  Typical computational techniques for vascular biomechanics represent the
blood vessel wall via either a membrane, a shell, or a 3D solid element. Each
of these formulations has its trade offs concerning accuracy, ease of
implementation, and computational costs. Despite the widespread use of these
formulations, a systematic comparison on the performance and accuracy of these
formulations for nonlinear vascular biomechanics is lacking. Therefore, the
decision regarding the optimal choice often relies on intuition or previous
experience, with unclear consequences of choosing one approach over the other.
Here, we present a systematic comparison among three different formulations to
represent vessel wall: (i) a nonlinear membrane model, (ii) a nonlinear,
rotation-free shell model, and (iii) a nonlinear 3D solid model. For the 3D
solid model, we consider two different implementations employing linear and
quadratic interpolation. We present comparison results in both idealized and
subject-specific mouse geometries. For the idealized cylindrical geometry, we
compare our results against the axisymmetric solution for three different wall
thickness to radius ratio. Subsequently, a comparison of these approaches is
presented in an idealized bifurcation model for regionally varying wall
thickness. Lastly, we present the comparison results for a subject-specific
mouse geometry with regionally varying material properties and wall thickness,
while incorporating the effect of external tissue surrounding the vessel wall.
