Related papers: Morphological instability of an invasive active-pa…
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…
We present an analogy between two unrelated instabilities. One is caused by the impact of a drop of water on a solid surface while the other one concerns a tumor that develops invasive cellular branches into the surrounding host tissue. In…
By analytically solving some simple models of phase-ordering kinetics, we suggest a mechanism for the onset of non-equilibrium behaviour in colloid-polymer mixtures. These mixtures can function as models of atomic systems; their physics…
Invasiveness, one of the hallmarks of tumor progression, represents the tumor's ability to expand into the host tissue by means of several complex biochemical and biomechanical processes. Since certain aspects of the problem present a…
In this paper, we develop a sharp interface tumor growth model in two dimensions to study the effect of both the intratumoral structure using a controlled necrotic core and the extratumoral nutrient supply from vasculature on tumor…
A phase-field approach describing the dynamics of a strained solid in contact with its melt is developed. By rigorous asymptotic analysis we show that the sharp-interface limit of this model recovers the continuum model equations for the…
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.…
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 linear stability of stratified two-phase flows in rectangular ducts is studied numerically. The linear stability analysis takes into account all possible infinitesimal three-dimensional disturbances and is carried out by solution of the…
The reactive-infiltration instability, which develops when a porous matrix is dissolved by a flowing fluid, contains two important length scales. Here we outline a linear stability analysis that simultaneously incorporates both scales. We…
Through modelling and simulations we show that material instabilities play a dominant role in the mechanical behavior of the fibrous collagen Extracellular Matrix (ECM), as observed when the ECM is deformed by contractile biological cells.…
This work focuses on the interfacial dynamics with interfacial mass flux in the presence of acceleration and surface tension. We employ the general matrix method to find the fundamental solutions for the linearized boundary value problem…
We study theoretically the shapes of biological tubes affected by various pathologies. When epithelial cells grow at an uncontrolled rate, the negative tension produced by their division provokes a buckling instability. Several shapes are…
Animal morphogenesis often involves significant shape changes of epithelial tissue sheets. Great progress has been made in understanding the underlying cellular driving forces and their coordination through biomechanical feedback loops.…
We study the influence of disorder strength on the interface roughening process in a phase-field model with locally conserved dynamics. We consider two cases where the mobility coefficient multiplying the locally conserved current is either…
We investigate the linear stability of a flat interface that separates a liquid layer from a fully-developed turbulent gas flow. In this context, linear-stability analysis involves the study of the dynamics of a small-amplitude wave on the…
Unstable dynamics characterizes the evolution of most solid tumors. Because of an increased failure of maintaining genome integrity, a cumulative increase in the levels of gene mutation and loss is observed. Previous work suggests that…
Cellularized tissue and polymer networks can both transition from floppy to rigid as a function of their control parameters, and, yet, the two systems often mechanically interact, which may affect their respective rigidities. To study this…
Two-dimensional Stokes flow with injection and suction is investigated through a second-order, perturbative mode-coupling approach. We examine the time-dependent disturbance of an initially circular interface separating two viscous fluids,…
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…