A pulsatile 3D flow relevant to thoracic hemodynamics: CFD - 4D Flow MRI comparison

Application Challenge AC7-04 © copyright ERCOFTAC 2021

Description

Introduction

The objective of the current Application Challenge is to provide a well-controlled environment and procedure to enable comparison between CFD and 4D Flow MRI. The experiment is designed to remove most classical sources of uncertainties inherent to the in vivo MRI such as moving deformable walls or undefined blood properties. The experimental MRI setup is shown in figure 1. The flow is studied within a component called (imaging) phantom. This latter term refers to an idealized object to calibrate or/and evaluate imaging devices in the field of biomedical imaging. In this study, the phantom has been designed to presents topological complexities analogous to the cardiovascular system (Fig. 2). Large Eddy Simulation (LES) has been conducted on the same geometry. Both the experiment and the simulation have been performed under a sinusoidal pulsatile flow, with flow conditions in the laminar-turbulent transition regime similar to what one can find in the cardiovascular system.

Figure 1: Schematic experimental setup

The methods described in this Application Challenge are mainly adapted from Puiseux et al. (2019) [2].

Relevance to Industrial Sector

4D Flow MRI (Magnetic Resonance Imaging) is a specific type of MRI sequences, which allows to image the velocity field of moving fluids such as blood. Therefore it represents an interesting opportunity for clinicians to detect and follow the evolution of cardiovascular diseases. However, this technique suffers from some limitations, which questions its accuracy and efficiency to measure relevant hemodynamic quantities. Although CFD accuracy depends on model assumptions, it also enables to bypass some of the limitations inherent to the MRI process in providing higher spatio-temporal resolutions and giving access to instantaneous and derived quantities. Thereby the idea of this Application Challenge is to use 4D Flow MRI and CFD to develop a reproducible method for enabling the comparison of the two methods.

Design or Assessment Parameters

Within the phantom, the velocity field with components in the three Cartesian directions was measured thanks to 4D Flow MRI. It was also measured in a transverse plane located at the inlet of the phantom by means of 2D cine PC-MRI. This latter technique is similar to 4D Flow MRI, but since it is performed only on a slice, it permits a higher spatio-temporal resolution. The velocity field was numerically predicted within the phantom as well, where the 2D cine PC-MRI data were used to specify the boundary conditions at the inlet.

Flow Domain Geometry

The flow phantom was constructed to generate a complex and realistic flow, such as that observed in the cardiovascular system. The aim was not to reproduce a patient-specific geometry, but to include several geometrical features yielding complex flow patterns analogous to in vivo flow patterns, while keeping the flow phantom relatively compact and well-controlled. A 26 mm inner diameter pipe bend was designed with a 50 mm radius of curvature to mimic aortic arch blood flows. A bifurcation was set in analogy with collateral arteries. The junction of the collateral duct and descending main pipe was designed to replicate the typical flow split that can be found in vivo between supraceliac and infrarenal arteries. Finally, a protuberance was attached at the intersection of the collateral and main branch to mimic blood flow patterns in an aortic aneurysm (Fig. 2). Typical flow structures expected are e.g. a flow recirculation in the aneurysm, regurgitation in the bifurcation, or strong longitudinal vorticity and secondary flow in the bent arch.

Figure 2: Analogy with the aorta - Orange: Aneurysm, Blue: Collateral, Green: Arch/Bend

An engineering drawing of the phantom is given in Figure 3. The phantom was 3D-printed and is made of Nylon PA 12 with a 60 μm geometric tolerance in one block and immersed within a silicon bath both for post-processing electromagnetism-induced eddy currents (also called Foucault's currents) effects on MRI images and for securing the phantom.

Figure 3: Engineering drawing of the phantom

Flow Physics and Fluid Dynamics Data

The fluid used in the experiment is a Newtonian blood-mimicking fluid with kinematic viscosity $\nu =4.02\times 10^{-6}$ m $^{2}$ /s and density $\rho =1020$ kg/m $^{3}$ . The fluid is assumed to be incompressible. The Reynolds number at the inlet is given by $Re={\frac {u_{bulk}D}{\nu }}$ where $u_{bulk}$ is the averaged inlet velocity and $D$ the diameter of the main duct. At peak systole (highest inlet velocity), a maximum $Re=1915$ at the inlet is measured and at end diastole (lowest flowrate) $Re=160$ . Thus the flow regime within the phantom lies in the laminar-turbulent transition, as expected in large arteries.