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Effect of Subject-Specific, Spatially Reduced, and Idealized Boundary Conditions on the Predicted Hemodynamic Environment in the Murine Aorta

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Abstract

Mouse models of atherosclerosis have become effective resources to study atherogenesis, including the relationship between hemodynamics and lesion development. Computational methods aid the prediction of the in vivo hemodynamic environment in the mouse vasculature, but careful selection of inflow and outflow boundary conditions (BCs) is warranted to promote model accuracy. Herein, we investigated the impact of animal-specific versus reduced/idealized flow boundary conditions on predicted blood flow patterns in the mouse thoracic aorta. Blood velocities were measured in the aortic root, arch branch vessel, and descending aorta in ApoE−/− mice using phase-contrast MRI. Computational geometries were derived from micro-CT imaging and combinations of high-fidelity or reduced/idealized MR-derived BCs were applied to predict the bulk flow field and hemodynamic metrics (e.g., wall shear stress, WSS; cross-flow index, CFI). Results demonstrate that pressure-free outlet BCs significantly overestimate outlet flow rates as compared to measured values. When compared to models that incorporate 3-component inlet velocity data [\(\mathop{v}\limits^{\rightharpoonup} \left( {v_{r} ,v_{\theta } ,v_{z} } \right)\)] and time-varying outlet mass flow splits [\(Q\left( t \right)\)] (i.e., high-fidelity model), neglecting in-plane inlet velocity components (i.e., \(\mathop{v}\limits^{\rightharpoonup} (v_{z}\))) leads to errors in WSS and CFI values ranging from 10 to 30% across the model domain whereas the application of a steady outlet mass flow splits results in negligible differences in these hemodynamics metrics. This investigation highlights that 3-component inlet velocity data and at least steady mass flow splits are required for accurate predictions of flow patterns in the mouse thoracic aorta.

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Notes

  1. Although a pressure gauge was not in-line during perfusion of the animals, due to possibility of equipment damage with the contrast agent, benchtop testing using an identical setup with tubing that had a diameter equivalent to the mouse aorta and high downstream resistance indicated the perfusion pressure was ~150 mmHg.

References

  1. Ateshian, G. A., J. J. Shim, S. A. Maas, and J. A. Weiss. Finite element framework for computational fluid dynamics in FEBio. J. Biomech. Eng. 140:021001, 2018.

    Article  Google Scholar 

  2. Breslow, J. L. Mouse models of atherosclerosis. Science. 272:685–688, 1996.

    Article  CAS  Google Scholar 

  3. Cebral, J. R., M. A. Castro, J. E. Burgess, R. S. Pergolizzi, M. J. Sheridan, and C. M. Putman. Characterization of cerebral aneurysms for assessing risk of rupture by using patient-specific computational hemodynamics models. AJNR Am. J. Neuroradiol. 26:2550–2559, 2005.

    PubMed  PubMed Central  Google Scholar 

  4. Cheng, C., D. Tempel, R. van Haperen, A. van der Baan, F. Grosveld, M. J. Daemen, R. Krams, and R. de Crom. Atherosclerotic lesion size and vulnerability are determined by patterns of fluid shear stress. Circulation. 113:2744–2753, 2006.

    Article  Google Scholar 

  5. De Wilde, D., B. Trachet, G. R. De Meyer, and P. Segers. Shear stress metrics and their relation to atherosclerosis: an in vivo follow-up study in atherosclerotic mice. Ann. Biomed. Eng. 44:2327–2338, 2016.

    Article  Google Scholar 

  6. Dice, L. R. Measures of the amount of ecologic association between species. Ecology. 26:297–302, 1945.

    Article  Google Scholar 

  7. Feintuch, A., P. Ruengsakulrach, A. Lin, J. Zhang, Y. Q. Zhou, J. Bishop, L. Davidson, D. Courtman, F. S. Foster, D. A. Steinman, R. M. Henkelman, and C. R. Ethier. Hemodynamics in the mouse aortic arch as assessed by MRI, ultrasound, and numerical modeling. Am. J. Physiol. Heart. Circ. Physiol. 292:H884-892, 2007.

    Article  CAS  Google Scholar 

  8. Gallo, D., G. De Santis, F. Negri, D. Tresoldi, R. Ponzini, D. Massai, M. A. Deriu, P. Segers, B. Verhegghe, G. Rizzo, and U. Morbiducci. On the use of in vivo measured flow rates as boundary conditions for image-based hemodynamic models of the human aorta: implications for indicators of abnormal flow. Ann. Biomed. Eng. 40:729–741, 2012.

    Article  CAS  Google Scholar 

  9. He, X., and D. N. Ku. Pulsatile flow in the human left coronary artery bifurcation: average conditions. J. Biomech. Eng. 118:74–82, 1996.

    Article  CAS  Google Scholar 

  10. He, Y., C. M. Terry, C. Nguyen, S. A. Berceli, Y. T. Shiu, and A. K. Cheung. Serial analysis of lumen geometry and hemodynamics in human arteriovenous fistula for hemodialysis using magnetic resonance imaging and computational fluid dynamics. J. Biomech. 46:165–169, 2013.

    Article  Google Scholar 

  11. Hoi, Y., B. A. Wasserman, E. G. Lakatta, and D. A. Steinman. Carotid bifurcation hemodynamics in older adults: effect of measured versus assumed flow waveform. J. Biomech. Eng. 132:071006, 2010.

    Article  Google Scholar 

  12. Hoi, Y., Y. Q. Zhou, X. Zhang, R. M. Henkelman, and D. A. Steinman. Correlation between local hemodynamics and lesion distribution in a novel aortic regurgitation murine model of atherosclerosis. Ann. Biomed. Eng. 39:1414–1422, 2011.

    Article  Google Scholar 

  13. Janssen, B. J., T. De Celle, J. J. Debets, A. E. Brouns, M. F. Callahan, and T. L. Smith. Effects of anesthetics on systemic hemodynamics in mice. Am. J. Physiol. Heart. Circ. Physiol. 287:H1618-1624, 2004.

    Article  CAS  Google Scholar 

  14. Jin, S., J. Oshinski, and D. P. Giddens. Effects of wall motion and compliance on flow patterns in the ascending aorta. J. Biomech. Eng. 125:347–354, 2003.

    Article  Google Scholar 

  15. Maas, S. A., B. J. Ellis, G. A. Ateshian, and J. A. Weiss. FEBio: finite elements for biomechanics. J. Biomech. Eng. 134:011005, 2012.

    Article  Google Scholar 

  16. Madhavan, S., and E. M. C. Kemmerling. The effect of inlet and outlet boundary conditions in image-based CFD modeling of aortic flow. Biomed Eng Online. 17:66, 2018.

    Article  Google Scholar 

  17. Marsden, A., and E. Kung. Multiscale Modeling of Cardiovascular Flows. In: Computational Bioengineering, edited by G. Zhang. Boca Raton: CRC Press, 2015.

    Google Scholar 

  18. McRobbie, D. W., E. A. Moore, M. J. Graves, and M. R. Prince. MRI from Picture to Proton. Cambridge: Cambridge University Press, 2006.

    Book  Google Scholar 

  19. Merino, H., S. Parthasarathy, and D. K. Singla. Partial ligation-induced carotid artery occlusion induces leukocyte recruitment and lipid accumulation–a shear stress model of atherosclerosis. Mol. Cell. Biochem. 372:267–273, 2013.

    Article  CAS  Google Scholar 

  20. Mohamied, Y., S. J. Sherwin, and P. D. Weinberg. Understanding the fluid mechanics behind transverse wall shear stress. J. Biomech. 50:102–109, 2017.

    Article  Google Scholar 

  21. Molony, D., J. Park, L. Zhou, C. Fleischer, H. Y. Sun, X. Hu, J. Oshinski, H. Samady, D. P. Giddens, and A. Rezvan. Bulk flow and near wall hemodynamics of the rabbit aortic arch: a 4D PC-MRI derived CFD study. J Biomech. Eng. 141(1):011003, 2018.

    Article  Google Scholar 

  22. Morbiducci, U., R. Ponzini, D. Gallo, C. Bignardi, and G. Rizzo. Inflow boundary conditions for image-based computational hemodynamics: impact of idealized versus measured velocity profiles in the human aorta. J. Biomech. 46:102–109, 2013.

    Article  Google Scholar 

  23. Murray, C. D. The physiological principle of minimum work: I. The vascular system and the cost of blood volume. Proc. Natl. Acad. Sci. U.S.A. 12:207–214, 1926.

    Article  CAS  Google Scholar 

  24. Nam, D., C. W. Ni, A. Rezvan, J. Suo, K. Budzyn, A. Llanos, D. Harrison, D. Giddens, and H. Jo. Partial carotid ligation is a model of acutely induced disturbed flow, leading to rapid endothelial dysfunction and atherosclerosis. Am. J. Physiol. Heart Circ. Physiol. 297:H1535-1543, 2009.

    Article  CAS  Google Scholar 

  25. Pirola, S., Z. Cheng, O. A. Jarral, D. P. O’Regan, J. R. Pepper, T. Athanasiou, and X. Y. Xu. On the choice of outlet boundary conditions for patient-specific analysis of aortic flow using computational fluid dynamics. J Biomech. 60:15–21, 2017.

    Article  CAS  Google Scholar 

  26. Samady, H., P. Eshtehardi, M. C. McDaniel, J. Suo, S. S. Dhawan, C. Maynard, L. H. Timmins, A. A. Quyyumi, and D. P. Giddens. Coronary artery wall shear stress is associated with progression and transformation of atherosclerotic plaque and arterial remodeling in patients with coronary artery disease. Circulation. 124:779–788, 2011.

    Article  CAS  Google Scholar 

  27. Seok J., H. S. Warren, A. G. Cuenca, M. N. Mindrinos, H. V. Baker, W. Xu, D. R. Richards, G. P. McDonald-Smith, H. Gao, L. Hennessy, C. C. Finnerty, C. M. López, S. Honari, E. E. Moore, J. P. Minei, J. Cuschieri, P. E. Bankey, J. L. Johnson, J. Sperry, A. B. Nathens, T. R. Billiar, M. A. West, M. G. Jeschke, M. B. Klein, R. L. Gamelli, N. S. Gibran, B. H. Brownstein, C. Miller-Graziano, S. E. Calvano, P. H. Mason, J. P. Cobb, L. G. Rahme, S. F. Lowry, R. V. Maier, L. L. Moldawer, D. N. Herndon, R. W. Davis, W. Xiao, R. G. Tompkins and L. r. S. C. R. P. Inflammation and Host Response to Injury. Genomic responses in mouse models poorly mimic human inflammatory diseases. Proc. Natl. Acad. Sci. U.S.A. 110: 3507–3512, 2013.

  28. Steinman, D. A. Image-based computational fluid dynamics modeling in realistic arterial geometries. Ann. Biomed. Eng. 30:483–497, 2002.

    Article  Google Scholar 

  29. Suo, J., D. E. Ferrara, D. Sorescu, R. E. Guldberg, W. R. Taylor, and D. P. Giddens. Hemodynamic shear stresses in mouse aortas: implications for atherogenesis. Arterioscler. Thromb. Vasc. Biol. 27:346–351, 2007.

    Article  CAS  Google Scholar 

  30. Taylor, C. A., and C. A. Figueroa. Patient-specific modeling of cardiovascular mechanics. Annu. Rev. Biomed. Eng. 11:109–134, 2009.

    Article  CAS  Google Scholar 

  31. Taylor, C. A., T. A. Fonte, and J. K. Min. Computational fluid dynamics applied to cardiac computed tomography for noninvasive quantification of fractional flow reserve: scientific basis. J. Am. Coll. Cardiol. 61:2233–2241, 2013.

    Article  Google Scholar 

  32. Trachet, B., J. Bols, G. De Santis, S. Vandenberghe, B. Loeys, and P. Segers. The impact of simplified boundary conditions and aortic arch inclusion on CFD simulations in the mouse aorta: a comparison with mouse-specific reference data. J. Biomech. Eng. 133:121006, 2011.

    Article  Google Scholar 

  33. Trachet, B., J. Bols, J. Degroote, B. Verhegghe, N. Stergiopulos, J. Vierendeels, and P. Segers. An animal-specific FSI model of the abdominal aorta in anesthetized mice. Ann. Biomed. Eng. 43:1298–1309, 2015.

    Article  Google Scholar 

  34. Trachet, B., A. Swillens, D. Van Loo, C. Casteleyn, A. De Paepe, B. Loeys, and P. Segers. The influence of aortic dimensions on calculated wall shear stress in the mouse aortic arch. Comput. Methods Biomech. Biomed. Eng. 12:491–499, 2009.

    Article  Google Scholar 

  35. Van Doormaal, M. A., A. Kazakidi, M. Wylezinska, A. Hunt, J. L. Tremoleda, A. Protti, Y. Bohraus, W. Gsell, P. D. Weinberg, and C. R. Ethier. Haemodynamics in the mouse aortic arch computed from MRI-derived velocities at the aortic root. J. R. Soc. Interface. 9:2834–2844, 2012.

    Article  Google Scholar 

  36. Willett, N. J., R. C. Long, K. Maiellaro-Rafferty, R. L. Sutliff, R. Shafer, J. N. Oshinski, D. P. Giddens, R. E. Guldberg, and W. R. Taylor. An in vivo murine model of low-magnitude oscillatory wall shear stress to address the molecular mechanisms of mechanotransduction–brief report. Arterioscler. Thromb. Vasc. Biol. 30:2099–2102, 2010.

    Article  CAS  Google Scholar 

  37. Zhu, H., J. Zhang, J. Shih, F. Lopez-Bertoni, J. R. Hagaman, N. Maeda, and M. H. Friedman. Differences in aortic arch geometry, hemodynamics, and plaque patterns between C57BL/6 and 129/SvEv mice. J. Biomech. Eng. 131:121005, 2009.

    Article  Google Scholar 

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Acknowledgments

MRI scans were performed at the University of Utah Preclinical Imaging Facility supported by NIH Grant S10 RR023017. Seg3D is an Open Source software project that is supported by the National Institute of General Medical Sciences of the National Institutes of Health under Grant Number P41 GM103545.

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Correspondence to Lucas H. Timmins.

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Associate Editor Stefan M. Duma oversaw the review of this article.

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Smith, K.A., Merchant, S.S., Hsu, E.W. et al. Effect of Subject-Specific, Spatially Reduced, and Idealized Boundary Conditions on the Predicted Hemodynamic Environment in the Murine Aorta. Ann Biomed Eng 49, 3255–3266 (2021). https://doi.org/10.1007/s10439-021-02851-7

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