Related papers: Minimal Morphoelastic Models of Solid Tumour Spher…
The precise role of the microenvironment on tumor growth is poorly understood. Whereas the tumor is in constant competition with the surrounding tissue, little is known about the mechanics of this interaction. Using a novel experimental…
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…
The speed and the versatility of today's computers open up new opportunities to simulate complex biological systems. Here we review a computational approach recently proposed by us to model large tumor cell populations and spheroids, and we…
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…
It is widely recognized that reciprocal interactions between cells and their microenvironment, via mechanical forces and biochemical signaling pathways, regulate cell behaviors during normal development, homeostasis and disease progression…
Multicellular tumor spheroids are an important {\it in vitro} model of the pre-vascular phase of solid tumors, for sizes well below the diagnostic limit: therefore a biophysical model of spheroids has the ability to shed light on the…
The inverse geometric approach to the modeling of the growth of circular objects revealing required features, such as the velocity of the growth and fractal behavior of their contours, is presented. It enables to reproduce some of the…
The mechanism by which cells measure the dimension of the organ in which they are embedded, and slow down their growth when the final size is reached, is a long-standing problem of developmental biology. The role of mechanics in this…
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 research has shifted from a purely gene-centric view to a more holistic understanding that recognizes the critical role of the tumour microenvironment, where mechanics and metabolism are key drivers of disease progression. However,…
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,…
Collective cell movement, characterized by multiple cells that are in contact for substantial periods of time and undergo correlated motion, plays a central role in cancer and embryogenesis. Recent imaging experiments have provided…
The internal and external mechanical environment plays an important role in tumorogenesis. As a proxy of an avascular early state tumor, we use multicellular spheroids, a composite material made of cells, extracellular matrix and permeating…
The mechanical behaviour of solid biological tissues has long been described using models based on classical continuum mechanics. However, the classical continuum theories of elasticity and viscoelasticity cannot easily capture the…
Most organisms grow according to simple laws, which in principle can be derived from energy conservation and scaling arguments, critically dependent on the relation between the metabolic rate B of energy flow and the organism mass m.…
A three-dimensional cell culture called a spheroid serves as a foundational entity in a wide variety of modern tissue engineering applications, including 3D-bioprinting and preclinical drug testing. Lack of oxygen within tissue spheroids…
Clinically, palpation is one of the important diagnostic methods to assess tumor malignancy. In laboratory research, it is well accepted that the bulk stiffness of the tumor and the surrounding tissue is closely correlated with the…
Uncontrolled growth of tumor cells in confined spaces leads to the accumulation of compressive stress within the tumor. Although the effects of tension within 3D extracellular matrices on tumor growth and invasion are well established, the…
Using formal asymptotic methods we derive a free boundary problem representing one of the simplest mathematical descriptions of the growth and death of a tumour or other biological tissue. The mathematical model takes the form of a closed…
Mathematical modeling in cancer has been growing in popularity and impact since its inception in 1932. The first theoretical mathematical modeling in cancer research was focused on understanding tumor growth laws and has grown to include…