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


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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Computational fluid dynamics


Coupled momentum method


Fluid–structure interaction


Gradient echo


Least squares error


Phase contrast magnetic resonance imaging


Pulse wave velocity


Random Sample Consensus


Reduced unified continuum


Spoiled gradient echo MRI




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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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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).

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