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Airway Wall Stiffening Increases Peak Wall Shear Stress: A Fluid–Structure Interaction Study in Rigid and Compliant Airways

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Abstract

The airflow characteristics in a computed tomography (CT) based human airway bifurcation model with rigid and compliant walls are investigated numerically. An in-house three-dimensional (3D) fluid–structure interaction (FSI) method is applied to simulate the flow at different Reynolds numbers and airway wall stiffness. As the Reynolds number increases, the airway wall deformation increases and the secondary flow becomes more prominent. It is found that the peak wall shear stress on the rigid airway wall can be five times stronger than that on the compliant airway wall. When adding tethering forces to the model, we find that these forces, which produce larger airway deformation than without tethering, lead to more skewed velocity profiles in the lower branches and further reduced wall shear stresses via a larger airway lumen. This implies that pathologic changes in the lung such as fibrosis or remodeling of the airway wall—both of which can serve to restrain airway wall motion—have the potential to increase wall shear stress and thus can form a positive feed-back loop for the development of altered flow profiles and airway remodeling. These observations are particularly interesting as we try to understand flow and structural changes seen in, for instance, asthma, emphysema, cystic fibrosis, and interstitial lung disease.

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Acknowledgments

This study was supported in part by NIH Grants R01-HL-064368, R01-EB-005823, and S10-RR-022421. We are grateful to Jiwoong Choi and Youbing Yin for assisting with generation of meshes and CT images of the airway model. We also thank TeraGrid via the Texas Advanced Computing Center for allocating computer time.

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Correspondence to Ching-Long Lin.

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Associate Editor Kenneth R. Lutchen oversaw the review of this article.

Appendix: Solver Validation

Appendix: Solver Validation

Different error analyses and several benchmark cases for verification and validation have been performed on the FSI solver.60 Here, the 3D FSI solver is further validated by performing simulations on a closely related problem of the flow in a collapsible tube, which has significance in many physiological systems such as blood flow in the circulation and airflow in the airway tree. Given its importance and complexity, the topic of flow through collapsible tubes has been extensively investigated for over 30 years. Kamm and Pedley18 provided a brief review of the subject, Heil and Jensen15 gave a more comprehensive review of the biological examples and the theoretical and computational developments, and Bertram4 reviewed the experimental side of the subject, and applications in medicine and engineering technologies. Figure A1a shows the typical setup of the problem: a flexible tube section of length l is mounted between two rigid tubes of lengths l up and l down, respectively. An external pressure p ext is imposed on the outside wall of the flexible tube section. The pressure at the exit of the downstream rigid tube l down is set to be constant, i.e., p down = 0. The radius R of the tube is 4 cm and the thickness h is R/20. The length l of the flexible tube is 10R, and the lengths of the upstream and downstream rigid tubes are R and 5R respectively. For the sake of comparison, all the parameters for this case are taken from those used in Marzo et al.’s study.30 The Young’s modulus E of the elastic tube is 4,559.4 Pa, and the Poisson’s ratio is 0.49. A constant flow is imposed at the inlet of the upstream rigid tube, and the Reynolds number is set to be 128. The meshes for fluid and structure domains have 25,578 tetrahedral elements and 3,996 shell triangle elements, respectively.

Figure A1
figure 13

(a) Schematic of flow though a collapsible tube; (b) Deformed collapsible tube at p ext = 1.4 Pa and Re = 128, with a maximum deformation of about 0.8R at the location 0.72l with respect to the beginning point of the flexible section; (c) Profiles of the deformed tube at plane y = 0 under different external pressures: (1) p ext = 0.0 Pa and (2) p ext = 1.42 Pa (the dash line is the un-deformed profile); (d) Non-dimensional pressure profiles along the flexible tube section; and (e) Deformation profiles of the flexible tube section extracted at y-symmetry (y = 0)

The deformation of the flexible section of the tube is determined by the transmural pressure between the internal pressure and external pressure. Initially p ext = 0, and the internal pressure is larger than p ext, and, thus, the flexible tube expands axisymmetrically under the positive transmural pressure. By increasing the external pressure, the transmural pressure decreases. Eventually the external pressure becomes larger than the internal pressure, and the flexible tube contracts under the negative transmural pressure. If the external pressure exceeds a critical value, then the axisymmetric deformation loses its stability, and the tube buckles non-axisymmetrically.15 Figure A1b exhibits one example of the non-axisymmetric collapse of the flexible tube. The extent and location of the strongest collapse vary with different external pressure values. Figure A1c shows the profiles of the deformed flexible tubes under different external pressures at p ext = 0.0 Pa and p ext = 1.42 Pa. It is found that at Re = 128, and with an external pressure p ext = 1.42 Pa, the maximum deformation is about 0.8R, and the location of the maximum collapse point is at 0.76. Figures A1d and A1e compare the fluid pressure and wall deformation profiles along the flexible section of the tube with Marzo et al.’s result,30 in which the pressure is non-dimensionalized by bending stiffness, and the deformation and axial distance are normalized with respect to radius R. Good agreement is found with the results obtained by Marzo et al. 30 Given the non-axisymmetric deformation of the tube, this example suggests that the FSI, which does not assume geometric similarity in expanding or contracting the airways, is a more suitable approach for realistic representation of airway deformation.

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Xia, G., Tawhai, M.H., Hoffman, E.A. et al. Airway Wall Stiffening Increases Peak Wall Shear Stress: A Fluid–Structure Interaction Study in Rigid and Compliant Airways. Ann Biomed Eng 38, 1836–1853 (2010). https://doi.org/10.1007/s10439-010-9956-y

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