Abstract
We use the Glazier-Graner-Hogeweg model to simulate three-dimensional (3D), single-phenotype, avascular tumors growing in an homogeneous tissue matrix (TM) supplying a single limiting nutrient. We study the effects of two parameters on tumor morphology: a diffusion-limitation parameter defined as the ratio of the tumor-substrate consumption rate to the substrate-transport rate, and the tumor-TM surface tension. This initial model omits necrosis and oxidative/hypoxic metabolism effects, which can further influence tumor morphology, but our simplified model still shows significant parameter dependencies. The diffusion-limitation parameter determines whether the growing solid tumor develops a smooth (noninvasive) or fingered (invasive) interface, as in our earlier two-dimensional (2D) simulations. The sensitivity of 3D tumor morphology to tumor-TM surface tension increases with the size of the diffusion-limitation parameter, as in 2D. The 3D results are unexpectedly close to those in 2D. Our results therefore may justify using simpler 2D simulations of tumor growth, instead of more realistic but more computationally expensive 3D simulations. While geometrical artifacts mean that 2D sections of connected 3D tumors may be disconnected, the morphologies of 3D simulated tumors nevertheless correlate with the morphologies of their 2D sections, especially for low-surface-tension tumors, allowing the use of 2D sections to partially reconstruct medically-important 3D-tumor structures.
Highlights
In [1] we studied the effects of nutrient limitation and surface tension in a simplified two-dimensional (2D) model of tumor invasion using the Glazier-Graner-Hogeweg (GGH) [2,3,4], as implemented in the CompuCell3D (CC3D) modeling environment [5,6,7,8,9,10]
Since we focus on the role of cell-cell adhesion and competition for nutrients at the tumor-TM interface where the tumor cells are alive and proliferating, as in [1], we simulate singlecell-type avascular tumors without angiogenesis, omitting necrotic and quiescent cells, which are absent at the tumor-TM interface during early stages of fingering
We show that the diffusion-limitation parameter G determines whether the 3D tumor has a uniform or fingered margin, while the tumor-TM surface tension c affects the detailed tumor morphology, as in 2D
Summary
In [1] we studied the effects of nutrient limitation and surface tension in a simplified two-dimensional (2D) model of tumor invasion using the Glazier-Graner-Hogeweg (GGH) ( known as the Cellular Potts Model) [2,3,4], as implemented in the CompuCell3D (CC3D) modeling environment [5,6,7,8,9,10]. In 2D, the selection of smooth-interface (noninvasive) vs fingered (invasive) growth depends on the tumor’s substrate-consumption rate per unit substrate-transport rate, the diffusion-limitation parameter G, while the detailed morphology depends on the tumor-tissuematrix (TM) surface tension c. Low concentrations of nutrients in the environment which cause tumor-cell competition, or cells with a very high substrate-consumption rate generate a fingering instability and irregular, invasive tumors. Our three-dimensional (3D) model extension of our 2D model [1], includes growing, spatially-extended tumor cells, surrounding TM represented as a nondiffusing field secreting nutrients, a diffusing field representing matrix-degrading enzymes (MDEs) that degrade TM, and a diffusing nutrient field (substrate) which governs the rate of tumor-cell growth. As in our 2D model we assume that all tumor cells are identical in their capacities and responses, and that the specific growth rate of tumor cells increases linearly with the local concentration of a single limiting substrate, with no concentration threshold for tumor cells to grow
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