Towards predicting shear-banding instabilities in lipid monolayers.

Langmuir monolayers are advantageous systems used to investigate how lipid membranes get involved in the physiology of many living structures, such as collapse phenomena in alveolar structures. Much work focuses on characterizing the pressure-bearing capacity of Langmuir films, expressed in the form of isotherm curves. These show that monolayers experience different phases during compression with an according evolution of their mechanical response, incurring into instability events when a critical stress threshold is overcome. Although well-known state equations, which establish an inverse relationship between surface pressure and area change, are able to properly describe monolayer behaviour during liquid expanded phase, the modelling of their nonlinear behaviour in the subsequent condensed region is still an open issue. In this regard, most efforts are addressed to explain out-of-plane collapse by modelling buckling and wrinkling mainly resorting to linearly elastic plate theory. However, some experiments on Langmuir monolayers also show in-plane instability phenomena leading to the formation of the so-called shear bands and, to date, no theoretical description of the onset of shear banding bifurcation in monolayers has been yet provided. For this reason, by adopting a macroscopic description, we here study material stability of the lipid monolayers and exploit an incremental approach to find the conditions that kindle shear bands. In particular, by starting from the widely assumed hypothesis that monolayers behave elastically in the solid-like region, in this work a hyperfoam hyperelastic potential is introduced as a new constitutive strategy to trace back the nonlinear response of monolayer response during densification. In this way, the obtained mechanical properties together with the adopted strain energy are successfully employed to reproduce the onset of shear banding exhibited by some lipid systems under different chemical and thermal conditions.

Growth and in vivo stresses traced through tumor mechanics enriched with predator-prey cells dynamics.

Mechanical stress accumulating during growth in solid tumors plays a crucial role in the tumor mechanobiology. Stresses arise as a consequence of the spatially inhomogeneous tissue growth due to the different activity of healthy and cancer cells inhabiting the various districts of the tissue, an additional piling up effect, induced by stress transferring across the scales, contributing to determine the total stress occurring at the macroscopic level. The spatially inhomogeneous growth rates accompany nonuniform and time-propagating stress profiles, which constitute mechanical barriers to nutrient transport and influence the intratumoral interstitial flow, in this way deciding the starved/feeded regions, with direct aftereffects on necrosis, angiogenesis, cancer aggressiveness and overall tumor mass size. Despite their ascertained role in tumor mechanobiology, stresses cannot be directly appraised neither from overall tumor size nor through standard non-invasive measurements. To date, the sole way for qualitatively revealing their presence within solid tumors is ex vivo, by engraving the excised masses and then observing opening between the cut edges. Therefore, to contribute to unveil stresses and their implications in tumors, it is first proposed a multiscale model where Volterra-Lotka (predator/prey-like) equations describing the interspecific (environment-mediated) competitions among healthy and cancer cells are coupled with equations of nonlinear poroelasticity. Then, an experimental study on mice injected subcutaneously with a suspension of two different cancer cell lines (MiaPaCa-2 and MDA.MB231) was conducted to provide experimental evidences that gave qualitative and some new quantitative confirmations of the theoretical model predictions.