Buckling instability in arteries.

Arteries can become tortuous in response to abnormal growth stimuli, genetic defects and aging. It is suggested that a buckling instability is a mechanism that might lead to artery tortuosity. Here, the buckling instability in arteries is studied by examining asymmetric modes of bifurcation of two-layer cylindrical structures that are residually stressed. These structures are loaded by an axial force, internal pressure and have nonlinear, anisotropic, hyperelastic responses to stresses. Strain-softening and reduced opening angle are shown to lower the critical internal pressure leading to buckling. In addition, the ratio of the media thickness to the adventitia thickness is shown to have a dramatic impact on arterial instability.

Effect of residual stress on peak cap stress in arteries.

Vulnerable plaques are a subset of atherosclerotic plaques that are prone to rupture when high stresses occur in the cap. The roles of residual stress, plaque morphology, and cap stiffness on the cap stress are not completely understood. Here, arteries are modeled within the framework of nonlinear elasticity as incompressible cylindrical structures that are residually stressed through differential growth. These structures are assumed to have a nonlinear, anisotropic, hyperelastic response to stresses in the media and adventitia layers and an isotropic response in the intima and necrotic layers. The effect of differential growth on the peak stress is explored in a simple, concentric geometry and it is shown that axial differential growth decreases the peak stress in the inner layer. Furthermore, morphological risk factors are explored. The peak stress in residually stressed cylinders is not greatly affected by changing the thickness of the intima. The thickness of the necrotic layer is shown to be the most important morphological feature that affects the peak stress in a residually stressed vessel.

Differential growth and residual stress in cylindrical elastic structures.

Cylindrical forms are among one of Nature's fundamental building blocks. They serve many different purposes, from sustaining body weight to carrying flows. Their mechanical properties are generated through the often complex arrangements of the walls. In particular, in many structures that have elastic responses, such as stems and arteries, the walls are in a state of tension generated by differential growth. Here, the effect of differential growth and residual stress on the overall mechanical response of the cylindrical structure is studied within the framework of morpho-elasticity.

Morpho-elastodynamics: the long-time dynamics of elastic growth.

As elastic tissues grow and remodel, they generate stresses that influence their mechanical states which influence the way growth proceeds. This complex feedback leads to a dynamic evolution of growth and stresses which can be modelled within the theory of exact nonlinear elasticity. Here, we first review the different theoretical results considering growth laws and then, we present a new approach to look at morphoelasticity as a continuous dynamical process. These evolution laws lead to new dynamical systems that can be studied by the classical methods of dynamical systems theory.