A nutrient-limited model for avascular cancer growth including cell proliferation, motility, and
death is presented. The model qualitatively reproduces commonly observed morphologies …

The desire to understand tumor complexity has given rise to mathematical models to
describe the tumor microenvironment. We present a new mathematical model for avascular …

We study solid tumor (carcinoma) growth in the nonlinear regime using boundary-integral
simulations. The tumor core is nonnecrotic and no inhibitor chemical species are present. A …

Scaling techniques were used to analyze the fractal nature of colonies of 15 cell lines
growing in vitro as well as of 16 types of tumor developing in vivo. All cell colonies were …

We present a physiologically structured lattice model for vascular tumor growth which
accounts for blood flow and structural adaptation of the vasculature, transport of oxygen …

The intracellular and extracellular dynamics that govern tumor growth and invasiveness in
vivo remain poorly understood. Cell genotype and phenotype, and nutrient, oxygen, and …

The structure and function of biological systems are considered to be closely related. The
present study addresses the question of how histological patterns of tumours are related to …

Competition for available nutrients is known to be crucial for cancer development. Based on
this fact, a model is proposed that can describe the manifold of morphologies and growth …

Tumor spheroids grown in vitro have been widely used as models of in vivo tumor growth
because they display many of the characteristics of in vivo growth, including the effects of …

In this paper, a mathematical model is presented to describe the evolution of an avascular
solid tumour in response to an externally-supplied nutrient. The growth of the tumour …