Related papers: Morphological stability for in silico models of av…
During the last decades, medical observations and multiscale data concerning tumor growth are mounting. At the same time, contemporary imaging techniques well established in clinical practice, provide a variety of information on real-time,…
We present a stochastic computational model of avascular tumors, emphasizing the detailed implementation of the first four so-called hallmarks of cancer: self-sufficiency in growth factors, resistance to growth inhibitors, avoidance of…
In the present article we demonstrate a new hybrid model of tumor growth. Our model is stochastic by tumor population development and strongly deterministic in cell motility dynamics and spatial propagation. In addition, it has excellent…
In this study, we model avascular tumour growth in epithelial tissue. This can help us to get a macroscopic view of the interaction between the tumour with its surrounding microenvironment and the physical changes within the tumour…
A nutrient-limited model for avascular cancer growth including cell proliferation, motility and death is presented. The model qualitatively reproduces commonly observed morphologies for primary tumors, and the simulated patterns are…
When modeling of tumor-driven angiogenesis, a major source of analytical and computational complexity is the strong coupling between the kinetic parameters of the relevant stochastic branching-and-growth of the capillary network, and the…
Adaptive therapy is a promising paradigm for treating cancers, that exploits competitive interactions between drug-sensitive and drug-resistant cells, thereby avoiding or delaying treatment failure due to evolution of drug resistance within…
Biological living systems in general exhibit complex and diverse dynamics. The latter, in particular, is essential, since diversification increases the odds of survival of an organism while reducing the risk of extinction of the population.…
To deal with permanent deformations and residual stresses, we consider a morphoelastic model for the scar formation as the result of wound healing after a skin trauma. Next to the mechanical components such as strain and displacements, the…
At present it is still quite difficult to match the vast knowledge on the behavior of individual tumor cells with macroscopic measurements on clinical tumors. On the modeling side, we already know how to deal with many molecular pathways…
Survival of living tumor cells underlies many influences such as nutrient saturation, oxygen level, drug concentrations or mechanical forces. Data-supported mathematical modeling can be a powerful tool to get a better understanding of cell…
We investigate avascular tumour growth as a two-phase process consisting of cells and liquid. Based on the one-dimensional continuum moving-boundary model formulated by (Byrne, King, McElwain, Preziosi, Applied Mathematics Letters, 2003,…
Strong experimental evidence has indicated that tumor growth belongs to the molecular beam epitaxy universality class. This type of growth is characterized by the constraint of cell proliferation to the tumor border, and surface diffusion…
In this survey article, a variety of systems modeling tumor growth are discussed. In accordance with the hallmarks of cancer, the described models incorporate the primary characteristics of cancer evolution. Specifically, we focus on…
We investigate the evolution of tumor growth relying on a nonlinear model of partial differential equations which incorporates mechanical laws for tissue compression combined with rules for nutrients availability and drug application.…
Solid tumours have the ability to assemble their own vascular network for optimizing their access to the vital nutrients. These new capillaries are morphologically different from normal physiological vessels. In particular, they have a much…
In the present article the diffusion equation is used to model the spatio-temporal dynamics of a tumor, taking into account the heterogeneous of the medium. This approach makes it possible to take into account the complex geometric shape of…
Survival models are used in various fields, such as the development of cancer treatment protocols. Although many statistical and machine learning models have been proposed to achieve accurate survival predictions, little attention has been…
Cancer is a very complex phenomenon that involves many different scales and situations. In this paper we consider a free boundary problem describing the evolution of a tumor colony and we derive a new asymptotic model for tumor growth. We…
Cancer is a disease of cellular regulation, often initiated by genetic mutation within cells, and leading to a heterogeneous cell population within tissues. In the competition for nutrients and growth space within the tumors the phenotype…