Related papers: Fingering instabilities in tissue invasion: an act…
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…
We present a two-dimensional continuum model of tumor growth, which treats the tissue as a composition of six distinct fluid phases; their dynamics are governed by the equations of mass and momentum conservation. Our model divides the…
Interfaces between stratified epithelia and their supporting stromas commonly exhibit irregular shapes. Undulations are particularly pronounced in dysplastic tissues and typically evolve into long, finger-like protrusions in carcinomas. In…
The displacement of a more viscous fluid by a less viscous one in a quasi-two dimensional geometry leads to the formation of complex fingering patterns. This fingering has been characterized by a most unstable wavelength, $\lambda_c$, which…
Understanding tumor invasion and metastasis is of crucial importance for both fundamental cancer research and clinical practice. In vitro experiments have established that the invasive growth of malignant tumors is characterized by the…
In this paper, we develop a sharp interface tumor growth model to study the effect of the tumor microenvironment using a complex far-field geometry that mimics a heterogeneous distribution of vasculature. Together with different nutrient…
Motivated by studies suggesting that the patterns exhibited by the collectively expanding fronts of thin cells during the closing of a wound [Mark et al., Biophys. J., 98:361-370, 2010] and the shapes of single cells crawling on surfaces…
The aim of this paper is to investigate the asymptotic behavior of a biphase tumor fluid flow derived by 2-scale homogenisation techniques in recent works. This biphase fluid flow model accounts for the capillary wall permeability, and the…
Motivated by experimental observations, we develop a mathematical model of chemotactically directed tumor growth. We present an analytical study of the model as well as a numerical one. The mathematical analysis shows that: (i) tumor cell…
This study proposes and explores a linear hydrodynamic thermo-elasticity system within mixture models, comprising fluid and solid phases, with a focus on biological tissues, particularly tumor-related phenomena. Although tumor growth is not…
We present in this paper an experimental study of the invasion activity during unstable drainage in a 2D random porous medium, when the (wetting) displaced fluid has a high viscosity with respect to that of the (non-wetting) displacing…
The invasion of one fluid into another of higher viscosity in a quasi-two dimensional geometry typically produces complex fingering patterns. Because interfacial tension suppresses short-wavelength fluctuations, its elimination by using…
Interstitial fluid flow is a feature of many solid tumours. In vitro Experiments have shown that such fluid flow can direct tumour cell movement upstream or downstream depending on the balance between the competing mechanisms of tensotaxis…
When a liquid viscous bridge between two parallel substrates is stretched by accelerating one substrate, its interface recedes in the radial direction. In some cases the interface becomes unstable. Such instability leads to the emergence of…
We develop a computational method for simulating the nonlinear dynamics of an elastic tumor-host interface. This work is motivated by the recent linear stability analysis of a two-phase tumor model with an elastic membrane interface in 2D.…
The process of one fluid pushing another is universally common while involving complex interfacial instabilities. Particularly, occurring in a myriad of natural and industrial processes, wavy fingering patterns frequently emerge when a less…
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…
Viscous fingering patterns can form at the interface between two immiscible fluids confined in the gap between a pair of flat plates; whenever the fluid with lower viscosity displaces the one of higher viscosity the interface is unstable.…
A rest fluid displaced by a less viscous fluid in a porous medium triggers the so-called Saffman-Taylor instability at their contact front and hence forms complicated finger-like patterns. When the two fluids are miscible, the surface…
In this work, we present a coupled 3D-1D model of solid tumor growth within a dynamically changing vascular network to facilitate realistic simulations of angiogenesis. Additionally, the model includes erosion of the extracellular matrix,…