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\emph{In vitro} experiments in which tumour cells are seeded in a gelatinous medium, or hydrogel, show how mechanical interactions between tumour cells and the tissue in which they are embedded, together with local levels of an…
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…
Tumor growth has a number of features in common with a physical process known as molecular beam epitaxy. Both growth processes are characterized by the constraint of growth development to the body border, and surface diffusion of…
Employing a novel two-dimensional computational model we have simulated the feedback between angiogenesis and tumor growth dynamics. Analyzing vessel formation and elongation towards the concentration gradient of the tumor-derived…
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…
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…
Various models of tumor growth are available in the litterature. A first class describes the evolution of the cell number density when considered as a continuous visco-elastic material with growth. A second class, describes the tumor as a…
Complex tumor-host interactions can significantly affect the growth dynamics and morphologies of progressing neoplasms. The growth of a confined solid tumor induces mechanical pressure and deformation of the surrounding microenvironment,…
One of the hallmarks of pre-migratory tumors is the progressive loss of compact morphology. To investigate how tumors may intrinsically regulate their shape during growth, we employ a three-dimensional (3D) vertex model of multicellular…
The problem of the onset and growth of solid tumour in homogeneous tissue is regarded using an approach based on local interaction between the tumoral and the sane tissue cells. The characteristic sizes and growth rates of spherical…
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…
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…
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…
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…
In this paper a macroscopic model of tumor cord growth is developed, relying on the mathematical theory of deformable porous media. Tumor is modeled as a saturated mixture of proliferating cells, extracellular fluid and extracellular…
Cells are dynamic systems characterized by temporal variations in biophysical properties such as stiffness and contractility. Recent studies show that the recruitment and release of actin filaments into and out of the cell cortex - a…
Several experiments have demonstrated the existence of an electro-mechanical effect in many biological tissues and hydrogels, and its actual influence on growth, migration, and pattern formation. Here, to model these interactions and…
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 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…
Growing experimental evidence highlights the relevant role of mechanics in the physiology of solid tumours, even in their early stages. While most of the mathematical models describe tumour growth as a volumetric increase of mass in the…