Front and domain growth in the presence of gravity

Modelling of chemotactic sprouting endothelial cells through an extracellular matrix

Sprouting angiogenesis is a core biological process critical to vascular development. Its accurate simulation, relevant to multiple facets of human health, is of broad, interdisciplinary appeal. This study presents an in-silico model replicating a microfluidic assay where endothelial cells sprout into a biomimetic extracellular matrix, specifically, a large-pore, low-concentration fibrin-based porous hydrogel, influenced by chemotactic factors. We introduce a novel approach by incorporating the extracellular matrix and chemotactic factor effects into a unified term using a single parameter, primarily focusing on modelling sprouting dynamics and morphology. This continuous model naturally describes chemotactic-induced sprouting with no need for additional rules. In addition, we extended our base model to account for matrix sensing and degradation, crucial aspects of angiogenesis. We validate our model via a hybrid in-silico experimental method, comparing the model predictions with experimental results derived from the microfluidic setup. Our results underscore the intricate relationship between the extracellular matrix structure and angiogenic sprouting, proposing a promising method for predicting the influence of the extracellular matrix on angiogenesis.

Stochastic phase segregation on surfaces

Phase separation and coarsening is a phenomenon commonly seen in binary physical and chemical systems that occur in nature. Often, thermal fluctuations, modelled as stochastic noise, are present in the system and the phase segregation process occurs on a surface. In this work, the segregation process is modelled via the Cahn-Hilliard-Cook model, which is a fourth-order parabolic stochastic system. Coarsening is analysed on two sample surfaces: a unit sphere and a dumbbell. On both surfaces, a statistical analysis of the growth rate is performed, and the influence of noise level and mobility is also investigated. For the spherical interface, it is also shown that a lognormal distribution fits the growth rate well.

Oscillatory instabilities in phase separation of binary mixtures: Fixing the thermodynamic driving

Binary liquid mixtures can show pronounced oscillations in the differential scanning calorimeter signal for the specific heat and in the turbidity when phase separation is induced by continuously ramping the temperature. For a fixed ramp rate, i.e., a linear temporal drift of temperature, only a small number of oscillations have been observed. In the present manuscript we describe an experimental setup where simultaneous video-microscopy and shadow-graph measurements can be performed on mixtures subjected to an arbitrary temporal temperature evolution. In particular, it can be adjusted to fix the thermodynamic driving force, which characterizes the rate of change of the composition of the coexisting phases. With this novel technique both the number of oscillations and the temperature interval where oscillations are observed increase significantly. This technique can easily be applied to a great variety of binary mixtures, permitting detailed investigations of their phase-separation kinetics under slowly ramping temperature.

Phase separation in the presence of spatially periodic forcing

We have investigated theoretically phase separation in the presence of spatially periodic forcing. From the analytic and numeric study of a suitably generalized Cahn-Hilliard equation in one and two dimensions, we find that the forcing amplitude necessary to generate a periodic kink-type state from small random initial conditions depends weakly on wave number. This amplitude is much larger than the one necessary to stabilize the periodic state, i.e., to prevent late-stage coarsening, once it is established. Surprisingly, the destabilizing mode is of long-wave type, which is in contrast to the well-known most rapidly growing coarsening mode in the unforced system. In the Allen-Cahn equation with nonconserved order parameter the relevant modes are always long wave. It appears feasible to observe these effects by imposing a temperature modulation by optical grating which then couples to concentration modulation via the (Ludwig-)Soret effect.

Filler-induced composition waves in phase-separating polymer blends

The influence of immobile filler particles (spheres, fibers, platelets) on polymer-blend phase separation is investigated computationally using a generalization of the Cahn-Hilliard-Cook (CHC) model. Simulation shows that the selective affinity of one of the polymers for the filler surface leads to the development of concentration waves about the filler particles at an early stage of phase separation in near critical composition blends. These "target" patterns are overtaken in late-stage phase separation by a growing "background" spinodal pattern characteristic of blends without filler particles. The linearized CHC model is used to estimate the number of composition oscillations emanating from isolated filler particles. In far-off-critical composition blends, an "encapsulation layer" grows at the surface of the filler rather than a target pattern. The results of these simulations compare favorably with experiments on filled phase-separating ultrathin blend films in which the filler particles are immobilized on a solid substrate.