Wrinkling instabilities for biologically relevant fiber-reinforced composite materials with a case study of Neo-Hookean/Ogden-Gasser-Holzapfel bilayer

Axonal tension contributes to consistent fold placement

Cortical folding is a critical process during brain development, resulting in morphologies that are both consistent and distinct between individuals and species. While earlier studies have highlighted important aspects of cortical folding, most existing computational models, based on the differential growth theory, fall short of explaining why folds tend to appear in particular locations. The axon tension hypothesis may provide insight into this conundrum; however, there has been significant controversy about a potential role of axonal tension during the gyrification. The common opinion in the field is that axonal tension is inadequate to drive gyrification, but we currently run the risk of discarding this hypothesis without comprehensively studying the role of axonal tension. Here we propose a novel bi-layered finite element model incorporating the two theories, including characteristic axonal tension in the subcortex and differential cortical growth. We show that axon tension can serve as a perturbation sufficient to trigger buckling in simulations; similarly to other types of perturbations, the natural stability behavior of the system tends to determine some characteristics of the folding morphology (e.g. the wavelength) while the perturbation determines the location of folds. Certain geometries, however, can interact or compete with the natural stability of the system to change the wavelength. When multiple perturbations are present, they similarly compete with each other. We found that an axon bundle of reasonable size will overpower up to a 5% thickness perturbation (typical in the literature) and determine fold placement. Finally, when multiple axon tracts are present, even a slight difference in axon stiffness, representing the heterogeneity of axonal connections, is enough to significantly change the folding pattern. While the simulations presented here are a very simple representation of white matter connectivity, our findings point to urgent future research on the role of axon connectivity in cortical folding.

Topographic de-adhesion in the viscoelastic limit

The superiority of many natural surfaces at resisting soft, sticky biofoulants have inspired the integration of dynamic topography with mechanical instability to promote self-cleaning artificial surfaces. The physics behind this novel mechanism is currently limited to elastic biofoulants where surface energy, bending stiffness and topographical wavelength are key factors. However, the viscoelastic nature of many biofoulants causes a complex interplay between these factors with time-dependent characteristics such as material softening and loading rate. Here, we enrich the current elastic theory of topographic de-adhesion using analytical and finite-element models to elucidate the nonlinear, time-dependent interaction of three physical, dimensionless parameters: biofoulant's stiffness reduction, the product of relaxation time and loading rate, and the critical strain for short-term elastic de-adhesion. Theoretical predictions, in good agreement with numerical simulations, provide insight into tuning these control parameters to optimize surface renewal via topographic de-adhesion in the viscoelastic regime.

Dynamic Luminal Topography: A Potential Strategy to Prevent Vascular Graft Thrombosis

Aim

Biologic interfaces play important roles in tissue function. The vascular lumen-blood interface represents a surface where dynamic interactions between the endothelium and circulating blood cells are critical in preventing thrombosis. The arterial lumen possesses a uniform wrinkled surface determined by the underlying internal elastic lamina. The function of this structure is not known, but computational analyses of artificial surfaces with dynamic topography, oscillating between smooth and wrinkled configurations, support the ability of this surface structure to shed adherent material (Genzer and Groenewold, 2006; Bixler and Bhushan, 2012; Li et al., 2014). We hypothesized that incorporating a luminal surface capable of cyclical wrinkling/flattening during the cardiac cycle into vascular graft technology may represent a novel mechanism of resisting platelet adhesion and thrombosis.

Methods and Results

Bilayer silicone grafts possessing luminal corrugations that cyclically wrinkle and flatten during pulsatile flow were fabricated based on material strain mismatch. When placed into a pulsatile flow circuit with activated platelets, these grafts exhibited significantly reduced platelet deposition compared to grafts with smooth luminal surfaces. Constrained wrinkled grafts with static topography during pulsatile flow were more susceptible to platelet accumulation than dynamic wrinkled grafts and behaved similar to the smooth grafts under pulsatile flow. Wrinkled grafts under continuous flow conditions also exhibited marked increases in platelet accumulation.

Conclusion

These findings provide evidence that grafts with dynamic luminal topography resist platelet accumulation and support the application of this structure in vascular graft technology to improve the performance of prosthetic grafts. They also suggest that this corrugated structure in arteries may represent an inherent, self-cleaning mechanism in the vasculature.

Delamination of open cylindrical shells from soft and adhesive Winkler's foundation

The interaction between thin elastic films and soft-adhesive foundations has recently gained interest due to technological applications that require control over such objects. Motivated by these applications we investigate the equilibrium configuration of an open cylindrical shell with natural curvature κ and bending modulus B that is adhered to soft and adhesive foundation with stiffness K. We derive an analytical model that predicts the delamination criterion, i.e., the critical natural curvature, κ_{cr}, at which delamination first occurs, and the ultimate shape of the shell. While in the case of a rigid foundation, K→∞, our model recovers the known two-states solution at which the shell either remains completely attached to the substrate or completely detaches from it, on a soft foundation our model predicts the emergence of a new branch of solutions. This branch corresponds to partially adhered shells, where the contact zone between the shell and the substrate is finite and scales as ℓ_{w}∼(B/K)^{1/4}. In addition, we find that the criterion for delamination depends on the total length of the shell along the curved direction, L. While relatively short shells, L∼ℓ_{w}, transform continuously between adhered and delaminated solutions, long shells, L≫ℓ_{w}, transform discontinuously. Notably, our work provides insights into the detachment phenomena of thin elastic sheets from soft and adhesive foundations.