A systematic comparison of membrane, shell, and 3D solid formulations for nonlinear vascular biomechanics

Typical computational methods for vascular biosolid mechanics represent the blood vessel wall as a membrane, shell, or 3D solid. Each of these formulations has advantages and disadvantages concerning accuracy, ease of implementation, and computational costs. Despite the widespread use of these formulations, a systematic comparison of the performance and accuracy of these formulations for nonlinear vascular biomechanics has remained wanting. 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 the vessel wall as: (i) a nonlinear membrane, (ii) a nonlinear, rotation-free shell, and (iii) a nonlinear 3D solid. For the 3D solid model, we consider two different implementations employing linear and quadratic interpolation. Convergence analysis for displacement and stress are presented for all formulations. We compare results in both idealized and subject-specific mouse aortic geometries. For the idealized cylindrical geometry, we compare our results against the axisymmetric solution for five different wall thickness-to-radius ratios. Subsequently, a comparison of these approaches is presented for an idealized arterial bifurcation having regionally varying wall thickness. Lastly, we compare results for a subject-specific mouse geometry with regionally varying material properties and wall thickness. External tissue support boundary conditions model the effect of perivascular tissue. Based on our results, the rotation-free shell formulation represents the most advantageous compromise between computational cost and accuracy for large scale vascular biomechanics applications that include complex geometries.