4D Flow MRI Pressure Estimation Using Velocity Measurement-Error-Based Weighted Least-Squares

Super-Resolving and Denoising 4D flow MRI of Neurofluids Using Physics-Guided Neural Networks

PURPOSE

To obtain high-resolution velocity fields of cerebrospinal fluid (CSF) and cerebral blood flow by applying a physics-guided neural network (div-mDCSRN-Flow) to 4D flow MRI.

METHODS

The div-mDCSRN-Flow network was developed to improve spatial resolution and denoise 4D flow MRI. The network was trained with patches of paired high-resolution and low-resolution synthetic 4D flow MRI data derived from computational fluid dynamic simulations of CSF flow within the cerebral ventricles of five healthy cases and five Alzheimer's disease cases. The loss function combined mean squared error with a binary cross-entropy term for segmentation and a divergence-based regularization term for the conservation of mass. Performance was assessed using synthetic 4D flow MRI in one healthy and one Alzheimer' disease cases, an in vitro study of healthy cerebral ventricles, and in vivo 4D flow imaging of CSF as well as flow in arterial and venous blood vessels. Comparison was performed to trilinear interpolation, divergence-free radial basis functions, divergence-free wavelets, 4DFlowNet, and our network without divergence constraints.

RESULTS

The proposed network div-mDCSRN-Flow outperformed other methods in reconstructing high-resolution velocity fields from synthetic 4D flow MRI in healthy and AD cases. The div-mDCSRN-Flow network reduced error by 22.5% relative to linear interpolation for in vitro core voxels and by 49.5% in edge voxels.

CONCLUSION

The results demonstrate generalizability of our 4D flow MRI super-resolution and denoising approach due to network training using flow patches and physics-based constraints. The mDCSRN-Flow network can facilitate MRI studies involving CSF flow measurements in cerebral ventricles and association of MRI-based flow metrics with cerebrovascular health.

Left ventricle diastolic vortex ring characterization in ischemic cardiomyopathy: insight into atrio-ventricular interplay

Diastolic vortex ring (VR) plays a key role in the blood-pumping function exerted by the left ventricle (LV), with altered VR structures being associated with LV dysfunction. Herein, we sought to characterize the VR diastolic alterations in ischemic cardiomyopathy (ICM) patients with systo-diastolic LV dysfunction, as compared to healthy controls, in order to provide a more comprehensive understanding of LV diastolic function. 4D Flow MRI data were acquired in ICM patients (n = 15) and healthy controls (n = 15). The λ2 method was used to extract VRs during early and late diastolic filling. Geometrical VR features, e.g., circularity index (CI), orientation (α), and inclination with respect to the LV outflow tract (ß), were extracted. Kinetic energy (KE), rate of viscous energy loss ( EL ˙ ), vorticity (W), and volume (V) were computed for each VR; the ratios with the respective quantities computed for the entire LV were derived. At peak E-wave, the VR was less circular (p = 0.032), formed a smaller α with the LV long-axis (p = 0.003) and a greater ß (p = 0.002) in ICM patients as compared to controls. At peak A-wave, CI was significantly increased (p = 0.034), while α was significantly smaller (p = 0.016) and β was significantly increased (p = 0.036) in ICM as compared to controls. At both peak E-wave and peak A-wave,EL ˙ VR / EL ˙ LV , WVR/WLV, and VVR/VLV significantly decreased in ICM patients vs. healthy controls. KEVR/VVR showed a significant decrease in ICM patients with respect to controls at peak E-wave, while VVR remained comparable between normal and pathologic conditions. In the analyzed ICM patients, the diastolic VRs showed alterations in terms of geometry and energetics. These derangements might be attributed to both structural and functional alterations affecting the infarcted wall region and the remote myocardium.

Enhanced echocardiographic assessment of intracardiac flow in congenital heart disease

BACKGROUND

4D flow magnetic resonance imaging (4D flow MRI) can assess and measure the complex flow patterns of the right ventricle (RV) in congenital heart diseases, but its limited availability makes the broad application of intracardiac flow assessment challenging. Color Doppler imaging velocity reconstruction from conventional echocardiography is an emerging alternative, but its validity against 4D flow MRI needs to be established.

OBJECTIVE

To compare intracardiac flow parameters measured by color Doppler velocity reconstruction (DoVeR) against parameters measured from 4D flow MRI.

METHODS

We analyzed 20 subjects, including 7 normal RVs and 13 abnormal RVs (10 with repaired Tetralogy of Fallot, and 3 with atrial-level shunts). Intracardiac flow parameters such as relative pressure difference, vortex strength, total kinetic energy, and viscous energy loss were quantified using DoVeR and 4D flow MRI. The agreement between the two methods was determined by comparing the spatial fields and quantifying the cross-correlation and normalized difference between time-series measurements.

RESULTS

The hemodynamic parameters obtained from DoVeR and 4D flow MRI showed similar flow characteristics and spatial distributions. The time evolutions of the parameters were also in good agreement between the two methods. The median correlation coefficient between the time-series of any parameter was between 0.87 and 0.92, and the median L2-norm deviation was between 10% to 14%.

CONCLUSIONS

Our study shows that DoVeR is a reliable alternative to 4D flow MRI for quantifying intracardiac hemodynamic parameters in the RV.

Cardiac MR modelling of systolic and diastolic blood pressure

AIMS

Blood pressure (BP) is a crucial factor in cardiovascular health and can affect cardiac imaging assessments. However, standard outpatient cardiovascular MR (CMR) imaging procedures do not typically include BP measurements prior to image acquisition. This study proposes that brachial systolic BP (SBP) and diastolic BP (DBP) can be modelled using patient characteristics and CMR data.

METHODS

In this multicentre study, 57 patients from the PREFER-CMR registry and 163 patients from other registries were used as the derivation cohort. All subjects had their brachial SBP and DBP measured using a sphygmomanometer. Multivariate linear regression analysis was applied to predict brachial BP. The model was subsequently validated in a cohort of 169 healthy individuals.

RESULTS

Age and left ventricular ejection fraction were associated with SBP. Aortic forward flow, body surface area and left ventricular mass index were associated with DBP. When applied to the validation cohort, the correlation coefficient between CMR-derived SBP and brachial SBP was (r=0.16, 95% CI 0.011 to 0.305, p=0.03), and CMR-derived DBP and brachial DBP was (r=0.27, 95% CI 0.122 to 0.403, p=0.0004). The area under the curve (AUC) for CMR-derived SBP to predict SBP>120 mmHg was 0.59, p=0.038. Moreover, CMR-derived DBP to predict DBP>80 mmHg had an AUC of 0.64, p=0.002.

CONCLUSION

CMR-derived SBP and DBP models can estimate brachial SBP and DBP. Such models may allow efficient prospective collection, as well as retrospective estimation of BP, which should be incorporated into assessments due to its critical effect on load-dependent parameters.

A Vector Fitting Approach for the Automated Estimation of Lumped Boundary Conditions of 1D Circulation Models

PURPOSE

The choice of appropriate boundary conditions is a crucial step in the development of cardiovascular models for blood flow simulations. The three-element Windkessel model is usually employed as a lumped boundary condition, providing a reduced order representation of the peripheral circulation. However, the systematic estimation of the Windkessel parameters remains an open problem. Moreover, the Windkessel model is not always adequate to model blood flow dynamics, which often require more elaborate boundary conditions. In this study, we propose a method for the estimation of the parameters of high order boundary conditions, including the Windkessel model, from pressure and flow rate waveforms at the truncation point. Moreover, we investigate the effect of adopting higher order boundary conditions, corresponding to equivalent circuits with more than one storage element, on the accuracy of the model.

METHOD

The proposed technique is based on Time-Domain Vector Fitting, a modeling algorithm that, given samples of the input and output of a system, such as pressure and flow waveforms, can derive a differential equation approximating their relation.

RESULTS

The capabilities of the proposed method are tested on a 1D circulation model consisting of the 55 largest human systemic arteries, to demonstrate its accuracy and its usefulness to estimate boundary conditions with order higher than the traditional Windkessel models. The proposed method is compared to other common estimation techniques, and its robustness in parameter estimation is verified in presence of noisy data and of physiological changes of aortic flow rate induced by mental stress.

CONCLUSION

Results suggest that the proposed method is able to accurately estimate boundary conditions of arbitrary order. Higher order boundary conditions can improve the accuracy of cardiovascular simulations, and Time-Domain Vector Fitting can automatically estimate them.

Automatic 4D Flow MRI Segmentation Using the Standardized Difference of Means Velocity

We present a method to automatically segment 4D flow magnetic resonance imaging (MRI) by identifying net flow effects using the standardized difference of means (SDM) velocity. The SDM velocity quantifies the ratio between the net flow and observed flow pulsatility in each voxel. Vessel segmentation is performed using an F-test, identifying voxels with significantly higher SDM velocity values than background voxels. We compare the SDM segmentation algorithm against pseudo-complex difference (PCD) intensity segmentation of 4D flow measurements in in vitro cerebral aneurysm models and 10 in vitro Circle of Willis (CoW) datasets. We also compared the SDM algorithm to convolutional neural network (CNN) segmentation in 5 thoracic vasculature datasets. The in vitro flow phantom geometry is known, while the ground truth geometries for the CoW and thoracic aortas are derived from high-resolution time-of-flight (TOF) magnetic resonance angiography and manual segmentation, respectively. The SDM algorithm demonstrates greater robustness than PCD and CNN approaches and can be applied to 4D flow data from other vascular territories. The SDM to PCD comparison demonstrated an approximate 48% increase in sensitivity in vitro and 70% increase in the CoW, respectively; the SDM and CNN sensitivities were similar. The vessel surface derived from the SDM method was 46% closer to the in vitro surfaces and 72% closer to the in vitro TOF surfaces than the PCD approach. The SDM and CNN approaches both accurately identify vessel surfaces. The SDM algorithm is a repeatable segmentation method, enabling reliable computation of hemodynamic metrics associated with cardiovascular disease.

Exploring the influence of nasal vestibule structure on nasal obstruction using CFD and Machine Learning method

Motivated by clinical findings about the nasal vestibule, this study analyzes the aerodynamic characteristics of the nasal vestibule and attempt to determine anatomical features which have a large influence on airflow through a combination of Computational Fluid Dynamics (CFD) and machine learning method. Firstly, the aerodynamic characteristics of the nasal vestibule are detailedly analyzed using the CFD method. Based on CFD simulation results, we divide the nasal vestibule into two types with distinctly different airflow patterns, which is consistent with clinical findings. Secondly, we explore the relationship between anatomical features and aerodynamic characteristics by developing a novel machine learning model which could predict airflow patterns based on several anatomical features. Feature mining is performed to determine the anatomical feature which has the greatest impact on respiratory function. The method is developed and validated on 41 unilateral nasal vestibules from 26 patients with nasal obstruction. The correctness of the CFD analysis and the developed model is verified by comparing them with clinical findings.

Motion-resolved real-time 4D flow MRI with low-rank and subspace modeling

PURPOSE

To develop a new motion-resolved real-time four-dimensional (4D) flow MRI method, which enables the quantification and visualization of blood flow velocities with three-directional flow encodings and volumetric coverage without electrocardiogram (ECG) synchronization and respiration control.

METHODS

An integrated imaging method is presented for real-time 4D flow MRI, which encompasses data acquisition, image reconstruction, and postprocessing. The proposed method features a specialized continuous ( k , t ) $$ \left(\mathbf{k},t\right) $$ -space acquisition scheme, which collects two sets of data (i.e., training data and imaging data) in an interleaved manner. By exploiting strong spatiotemporal correlation of 4D flow data, it reconstructs time-series images from highly-undersampled ( k , t ) $$ \left(\mathbf{k},t\right) $$ -space measurements with a low-rank and subspace model. Through data-binning-based postprocessing, it constructs a five-dimensional dataset (i.e., x-y-z-cardiac-respiratory), from which respiration-dependent flow information is further analyzed. The proposed method was evaluated in aortic flow imaging experiments with ten healthy subjects and two patients with atrial fibrillation.

RESULTS

The proposed method achieves 2.4 mm isotropic spatial resolution and 34.4 ms temporal resolution for measuring the blood flow of the aorta. For the healthy subjects, it provides flow measurements in good agreement with those from the conventional 4D flow MRI technique. For the patients with atrial fibrillation, it is able to resolve beat-by-beat pathological flow variations, which cannot be obtained from the conventional technique. The postprocessing further provides respiration-dependent flow information.

CONCLUSION

The proposed method enables high-resolution motion-resolved real-time 4D flow imaging without ECG gating and respiration control. It is able to resolve beat-by-beat blood flow variations as well as respiration-dependent flow information.

Physics-informed compressed sensing for PC-MRI: an inverse Navier-Stokes problem

We formulate a physics-informed compressed sensing (PICS) method for the reconstruction of velocity fields from noisy and sparse phase-contrast magnetic resonance signals. The method solves an inverse Navier-Stokes boundary value problem, which permits us to jointly reconstruct and segment the velocity field, and at the same time infer hidden quantities such as the hydrodynamic pressure and the wall shear stress. Using a Bayesian framework, we regularize the problem by introducing a priori information about the unknown parameters in the form of Gaussian random fields. This prior information is updated using the Navier-Stokes problem, an energy-based segmentation functional, and by requiring that the reconstruction is consistent with the k-space signals. We create an algorithm that solves this inverse problem, and test it for noisy and sparse k-space signals of the flow through a converging nozzle. We find that the method is capable of reconstructing and segmenting the velocity fields from sparsely-sampled (15% k-space coverage), low (~10) signal-to-noise ratio (SNR) signals, and that the reconstructed velocity field compares well with that derived from fully-sampled (100% k-space coverage) high (>40) SNR signals of the same flow.

Wall Shear Stress Estimation for 4D Flow MRI Using Navier-Stokes Equation Correction

This study introduces a novel wall shear stress (WSS) estimation method for 4D flow MRI. The method improves the WSS accuracy by using the reconstructed pressure gradient and the flow-physics constraints to correct velocity gradient estimation. The method was tested on synthetic 4D flow data of analytical Womersley flow and flow in cerebral aneurysms and applied to in vivo 4D flow data acquired in cerebral aneurysms and aortas. The proposed method's performance was compared to the state-of-the-art method based on smooth-spline fitting of velocity profile and the WSS calculated from uncorrected velocity gradient. The proposed method improved the WSS accuracy by as much as 100% for the Womersley flow and reduced the underestimation of mean WSS by 39 to 50% for the synthetic aneurysmal flow. The predicted mean WSS from the in vivo aneurysmal data using the proposed method was 31 to 50% higher than the other methods. The predicted aortic WSS using the proposed method was 3 to 6 times higher than the other methods and was consistent with previous CFD studies and the results from recently developed methods that take into account the limited spatial resolution of 4D flow MRI. The proposed method improves the accuracy of WSS estimation from 4D flow MRI, which can help predict blood vessel remodeling and progression of cardiovascular diseases.

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.

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.

A multi-modality approach for enhancing 4D flow magnetic resonance imaging via sparse representation

This work evaluates and applies a multi-modality approach to enhance blood flow measurements and haemodynamic analysis with phase-contrast magnetic resonance imaging (4D flow MRI) in cerebral aneurysms (CAs). Using a library of high-resolution velocity fields from patient-specific computational fluid dynamic simulations and in vitro particle tracking velocimetry measurements, the flow field of 4D flow MRI data is reconstructed as the sparse representation of the library. The method was evaluated with synthetic 4D flow MRI data in two CAs. The reconstruction enhanced the spatial resolution and velocity accuracy of the synthetic MRI data, leading to reliable pressure and wall shear stress (WSS) evaluation. The method was applied on in vivo 4D flow MRI data acquired in the same CAs. The reconstruction increased the velocity and WSS by 6-13% and 39-61%, respectively, suggesting that the accuracy of these quantities was improved since the raw MRI data underestimated the velocity and WSS by 10-20% and 40-50%, respectively. The computed pressure fields from the reconstructed data were consistent with the observed flow structures. The results suggest that using the sparse representation flow reconstruction with in vivo 4D flow MRI enhances blood flow measurement and haemodynamic analysis.

Noninvasive quantification of cerebrovascular pressure changes using 4D Flow MRI

PURPOSE

Hemodynamic alterations are indicative of cerebrovascular disease. However, the narrow and tortuous cerebrovasculature complicates image-based assessment, especially when quantifying relative pressure. Here, we present a systematic evaluation of image-based cerebrovascular relative pressure mapping, investigating the accuracy of the routinely used reduced Bernoulli (RB), the extended unsteady Bernoulli (UB), and the full-field virtual work-energy relative pressure ( ν WERP) method.

METHODS

Patient-specific in silico models were used to generate synthetic cerebrovascular 4D Flow MRI, with RB, UB, and ν WERP performance quantified as a function of spatiotemporal sampling and image noise. Cerebrovascular relative pressures were also derived in 4D Flow MRI from healthy volunteers ( n = 8 ), acquired at two spatial resolutions (dx = 1.1 and 0.8 mm).

RESULTS

The in silico analysis indicate that accurate relative pressure estimations are inherently coupled to spatial sampling: at dx = 1.0 mm high errors are reported for all methods; at dx = 0.5 mm ν WERP recovers relative pressures at a mean error of 0.02 ± 0.25 mm Hg, while errors remain higher for RB and UB (mean error of -2.18 ± 1.91 and -2.18 ± 1.87 mm Hg, respectively). The dependence on spatial sampling is also indicated in vivo, albeit with higher correlative dependence between resolutions using ν WERP (k = 0.64, R2 = 0.81 for dx = 1.1 vs. 0.8 mm) than with RB or UB (k = 0.04, R2 = 0.03, and k = 0.07, R2 = 0.07, respectively).

CONCLUSION

Image-based full-field methods such as ν WERP enable cerebrovascular relative pressure mapping; however, accuracy is directly dependent on utilized spatial resolution.

Divergence-Free Constrained Phase Unwrapping and Denoising for 4D Flow MRI Using Weighted Least-Squares

A novel divergence-free constrained phase unwrapping method was proposed and evaluated for 4D flow MRI. The unwrapped phase field was obtained by integrating the phase variations estimated from the wrapped phase data using weighted least-squares. The divergence-free constraint for incompressible blood flow was incorporated to regulate and denoise the resulting phase field. The proposed method was tested on synthetic phase data of left ventricular flow and in vitro 4D flow measurement of Poiseuille flow. The method was additionally applied to in vivo 4D flow measurements in the thoracic aorta from 30 human subjects. The performance of the proposed method was compared to the state-of-the-art 4D single-step Laplacian algorithm. The synthetic phase data were completely unwrapped by the proposed method for all the cases with velocity encoding (venc) as low as 20% of the maximum velocity and signal-to-noise ratio as low as 5. The in vitro Poiseuille flow data were completely unwrapped with a 60% increase in the velocity-to-noise ratio. For the in-vivo aortic datasets with venc ratio less than 0.4, the proposed method significantly improved the success rate by as much as 40% and reduced the velocity error levels by a factor of 10 compared to the state-of-the-art method. The divergence-free constrained method exhibits reliability and robustness on phase unwrapping and shows improved accuracy of velocity and hemodynamic quantities by unwrapping the low-venc 4D flow MRI data.

Structural Heart 4D Flow MRI for Hemodynamic Assessment: How We Do It

MRI is an essential diagnostic tool in the anatomic and functional evaluation of cardiovascular disease. In many practices, 2D phase-contrast (2D-PC) has been used for blood flow quantification. 4D Flow MRI is a time-resolved volumetric acquisition that captures the vector field of blood flow along with anatomic images. 4D Flow MRI provides a simpler acquisition compared to 2D-PC and facilitates a more accurate and comprehensive hemodynamic assessment. Advancements in accelerated imaging have significantly shortened scan times of 4D Flow MRI while preserving image quality, enabling this technology to transition from the research arena to routine clinical practice. In this article, we review technical optimization based on our clinical experience of over 10 years with 4D Flow MRI. We also present pearls and pitfalls in the practical application of 4D Flow MRI, including how to quantify cardiovascular shunts, valvular or vascular stenosis, and valvular regurgitation. As experience increases, and as 4D Flow sequences and post-processing software become more broadly available, 4D Flow MRI will likely become an essential component of cardiac imaging for practices involved in the management of congenital and acquired structural heart disease.