Related papers: On a nonlinear model for tumor growth in a cellula…
In this contribution, the non-local, integro-partial differential system of equations proposed by Hillen et al. (Bull. Math. Biol. 75, 2013, no.1, 161-184) to account for the the tumor growth paradox (or the observation that some incomplete…
Tumor growth from a single transformed cancer cell up to a clinically apparent mass spans many spatial and temporal orders of magnitude. Implementation of cellular automata simulations of such tumor growth can be straightforward but…
We analyze a phase field model for tumor growth consisting of a Cahn-Hilliard-Brinkman system, ruling the evolution of the tumor mass, coupled with an advection-reaction-diffusion equation for a chemical species acting as a nutrient. The…
At the continuous level, we consider two types of tumor growth models: the cell density model, which is based on the fluid mechanical construction, is more favorable for scientific interpretation and numerical simulations; and the free…
Background: Radiotherapy outcomes are usually predicted using the Linear Quadratic model. However, this model does not integrate complex features of tumor growth, in particular cell cycle regulation. Methods: In this paper, we propose a…
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 this work, we present a phase-field model for tumour growth, where a diffuse interface separates a tumour from the surrounding host tissue. In our model, we consider transport processes by an internal, non-solenoidal velocity field. We…
The mathematical modeling of tumor growth leads to singular stiff pressure law limits for porous medium equations with a source term. Such asymptotic problems give rise to free boundaries, which, in the absence of active motion, are…
Understanding how microenvironmental heterogeneity influences tumor progression is essential for advancing both cancer biology and therapeutic strategies. In this study, we develop a cellular automata (CA) model to simulate tumor growth…
A major goal of modern computational biology is to simulate the collective behaviour of large cell populations starting from the intricate web of molecular interactions occurring at the microscopic level. In this paper we describe a…
Mathematical modelling of tumor growth is one of the most useful and inexpensive approaches to determine and predict the stage, size and progression of tumors in realistic geometries. Moreover, these models has been used to get an insight…
Known as one of the hallmarks of cancer [30], cancer cell invasion of human body tissue is a complicated spatio-temporal multiscale process which enables a localised solid tumour to transform into a systemic, metastatic and fatal disease.…
Predictive modeling of the evolutionary dynamics of cancer is a challenge issue in computational cancer biology. In this paper, we propose a general mathematical model framework for the evolutionary dynamics of cancer with plasticity and…
We investigate a multiphase Cahn-Hilliard model for tumor growth with general source terms. The multiphase approach allows us to consider multiple cell types and multiple chemical species (oxygen and/or nutrients) that are consumed by the…
This paper deals with a nonlinear system of partial differential equations modeling a simplified tumor-induced angiogenesis taking into account only the interplay between tumor angiogenic factors and endothelial cells. Considered model…
A novel numerical technique has been proposed to solve a two-phase tumour growth model in one spatial dimension without needing to account for the boundary dynamics explicitly. The equivalence to the standard definition of a weak solution…
In this paper we study a tumor growth model with nutrients. The model presents dynamic patch solutions due to the contact inhibition among the tumor cells. We show that when the nutrients do not diffuse and the cells do not die, the tumor…
In this paper, we study a nonlinearly coupled initial-boundary value problem describing the evolution of brain tumor growth including lactate metabolism. In our modeling approach, we also take into account the viscoelastic properties of the…
A systematic understanding of the evolution and growth dynamics of invasive solid tumors in response to different chemotherapy strategies is crucial for the development of individually optimized oncotherapy. Here, we develop a hybrid…
Mathematical models that describe the tumor growth process have been formulated by several authors in order to understand how cancer develops and to develop new treatment approaches. In this study, it is aimed to investigate the long-time…