关键词: binary fractal fibers, binary cell elements, regular binary fractals, multiplecell elements, regular multifractals, avascular, continuous-discrete model, p27 gene, tumor growth, numerical simulation, multi-scale

Abstract: A multi-scale continuous-discrete model based on the effects of the p27 gene control is built to simulate the avascular tumor growth. At the tissue level, the continuous Eulerian model is adopted to determine the distribution of the concentration of oxygen, the extracellular matrix (ECM), and the matrix-degradative enzyme (MDE). At the cellular level, the discrete Lagrangien model is adopted to determine the movement, the proliferation, and the death of single tumor cells (TCs). At the genetic level, whether a cell is committed to mitosis is determined by solving a set of equations modeling the effects of the p27 gene control. The avascular morphological evolution of the solid tumor growth is simulated, including the radius of the solid tumor, the number of the TCs, the oxygen distribution over time, and the inhibiting effect of the up-regulating p27 gene expression.

Key words: binary fractal fibers, binary cell elements, regular binary fractals, multiplecell elements, regular multifractals, avascular, multi-scale, p27 gene, numerical simulation, continuous-discrete model, tumor growth