Insights into the micromechanics of stress-relaxation and creep behaviours in the aortic valve

Viscoelastic attributes of the aortic valve (AV) tissue are, in part, reflected in stress-relaxation and creep behaviours observed in vitro. While the extent of AV time-dependent behaviour under physiological conditions is not yet fully understood, in vitro the tissue exhibits clear stress-relaxation but minimal creep under equi-biaxial loading, in contrast to uniaxial loading where creep is evidently exhibited. Tissue-level stress-relaxation behaviour follows the form of (single and double) Maxwell-type exponential decay relaxation modes, and creep occurs in the form of exponential primary followed by linear secondary creep modes. This paper aims to provide an explanation for these behaviours based on the AV microstructural (i.e. fibre-level) mechanics. The kinematics of AV microstructural reorganisation is investigated experimentally using confocal microscopy to track the interstitial cell nuclei as markers of AV microstructural reorganisation under uniaxial loading. A theoretical framework is then applied to describe the experimentally observed kinematics in mathematical terms. Using this framework it is shown that at the microstructural level, AV stress-relaxation and creep behaviours both stem from the same dissipative kinematics of fibre-fibre and fibre-matrix interactions, that occur as a consequence of microstructural reorganisation due to the applied tissue-level loads. It is additionally shown that the proposed dissipative kinematics correctly predict the nature of relaxation and creep behaviours, i.e. the type and the number of modes involved. Further analysis is presented to demonstrate that the origin of the minimal creep behaviour under equi-biaxial loading can be explained to stem from tissue-level loading boundary conditions. These key findings help to better understand the underlying causes of AV stress-relaxation and creep behaviours in vivo, and why these may differ from the behaviours observed under non-physiological in vitro loading.