A computational framework for modeling fluid and solid stresses in porous tissues with application to the trabeculated embryonic heart
- 1Department of Mechanical Engineering, Bucknell University, Lewisburg, Pennsylvania, United States of America
- 2Department of Biomedical Engineering, Bucknell University, Lewisburg, Pennsylvania, United States of America
Abstract
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. Author summary: Many biological tissues are porous, allowing the passage of fluids such as blood, lymph, and interstitial fluid across the tissue with varying levels of resistance. One important example is the porous, trabecular tissue filling the ventricles of the developing heart before formation of coronary circulation. The response of this trabecular region to mechanical load suggests it is an important sensor and actuator for mechanotransduction. Although computational modeling of fluid flow interacting with complex, porous, elastic tissue can help elucidate details of mechanotransduction, the analysis is computationally intensive, propagates uncertainties from image analysis and meshing, and does not easily allow parameter studies. We addressed this challenge with anatomical studies of the 12.5-day mouse heart, followed by three levels of modeling, integrating single-pore simulations, layered models of solid and porous regions with impinging fluid, and continuum representations of the porous region. The continuum model was efficient and agreed well with explicit pore representations. A ventricular model of 12.5-day mouse demonstrated application to more realistic geometry. We also developed methods to estimate local stress from continuum-based calculations. This approach enables efficient, whole-organ parametric analyses of fluid flow, circumventing the need for computationally expensive explicit pore modeling.
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BibTeX
@article{buffinton2026computational,
title = {{A computational framework for modeling fluid and solid stresses in porous tissues with application to the trabeculated embryonic heart}},
author = {Christine Miller Buffinton and James W. Baish},
journal = {PLOS Computational Biology},
year = {2026},
month = oct,
doi = {10.1371/journal.pcbi.1014896},
url = {https://journals.plos.org/ploscompbiol/article?id=10.1371/journal.pcbi.1014896},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - A computational framework for modeling fluid and solid stresses in porous tissues with application to the trabeculated embryonic heart
AU - Christine Miller Buffinton
AU - James W. Baish
PY - 2026
DA - 2026/10/23
JO - PLOS Computational Biology
DO - 10.1371/journal.pcbi.1014896
UR - https://journals.plos.org/ploscompbiol/article?id=10.1371/journal.pcbi.1014896
AB - 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. Author summary: Many biological tissues are porous, allowing the passage of fluids such as blood, lymph, and interstitial fluid across the tissue with varying levels of resistance. One important example is the porous, trabecular tissue filling the ventricles of the developing heart before formation of coronary circulation. The response of this trabecular region to mechanical load suggests it is an important sensor and actuator for mechanotransduction. Although computational modeling of fluid flow interacting with complex, porous, elastic tissue can help elucidate details of mechanotransduction, the analysis is computationally intensive, propagates uncertainties from image analysis and meshing, and does not easily allow parameter studies. We addressed this challenge with anatomical studies of the 12.5-day mouse heart, followed by three levels of modeling, integrating single-pore simulations, layered models of solid and porous regions with impinging fluid, and continuum representations of the porous region. The continuum model was efficient and agreed well with explicit pore representations. A ventricular model of 12.5-day mouse demonstrated application to more realistic geometry. We also developed methods to estimate local stress from continuum-based calculations. This approach enables efficient, whole-organ parametric analyses of fluid flow, circumventing the need for computationally expensive explicit pore modeling.
SN - 1553-7358
SN - 1553-734X
ER -