Kou Wenjun, Griffith Boyce E, Pandolfino John E, Kahrilas Peter J, Patankar Neelesh A
Theoretical and Applied Mechanics, Northwestern University, 2145 Sheridan Road, Evanston, Illinois 60208, USA.
Departments of Mathematics and Biomedical Engineering, University of North Carolina at Chapel Hill, Phillips Hall, Campus Box 3250, Chapel Hill, North Carolina 27599-3250, USA.
J Comput Phys. 2017 Oct 1;348:433-459. doi: 10.1016/j.jcp.2017.07.025. Epub 2017 Jul 18.
In this work, we extend our previous esophageal transport model using an immersed boundary (IB) method with discrete fiber-based structural model, to one using a continuum mechanics-based model that is approximated based on finite elements (IB-FE). To deal with the leakage of flow when the Lagrangian mesh becomes coarser than the fluid mesh, we employ adaptive interaction quadrature points to deal with Lagrangian-Eulerian interaction equations based on a previous work (Griffith and Luo [1]). In particular, we introduce a new anisotropic adaptive interaction quadrature rule. The new rule permits us to vary the interaction quadrature points not only at each time-step and element but also at different orientations per element. This helps to avoid the leakage issue without sacrificing the computational efficiency and accuracy in dealing with the interaction equations. For the material model, we extend our previous fiber-based model to a continuum-based model. We present formulations for general fiber-reinforced material models in the IB-FE framework. The new material model can handle non-linear elasticity and fiber-matrix interactions, and thus permits us to consider more realistic material behavior of biological tissues. To validate our method, we first study a case in which a three-dimensional short tube is dilated. Results on the pressure-displacement relationship and the stress distribution matches very well with those obtained from the implicit FE method. We remark that in our IB-FE case, the three-dimensional tube undergoes a very large deformation and the Lagrangian mesh-size becomes about 6 times of Eulerian mesh-size in the circumferential orientation. To validate the performance of the method in handling fiber-matrix material models, we perform a second study on dilating a long fiber-reinforced tube. Errors are small when we compare numerical solutions with analytical solutions. The technique is then applied to the problem of esophageal transport. We use two fiber-reinforced models for the esophageal tissue: a bi-linear model and an exponential model. We present three cases on esophageal transport that differ in the material model and the muscle fiber architecture. The overall transport features are consistent with those observed from the previous model. We remark that the continuum-based model can handle more realistic and complicated material behavior. This is demonstrated in our third case where a spatially varying fiber architecture is included based on experimental study. We find that this unique muscle fiber architecture could generate a so-called pressure transition zone, which is a luminal pressure pattern that is of clinical interest. This suggests an important role of muscle fiber architecture in esophageal transport.
在这项工作中，我们将先前使用基于离散纤维结构模型的浸入边界（IB）方法的食管传输模型扩展为使用基于连续介质力学且基于有限元近似的模型（IB - FE）。为了处理拉格朗日网格比流体网格更粗时的流动泄漏问题，我们基于先前的工作（格里菲斯和罗[1]）采用自适应相互作用求积点来处理拉格朗日 - 欧拉相互作用方程。特别地，我们引入了一种新的各向异性自适应相互作用求积规则。新规则允许我们不仅在每个时间步和单元处，而且在每个单元的不同方向上改变相互作用求积点。这有助于避免泄漏问题，同时在处理相互作用方程时不牺牲计算效率和精度。对于材料模型，我们将先前基于纤维的模型扩展为基于连续介质的模型。我们在IB - FE框架中给出了一般纤维增强材料模型的公式。新的材料模型可以处理非线性弹性和纤维 - 基体相互作用，从而使我们能够考虑生物组织更现实的材料行为。为了验证我们的方法，我们首先研究一个三维短管扩张的案例。压力 - 位移关系和应力分布的结果与从隐式有限元方法获得的结果非常吻合。我们注意到在我们的IB - FE案例中，三维管经历了非常大的变形，并且拉格朗日网格尺寸在圆周方向上变为欧拉网格尺寸的约6倍。为了验证该方法在处理纤维 - 基体材料模型方面的性能，我们对长纤维增强管的扩张进行了第二项研究。当我们将数值解与解析解进行比较时，误差很小。然后将该技术应用于食管传输问题。我们对食管组织使用了两种纤维增强模型：双线性模型和指数模型。我们给出了三种食管传输案例，它们在材料模型和肌纤维结构方面有所不同。整体传输特征与先前模型中观察到的特征一致。我们注意到基于连续介质的模型可以处理更现实和复杂的材料行为。这在我们的第三个案例中得到了证明，该案例基于实验研究纳入了空间变化的纤维结构。我们发现这种独特的肌纤维结构可以产生所谓的压力过渡区，这是一种具有临床意义的腔内压力模式。这表明肌纤维结构在食管传输中起着重要作用。
