Publications

The structure and dynamics of important biological quasi-two-dimensional systems, ranging from cytoskeletal gels to tissues, are controlled by nematic order, flow, defects and activity. Continuum hydrodynamic descriptions combined with numerical simulations have been used to understand such complex systems. The development of thermodynamically consistent theories and numerical methods to model active nemato-hydrodynamics is eased by mathematical formalisms enabling systematic derivations and structured-preserving algorithms. Alternative to classical nonequilibrium thermodynamics and bracket formalisms, here we develop a theoretical and computational framework for active nematics based on Onsager's variational formalism to irreversible thermodynamics, according to which the dynamics result from the minimization of a Rayleighian functional capturing the competition between free-energy release, dissipation and activity. We show that two standard incompressible models of active nemato-hydrodynamics can be framed in the variational formalism, and develop a new compressible model for density-dependent active nemato-hydrodynamics relevant to model actomyosin gels. We show that the variational principle enables a direct and transparent derivation not only of the governing equations, but also of the finite element numerical scheme. We exercise this model in two representative examples of active nemato-hydrodynamics relevant to the actin cytoskeleton during wound healing and to the dynamics of confined colonies of elongated cells.

JTD Keywords: Active nematics, Bracket formulation, Equations, Finite element metho, Hydrodynamics, Instabilities, Model, Nematic defects, Onsager's variational formalism, Principle, Wound healing

[Figure: see text].

JTD Keywords: activation, cell extrusion, contraction, drives, homeostasis, interface, junctions, kinase, tension, Adhesion, Article, Cell membranes, Chemical activation, Cytology, E-cadherin, Epithelial monolayers, Epithelium, Homoeostasis, Human, Mechanical instabilities, Monolayers, Morphological transformations, Morphology, Normal tissue, Oncogenics, Soft substrates, Substrates, Tissue, Tissue mechanics, Tissue morphology, Tumor development

In this work, we study the mechanics of metamaterial sheets inspired by the pellicle of Euglenids. They are composed of interlocking elastic rods which can freely slide along their edges. We characterize the kinematics and the mechanics of these structures using the special Cosserat theory of rods and by assuming axisymmetric deformations of the tubular assembly. Through an asymptotic expansion, we investigate both structures that comprise a discrete number of rods and the limit case of a sheet composed by infinitely many rods. We apply our theoretical framework to investigate the stability of these structures in the presence of an axial load. Through a linear analysis, we compute the critical buckling force for both the discrete and the continuous case. For the latter, we also perform a numerical post-buckling analysis, studying the non-linear evolution of the bifurcation through finite elements simulations.

JTD Keywords: Biomimetic structures, Elastic structures, Helical rods, Mechanical instabilities, Metamaterials, Post-buckling analysis

Numerical studies of the intervertebral disc (IVD) are important to better understand the load transfer and the mechanobiological processes within the disc. Among the relevant calculations, fluid-related outputs are critical to describe and explore accurately the tissue properties. Porohyperelastic finite element models of IVD can describe accurately the disc behaviour at the organ level and allow the inclusion of fluid effects. However, results may be affected by numerical instabilities when fast load rates are applied. We hypothesized that such instabilities would appear preferentially at material discontinuities such as the annulus-nucleus boundary and should be considered when testing mesh convergence. A L4-L5 IVD model including the nucleus, annulus and cartilage endplates were tested under pure rotational loads, with different levels of mesh refinement. The effect of load relaxation and swelling were also studied. Simulations indicated that fluid velocity oscillations appeared due to numerical instability of the pore pressure spatial derivative at material discontinuities. Applying local refinement only was not enough to eliminate these oscillations. In fact, mesh refinements had to be local, material-dependent, and supplemented by the creation of a material transition zone, including interpolated material properties. Results also indicated that oscillations vanished along load relaxation, and faster attenuation occurred with the incorporation of the osmotic pressure. We concluded that material discontinuities are a major cause of instability for poromechanical calculations in multi-tissue models when load velocities are simulated. A strategy was presented to address these instabilities and recommendations on the use of IVD porohyperelastic models were given.

JTD Keywords: Fast loads, Intervertebral disc, Numerical instabilities, Poroelastic model