tumour growth data. Various models have been proposed to explain the biological significance and foundations of these functions. However, no model has been found to fully explain all three or the relationships between them.
We propose a simple cancer cell population dynamics model that provides a biological interpretation for these sigmoids' ability to represent tumour growth.
We show that the three sigmoids can be derived from the model and are in fact a single solution subject to the continuous variation of parameters describing the decay of the proliferation fraction and/or cell quiescence. We use the model to generate proliferation fraction profiles for each sigmoid and comment on the significance of the differences relative to cell cycle-specific and non-cell cycle-specific therapies.
一类被称为广义冯·贝塔朗菲、冈珀茨和广义逻辑斯蒂的S形函数已被用于拟合肿瘤生长数据。人们提出了各种模型来解释这些函数的生物学意义和基础。然而，尚未发现有模型能完全解释这三种函数或它们之间的关系。
我们提出了一个简单的癌细胞群体动力学模型，该模型为这些S形函数表示肿瘤生长的能力提供了生物学解释。
我们表明，这三种S形函数可以从该模型推导得出，实际上它们是一个单一解，取决于描述增殖分数衰减和/或细胞静止的参数的连续变化。我们使用该模型为每个S形函数生成增殖分数分布图，并评论相对于细胞周期特异性和非细胞周期特异性疗法而言差异的意义。
