Department of Surgery, University of Michigan, Ann Arbor, MI, USA.
Mines Saint-Étienne, Univ Lyon, Univ Jean Monnet, INSERM, U 1059 Sainbiose, Centre CIS, 42023, Saint-Étienne, France.
Sci Rep. 2020 Oct 16;10(1):17528. doi: 10.1038/s41598-020-74277-5.
We implement a nonlinear rotation-free shell formulation capable of handling large deformations for applications in vascular biomechanics. The formulation employs a previously reported shell element that calculates both the membrane and bending behavior via displacement degrees of freedom for a triangular element. The thickness stretch is statically condensed to enforce vessel wall incompressibility via a plane stress condition. Consequently, the formulation allows incorporation of appropriate 3D constitutive material models. We also incorporate external tissue support conditions to model the effect of surrounding tissue. We present theoretical and variational details of the formulation and verify our implementation against axisymmetric results and literature data. We also adapt a previously reported prestress methodology to identify the unloaded configuration corresponding to the medically imaged in vivo vessel geometry. We verify the prestress methodology in an idealized bifurcation model and demonstrate the significance of including prestress. Lastly, we demonstrate the robustness of our formulation via its application to mouse-specific models of arterial mechanics using an experimentally informed four-fiber constitutive model.
我们实现了一种非线性无旋转壳公式，能够处理血管生物力学应用中的大变形。该公式采用了先前报道的壳元，通过三角形单元的位移自由度来计算膜和弯曲行为。厚度拉伸通过平面应力条件进行静态凝聚，以强制血管壁不可压缩性。因此，该公式允许结合适当的 3D 本构材料模型。我们还结合了外部组织支撑条件来模拟周围组织的影响。我们介绍了公式的理论和变分细节，并通过轴对称结果和文献数据验证了我们的实现。我们还采用了先前报道的预应力方法来确定与医学成像的体内血管几何形状相对应的空载配置。我们在理想化的分叉模型中验证了预应力方法，并证明了包括预应力的重要性。最后，我们通过将其应用于使用实验启发的四纤维本构模型的特定于小鼠的动脉力学模型来证明我们的公式的稳健性。
