N. Nguyen2, N. Nath3, L. Deseri2, E. Tzeng3, S. Velankar2, L. Pocivavsek1 1University Of Chicago,Surgery,Chicago, IL, USA 2University Of Pittsburg,Engineering,Pittsburgh, PA, USA 3University Of Pittsburg,Surgery,Pittsburgh, PA, USA
Introduction: Wrinkling is a ubiquitous surface phenomenon in many biological tissues and is believed to play an important role in arterial health. Recent work of Pocivavsek et al. proposed that arterial luminal wrinkling is used as a mechanical anti-fouling mechanism in arteries. This topography driven surface renewal is the first model to propose and validate a structure-function mechanism for arterial wrinkles. As arteries are highly nonlinear, anisotropic, multilayered composite systems, it is necessary to investigate wrinkling incorporating these material characteristics.
Methods: Though several studies have examined surface wrinkling mechanisms with non-linear isotropic material relationships, wrinkling associated with anisotropic constitutive models such as Ogden-Gasser-Holzapfel (OGH), which has been widely employed for its capability of describing complex heterogeneous and fiber-reinforced aspects of soft biological tissues and in particular arteries, still requires investigation. Here, the effects of OGH parameters such as fibers’ orientation, stiffness, and dispersion on the critical onset of wrinkling, wrinkle wavelength and amplitude are elucidated through analysis of a bilayer system composed of a thin, stiff Neo-hookean membrane and a soft OGH substrate subjected to compression. Critical contractile strain at which wrinkles occur is predicted using both finite element analysis and analytical linear perturbation approach.
Results: Our data (see figure) suggest that beside stiffness mismatch, the traditional biomechanical parameter associated with wrinkling, anisotropic features associated with fiber stiffness and distribution might be used in natural layered systems to adjust and control wrinkling and subsequent folding behaviors. In general, the addition of fibers with even marginally larger moduli than the surrounding matrix, tends to increase the critical strain for wrinkling. Fibers oriented in the x-z plane have the weakest perturbation while fibers in the x-y plane the strongest. Further analysis of a bilayer system with fibers in the (x-y) plane subjected to compression in the x direction shows a complex dependence of critical wrinkling strain on fiber angle, stiffness and dispersion. This behavior is captured by an approximation utilizing the linearized anisotropic properties derived from OGH model.
Conclusion: We conclude that global fiber orientation has the strongest impact on the critical strain of wrinkle onset. Such understanding of wrinkling in this artery wall-like system will aid the process of answering the role of wrinkling mechanisms in biological artery in addition to the design of its synthetic counterparts.
