Metastatic tumours often invade healthy neighbouring tissues by forming multicellular finger-like protrusions emerging from the cancer mass. To understand the mechanical context behind this phenomenon, we here develop a minimalist fluid model of a self-propelled, growing biological tissue. The theory involves only four mechanical parameters and remains analytically trackable in various settings. As an application of the model, we study the evolution of a two-dimensional circular droplet made of our active and expanding fluid, and embedded in a passive non-growing tissue. This system could be used to model the evolution of a carcinoma in an epithelial layer. We find that our description can explain the propensity of tumour tissues to fingering instabilities, as conditioned by the magnitude of active traction and the growth kinetics. We are also able to derive predictions for the tumour size at the onset of metastasis, and for the number of subsequent invasive fingers. Our active fluid model may help describe a wider range of biological processes, including wound healing and developmental patterning.
We numerically study the translocation
dynamics of double emulsion
drops with multiple close-packed inner droplets within constrictions.
Such liquid architectures, which we refer to as HIPdEs (high-internal
phase double emulsions), consist of a ternary fluid, in which monodisperse
droplets are encapsulated within a larger drop in turn immersed in
a bulk fluid. Extensive two-dimensional lattice Boltzmann simulations
show that if the area fraction of the internal drops is close to the
packing fraction limit of hard spheres and the height of the channel
is much smaller than the typical size of the emulsion, the crossing
yields permanent shape deformations persistent over long periods of
time. Morphological changes and rheological response are quantitatively
assessed in terms of the structure of the velocity field, circularity
of the emulsion, and rate of energy dissipated by viscous forces.
Our results may be used to improve the design of soft mesoscale porous
materials, which employ HIPdEs as templates for tissue engineering
applications.
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