A computational framework for modeling fluid and solid stresses in porous tissues with application to the trabeculated embryonic heart

This study provides a framework for efficient solutions of computational fluid-solid interaction models of porous tissue, with a focus on blood flow through the developing heart wall in the critical chamber and valve formation stages, when trabeculation fills much of the ventricles. This porous, trabeculated tissue is the site of complex mechanotransduction processes, but accurately estimating solid and fluid stresses within such intricate geometries is difficult. We addressed this with three levels of modeling and verification. Images of E12.5 mouse ventricles were first obtained through confocal microscopy and 3D reconstruction. These guided creation of explicit pore-scale finite element simulations with fluid-solid interaction. Idealized and image-derived unit cells were analyzed to determine hydraulic permeability. Next, a multi-pore representation of the ventricular wall was solved with full fluid and solid equations. A continuum model based on Brinkman equations then replaced the explicit pore structure, and sensitivity to permeability was evaluated in terms of fluid flow in the open channel and porous region. Permeabilities obtained from unit-cell simulations followed trends from Kozeny-Carman solid-pore and fiber theory for the rigid case, while simulations for hyperelastic unit-cell material quantified the effects of tissue elasticity. Comparison of continuum and explicit model results showed the Brinkman equation, which incorporates the diffusion of shear stress from flow in the free fluid into the porous media, but not explicitly inertial effects, could significantly improve the accuracy of continuum models compared to Darcy's law. A 3D model of blood flow through the ventricles of the developing mouse heart demonstrated the application of the technique to more realistic geometry, showed locations of peak solid and shear stress, and produced physiologically reasonable flow. Furthermore, we developed methodologies to estimate local wall shear and solid stress from continuum-based calculations. This approach can enable efficient, whole-organ parametric analyses of fluid flow, circumventing the need for computationally expensive explicit pore modeling.