Related papers: Analyzing the Dynamic Relationship between Tumor G…
Most cancers in humans are large, measuring centimeters in diameter, composed of many billions of cells. An equivalent mass of normal cells would be highly heterogeneous as a result of the mutations that occur during each cell division.…
Due to over-metabolism, the tumour cells become hypoxic. To overcome this situation tumour cells secret several chemical substrates to attract nearby blood vessels towards it (angiogenesis). Transition from avascular to vascular tumour is…
Acidosis in tumors arises from reprogrammed metabolism and compromised vasculature, creating a harsh, acidic microenvironment that drives the evolutionary selection of acid-resistant cell phenotypes. A mathematical model is proposed to…
Currently, most of the basic mechanisms governing tumor-immune system interactions, in combination with modulations of tumor-associated vasculature, are far from being completely understood. Here, we propose a mathematical model of…
Cytotoxic chemotherapy is a common treatment for advanced prostate cancer. These tumors are also known to rely on angiogenesis, i.e., the growth of local microvasculature via chemical signaling produced by the tumor. Thus, several clinical…
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,…
In this work, we present and analyze a mathematical model for tumor growth incorporating ECM erosion, interstitial flow, and the effect of vascular flow and nutrient transport. The model is of phase-field or diffused-interface type in which…
The work presents a study of the non-linear mathematical model of tumor growth, proposed by Kolev and Zubik-Kowal (2011). The model is described by a system composed of four partial differential equations that represent the evolution of the…
In this paper, we consider a free boundary problem modeling the growth of spherically symmetric necrotic tumors with angiogenesis and a $\omega$-periodic supply $\phi(t)$ of external nutrients. In the model, the consumption rate of the…
We argue that volumetric growth dynamics of a solid cancer depend on the tumor system's overall surface extension. While this at first may seem evident, to our knowledge, so far no theoretical argument has been presented explaining this…
In this paper we present a study of local dynamics of the growth of cancer tumor and healthy cells considering the presence of nutrients in the system. We also analyze the evolution of system if we take indirectly into account the level of…
We have extended our previously developed 3D multi-scale agent-based brain tumor model to simulate cancer heterogeneity and to analyze its impact across the scales of interest. While our algorithm continues to employ an epidermal growth…
Hot spots in tumors are regions of high vascular density in the center of the tumor and their analysis is an important diagnostic tool in cancer treatment. We present a model for vascular remodeling in tumors predicting that the formation…
We consider a phase-field model of prostate cancer growth with chemotherapy and antiangiogenic therapy effects which is introduced in [2]. It is comprised of phase-field equation to describe tumor growth, which is coupled to a…
Tumor cells develop different features to adapt to environmental conditions. A prominent example is the ability of tumor cells to switch between migratory and proliferative phenotypes, a phenomenon known as go-or-grow mechanism. It is…
A model is proposed to study the process of hypoxia-induced angiogenesis in cancer cells. The model accounts for the role played by the vascular endothelial growth factor (VEGF)-A in regulating the oxygen intake. VEGF-A is dynamically…
The physics of solid tumor growth can be considered at three distinct size scales: the tumor scale, the cell-extracellular matrix (ECM) scale and the sub-cellular scale. In this paper we consider the tumor scale in the interest of…
We present a multiphase mathematical model for tumor growth which incorporates the remodeling of the extracellular matrix and describes the formation of fibrotic tissue by tumor cells. We also detail a full qualitative analysis of the…
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…
We consider a free boundary tumor model under the presence of angiogenesis and time delays in the process of proliferation, in which the cell location is incorporated. It is assumed that the tumor attracts blood vessels at a rate…