A Stokes-consistent backflow stabilization for physiological flows

In computational fluid dynamics incoming flow at open boundaries, or \emph{backflow}, often yields to unphysical instabilities for high Reynolds numbers. It is widely accepted that this is due to the incoming energy arising from the convection term, which cannot be \emph{a priori} controlled when the velocity field is unknown at the boundary. In order to improve the robustness of the numerical simulations, we propose a stabilized formulation based on a penalization of the residual of a weak Stokes problem on the open boundary, whose viscous part controls the incoming convective energy, while the inertial term contributes to the kinetic energy. We also present different strategies for the approximation of the boundary pressure gradient, which is needed for defining the stabilization term. The method has the advantage that it does not require neither artificial modifications or extensions of the computational domain. Moreover, it is consistent with the Womersley solution. We illustrate our approach on numerical examples ~- both academic and real-life -~ relevant to blood and respiratory flows. The results also show that the stabilization parameter can be reduced with the mesh size

A tangential regularization method for backflow stabilization in hemodynamics

In computational simulations of fluid flows, instabilities at the Neumann boundaries may appear during backflow regime. It is widely accepted that this is due to the incoming energy at the boundary, coming from the convection term, which cannot be controlled when the velocity field is unknown. We propose a stabilized formulation based on a local regularization of the fluid velocity along the tangential directions on the Neumann boundaries. The stabilization term is proportional to the amount of backflow, and does not require any further assumption on the velocity profile. The perfomance of the method is assessed on a twoand three-dimensional Womersley flows, as well as considering a hemodynamic physiological regime in a patient-specific aortic geometry

On monolithic and Chorin–Temam schemes for incompressible flows in moving domains

Several time discretization schemes for the incompressible Navier–Stokes equations (iNSE) in moving domains have been proposed. Here we introduce them in a unified fashion, allowing a common well posedness and time stability analysis. It can be therefore shown that only a particular choice of the numerical scheme ensures such properties. The analysis is performed for monolithic and Chorin–Temam schemes. Results are supported by numerical experiments

A tangential regularization method for backflow stabilization in hemodynamics

In computational simulations of fluid flows, instabilities at the Neumann boundaries may appear during backflow regime. It is widely accepted that this is due to the incoming energy at the boundary, coming from the convection term, which cannot be controlled when the velocity field is unknown. We propose a stabilized formulation based on a local regularization of the fluid velocity along the tangential directions on the Neumann boundaries. The stabilization term is proportional to the amount of backflow, and does not require any further assumption on the velocity profile. The perfomance of the method is assessed on a two- and three-dimensional Womersley flows, as well as considering a hemodynamic physiological regime in a patient-specific aortic geometry

A distributed resistance inverse method for flow obstacle identification from internal velocity measurements

We present a penalization parameter method for obstacle identification in an incompressible fluid flow for a modified version of the Oseen equations. The proposed method consist in adding a high resistance potential to the system such that some subset of its boundary support represents the obstacle. This allows to work in a fixed domain and highly simplify the solution of the inverse problem via some suitable cost functional. Existence of minimizers and first and second order optimality conditions are derived through the differentiability of the solutions of the Oseen equation with respect to the potential. Finally, several numerical experiments using Navier-Stokes flow illustrate the applicability of the method, for the localization of a bi-dimensional cardiac valve from MRI and ultrasound flow type imaging data

A comparison of phase unwrapping methods in velocity-encoded MRI for aortic flows

Purpose: The phase of a MRI signal is used to encode the velocity of blood flow. Phase unwrapping artifacts may appear when aiming to improve the velocity-to-noise ratio (VNR) of the measured velocity field. This study aims to compare various unwrapping algorithms on ground-truth synthetic data generated using computational fluid dynamics (CFD) simulations. Methods: We compare four different phase unwrapping algorithms on two different synthetic datasets of four-dimensional flow MRI and 26 datasets of 2D PC-MRI acquisitions including the ascending and descending aorta. The synthetic datasets are constructed using CFD simulations of an aorta with a coarctation, with different levels of spatiotemporal resolutions and noise. The error of the unwrapped images was assessed by comparison against the ground truth velocity field in the synthetic data and dual-VENC reconstructions in the in vivo data. Results: Using the unwrapping algorithms, we were able to remove aliased voxels in the data almost entirely, reducing the L2-error compared to the ground truth by 50%–80%. Results indicated that the best choice of algorithm depend on the spatiotemporal resolution and noise level of the dataset. Temporal unwrapping is most successful with a high temporal and low spatial resolution ((Figure presented.) ms, (Figure presented.) mm), reducing the L2-error by 70%–85%, while Laplacian unwrapping performs better with a lower temporal or better spatial resolution ((Figure presented.) ms, (Figure presented.) mm), especially for signal-to-noise ratio (SNR) 12 as opposed to SNR 15, with an error reduction of 55%–85% compared to the 50%–75% achieved by the Temporal method. The differences in performance between the methods are statistically significant. Conclusions: The temporal method and spatiotemporal Laplacian method provide the best results, with the spatiotemporal Laplacian being more robust. However, single- (Figure presented.) methods only situationally and not generally reach the performance of dual- (Figure presented.) unwrapping methods.</p

Automatic Mapping of Atrial Fiber Orientations for Patient-Specific Modeling of Cardiac Electromechanics using Image-Registration

Knowledge of appropriate local fiber architecture is necessary to simulate patient-specific electromechanics in the human heart. However, it is not yet possible to reliably measure in-vivo fiber directions, especially in human atria. Thus, we present a method which defines the fiber architecture in arbitrarily shaped atria using image registration and reorientation methods based on atlas atria with fibers predefined from detailed histological observations. Thereby, it is possible to generate detailed fiber families in every new patient-specific geometry in an automated, time-efficient process. We demonstrate the good performance of the image registration and fiber definition on ten differently shaped human atria. Additionally, we show that characteristics of the electrophysiological activation pattern which appear in the atlas atria also appear in the patients' atria. We arrive at analogous conclusions for coupled electro-mechano-hemodynamical computations

Comparison of Improved Unidirectional Dual Velocity-Encoding MRI Methods

Background: In phase-contrast (PC) MRI, several dual velocity encoding methods have been proposed to robustly increase velocity-to-noise ratio (VNR), including a standard dual-VENC (SDV), an optimal dual-VENC (ODV), and bi- and triconditional methods. Purpose: To develop a correction method for the ODV approach and to perform a comparison between methods. Study Type: Case–control study. Population: Twenty-six volunteers. Field Strength/Sequence: 1.5 T phase-contrast MRI with VENCs of 50, 75, and 150 cm/second. Assessment: Since we acquired single-VENC protocols, we used the background phase from high-VENC (VENCH) to reconstruct the low-VENC (VENCL) phase. We implemented and compared the unwrapping methods for different noise levels and also developed a correction of the ODV method. Statistical Tests: Shapiro–Wilk's normality test, two-way analysis of variance with homogeneity of variances was performed using Levene's test, and the significance level was adjusted by Tukey's multiple post hoc analysis with Bonferroni (P &lt; 0.05). Results: Statistical analysis revealed no extreme outliers, normally distributed residuals, and homogeneous variances. We found statistically significant interaction between noise levels and the unwrapping methods. This implies that the number of non-unwrapped pixels increased with the noise level. We found that for β = VENCL/VENCH = 1/2, unwrapping methods were more robust to noise. The post hoc test showed a significant difference between the ODV corrected and the other methods, offering the best results regarding the number of unwrapped pixels. Data Conclusions: All methods performed similarly without noise, but the ODV corrected method was more robust to noise at the price of a higher computational time. Level of Evidence: 4. Technical Efficacy Stage: 1.</p

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

While the clinical gold standard for pressure difference measurements is invasive catheterization, 4D Flow MRI is a promising tool for enabling a non-invasive quantification, by linking highly spatially resolved velocity measurements with pressure differences via the incompressible Navier–Stokes equations. In this work we provide a validation and comparison with phantom and clinical patient data of pressure difference maps estimators. We compare the classical Pressure Poisson Estimator (PPE) and the new Stokes Estimator (STE) against catheter pressure measurements under a variety of stenosis severities and flow intensities. Specifically, we use several 4D Flow data sets of realistic aortic phantoms with different anatomic and hemodynamic severities and two patients with aortic coarctation. The phantom data sets are enriched by subsampling to lower resolutions, modification of the segmentation and addition of synthetic noise, in order to study the sensitivity of the pressure difference estimators to these factors. Overall, the STE method yields more accurate results than the PPE method compared to catheterization data. The superiority of the STE becomes more evident at increasing Reynolds numbers with a better capacity of capturing pressure gradients in strongly convective flow regimes. The results indicate an improved robustness of the STE method with respect to variation in lumen segmentation. However, with heuristic removal of the wall-voxels, the PPE can reach a comparable accuracy for lower Reynolds’ numbers