Division of Theoretical Physics, P.N. Lebedev Physical Institute of the Russian Academy of Sciences, 53 Leninskii Prospekt, Moscow, Russia, 119991.
Peoples' Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya St, Moscow, Russia, 117198.
J Math Biol. 2020 Feb;80(3):601-626. doi: 10.1007/s00285-019-01434-4. Epub 2019 Oct 1.
A new continuous spatially-distributed model of solid tumor growth and progression is presented. The model explicitly accounts for mutations/epimutations of tumor cells which take place upon their division. The tumor grows in normal tissue and its progression is driven only by competition between populations of malignant cells for limited nutrient supply. Two reasons for the motion of tumor cells in space are taken into consideration, i.e., their intrinsic motility and convective fluxes, which arise due to proliferation of tumor cells. The model is applied to investigation of solid tumor progression under phenotypic alterations that inversely affect cell proliferation rate and cell motility by increasing the value of one of the parameters at the expense of another.It is demonstrated that the crucial feature that gives evolutionary advantage to a cell population is the speed of its intergrowth into surrounding normal tissue. Of note, increase in tumor intergrowth speed in not always associated with increase in motility of tumor cells. Depending on the parameters of functions, that describe phenotypic alterations, tumor cellular composition may evolve towards: (1) maximization of cell proliferation rate, (2) maximization of cell motility, (3) non-extremum values of cell proliferation rate and motility. Scenarios are found, where after initial tendency for maximization of cell proliferation rate, the direction of tumor progression sharply switches to maximization of cell motility, which is accompanied by decrease in total speed of tumor growth.
提出了一种新的连续空间分布的实体瘤生长和进展模型。该模型明确考虑了肿瘤细胞分裂时发生的突变/表观突变。肿瘤在正常组织中生长，其进展仅由恶性细胞群体为有限的营养供应而竞争驱动。考虑了肿瘤细胞在空间中运动的两个原因，即它们的内在运动性和由于肿瘤细胞增殖而产生的对流通量。该模型应用于研究在表型改变下的实体瘤进展，表型改变通过增加一个参数的值而以牺牲另一个参数的值来反向影响细胞增殖率和细胞迁移率。结果表明，赋予细胞群体进化优势的关键特征是其向周围正常组织中过度生长的速度。值得注意的是，肿瘤过度生长速度的增加并不总是与肿瘤细胞迁移率的增加相关。取决于描述表型改变的函数的参数，肿瘤细胞组成可能会朝着以下方向进化：（1）最大化细胞增殖率，（2）最大化细胞迁移率，（3）非极值细胞增殖率和迁移率。发现了一些情况，在最初倾向于最大化细胞增殖率之后，肿瘤进展的方向急剧转向最大化细胞迁移率，这伴随着肿瘤生长总速度的降低。
