RESUMEN

In this work, we present a mathematical model of cell growth in the pores of a perfusion bioreactor through which a nutrient solution is pumped. We have developed a 2-D vertex model that allows us to reproduce the microscopic dynamics of the microenvironment of cells and describe the occupation of the pore space with cells. In this model, each cell is represented by a polygon; the number of vertices and shapes may change over time. The model includes mitotic cell division and intercalation. We study the impact of two factors on cell growth. On the one hand, we consider a channel of variable cross-section, which models a scaffold with a porosity gradient. On the other hand, a cluster of cells grows under the influence of a nutrient solution flow, which establishes a non-uniform distribution of shear stresses in the pore space. We present the results of numerical simulation of the tissue growth in a wavy channel. The model allows us to obtain complete microscopic information that includes the dynamics of intracellular pressure, the local elastic energy, and the characteristics of cell populations. As we showed, in a functional-graded scaffold, the distribution of the shear stresses in the pore space has a complicated structure, which implies the possibility of controlling the growth zones by varying the pore geometry.

RESUMEN

This article provides the results of a theoretical and experimental study of buoyancy-driven instabilities triggered by a neutralization reaction in an immiscible two-layer system placed in a vertical Hele-Shaw cell. Flow patterns are predicted by a reaction-induced buoyancy number [Formula: see text], which we define as the ratio of densities of the reaction zone and the lower layer. In experiments, we observed the development of cellular convection ([Formula: see text]), the fingering process with an aligned line of fingertips at a slightly denser reaction zone ([Formula: see text]) and the typical Rayleigh-Taylor convection for [Formula: see text]. A mathematical model includes a set of reaction-diffusion-convection equations written in the Hele-Shaw approximation. The model's novelty is that it accounts for the water produced during the reaction, a commonly neglected effect. The persisting regularity of the fingering during the collapse of the reaction zone is explained by the dynamic release of water, which compensates for the heavy fluid falling and stabilizes the pattern. Finally, we present a stability map on the plane of the initial concentrations of solutions. Good agreement between the experimental data and theoretical results is observed. This article is part of the theme issue 'New trends in pattern formation and nonlinear dynamics of extended systems'.

RESUMEN

According to recent studies, cancer is an evolving complex ecosystem. It means that tumor cells are well differentiated and involved in heterotypic interactions with their microenvironment competing for available resources to proliferate and survive. In this paper, we propose a chemo-mechanical model for the growth of specific subtypes of an invasive breast carcinoma. The model suggests that a carcinoma is a heterogeneous entity comprising cells of different phenotypes, which perform different functions in a tumor. Every cell is represented by an elastic polygon changing its form and size under pressure from the tissue. The mechanical model is based on the elastic potential energy of the tissue including the effects of contractile forces within the cell perimeter and the elastic resistance to stretching or compressing the cell with respect to the reference area. A tissue can evolve via mechanisms of cell division and intercalation. The phenotype of each cell is determined by its environment and can dynamically change via an epithelial-mesenchymal transition and vice versa. The phenotype defines the cell adhesion to the adjacent tissue and the ability to divide. In this part, we focus on the forms of collective migration of large groups of cells. Numerical simulations show the different architectural subtypes of invasive carcinoma. For each communication, we examine the dynamics of the cell population and evaluate the complexity of the pattern in terms of the synergistic paradigm. The patterns are compared with the morphological structures previously identified in clinical studies.

Asunto(s)

Neoplasias de la Mama/patología , Movimiento Celular , Modelos Biológicos , Fenómenos Biomecánicos , Recuento de Células , División Celular , Proliferación Celular , Simulación por Computador , Epitelio/patología , Femenino , Humanos , Invasividad Neoplásica , Análisis Numérico Asistido por Computador , Fenotipo , Células del Estroma/patología

RESUMEN

We present a theoretical study on pattern formation occurring in miscible fluids reacting by a second-order reaction A+B→C in a vertical Hele-Shaw cell under constant gravity. We have recently reported that the concentration-dependent diffusion of species coupled with a frontal neutralization reaction can produce a multilayer system where low-density depleted zones could be embedded between the denser layers. This leads to the excitation of chemoconvective modes spatially separated from each other by a motionless fluid. In this Rapid Communication, we show that the layers can interact via a diffusion mechanism. Since diffusively coupled instabilities initially have different wavelengths, this causes a long-wave modulation of one pattern by another. We have developed a mathematical model which includes a system of reaction-diffusion-convection equations. The linear stability of a transient base state is studied by calculating the growth rate of the Lyapunov exponent for each unstable layer. Numerical simulations supported by phase portrait reconstruction and Fourier spectra calculation have revealed that nonlinear dynamics consistently passes through (i) a perfect spatially periodic system of chemoconvective cells, (ii) a quasiperiodic system of the same cells, and (iii) a disordered fingering structure. We show that in this system, the coordinate codirected to the reaction front paradoxically plays the role of time, time itself acts as a bifurcation parameter, and a complete spatial analog of the two-frequency torus breakup is observed.

RESUMEN

Continuous-flow microreactors are an important development in chemical engineering technology, since pharmaceutical production needs flexibility in reconfiguring the synthesis system rather than large volumes of product yield. Microreactors of this type have a special vessel, in which the convective vortices are organized to mix the reagents to increase the product output. We propose a new type of micromixer based on the intensive relaxation oscillations induced by a fundamental effect discovered recently. The mechanism of these oscillations was found to be a coupling of the solutal Marangoni effect, buoyancy and diffusion. The phenomenon can be observed in the vicinity of an air⁻liquid (or liquid⁻liquid) interface with inhomogeneous concentration of a surface-active solute. Important features of the oscillations are demonstrated experimentally and numerically. The periodicity of the oscillations is a result of the repeated regeneration of the Marangoni driving force. This feature is used in our design of a micromixer with a single air bubble inside the reaction zone. We show that the micromixer does not consume external energy and adapts to the medium state due to feedback. It switches on automatically each time when a concentration inhomogeneity in the reaction zone occurs, and stops mixing when the solution becomes sufficiently uniform.

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We consider the effect of a partially contaminated interface on the steady thermocapillary flow developed in a two-dimensional slot of finite extent. The contamination is due to the presence of an insoluble surfactant which is carried away by the flow and forms a region of stagnant surface. This problem, first studied in the classical theoretical paper by Carpenter and Homsy (1985, J. Fluid Mech. 155, 429), is revisited thanks to new experimental data. We show that there is a qualitative agreement between above theory and our experiments: two different regions simultaneously coexist on the surface, one of which is free from surfactant and subject to vigorous Marangoni flow, while the other is stagnant and subject to creeping flow with the surface velocity smaller about two orders of magnitude. We found, however, significant disagreement between theory predictions for the extent of a stagnant surface region and newly obtained experimental data. In this paper, we provide an explanation for this discrepancy demonstrating that the surface temperature distribution is far from suggested earlier. Another effect, not previously taken into account, is a possible phase transition experienced by the surfactant. We obtain a correct analytic solution for the position of the edge of the stagnation zone and compare it with the experimental data.

RESUMEN

We report shock-wave-like structures that are strikingly different from previously observed fingering instabilities, which occur in a two-layer system of miscible fluids reacting by a second-order reaction A+B→S in a vertical Hele-Shaw cell. While the traditional analysis expects the occurrence of a diffusion-controlled convection, we show both experimentally and theoretically that the exothermic neutralization reaction can also trigger a wave with a perfectly planar front and nearly discontinuous change in density across the front. This wave propagates fast compared with the characteristic diffusion times and separates the motionless fluid and the area with anomalously intense convective mixing. We explain its mechanism and introduce a new dimensionless parameter, which allows to predict the appearance of such a pattern in other systems. Moreover, we show that our governing equations, taken in the inviscid limit, are formally analogous to well-known shallow-water equations and adiabatic gas flow equations. Based on this analogy, we define the critical velocity for the onset of the shock wave which is found to be in the perfect agreement with the experiments.

RESUMEN

We report on chemoconvective pattern formation phenomena observed in a two-layer system of miscible fluids filling a vertical Hele-Shaw cell. We show both experimentally and theoretically that the concentration-dependent diffusion coupled with frontal acid-base neutralization can give rise to the formation of a local unstable zone low in density, resulting in a perfectly regular cell-type convective pattern. The described effect gives an example of yet another powerful mechanism which allows the reaction-diffusion processes to govern the flow of reacting fluids under gravity conditions.