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Validation of the Reduced Unified Continuum Formulation Against In Vitro 4D-Flow MRI

Abstract

We previously introduced and verified the reduced unified continuum formulation for vascular fluid–structure interaction (FSI) against Womersley’s deformable wall theory. Our present work seeks to investigate its performance in a patient-specific aortic setting in which assumptions of idealized geometries and velocity profiles are invalid. Specifically, we leveraged 2D magnetic resonance imaging (MRI) and 4D-flow MRI to extract high-resolution anatomical and hemodynamic information from an in vitro flow circuit embedding a compliant 3D-printed aortic phantom. To accurately reflect experimental conditions, we numerically implemented viscoelastic external tissue support, vascular tissue prestressing, and skew boundary conditions enabling in-plane vascular motion at each inlet and outlet. Validation of our formulation is achieved through close quantitative agreement in pressures, lumen area changes, pulse wave velocity, and early systolic velocities, as well as qualitative agreement in late systolic flow structures. Our validated suite of FSI techniques offers a computationally efficient approach for numerical simulation of vascular hemodynamics. This study is among the first to validate a cardiovascular FSI formulation against an in vitro flow circuit involving a compliant vascular phantom of complex patient-specific anatomy.

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Abbreviations

CFD:

Computational fluid dynamics

CMM:

Coupled momentum method

FSI:

Fluid–structure interaction

GRE:

Gradient echo

LSE:

Least squares error

PC-MRI:

Phase contrast magnetic resonance imaging

PWV:

Pulse wave velocity

RANSAC:

Random Sample Consensus

RUC:

Reduced unified continuum

SPGR:

Spoiled gradient echo MRI

TTF:

Time-to-foot

References

  1. Alastruey, J., Numerical modelling of pulse wave propagation in the cardiovascular system: development, validation and clinical applications. PhD thesis, Imperial College London, 2006.

  2. Annio, G., R. Torii, A. Ducci, V. Muthurangu, V. Tsang, and G. Burriesci, Experimental validation of enhanced magnetic resonance imaging (EMRI) using particle image velocimetry (PIV). Ann. Biomed. Eng. 49:3481–3493, 2021.

    Article  Google Scholar 

  3. Bazilevs, Y., M.-C. Hsu, Y. Zhang, W. Wang, T. Kvamsdal, S. Hentschel, and J. Isaksen, Computational vascular fluid-structure interaction: methodology and application to cerebral aneurysms. Biomech. Model. Mechanobiol. 9(4):481–498, 2010.

    CAS  Article  Google Scholar 

  4. Biglino, G., D. Cosentino, J. Steeden, L. De Nova, M. Castelli, H. Ntsinjana, G. Pennati, A. Taylor, and S. Schievano, Using 4D cardiovascular magnetic resonance imaging to validate computational fluid dynamics: a case study. Front. Pediatr. 3:107, 2015.

    Article  Google Scholar 

  5. Biglino, G., P. Verschueren, R. Zegels, A. Taylor, and S. Schievano, Rapid prototyping compliant arterial phantoms for in-vitro studies and device testing. J. Cardiovasc. Magn. Reson. 15:2, 2013.

    Article  Google Scholar 

  6. Cheng, Z., C. Juli, N. Wood, R. Gibbs, and X. Xu, Predicting flow in aortic dissection: comparison of computational model with PC-MRI velocity measurements. Med. Eng. Phys. 36(9), 1176–1184, 2014.

    CAS  Article  Google Scholar 

  7. Figueroa, C., I. Vignon-Clementel, K. Jansen, T. Hughes, and C. Taylor, A coupled momentum method for modeling blood flow in three-dimensional deformable arteries. Comput. Methods Appl. Mech. Eng. 195:5685–5706, 2006.

    Article  Google Scholar 

  8. Fonken, J., E. Maas, A. Nievergeld, M. van Sambeek, F. van de Vosse, and R. Lopata, Ultrasound-based fluid-structure interaction modeling of abdominal aortic aneurysms incorporating pre-stress. Front. Physiol. 12:1255, 2021.

    Article  Google Scholar 

  9. González Ballester, M., A. Zisserman, and M. Brady, Estimation of the partial volume effect in MRI. Med. Image Anal. 6(4):389–405, 2000.

  10. Griffiths, D., Treatment of skew boundary conditions in finite element analysis. Comput. Struct. 36(6):1009–1012, 1990.

    Article  Google Scholar 

  11. Ho, W., I. Tshimanga, M. Ngoepe, M. Jermy, and P. Geoghegan, Evaluation of a desktop 3D printed rigid refractive-indexed-matched flow phantom for PIV measurements on cerebral aneurysms. Cardiovasc. Eng. Technol. 11(1), 14–23, 2020.

    CAS  Article  Google Scholar 

  12. Hsu, M.-C. and Y. Bazilevs, Blood vessel tissue prestress modeling for vascular fluid-structure interaction simulation. Finite Elem. Anal. Des. 47(6), 593–599, 2011.

    Article  Google Scholar 

  13. Ionita, C., M. Mokin, N. Varble, D. Bednarek, J. Xiang, K. Snyde, A. Siddiqui, E. Levy, H. Meng, and S. Rudin, Challenges and limitations of patient-specific vascular phantom fabrication using 3D Polyjet printing. Proc. SPIE 9038:90380M, 2014.

    PubMed  PubMed Central  Google Scholar 

  14. Kaiser, A. N. Schiavone, J. Eaton, and A. Marsden, Validation of immersed boundary simulations of heart valve hemodynamics against in vitro 4D flow MRI data. https://arxiv.org/2111.00720[q-bio.TO], 2021.

  15. Knoops, P., G. Biglino, A. Hughes, K. Parker, L. Xu, S. Schievano, and R. Torii, A mock circulatory system incorporating a compliant 3D-printed anatomical model to investigate pulmonary hemodynamics. Artif. Organs 41(7):637–646, 2017.

    CAS  Article  Google Scholar 

  16. Kolyva, C., G. Biglino, J. Pepper, and A. Khir, A mock circulatory system with physiological distribution of terminal resistance and compliance: application for testing the intra-aortic balloon pump. Artif. Organs 36(3):E62–E70, 2012.

    CAS  Article  Google Scholar 

  17. Ku, J., M. Draney, F. Arko, W. Lee, F. Chan, N. Pelc, C. Zarins, and C. Taylor, In vivo validation of numerical prediction of blood flow in arterial bypass grafts. Ann. Biomed. Eng. 30(6):743–752, 2002.

    Article  Google Scholar 

  18. Kung, E., A. Les, C. Figueroa, F. Medina, K. Arcaute, R. Wicker, M. McConnell, and C. Taylor, In vitro validation of finite element analysis of blood flow in deformable models. Ann. Biomed. Eng. 39:1947–1960, 2011.

    Article  Google Scholar 

  19. Kung, E., A. Les, F. Medina, R. Wicker, M. McConnell, and C. Taylor, In vitro validation of finite-element model of AAA hemodynamics incorporating realistic outlet boundary conditions. J. Biomech. Eng. 133(4):041003, 2011.

    Article  Google Scholar 

  20. Lan, H., A. Updegrove, N. Wilson, G. Maher, S. Shadden, and A. Marsden, A re-engineered software interface and workflow for the open-source simvascular cardiovascular modeling package. J. Biomech. Eng. 140(2):0245011–02450111, 2018.

    Article  Google Scholar 

  21. Lan, I., J. Liu, W. Yang, and A. Marsden, Numerical investigation of abdominal aortic aneurysm hemodynamics using the reduced unified continuum formulation for vascular fluid–structure interaction. Forces Mech. 7:100089, 2022.

    Article  Google Scholar 

  22. Lan, I., J. Liu, W. Yang, and A. Marsden, A reduced unified continuum formulation for vascular fluid-structure interaction. Comput. Methods Appl. Mech. Eng. 394:114852, 2022.

    Article  Google Scholar 

  23. Liu, J., I. Lan, O. Tikenogullari, and A. Marsden. A note on the accuracy of the generalized-\(\alpha\) scheme for the incompressible Navier–Stokes equations. Int. J. Numer. Methods Eng. 122:638–651, 2021.

    Article  Google Scholar 

  24. Liu, J., M. Latorre, and A. Marsden, A continuum and computational framework for viscoelastodynamics: I. finite deformation linear models. Comput. Methods Appl. Mech. Eng. 385:114059, 2021.

  25. Liu, J. and A. Marsden, A unified continuum and variational multiscale formulation for fluids, solids, and fluid–structure interaction. Comput. Methods Appl. Mech. Eng. 337:549–597, 2018.

    Article  Google Scholar 

  26. Liu, J., A. Marsden, and Z. Tao, An energy-stable mixed formulation for isogeometric analysis of incompressible hyperelastodynamics. Int. J. Numer. Methods Eng. 120:937–963, 2019.

    Article  Google Scholar 

  27. Liu, J., W. Yang, M. Dong, and A. Marsden, The nested block preconditioning technique for the incompressible Navier–Stokes equations with emphasis on hemodynamic simulations. Comput. Methods Appl. Mech. Eng. 367:113122, 2020.

    Article  Google Scholar 

  28. Long, Q., X. Xu, B. Ariff, S. Thom, A. Hughes, and A. Stanton, Reconstruction of blood flow patterns in a human carotid bifurcation: a combined CFD and MRI study. J. Magn. Reson. Imaging 11(3):299–311, 2000.

    CAS  Article  Google Scholar 

  29. Markl, M., W. Wallis, S. Brendecke, J. Simon, A. Frydrychowicz, and A. Harloff, Estimation of global aortic pulse wave velocity by flow-sensitive 4D MRI. Magn. Reson. Med. 63(6):1575–1582, 2010.

    Article  Google Scholar 

  30. Moireau, P., N. Xiao, M. Astorino, C. Figueroa, D. Chapelle, C. Taylor, and J. Gerbeau, External tissue support and fluid–structure simulation in blood flows. Biomech. Model. Mechanobiol. 11:1–18, 2012.

    CAS  Article  Google Scholar 

  31. Polanczyk, A., M. Klinger, J. Nanobachvili, I. Huk, and C. Neumayer, Artificial circulatory model for analysis of human and artificial vessels. Appl. Sci. 8:1017, 2018.

    Article  Google Scholar 

  32. Pons, R., A. Guala, J. Rodríguez-Palomares, J. Cajas, L. Dux-Santoy, G. Teixidó-Tura, J. Molins, M. Vázquez, A. Evangelista, and J. Martorell, Fluid–structure interaction simulations outperform computational fluid dynamics in the description of thoracic aorta haemodynamics and in the differentiation of progressive dilation in Marfan syndrome patients. R. Soc. Open Sci. 7(2):191752, 2020.

    CAS  Article  Google Scholar 

  33. Saitta, S., S. Pirola, F. Piatti, E. Votta, F. Lucherini, F. Pluchinotta, M. Carminati, M. Lombardi, C. Geppert, F. Cuomo, C. Figueroa, X. Xu, and A. Redaelli, Evaluation of 4D flow MRI-based non-invasive pressure assessment in aortic coarctations. J. Biomech. 94:13–21, 2019.

    Article  Google Scholar 

  34. Schiavazzi, D., F. Coletti, G. Iaccarino, and J. Eaton, A matching pursuit approach to solenoidal filtering of three-dimensional velocity measurements. J. Comput. Phys. 263(C):206–221, 2014.

  35. Tanné, D., E. Bertrand, L. Kadem, P. Pibarot, and R. Rieu, Assessment of left heart and pulmonary circulation flow dynamics by a new pulsed mock circulatory system. Exp. Fluids 48:837–850, 2010.

    Article  Google Scholar 

  36. Urbina, J., J. Sotelo, D. Springmüller, C. Montalba, K. Letelier, C. Tejos, P. Irarrázaval, M. Andia, R. Razavi, I. Valverde, and S. Uribe, Realistic aortic phantom to study hemodynamics using MRI and cardiac catheterization in normal and aortic coarctation conditions. Ann. Biomed. Eng. 45:525–541, 2017.

    Article  Google Scholar 

  37. Zhou, J., M. Esmaily-Moghadam, T. Conover, T.-Y. Hsia, A. Marsden, R. Figliola, and The MOCHA Investigators, In vitro assessment of the assisted bidirectional glenn procedure for stage one single ventricle repair. Cardiovasc. Eng. Technol. 6(3):256–267, 2015.

  38. Zimmermann, J., M. Loecher, F. Kolawole, K. Bäumler, K. Gifford, S. Dual, M. Levenston, A. Marsden, and D. Ennis, On the impact of vessel wall stiffness on quantitative flow dynamics in a synthetic model of the thoracic aorta. Sci. Rep. 11(1):6703, 2021.

    CAS  Article  Google Scholar 

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Acknowledgments

This work was supported by the National Institutes of Health [Grant Nos. 1R01HL121754, 1R01HL123689, R01EB01830204], National Natural Science Foundation of China [Grant No. 12172160], and Guangdong-Hong Kong-Macao Joint Laboratory for Data-Driven Fluid Mechanics and Engineering Applications [Grant No. 2020B1212030001]. Ingrid S. Lan was supported by the National Science Foundation (NSF) Graduate Research Fellowship and Stanford Graduate Fellowship in Science and Engineering. Computational resources were provided by the Stanford Research Computing Center and Extreme Science and Engineering Discovery Environment supported by NSF [Grant No. ACI-1053575].

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No benefits in any form have been or will be received from a commercial party related directly or indirectly to the subject of this manuscript.

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Correspondence to Alison L. Marsden.

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Lan, I.S., Liu, J., Yang, W. et al. Validation of the Reduced Unified Continuum Formulation Against In Vitro 4D-Flow MRI. Ann Biomed Eng (2022). https://doi.org/10.1007/s10439-022-03038-4

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Keywords

  • Fluid–structure interaction
  • Pulse wave velocity
  • Magnetic resonance imaging
  • Compliant 3D printing
  • In vitro validation