Validation of 4D Flow based relative pressure maps in aortic flows

4Dflow-VP-Net: A deep convolutional neural network for noninvasive estimation of relative pressures in stenotic flows from 4D flow MRI

PURPOSE

To estimate relative transvalvular pressure gradient (TVPG) noninvasively from 4D flow MRI.

METHODS

A novel deep learning-based approach is proposed to estimate pressure gradient across stenosis from four-dimensional flow MRI (4D flow MRI) velocities. A deep neural network 4D flow Velocity-to-Presure Network (4Dflow-VP-Net) was trained to learn the spatiotemporal relationship between velocities and pressure in stenotic vessels. Training data were simulated by computational fluid dynamics (CFD) for different pulsatile flow conditions under an aortic flow waveform. The network was tested to predict pressure from CFD-simulated velocity data, in vitro 4D flow MRI data, and in vivo 4D flow MRI data of patients with both moderate and severe aortic stenosis. TVPG derived from 4Dflow-VP-Net was compared to catheter-based pressure measurements for available flow rates, in vitro and Doppler echocardiography-based pressure measurement, in vivo.

RESULTS

Relative pressures calculated by 4Dflow-VP-Net and in vitro pressure catheterization revealed strong correlation (r2  = 0.91). Correlations analysis of TVPG from reference CFD and 4Dflow-VP-Net for 450 simulated flow conditions showed strong correlation (r2  = 0.99). TVPG from in vitro MRI had a correlation coefficient of r2  = 0.98 with reference CFD. 4Dflow-VP-Net, applied to 4D flow MRI in 16 patients, showed comparable TVPG measurement with Doppler echocardiography (r2  = 0.85). Bland-Altman analysis of TVPG measurements showed mean bias and limits of agreement of -0.20 ± 2.07 mmHg and 0.19 ± 0.45 mmHg for CFD-simulated velocities and in vitro 4D flow velocities. In patients, overestimation of Doppler echocardiography relative to TVPG from 4Dflow-VP-Net (10.99 ± 6.77 mmHg) was observed.

CONCLUSION

The proposed approach can predict relative pressure in both in vitro and in vivo 4D flow MRI of aortic stenotic patients with high fidelity.

Relative pressure estimation from 4D flow MRI using generalized Bernoulli equation in a phantom model of arterial stenosis

OBJECTIVE

Arterial stenosis is a significant cardiovascular disease requiring accurate estimation of the pressure gradients for determining hemodynamic significance. In this paper, we propose Generalized Bernoulli Equation (GBE) utilizing interpolated-based method to estimate relative pressures using streamlines and pathlines from 4D Flow MRI.

METHODS

4D Flow MRI data in a stenotic phantom model and computational fluid dynamics simulated velocities generated under identical flow conditions were processed by Generalized Bernoulli Equation (GBE), Reduced Bernoulli Equations (RBE), as well as the Simple Bernoulli Equation (SBE) which is clinically prevalent. Pressures derived from 4D flow MRI and noise corrupted CFD velocities were compared with pressures generated directly with CFD as well as pressures obtained using Millar catheters under identical flow conditions.

RESULTS

It was found that SBE and RBE methods underestimated the relative pressure for lower flow rates while overestimating the relative pressure at higher flow rates. Specifically, compared to the reference pressure, SBE underestimated the maximum relative pressure by 22[Formula: see text] for a pulsatile flow data with peak flow rate [Formula: see text] and overestimated by around 40[Formula: see text] when [Formula: see text]. In contrast, for GBE method the relative pressure values were overestimated by 15[Formula: see text] with [Formula: see text]and around 10[Formula: see text] with [Formula: see text].

CONCLUSION

GBE methods showed robust performance to additive image noise compared to other methods. Our findings indicate that GBE pressure estimation over pathlines attains the highest level of accuracy compared to GBE over streamlines, and the SBE and RBE methods.

The impact of 4D-Flow MRI spatial resolution on patient-specific CFD simulations of the thoracic aorta

Magnetic Resonance Imaging (MRI) is considered the gold standard of medical imaging technologies as it allows for accurate imaging of blood vessels. 4-Dimensional Flow Magnetic Resonance Imaging (4D-Flow MRI) is built on conventional MRI, and provides flow data in the three vector directions and a time resolved magnitude data set. As such it can be used to retrospectively calculate haemodynamic parameters of interest, such as Wall Shear Stress (WSS). However, multiple studies have indicated that a significant limitation of the imaging technique is the spatiotemporal resolution that is currently available. Recent advances have proposed and successfully integrated 4D-Flow MRI imaging techniques with Computational Fluid Dynamics (CFD) to produce patient-specific simulations that have the potential to aid in treatments,surgical decision making, and risk stratification. However, the consequences of using insufficient 4D-Flow MRI spatial resolutions on any patient-specific CFD simulations is currently unclear, despite being a recognised limitation. The research presented in this study aims to quantify the inaccuracies in patient-specific 4D-Flow MRI based CFD simulations that can be attributed to insufficient spatial resolutions when acquiring 4D-Flow MRI data. For this research, a patient has undergone four 4D-Flow MRI scans acquired at various isotropic spatial resolutions and patient-specific CFD simulations have subsequently been run using geometry and velocity data produced from each scan. It was found that compared to CFD simulations based on a \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$1.5\,{\text {mm}} \times 1.5\,{\text {mm}} \times 1.5\,{\text {mm}}$$\end{document}1.5mm×1.5mm×1.5mm, using a spatial resolution of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$4\,{\text {mm}} \times 4\,{\text {mm}} \times 4\,{\text {mm}}$$\end{document}4mm×4mm×4mm substantially underestimated the maximum velocity magnitude at peak systole by \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$110.55\%$$\end{document}110.55%. The impacts of 4D-Flow MRI spatial resolution on WSS calculated from CFD simulations have been investigated and it has been shown that WSS is underestimated in CFD simulations that are based on a coarse 4D-Flow MRI spatial resolution. The authors have concluded that a minimum 4D-Flow MRI spatial resolution of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$1.5\,{\text {mm}} \times 1.5\,{\text {mm}} \times 1.5\,{\text {mm}}$$\end{document}1.5mm×1.5mm×1.5mm must be used when acquiring 4D-Flow MRI data to perform patient-specific CFD simulations. A coarser spatial resolution will produce substantial differences within the flow field and geometry.

Assessment of 4D flow MRI's quality by verifying its Navier-Stokes compatibility

4D Flow Magnetic Resonance Imaging (MRI) is the state-of-the-art technique to comprehensively measure the complex spatio-temporal and multidirectional patterns of blood flow. However, it is subject to artifacts such as noise and aliasing, which due to the 3D and dynamic structure is difficult to detect in clinical practice. In this work, a new mathematical and computational model to determine the quality of 4D Flow MRI is presented. The model is derived by assuming the true velocity satisfies the incompressible Navier-Stokes equations and that can be decomposed by the measurements u→meas plus an extra field w→ . Therefore, a non-linear problem with w→ as unknown arises, which serves as a measure of data quality. A stabilized finite element formulation tailored to this problem is proposed and analyzed. Then, extensive numerical examples-using synthetic 4D Flow MRI data as well as real measurements on experimental phantom and subjects-illustrate the ability to use w→ for assessing the quality of 4D Flow MRI measurements over space and time.

On the numerical treatment of viscous and convective effects in relative pressure reconstruction methods

The mechanism of many cardiovascular diseases can be understood by studying the pressure distribution in blood vessels. Direct pressure measurements, however, require invasive probing and provide only single-point data. Alternatively, relative pressure fields can be reconstructed from imaging-based velocity measurements by considering viscous and inertial forces. Both contributions can be potential troublemakers in pressure reconstruction: the former due to its higher-order derivatives, and the latter because of the quadratic nonlinearity in the convective acceleration. Viscous and convective terms can be treated in various forms, which, although equivalent for ideal measurements, can perform differently in practice. In fact, multiple versions are often used in literature, with no apparent consensus on the more suitable variants. In this context, the present work investigates the performance of different versions of relative pressure estimators. For viscous effects, in particular, two new modified estimators are presented to circumvent second-order differentiation without requiring surface integrals. In-silico and in-vitro data in the typical regime of cerebrovascular flows are considered, allowing a systematic noise sensitivity study. Convective terms are shown to be the main source of error, even for flows with pronounced viscous component. Moreover, the conservation (often integrated) form of convection exhibits higher noise sensitivity than the standard convective description, in all three families of estimators considered here. For the classical pressure Poisson estimator, the present modified version of the viscous term tends to yield better accuracy than the (recently introduced) integrated form, although this effect is in most cases negligible when compared to convection-related errors.

Unlocking the Non-invasive Assessment of Conduit and Reservoir Function in the Aorta

Aortic surgeries in congenital conditions, such as hypoplastic left heart syndrome (HLHS), aim to restore and maintain the conduit and reservoir functions of the aorta. We proposed a method to assess these two functions based on 4D flow MRI, and we applied it to study the aorta in pre-Fontan HLHS. Ten pre-Fontan HLHS patients and six age-matched controls were studied to derive the advective pressure difference and viscous dissipation for conduit function, and pulse wave velocity and elastic modulus for reservoir function. The reconstructed neo-aorta in HLHS subjects achieved a good conduit function at a cost of an impaired reservoir function (69.7% increase of elastic modulus). The native descending HLHS aorta displayed enhanced reservoir (elastic modulus being 18.4% smaller) but impaired conduit function (three-fold increase in peak advection). A non-invasive and comprehensive assessment of aortic conduit and reservoir functions is feasible and has potentially clinical relevance in congenital vascular conditions.