Multiscale and Multiaxial Mechanics of Vascular Smooth Muscle.

Mathematical models can facilitate an integrative understanding of the complexity underlying biological structure and function, but they must be informed and validated by empirical data. Uniaxial contraction of an arterial ring is a well-used in vitro approach for studying characteristics of smooth muscle contractility even though this experimental arrangement does not mimic the in vivo vascular geometry or loading. In contrast, biaxial contraction of an inflated and axially extended excised vessel provides broader information, both passive and active, under more realistic conditions. Few investigations have compared these two in vitro approaches directly, namely how their results overlap, how they differ, or if each provides unique complementary information. Toward this end, we present, to our knowledge, a new multiscale mathematical model of arterial contractility accounting for structural and functional constituents at molecular, cellular, and tissue levels. The artery is assumed to be a thick-walled incompressible cylinder described by an anisotropic model of the extracellular matrix and, to our knowledge, novel model of smooth muscle contractility. The latter includes a 3D structural sensitivity to deformation, including microscale muscle filament overlap and filament lattice spacing. The overall model captures uniaxial and biaxial experimental contraction data, which was not possible when accounting for filament overlap alone. The model also enables parameter sensitivity studies, which confirmed that uniaxial contraction tests are not as efficient as biaxial tests for identifying changes in vascular smooth muscle function.