Front Instabilities and Invasiveness of Simulated Avascular Tumors

Abstract

We study the interface morphology of a 2D simulation of an avascular tumor composed of identical cells growing in an homogeneous healthy tissue matrix (TM), in order to understand the origin of the morphological changes often observed during real tumor growth. We use the GlazierGranerHogeweg model, which treats tumor cells as extended, deformable objects, to study the effects of two parameters: a dimensionless diffusion-limitation parameter defined as the ratio of the tumor consumption rate to the substrate transport rate, and the tumor-TM surface tension. We model TM as a nondiffusing field, neglecting the TM pressure and haptotactic repulsion acting on a real growing tumor; thus our model is appropriate for studying tumors with highly motile cells, e.g., gliomas. We show that the diffusion-limitation parameter determines whether the growing tumor develops a smooth (noninvasive) or fingered (invasive) interface, and that the sensitivity of tumor morphology to tumor-TM surface tension increases with the size of the dimensionless diffusion-limitation parameter. For large diffusion-limitation parameters we find a transition (missed in previous work) between dendritic structures, produced when tumor-TM surface tension is high, and seaweed-like structures, produced when tumor-TM surface tension is low. This observation leads to a direct analogy between the mathematics and dynamics of tumors and those observed in nonbiological directional solidification. Our results are also consistent with biological observation that hypoxia promotes invasive growth of tumor cells by inducing higher levels of receptors for scatter factors that weaken cell-cell adhesion and increase cell motility. These findings suggest that tumor

Curvature-Dependent Elastic Properties of Liquid-Ordered Domains Result in Inverted Domain Sorting on Uniaxially Compressed Vesicles

“…For e ¼ 0, i.e., no attraction between cells, T ¼ 0 and the tumor front is always stable as found in the long-wavelength limit and various tumor models [17,26]. In the more realistic radial case, a necrotic core develops quickly, all the proliferative activity being confined in a ring of quasiconstant width l with a radius RðtÞ growing linearly in time (dR=dt ¼ _ R ¼ U) as observed in vivo [16] [ Fig.…”

The impact of adhesion on cellular invasion processes in cancer and development

“…Direct representations of adhesion were first considered in the context of individual cell-based models (Turner & Sherratt 2002;Turner et al 2004;Grygierzec et al 2004). In recent years, this modelling approach has been developed significantly by Anderson and coworkers, in a series of sophisticated studies into the ways in which changes in cell-cell and cell-5 A c c e p t e d m a n u s c r i p t matrix adhesion interact with other aspects of the invasive phenotype (Anderson et al 2006Ramis-Conde et al 2008;Poplawski et al 2009). …”

The influence of soluble fragments of extracellular matrix (ECM) on tumor growth and morphology

“…For nutrient-poor tumor growth, increasing adhesion can limit the rate of tumor fragmentation and the extent of tissue invasion [17]. Morphological instabilities were observed for nutrient-poor tumor growth, with the degree of instability increasing greatly with decreasing surface tension [23]. The fingering tumor cell population generally have low cell adhesion and oxygen consumption rates [32] and are observed for a combination of the strength of cell-cell adhesion and haptotaxis [33].…”

“…Instability provides a mechanism for tumor invasion that does not require development of a neovasculature to supply essential nutrients. Poplawski et al [23,24] demonstrated that the development of instability depends primarily on the diffusional limitation parameter (ratio of tumor growth rate to diffusion rate of nutrients) while the morphological details depend on cell-cell adhesion. The lack of competition for nutrients (high nutrient environment) promotes spherical, noninvasive tumors.…”