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.

Keywords: Compliant 3D printing; Fluid–structure interaction; In vitro validation; Magnetic resonance imaging; Pulse wave velocity.

FIGURE 1.

(a) Print-ready 3D STL model of a patient-specific thoracic aorta, annotated with the caps and landmark slices for 2D cine PC-MRI and 2D cine GRE MRI. (b) The resulting compliant 3D-printed flow phantom with 2-cm extensions on all five caps to facilitate connection to custom barbed model-tubing transition elements. (c) MRI-compatible in vitro flow circuit consisting of a programmable flow pump, a fluid reservoir, tubing with pinch valves serving as resistance elements, and two sealed air compression chambers (${\mathit{C}}_1,{\mathit{C}}_2$) serving as capacitance elements. A flow transducer and two pressure transducers were inserted for resistance and capacitance tuning prior to transfer of the flow circuit into the MRI scanner. Red arrows indicate the direction of flow.

FIGURE 2.

Schematic of numerical simulation methods incorporating data from four MRI sequences. The anatomical model was segmented from the 3D SPGR scan. Velocities from 2D cine PC-MRI were integrated over lumen areas from 2D cine GRE MRI to generate the volumetric flow rates prescribed at BCA, LCA, and LSA with idealized parabolic velocity profiles. The outlet pressure measured by a pressure transducer was prescribed. Velocities from 4D-flow MRI were masked by lumen contours from 2D cine GRE MRI to generate the velocity profiles prescribed at inlet in Sim-4DMRI. These 4D-flow velocities were integrated to generate the volumetric flow rates prescribed at inlet with parabolic velocity profiles in Sim-Idealized.

FIGURE 3.

Comparison of experimental and simulated volumetric flow rates and pressures over time at the five caps. In both Sim-4DMRI and Sim-Idealized, in-plane motion of the wall boundary rings is enabled, and the prescribed damping constant is ${\mathit{c}}^{\mathrm{s}}=3\times {10}^5\mathrm{g}/\left({\mathrm{c}\mathrm{m}}^2\mathrm{s}\right)$. Sim-Idealized represents the only simulation in which experimental three-component velocities from 4D-flow MRI were not prescribed at the inlet.

FIGURE 4.

Comparison of experimental and simulated relative areas over time at the six 2D scan landmarks along the aortic arch. In both Sim-4DMRI and Sim-Idealized, in-plane motion of the wall boundary rings is enabled, and the prescribed damping constant is ${\mathit{c}}^{\mathrm{s}}=3\times {10}^5\mathrm{g}/\left({\mathrm{c}\mathrm{m}}^2\mathrm{s}\right)$. We note that the experimentally measured areas do not exhibit periodicity, displaying a sharp jump from $\mathit{t}=0.98\mathrm{s}$ to the artificially repeated $\mathit{t}=0.0$ value for $\mathit{t}=1.0\mathrm{s}$.

FIGURE 5.

Experimental 4D-flow MRI (top), Sim-4DMRI (middle), and (C) Sim-Idealized (bottom) velocity profiles at 6 evenly spaced temporal frames spanning the systolic phase of the cardiac cycle. All six 2D scan landmarks along the aortic arch are included.

FIGURE 6.

Experimental 4D-flow MRI (top), Sim-4DMRI (middle), and Sim-Idealized (bottom) velocity profiles on a sagittal plane at 6 evenly spaced temporal frames spanning the systolic phase of the cardiac cycle.

FIGURE 7.

Streamlines computed from experimental 4D-flow MRI (top), Sim-4DMRI (middle), and Sim-Idealized (bottom) velocities at 6 evenly spaced temporal frames spanning the systolic phase of the cardiac cycle. The left (L, top) and right (R, bottom) lateral sides are annotated.

FIGURE 8.

Numerical pulse wave velocity (PWV) computation for Sim-4DMRI using (A) 50 equidistant normal slices along the descending aorta. (B) Simulated pressure waveforms and lines used to determine times-to-foot (TTFs) are plotted for the five representative yellow slices. (C) Experimental (purple) and numerical (black) PWV estimates determined as slopes of linear regressions, performed with either least squares error (LSE) or Random Sample Consensus (RANSAC), relating TTF to the distance along the descending aortic centerline. The time delay seen in the numerical results relative to the experimental results is a consequence of the use of pressure rather than flow waveforms.