Department of Mechanical Engineering, Columbia University, New York, NY 10027.
Department of Biomedical Engineering, University of Utah, Salt Lake City, UT 84112.
J Biomech Eng. 2021 Sep 1;143(9). doi: 10.1115/1.4050646.
In biomechanics, solid-fluid mixtures have commonly been used to model the response of hydrated biological tissues. In cartilage mechanics, this type of mixture, where the fluid and solid constituents are both assumed to be intrinsically incompressible, is often called a biphasic material. Various physiological processes involve the interaction of a viscous fluid with a porous-hydrated tissue, as encountered in synovial joint lubrication, cardiovascular mechanics, and respiratory mechanics. The objective of this study was to implement a finite element solver in the open-source software febio that models dynamic interactions between a viscous fluid and a biphasic domain, accommodating finite deformations of both domains as well as fluid exchanges between them. For compatibility with our recent implementation of solvers for computational fluid dynamics (CFD) and fluid-structure interactions (FSI), where the fluid is slightly compressible, this study employs a novel hybrid biphasic formulation where the porous skeleton is intrinsically incompressible but the fluid is also slightly compressible. The resulting biphasic-FSI (BFSI) implementation is verified against published analytical and numerical benchmark problems, as well as novel analytical solutions derived for the purposes of this study. An illustration of this BFSI solver is presented for two-dimensional (2D) airflow through a simulated face mask under five cycles of breathing, showing that masks significantly reduce air dispersion compared to the no-mask control analysis. In addition, we model three-dimensional (3D) blood flow in a bifurcated carotid artery assuming porous arterial walls and verify that mass is conserved across all fluid-permeable boundaries. The successful formulation and implementation of this BFSI solver offers enhanced multiphysics modeling capabilities that are accessible via an open-source software platform.
在生物力学中，固液混合物通常被用于模拟水合生物组织的响应。在软骨力学中，这种混合物，其中液体和固体成分都被假设为固有不可压缩的，通常被称为双相材料。各种生理过程涉及粘性流体与多孔水合组织的相互作用，如在滑液关节润滑、心血管力学和呼吸力学中遇到的情况。本研究的目的是在开源软件 febio 中实现一个有限元求解器，该求解器可以模拟粘性流体和双相域之间的动态相互作用，适应两个域的有限变形以及它们之间的流体交换。为了与我们最近实现的计算流体动力学（CFD）和流固相互作用（FSI）求解器兼容，其中流体略有可压缩性，本研究采用了一种新的混合双相公式，其中多孔骨架固有不可压缩，但流体也略有可压缩性。所得到的双相-FSI（BFSI）实现通过与已发表的分析和数值基准问题以及为研究目的推导的新分析解进行验证。通过对模拟面罩下二维（2D）气流在五次呼吸循环中的流动进行演示，展示了面罩与无面罩对照分析相比显著减少了空气分散。此外，我们还假设多孔动脉壁进行三维（3D）血流在分叉颈动脉中的流动，并验证了所有可渗透流体边界的质量守恒。这种 BFSI 求解器的成功公式化和实现提供了增强的多物理建模能力，可通过开源软件平台访问。
