The impact of MRI-based inflow for the hemodynamic evaluation of aortic coarctation

Impact of turbulence modeling on the simulation of blood flow in aortic coarctation

Numerical simulations of pulsatile blood flow in an aortic coarctation require the use of turbulence modeling. This paper considers three models from the class of large eddy simulation (LES) models (Smagorinsky, Vreman, σ -model) and one model from the class of variational multiscale models (residual-based) within a finite element framework. The influence of these models on the estimation of clinically relevant biomarkers used to assess the degree of severity of the pathological condition (pressure difference, secondary flow degree, normalized flow displacement, wall shear stress) is investigated in detail. The simulations show that most methods are consistent in terms of severity indicators such as pressure difference and stenotic velocity. Moreover, using second-order velocity finite elements, different turbulence models might lead to considerably different results concerning other clinically relevant quantities such as wall shear stresses. These differences may be attributed to differences in numerical dissipation introduced by the turbulence models.

Quantitative Complexity Theory (QCT) in Integrative Analysis of Cardiovascular Hemodynamic Response to Posture Change

The explanation of physiological mechanisms involved in adaptation of the cardiovascular system to intrinsic and environmental demands is crucial for both basic science and clinical research. Computational algorithms integrating multivariable data that comprehensively depict complex mechanisms of cardiovascular reactivity are currently being intensively researched. Quantitative Complexity Theory (QCT) provides quantitative and holistic information on the state of multi-functional dynamic systems. The present paper aimed to describe the application of QCT in an integrative analysis of the cardiovascular hemodynamic response to posture change. Three subjects that underwent head-up tilt testing under beat-by-beat hemodynamic monitoring (impedance cardiography) were discussed in relation to the complexity trends calculated using QCT software. Complexity has been shown to be a sensitive marker of a cardiovascular hemodynamic response to orthostatic stress and vasodilator administration, and its increase has preceded changes in standard cardiovascular parameters. Complexity profiling has provided a detailed assessment of individual hemodynamic patterns of syncope. Different stimuli and complexity settings produce results of different clinical usability.

Scale-Resolving Simulations of Steady and Pulsatile Flow Through Healthy and Stenotic Heart Valves

Blood-flow downstream of stenotic and healthy aortic valves exhibits intermittent random fluctuations in the velocity field which are associated with turbulence. Such flows warrant the use of computationally demanding scale-resolving models. The aim of this work was to compute and quantify this turbulent flow in healthy and stenotic heart valves for steady and pulsatile flow conditions. Large eddy simulations (LESs) and Reynolds-averaged Navier-Stokes (RANS) simulations were used to compute the flow field at inlet Reynolds numbers of 2700 and 5400 for valves with an opening area of 70 mm2 and 175 mm2 and their projected orifice-plate type counterparts. Power spectra and turbulent kinetic energy were quantified on the centerline. Projected geometries exhibited an increased pressure-drop (>90%) and elevated turbulent kinetic energy levels (>147%). Turbulence production was an order of magnitude higher in stenotic heart valves compared to healthy valves. Pulsatile flow stabilizes flow in the acceleration phase, whereas onset of deceleration triggered (healthy valve) or amplified (stenotic valve) turbulence. Simplification of the aortic valve by projecting the orifice area should be avoided in computational fluid dynamics (CFD). RANS simulations may be used to predict the transvalvular pressure-drop, but scale-resolving models are recommended when detailed information of the flow field is required.

Personalized Pre- and Post-Operative Hemodynamic Assessment of Aortic Coarctation from 3D Rotational Angiography

PURPOSE

Coarctation of Aorta (CoA) is a congenital disease consisting of a narrowing that obstructs the systemic blood flow. This proof-of-concept study aimed to develop a framework for automatically and robustly personalizing aortic hemodynamic computations for the assessment of pre- and post-intervention CoA patients from 3D rotational angiography (3DRA) data.

METHODS

We propose a framework that combines hemodynamic modelling and machine learning (ML) based techniques, and rely on 3DRA data for non-invasive pressure computation in CoA patients. The key features of our framework are a parameter estimation method for calibrating inlet and outlet boundary conditions, and regional mechanical wall properties, to ensure that the computational results match the patient-specific measurements, and an improved ML based pressure drop model capable of predicting the instantaneous pressure drop for a wide range of flow conditions and anatomical CoA variations.

RESULTS

We evaluated the framework by investigating 6 patient datasets, under pre- and post-operative setting, and, since all calibration procedures converged successfully, the proposed approach is deemed robust. We compared the peak-to-peak and the cycle-averaged pressure drop computed using the reduced-order hemodynamic model with the catheter based measurements, before and after virtual and actual stenting. The mean absolute error for the peak-to-peak pressure drop, which is the most relevant measure for clinical decision making, was 2.98 mmHg for the pre- and 2.11 mmHg for the post-operative setting. Moreover, the proposed method is computationally efficient: the average execution time was of only [Formula: see text] minutes on a standard hardware configuration.

CONCLUSION

The use of 3DRA for hemodynamic modelling could allow for a complete hemodynamic assessment, as well as virtual interventions or surgeries and predictive modeling. However, before such an approach can be used routinely, significant advancements are required for automating the workflow.

Deep Learning Based Centerline-Aggregated Aortic Hemodynamics: An Efficient Alternative to Numerical Modelling of Hemodynamics

Image-based patient-specific modelling of hemodynamics are gaining increased popularity as a diagnosis and outcome prediction solution for a variety of cardiovascular diseases. While their potential to improve diagnostic capabilities and thereby clinical outcome is widely recognized, these methods require considerable computational resources since they are mostly based on conventional numerical methods such as computational fluid dynamics (CFD). As an alternative to the numerical methods, we propose a machine learning (ML) based approach to calculate patient-specific hemodynamic parameters. Compared to CFD based methods, our approach holds the benefit of being able to calculate a patient-specific hemodynamic outcome instantly with little need for computational power. In this proof-of-concept study, we present a deep artificial neural network (ANN) capable of computing hemodynamics for patients with aortic coarctation in a centerline aggregated (i.e. locally averaged) form. Considering the complex relation between vessels shape and hemodynamics on the one hand and the limited availability of suitable clinical data on the other, a sufficient accuracy of the ANN may however not be achieved with available data only. Another key aspect of this study is therefore the successful augmentation of available clinical data. Using a statistical shape model, additional training data was generated which substantially increased the ANNs accuracy, showcasing the ability of ML based methods to perform in-silico modelling tasks previously requiring resource intensive CFD simulations.

Effects of Uncertainty of Outlet Boundary Conditions in a Patient-Specific Case of Aortic Coarctation

Computational Fluid Dynamics (CFD) simulations of blood flow are widely used to compute a variety of hemodynamic indicators such as velocity, time-varying wall shear stress, pressure drop, and energy losses. One of the major advances of this approach is that it is non-invasive. The accuracy of the cardiovascular simulations depends directly on the level of certainty on input parameters due to the modelling assumptions or computational settings. Physiologically suitable boundary conditions at the inlet and outlet of the computational domain are needed to perform a patient-specific CFD analysis. These conditions are often affected by uncertainties, whose impact can be quantified through a stochastic approach. A methodology based on a full propagation of the uncertainty from clinical data to model results is proposed here. It was possible to estimate the confidence associated with model predictions, differently than by deterministic simulations. We evaluated the effect of using three-element Windkessel models as the outflow boundary conditions of a patient-specific aortic coarctation model. A parameter was introduced to calibrate the resistances of the Windkessel model at the outlets. The generalized Polynomial Chaos method was adopted to perform the stochastic analysis, starting from a few deterministic simulations. Our results show that the uncertainty of the input parameter gave a remarkable variability on the volume flow rate waveform at the systolic peak simulating the conditions before the treatment. The same uncertain parameter had a slighter effect on other quantities of interest, such as the pressure gradient. Furthermore, the results highlight that the fine-tuning of Windkessel resistances is not necessary to simulate the post-stenting scenario.

Assessment of turbulent blood flow and wall shear stress in aortic coarctation using image-based simulations

In this study, we analyzed turbulent flows through a phantom (a 180[Formula: see text] bend with narrowing) at peak systole and a patient-specific coarctation of the aorta (CoA), with a pulsating flow, using magnetic resonance imaging (MRI) and computational fluid dynamics (CFD). For MRI, a 4D-flow MRI is performed using a 3T scanner. For CFD, the standard [Formula: see text], shear stress transport [Formula: see text], and Reynolds stress (RSM) models are applied. A good agreement between measured and simulated velocity is obtained for the phantom, especially for CFD with RSM. The wall shear stress (WSS) shows significant differences between CFD and MRI in absolute values, due to the limited near-wall resolution of MRI. However, normalized WSS shows qualitatively very similar distributions of the local values between MRI and CFD. Finally, a direct comparison between in vivo 4D-flow MRI and CFD with the RSM turbulence model is performed in the CoA. MRI can properly identify regions with locally elevated or suppressed WSS. If the exact values of the WSS are necessary, CFD is the preferred method. For future applications, we recommend the use of the combined MRI/CFD method for analysis and evaluation of the local flow patterns and WSS in the aorta.

The effect of coarctation degrees on wall shear stress indices

Coarctation of the aorta (CoA) is a congenital tightening of the proximal descending aorta. Flow quantification can be immensely valuable for an early and accurate diagnosis. However, there is a lack of appropriate diagnostic approaches for a variety of cardiovascular diseases, such as CoA. An accurate understanding of the disease depends on measurements of the global haemodynamics (criteria for heart function) and also the local haemodynamics (detailed data on the dynamics of blood flow). Playing a significant role in clinical processes, wall shear stress (WSS) cannot be measured clinically; thus, computation tools are needed to give an insight into this crucial haemodynamic parameter. In the present study, in order to enable the progress of non-invasive approaches that quantify global and local haemodynamics for different CoA severities, innovative computational blueprint simulations that include fluid-solid interaction models are developed. Since there is no clear approach for managing the CoA regarding its severity, this study proposes the use of WSS indices and pressure gradient to better establish a framework for treatment procedures in CoA patients with different severities. This provides a platform for improving CoA therapy on a patient-specific level, in which physicians can perform treatment methods based on WSS indices on top of using a mere experience. Results show how severe CoA affects the aorta in comparison to the milder cases, which can give the medical community valuable information before and after any intervention.

Hemodynamic Modeling of Biological Aortic Valve Replacement Using Preoperative Data Only

Objectives: Prediction of aortic hemodynamics after aortic valve replacement (AVR) could help optimize treatment planning and improve outcomes. This study aims to demonstrate an approach to predict postoperative maximum velocity, maximum pressure gradient, secondary flow degree (SFD), and normalized flow displacement (NFD) in patients receiving biological AVR.

Methods: Virtual AVR was performed for 10 patients, who received actual AVR with a biological prosthesis. The virtual AVRs used only preoperative anatomical and 4D flow MRI data. Subsequently, computational fluid dynamics (CFD) simulations were performed and the abovementioned hemodynamic parameters compared between postoperative 4D flow MRI data and CFD results.

Results: For maximum velocities and pressure gradients, postoperative 4D flow MRI data and CFD results were strongly correlated (R² = 0.75 and R² = 0.81) with low root mean square error (0.21 m/s and 3.8 mmHg). SFD and NFD were moderately and weakly correlated at R² = 0.44 and R² = 0.20, respectively. Flow visualization through streamlines indicates good qualitative agreement between 4D flow MRI data and CFD results in most cases.

Conclusion: The approach presented here seems suitable to estimate postoperative maximum velocity and pressure gradient in patients receiving biological AVR, using only preoperative MRI data. The workflow can be performed in a reasonable time frame and offers a method to estimate postoperative valve prosthesis performance and to identify patients at risk of patient-prosthesis mismatch preoperatively. Novel parameters, such as SFD and NFD, appear to be more sensitive, and estimation seems harder. Further workflow optimization and validation of results seems warranted.

Numerical investigation of patient-specific thoracic aortic aneurysms and comparison with normal subject via computational fluid dynamics (CFD)

Vascular hemodynamics play an important role in cardiovascular diseases. This work aimed to investigate the effects of an increase in ascending aortic diameter (AAD) on hemodynamics throughout a cardiac cycle for real patients. In this study, two scans of thoracic aortic aneurysm (TAA) subject with different AADs (42.94 mm and 48.01 mm) and a scan of a normal subject (19.81 mm) were analyzed to assess the effects of hemodynamics on the progression of TAA with the same flow rate. Real-patient aortic geometries were scanned by computed tomography angiography (CTA), and steady and pulsatile flow conditions were used to simulate real patient aortic geometries. Aortic arches were obtained from routine clinical scans. Computational fluid dynamics (CFD) simulations were performed with in vivo boundary conditions, and 3D Navier-Stokes equations were solved by a UDF (user-defined function) code defining a real cardiac cycle of one patient using Fourier series (FS). Wall shear stress (WSS) and pressure distributions were presented from normal subject to TAA cases. The results show that during the peak systolic phase pressure load increased by 18.56% from normal subject to TAA case 1 and by 23.8% from normal subject to TAA case 2 in the aneurysm region. It is concluded that although overall WSS increased in aneurysm cases but was low in dilatation areas. As a result, abnormal changes in WSS and higher pressure load may lead to rupture and risk of further dilatation. CFD simulations were highly effective to guide clinical predictions and assess the progress of aneurysm regions in case of early surgical intervention. Graphical abstract.

Assessment of hemodynamic responses to exercise in aortic coarctation using MRI-ergometry in combination with computational fluid dynamics

In patients with aortic coarctation it would be desirable to assess pressure gradients as well as information about blood flow profiles at rest and during exercise. We aimed to assess the hemodynamic responses to physical exercise by combining MRI-ergometry with computational fluid dynamics (CFD). MRI was performed on 20 patients with aortic coarctation (13 men, 7 women, mean age 21.5 ± 13.7 years) at rest and during ergometry. Peak systolic pressure gradients, wall shear stress (WSS), secondary flow degree (SFD) and normalized flow displacement (NFD) were calculated using CFD. Stroke volume was determined based on MRI. On average, the pressure gradient was 18.0 ± 16.6 mmHg at rest and increased to 28.5 ± 22.6 mmHg (p < 0.001) during exercise. A significant increase in cardiac index was observed (p < 0.001), which was mainly driven by an increase in heart rate (p < 0.001). WSS significantly increased during exercise (p = 0.006), whereas SFD and NFD remained unchanged. The combination of MRI-ergometry with CFD allows assessing pressure gradients as well as flow profiles during physical exercise. This concept has the potential to serve as an alternative to cardiac catheterization with pharmacological stress testing and provides hemodynamic information valuable for studying the pathophysiology of aortic coarctation.

Computational fluid dynamics: a primer for congenital heart disease clinicians

Computational fluid dynamics has become an important tool for studying blood flow dynamics. As an in-silico collection of methods, computational fluid dynamics is noninvasive and provides numerical values for the most important parameters of blood flow, such as velocity and pressure that are crucial in hemodynamic studies. In this primer, we briefly explain the basic theory and workflow of the two most commonly applied computational fluid dynamics techniques used in the congenital heart disease literature: the finite element method and the finite volume method. We define important terminology and include specific examples of how using these methods can answer important clinical questions in congenital cardiac surgery planning and perioperative patient management.

Assessment of a biofluid mechanics-based model for calculating portal pressure in canines

BACKGROUND

Portal hypertension is a severe complication caused by various chronic liver diseases. The standard methods for detecting portal hypertension (hepatic venous pressure gradient and free portal pressure) are available in only a few hospitals due to their technical difficulty and invasiveness; thus, non-invasive measuring methods are needed. This study aimed to establish and assess a novel model to calculate free portal pressure based on biofluid mechanics.

RESULT

Comparison of each dog's virtual and actual free portal pressure showed that a biofluid mechanics-based model could accurately predict free portal pressure (mean difference: -0.220, 95% CI: - 0.738 to 0.298; upper limit of agreement: 2.24, 95% CI: 1.34 to 3.14; lower limit of agreement: -2.68, 95% CI: - 3.58 to - 1.78; intraclass correlation coefficient: 0.98, 95% CI: 0.96 to 0.99; concordance correlation coefficient: 0.97, 95% CI: 0.93 to 0.99) and had a high AUC (0.984, 95% CI: 0.834 to 1.000), sensitivity (92.3, 95% CI: 64.0 to 99.8), specificity (91.7, 95% CI: 61.5 to 99.8), positive likelihood ratio (11.1, 95% CI: 1.7 to 72.8), and low negative likelihood ratio (0.08, 95% CI: 0.01 to 0.6) for detecting portal hypertension.

CONCLUSIONS

Our study suggests that the biofluid mechanics-based model was able to accurately predict free portal pressure and detect portal hypertension in canines. With further research and validation, this model might be applicable for calculating human portal pressure, detecting portal hypertensive patients, and evaluating disease progression and treatment efficacy.

Establishment and assessment of the hepatic venous pressure gradient using biofluid mechanics (HVPGBFM): protocol for a prospective, randomised, non-controlled, multicentre study

INTRODUCTION

Portal hypertension (PH) is a severe disease with a poor outcome. Hepatic venous pressure gradient (HVPG), the current gold standard to detect PH, is available only in few hospitals due to its invasiveness and technical difficulty. This study aimed to establish and assess a novel model to calculate HVPG based on biofluid mechanics.

METHODS AND ANALYSIS

This is a prospective, randomised, non-controlled, multicentre trial. A total of 248 patients will be recruited in this study, and each patient will undergo CT, blood tests, Doppler ultrasound and HVPG measurement. The study consists of two independent and consecutive cohorts: original cohort (124 patients) and validation cohort (124 patients). The researchers will establish and improve the HVPG using biofluid mechanics (HVPG_BFM)model in the original cohort and assess the model in the validation cohort.

ETHICS AND DISSEMINATION

The study was approved by the Scientific Research Projects Approval Determination of Independent Ethics Committee of Shanghai Ninth People's Hospital Affiliated to Shanghai Jiao Tong University School of Medicine (approval number 2017-430 T326). Study findings will be disseminated through peer-reviewed publications and conference presentations.

TRIAL REGISTRATION NUMBER

NCT03470389.

Three-dimensional rotational angiography in congenital heart disease: Present status and evolving future

Three-dimensional rotational angiography (3D-RA) enables volumetric imaging through rotation of the C-arm of an angiographic system and real-time 3D reconstruction during cardiac catheterization procedures. In the field of congenital heart disease (CHD), 3D-RA has gained considerable traction, owing to its capability for enhanced visualization of spatial relationships in complex cardiac morphologies and real time image guidance in an intricate interventional environment. This review provides an overview of the current applications, strengths, and limitations of 3D-RA acquisition in the management of CHD and potential future directions. In addition, issues of dosimetry, radiation exposure, and optimization strategies will be reviewed. Further implementation of 3D-RA will be driven by patient benefits relative to existing 3D imaging capabilities and fusion techniques balanced against radiation exposure.

Evaluation of 4D flow MRI-based non-invasive pressure assessment in aortic coarctations

Severity of aortic coarctation (CoA) is currently assessed by estimating trans-coarctation pressure drops through cardiac catheterization or echocardiography. In principle, more detailed information could be obtained non-invasively based on space- and time-resolved magnetic resonance imaging (4D flow) data. Yet the limitations of this imaging technique require testing the accuracy of 4D flow-derived hemodynamic quantities against other methodologies. With the objective of assessing the feasibility and accuracy of this non-invasive method to support the clinical diagnosis of CoA, we developed an algorithm (4DF-FEPPE) to obtain relative pressure distributions from 4D flow data by solving the Poisson pressure equation. 4DF-FEPPE was tested against results from a patient-specific fluid-structure interaction (FSI) simulation, whose patient-specific boundary conditions were prescribed based on 4D flow data. Since numerical simulations provide noise-free pressure fields on fine spatial and temporal scales, our analysis allowed to assess the uncertainties related to 4D flow noise and limited resolution. 4DF-FEPPE and FSI results were compared on a series of cross-sections along the aorta. Bland-Altman analysis revealed very good agreement between the two methodologies in terms of instantaneous data at peak systole, end-diastole and time-averaged values: biases (means of differences) were +0.4 mmHg, -1.1 mmHg and +0.6 mmHg, respectively. Limits of agreement (2 SD) were ±0.978 mmHg, ±1.06 mmHg and ±1.97 mmHg, respectively. Peak-to-peak and maximum trans-coarctation pressure drops obtained with 4DF-FEPPE differed from FSI results by 0.75 mmHg and -1.34 mmHg respectively. The present study considers important validation aspects of non-invasive pressure difference estimation based on 4D flow MRI, showing the potential of this technology to be more broadly applied to the clinical practice.

Suitability of lattice Boltzmann inlet and outlet boundary conditions for simulating flow in image-derived vasculature

The lattice Boltzmann method (LBM) is a popular alternative to solving the Navier-Stokes equations for modeling blood flow. When simulating flow using the LBM, several choices for inlet and outlet boundary conditions exist. While boundary conditions in the LBM have been evaluated in idealized geometries, there have been no extensive comparisons in image-derived vasculature, where the geometries are highly complex. In this study, the Zou-He (ZH) and finite difference (FD) boundary conditions were evaluated in image-derived vascular geometries by comparing their stability, accuracy, and run times. The boundary conditions were compared in four arteries: a coarctation of the aorta, dissected aorta, femoral artery, and left coronary artery. The FD boundary condition was more stable than ZH in all four geometries. In general, simulations using the ZH and FD method showed similar convergence rates within each geometry. However, the ZH method proved to be slightly more accurate compared with experimental flow using three-dimensional printed vasculature. The total run times necessary for simulations using the ZH boundary condition were significantly higher as the ZH method required a larger relaxation time, grid resolution, and number of time steps for a simulation representing the same physiological time. Finally, a new inlet velocity profile algorithm is presented for complex inlet geometries. Overall, results indicated that the FD method should generally be used for large-scale blood flow simulations in image-derived vasculature geometries. This study can serve as a guide to researchers interested in using the LBM to simulate blood flow.

A Hybrid Experimental-Computational Modeling Framework for Cardiovascular Device Testing

Significant advances in biomedical science often leverage powerful computational and experimental modeling platforms. We present a framework named physiology simulation coupled experiment ("PSCOPE") that can capitalize on the strengths of both types of platforms in a single hybrid model. PSCOPE uses an iterative method to couple an in vitro mock circuit to a lumped-parameter numerical simulation of physiology, obtaining closed-loop feedback between the two. We first compared the results of Fontan graft obstruction scenarios modeled using both PSCOPE and an established multiscale computational fluid dynamics method; the normalized root-mean-square error values of important physiologic parameters were between 0.1% and 2.1%, confirming the fidelity of the PSCOPE framework. Next, we demonstrate an example application of PSCOPE to model a scenario beyond the current capabilities of multiscale computational methods-the implantation of a Jarvik 2000 blood pump for cavopulmonary support in the single-ventricle circulation; we found that the commercial Jarvik 2000 controller can be modified to produce a suitable rotor speed for augmenting cardiac output by approximately 20% while maintaining blood pressures within safe ranges. The unified modeling framework enables a testing environment which simultaneously operates a medical device and performs computational simulations of the resulting physiology, providing a tool for physically testing medical devices with simulated physiologic feedback.

Hodge decomposition of wall shear stress vector fields characterizing biological flows

A discrete boundary-sensitive Hodge decomposition is proposed as a central tool for the analysis of wall shear stress (WSS) vector fields in aortic blood flows. The method is based on novel results for the smooth and discrete Hodge-Morrey-Friedrichs decomposition on manifolds with boundary and subdivides the WSS vector field into five components: gradient (curl-free), co-gradient (divergence-free) and three harmonic fields induced from the boundary, which are called the centre, Neumann and Dirichlet fields. First, an analysis of WSS in several simulated simplified phantom geometries (duct and idealized aorta) was performed in order to understand the nature of the five components. It was shown that the decomposition is able to distinguish harmonic blood flow arising from the inlet from harmonic circulations induced by the interior topology of the geometry. Finally, a comparative analysis of 11 patients with coarctation of the aorta (CoA) before and after treatment as well as 10 control patients was done. The study shows a significant difference between the CoA patients before and after the treatment, and the healthy controls. This means a global difference between aortic shapes of diseased and healthy subjects, thus leading to a new type of WSS-based analysis and classification of pathological and physiological blood flow.

Uncertainty Quantification for Non-invasive Assessment of Pressure Drop Across a Coarctation of the Aorta Using CFD

PURPOSE

Numerical assessment of the pressure drop across an aortic coarctation using CFD is a promising approach to replace invasive catheter-based measurements. The aim of this study was to investigate and quantify the uncertainty of numerical calculation of the pressure drop introduced during two essential steps of medical image processing: segmentation of the patient-specific geometry and measurement of patient-specific flow rates from 4D-flow-MRI.

METHODS

Based on the baseline segmentation, geometries with different stenosis diameters were generated for a sample of ten patients. The pressure drop generated by these geometries was calculated for different volume flow rates using computational fluid dynamics. Based on these simulations, a second order polynomial fit was calculated. Based on these polynomial fits an uncertainty of pressure drop calculation was quantified.

RESULTS

The calculated pressure drop values varied strongly between the patients. In four patients, pressure drops above and below the clinical threshold of 20 mmHg were found. The median standard deviation of the pressure drop was 2.3 mmHg. The sensitivity of the pressure drop toward changes in the volume flow rate or the stenosis geometry varied between patients.

CONCLUSION

The uncertainty of numerical pressure drop calculation introduced by uncertainties during image segmentation and measurement of volume flow rates was comparable to the uncertainty of pressure drop measurements using invasive catheterization. However, in some patients this uncertainty would have led to different treatment decision. Therefore, patient-specific uncertainty assessment might help to better understand the reliability of a numerically calculated biomarker as the pressure drop across an aortic coarctation.

Towards a Computational Framework for Modeling the Impact of Aortic Coarctations Upon Left Ventricular Load

Computational fluid dynamics (CFD) models of blood flow in the left ventricle (LV) and aorta are important tools for analyzing the mechanistic links between myocardial deformation and flow patterns. Typically, the use of image-based kinematic CFD models prevails in applications such as predicting the acute response to interventions which alter LV afterload conditions. However, such models are limited in their ability to analyze any impacts upon LV load or key biomarkers known to be implicated in driving remodeling processes as LV function is not accounted for in a mechanistic sense. This study addresses these limitations by reporting on progress made toward a novel electro-mechano-fluidic (EMF) model that represents the entire physics of LV electromechanics (EM) based on first principles. A biophysically detailed finite element (FE) model of LV EM was coupled with a FE-based CFD solver for moving domains using an arbitrary Eulerian-Lagrangian (ALE) formulation. Two clinical cases of patients suffering from aortic coarctations (CoA) were built and parameterized based on clinical data under pre-treatment conditions. For one patient case simulations under post-treatment conditions after geometric repair of CoA by a virtual stenting procedure were compared against pre-treatment results. Numerical stability of the approach was demonstrated by analyzing mesh quality and solver performance under the significantly large deformations of the LV blood pool. Further, computational tractability and compatibility with clinical time scales were investigated by performing strong scaling benchmarks up to 1536 compute cores. The overall cost of the entire workflow for building, fitting and executing EMF simulations was comparable to those reported for image-based kinematic models, suggesting that EMF models show potential of evolving into a viable clinical research tool.

Computational study of aortic hemodynamics for patients with an abnormal aortic valve: The importance of secondary flow at the ascending aorta inlet

Blood flow in the aorta is helical, but most computational studies ignore the presence of secondary flow components at the ascending aorta (AAo) inlet. The aim of this study is to ascertain the importance of inlet boundary conditions (BCs) in computational analysis of flow patterns in the thoracic aorta based on patient-specific images, with a particular focus on patients with an abnormal aortic valve. Two cases were studied: one presenting a severe aortic valve stenosis and the other with a mechanical valve. For both aorta models, three inlet BCs were compared; these included the flat profile and 1D through-plane velocity and 3D phase-contrast magnetic resonance imaging derived velocity profiles, with the latter being used for benchmarking. Our results showed that peak and mean velocities at the proximal end of the ascending aorta were underestimated by up to 41% when the secondary flow components were neglected. The results for helical flow descriptors highlighted the strong influence of secondary velocities on the helical flow structure in the AAo. Differences in all wall shear stress (WSS)-derived indices were much more pronounced in the AAo and aortic arch (AA) than in the descending aorta (DAo). Overall, this study demonstrates that using 3D velocity profiles as inlet BC is essential for patient-specific analysis of hemodynamics and WSS in the AAo and AA in the presence of an abnormal aortic valve. However, predicted flow in the DAo is less sensitive to the secondary velocities imposed at the inlet; hence, the 1D through-plane profile could be a sufficient inlet BC for studies focusing on distal regions of the thoracic aorta.

Model-Based Therapy Planning Allows Prediction of Haemodynamic Outcome after Aortic Valve Replacement

Optimizing treatment planning is essential for advances in patient care and outcomes. Precisely tailored therapy for each patient remains a yearned-for goal. Cardiovascular modelling has the potential to simulate and predict the functional response before the actual intervention is performed. The objective of this study was to proof the validity of model-based prediction of haemodynamic outcome after aortic valve replacement. In a prospective study design virtual (model-based) treatment of the valve and the surrounding vasculature were performed alongside the actual surgical procedure (control group). The resulting predictions of anatomic and haemodynamic outcome based on information from magnetic resonance imaging before the procedure were compared to post-operative imaging assessment of the surgical control group in ten patients. Predicted vs. post-operative peak velocities across the valve were comparable (2.97 ± 1.12 vs. 2.68 ± 0.67 m/s; p = 0.362). In wall shear stress (17.3 ± 12.3 Pa vs. 16.7 ± 16.84 Pa; p = 0.803) and secondary flow degree (0.44 ± 0.32 vs. 0.49 ± 0.23; p = 0.277) significant linear correlations (p < 0.001) were found between predicted and post-operative outcomes. Between groups blood flow patterns showed good agreement (helicity p = 0.852, vorticity p = 0.185, eccentricity p = 0.333). Model-based therapy planning is able to accurately predict post-operative haemodynamics after aortic valve replacement. These validated virtual treatment procedures open up promising opportunities for individually targeted interventions.

Hemodynamic Evaluation of a Biological and Mechanical Aortic Valve Prosthesis Using Patient-Specific MRI-Based CFD

Modeling different treatment options before a procedure is performed is a promising approach for surgical decision making and patient care in heart valve disease. This study investigated the hemodynamic impact of different prostheses through patient-specific MRI-based CFD simulations. Ten time-resolved MRI data sets with and without velocity encoding were obtained to reconstruct the aorta and set hemodynamic boundary conditions for simulations. Aortic hemodynamics after virtual valve replacement with a biological and mechanical valve prosthesis were investigated. Wall shear stress (WSS), secondary flow degree (SFD), transvalvular pressure drop (TPD), turbulent kinetic energy (TKE), and normalized flow displacement (NFD) were evaluated to characterize valve-induced hemodynamics. The biological prostheses induced significantly higher WSS (medians: 9.3 vs. 8.6 Pa, P = 0.027) and SFD (means: 0.78 vs. 0.49, P = 0.002) in the ascending aorta, TPD (medians: 11.4 vs. 2.7 mm Hg, P = 0.002), TKE (means: 400 vs. 283 cm² /s² , P = 0.037), and NFD (means: 0.0994 vs. 0.0607, P = 0.020) than the mechanical prostheses. The differences between the prosthesis types showed great inter-patient variability, however. Given this variability, a patient-specific evaluation is warranted. In conclusion, MRI-based CFD offers an opportunity to assess the interactions between prosthesis and patient-specific boundary conditions, which may help in optimizing surgical decision making and providing additional guidance to clinicians.

Modeling of coarctation of aorta in human fetuses using 3D/4D fetal echocardiography and computational fluid dynamics

OBJECTIVES

We sought to develop a hemodynamic model of aortic and ductal arches using computational fluid dynamics (CFD) and 3D/4D spatio-temporal image correlation (STIC) fetal echocardiography and to investigate the hemodynamics of coarctation of aorta (CoA) in human fetuses using this approach.

METHODS

We obtained 3D/4D STIC fetal echocardiographic images of the aortic and ductal arches (DA) in five normal fetuses. Based on these images, we simulated the hemodynamics in the two arches using CFD. Subsequently, we reduced the dimensions of aortic isthmus from 100% to 85%, 70%, 55%, 40%, and 25% of the original dimension digitally. Numerical simulation was repeated in each condition, and flow profile, velocity, pressure, and wall shear stress (WSS) were compared with those of the baseline normal aortic and ductal arches.

RESULTS

With the progressive narrowing in the aortic isthmus, there were alterations in the flow profile, velocity, pressure, and WSS. The downstream vortexes disappeared, and the double helix profile became single helix. When the aortic isthmus reduced by 55% in dimension, there was an exponential increase in velocity and WSS and decrease in pressure.

CONCLUSIONS

The aortic and ductal arch geometry and flow lead to the alterations in flow profile, velocity, pressure, and WSS in the aortic isthmus in normal and CoA models, which are conductive of ductal issue migration into these areas. A 55% reduction in the dimension of aortic isthmus is associated with exponential change in velocity, pressure, and WSS, a probable threshold for hemodynamically significant CoA.

Validation of numerical simulation methods in aortic arch using 4D Flow MRI

Computational fluid dynamics (CFD) are the gold standard in studying blood flow dynamics. However, CFD results are dependent on the boundary conditions and the computation model. The purpose of this study was to validate CFD methods using comparison with actual measurements of the blood flow vector obtained with four-dimensional (4D) flow magnetic resonance imaging (MRI). 4D Flow MRI was performed on a healthy adult and a child with double-aortic arch. The aortic lumen was segmented to visualize the blood flow. The CFD analyses were performed for the same geometries based on three turbulent models: laminar, large eddy simulation (LES), and the renormalization group k–ε model (RNG k–ε). The flow-velocity vector components, namely the wall shear stress (WSS) and flow energy loss (EL), of the MRI and CFD results were compared. The flow rate of the MRI results was underestimated in small vessels, including the neck vessels. Spiral flow in the ascending aorta caused by the left ventricular twist was observed by MRI. Secondary flow distal to the aortic arch was well realized in both CFD and MRI. The average correlation coefficients of the velocity vector components of MRI and CFD for the child were the highest for the RNG k–ε model (0.530 in ascending aorta, 0.768 in the aortic arch, 0.584 in the descending aorta). The WSS and EL values of MRI were less than half of those of CFD, but the WSS distribution patterns were quite similar. The WSS and EL estimates were higher in RNG k–ε and LES than in the laminar model because of eddy viscosity. The CFD computation realized accurate flow distal to the aortic arch, and the WSS distribution was well simulated compared to actual measurement using 4D Flow MRI. However, the helical flow was not simulated in the ascending aorta. The accuracy was enhanced by using the turbulence model, and the RNG k–ε model showed the highest correlation with 4D Flow MRI.

[Numerical flow simulation : A new method for assessing nasal breathing]

The current options for objective assessment of nasal breathing are limited. The maximum they can determine is the total nasal resistance. Possibilities to analyze the endonasal airstream are lacking. In contrast, numerical flow simulation is able to provide detailed information of the flow field within the nasal cavity. Thus, it has the potential to analyze the nasal airstream of an individual patient in a comprehensive manner and only a computed tomography (CT) scan of the paranasal sinuses is required. The clinical application is still limited due to the necessary technical and personnel resources. In particular, a statistically based referential characterization of normal nasal breathing does not yet exist in order to be able to compare and classify the simulation results.

Multidirectional WSS disturbances in stenotic turbulent flows: A pre- and post-intervention study in an aortic coarctation

Wall shear stress (WSS) disturbances are commonly expressed at sites of abnormal flow obstructions and may play an essential role in the pathogenesis of various vascular diseases. In laminar flows these disturbances have recently been assessed by the transverse wall shear stress (transWSS), which accounts for the WSS multidirectionality. Site-specific estimations of WSS disturbances in pulsatile transitional and turbulent type of flows are more challenging due to continuous and unpredictable changes in WSS behavior. In these complex flow settings, the transWSS may serve as a more comprehensive descriptor for assessing WSS disturbances of general nature compared to commonly used parameters. In this study large eddy simulations (LES) were used to investigate the transWSS properties in flows subjected to different pathological turbulent flow conditions, governed by a patient-specific model of an aortic coarctation pre and post balloon angioplasty. Results showed that regions of strong near-wall turbulence were collocated with regions of elevated transWSS and turbulent WSS, while in more transitional-like near-wall flow regions a closer resemblance was found between transWSS and low, and oscillatory WSS. Within the frame of this study, the transWSS parameter demonstrated a more multi-featured picture of WSS disturbances when exposed to different types of flow regimes, characteristics which were not depicted by the other parameters alone.

MRI-based computational hemodynamics in patients with aortic coarctation using the lattice Boltzmann methods: Clinical validation study

Purpose

To introduce a scheme based on a recent technique in computational hemodynamics, known as the lattice Boltzmann methods (LBM), to noninvasively measure pressure gradients in patients with a coarctation of the aorta (CoA). To provide evidence on the accuracy of the proposed scheme, the computed pressure drop values are compared against those obtained using the reference standard method of catheterization.

Materials and Methods

Pre‐ and posttreatment LBM‐based pressure gradients for 12 patients with CoA were simulated for the time point of peak systole using the open source library OpenLB. Four‐dimensional (4D) flow‐sensitive phase‐contrast MRI at 1.5 Tesla was used to acquire flow and to setup the simulation. The vascular geometry was reconstructed using 3D whole‐heart MRI. Patients underwent pre‐ and postinterventional pressure catheterization as a reference standard.

Results

There is a significant linear correlation between the pretreatment catheter pressure drops and those computed based on the LBM simulation, r=.85, P<.001. The bias was ‐0.58 ± 4.1 mmHg and was not significant ( P=0.64) with a 95% confidence interval (CI) of ‐3.22 to 2.06. For the posttreatment results, the bias was larger and at ‐2.54 ± 3.53 mmHg with a 95% CI of ‐0.17 to ‐4.91 mmHg.

Conclusion

The results indicate a reasonable agreement between the simulation results and the catheter measurements. LBM‐based computational hemodynamics can be considered as an alternative to more traditional computational fluid dynamics schemes for noninvasive pressure calculations and can assist in diagnosis and therapy planning.

Level of Evidence: 3

J. Magn. Reson. Imaging 2017;45:139–146.

Effects of Renal Denervation on Renal Artery Function in Humans: Preliminary Study

Aim

To study the effects of RD on renal artery wall function non-invasively using magnetic resonance.

Methods and Results

32 patients undergoing RD were included. A 3.0 Tesla magnetic resonance of the renal arteries was performed before RD and after 6-month. We quantified the vessel sharpness of both renal arteries using a quantitative analysis tool (Soap-Bubble®). In 17 patients we assessed the maximal and minimal cross-sectional area of both arteries, peak velocity, mean flow, and renal artery distensibility. In a subset of patients wall shear stress was assessed with computational flow dynamics. Neither renal artery sharpness nor renal artery distensibility differed significantly. A significant increase in minimal and maximal areas (by 25.3%, p = 0.008, and 24.6%, p = 0.007, respectively), peak velocity (by 16.9%, p = 0.021), and mean flow (by 22.4%, p = 0.007) was observed after RD. Wall shear stress significantly decreased (by 25%, p = 0.029). These effects were observed in blood pressure responders and non-responders.

Conclusions

RD is not associated with adverse effects at renal artery level, and leads to an increase in cross-sectional areas, velocity and flow and a decrease in wall shear stress.

Quantitative Assessment of Turbulence and Flow Eccentricity in an Aortic Coarctation: Impact of Virtual Interventions

Turbulence and flow eccentricity can be measured by magnetic resonance imaging (MRI) and may play an important role in the pathogenesis of numerous cardiovascular diseases. In the present study, we propose quantitative techniques to assess turbulent kinetic energy (TKE) and flow eccentricity that could assist in the evaluation and treatment of stenotic severities. These hemodynamic parameters were studied in a pre-treated aortic coarctation (CoA) and after several virtual interventions using computational fluid dynamics (CFD), to demonstrate the effect of different dilatation options on the flow field. Patient-specific geometry and flow conditions were derived from MRI data. The unsteady pulsatile flow was resolved by large eddy simulation including non-Newtonian blood rheology. Results showed an inverse asymptotic relationship between the total amount of TKE and degree of dilatation of the stenosis, where turbulent flow proximal the constriction limits the possible improvement by treating the CoA alone. Spatiotemporal maps of TKE and flow eccentricity could be linked to the characteristics of the jet, where improved flow conditions were favored by an eccentric dilatation of the CoA. By including these flow markers into a combined MRI-CFD intervention framework, CoA therapy has not only the possibility to produce predictions via simulation, but can also be validated pre- and immediate post treatment, as well as during follow-up studies.

Assessment of altered three-dimensional blood characteristics in aortic disease by velocity distribution analysis

PURPOSE

To test the feasibility of velocity distribution analysis for identifying altered three-dimensional (3D) flow characteristics in patients with aortic disease based on 4D flow MRI volumetric analysis.

METHODS

Forty patients with aortic (Ao) dilation (mid ascending aortic diameter MAA = 40 ± 7 mm, age = 56 ± 17 years, 11 females) underwent cardiovascular MRI. Four groups were retrospectively defined: mild Ao dilation (n = 10; MAA < 35 mm); moderate Ao dilation (n = 10; 35 < MAA < 45 mm); severe Ao dilation (n = 10; MAA > 45 mm); Ao dilation+aortic stenosis AS (n = 10; MAA > 35 mm and peak velocity > 2.5 m/s). The 3D PC-MR angiograms were computed and used to obtain a 3D segmentation of the aorta which was divided into four segments: root, ascending aorta, arch, descending aorta. Radial chart displays were used to visualize multiple parameters representing segmental changes in the 3D velocity distribution associated with aortic disease.

RESULTS

Changes in the velocity field and geometry between cohorts resulted in distinct hemodynamic patterns for each aortic segment. Disease progression from mild to Ao dilation + AS resulted in significant differences (P < 0.05) in flow parameters across cohorts and increased radial chart size for root and ascending aorta segments by 146% and 99%, respectively.

CONCLUSION

Volumetric 4D velocity distribution analysis has the potential to identify characteristic changes in regional blood flow patterns in patients with aortic disease.

Methodology for implementing patient-specific spatial boundary condition during a cardiac cycle from phase-contrast MRI for hemodynamic assessment

Pulmonary insufficiency (PI) can render the right ventricle dysfunctional due to volume overloading and hypertrophy. The treatment requires a pulmonary valve replacement surgery. However, determining the right time for the valve replacement surgery has been difficult with currently employed clinical techniques such as, echocardiography and cardiac MRI. Therefore, there is a clinical need to improve the diagnosis of PI by using patient-specific (PS) hemodynamic endpoints. While there are many reported studies on the use of PS geometry with time varying boundary conditions (BC) for hemodynamic computation, few use spatially varying PS velocity measurement at each time point of the cardiac cycle. In other words, the gap is that, there are limited number of studies which implement both spatially- and time-varying physiologic BC directly with patient specific geometry. The uniqueness of this research is in the incorporation of spatially varying PS velocity data obtained from phase-contrast MRI (PC-MRI) at each time point of the cardiac cycle with PS geometry obtained from angiographic MRI. This methodology was applied to model the complex developing flow in human pulmonary artery (PA) distal to pulmonary valve, in a normal and a subject with PI. To validate the methodology, the flow rates from the proposed method were compared with those obtained using QFlow software, which is a standard of care clinical technique. For the normal subject, the computed time average flow rates from this study differed from those obtained using the standard of care technique (QFlow) by 0.8 ml/s (0.9%) at the main PA, by 2 ml/s (3.4%) at the left PA and by 1.4 ml/s (3.8%) at the right PA. For the subject with PI, the difference was 7 ml/s (12.4%) at the main PA, 5.5 ml/s (22.6%) at the left PA and 4.9 ml/s (18.0%) at the right PA. The higher percentage differences for the subject with PI, was the result of overall lower values of the forward mean flow rate caused by excessive flow regurgitation. This methodology is expected to provide improved computational results when PS geometry from angiographic MRI is used in conjunction with PS PC-MRI data for solving the flow field.

Accelerated analysis of three-dimensional blood flow of the thoracic aorta in stroke patients

To test if new software accelerates analysis of in vivo acquired 4D flow MRI data. Respiration-gated and ECG-synchronized 4D flow MRI of the aorta was performed in 20 stroke patients using a routine 3-Tesla MRI system (TIMTRIO, Siemens, Germany). 3D blood flow data was processed by one experienced observer using new (A = MEVISFlow) and widely-used software (B = EnSight + Velomap-/FlowTool). Evaluation included: inter-/intra-observer variability of software A and inter-software comparison regarding (1) blood flow quantification (total-/peak flow) and (2) flow visualisation, plus (3) measurement of the time required for visualization and quantification of data (software A&B). (1) Inter-/intra-observer agreement of software A (mean difference ≤5.2 and ≤0.9 %, respectively) and inter-software agreement (mean difference ≤ 2.2 %) was high with high correlation of peak and total blood flow (r ≥ 0.74; p < 0.001 and r ≥ 0.91; p < 0.001). (2) Comparison of blood flow visualization showed substantial agreement (κ ≥ 0.68). (3) Data-analysis was three times faster when using software A [18:10 (±1:29) vs. 58:30 (±5:28) min; p < 0.0001]. Acceleration of blood flow quantification and visualisation using new software strongly facilitates future applications of 4D flow MRI and thus enables its usage in larger patient cohorts in clinical research and routine.

MRI-based computational fluid dynamics for diagnosis and treatment prediction: clinical validation study in patients with coarctation of aorta

PURPOSE

To reduce the need for diagnostic catheterization and optimize treatment in a variety of congenital heart diseases, magnetic resonance imaging (MRI)-based computational fluid dynamics (CFD) is proposed. However, data about the accuracy of CFD in a clinical context are still sparse. To fill this gap, this study compares MRI-based CFD to catheterization in the coarctation of aorta (CoA) setting.

MATERIALS AND METHODS

Thirteen patients with CoA were investigated by routine MRI prior to catheterization. 3D whole-heart MRI was used to reconstruct geometries and 4D flow-sensitive phase-contrast MRI was used to acquire flows. Peak systolic flows were simulated using the program FLUENT.

RESULTS

Peak systolic pressure drops in CoA measured by catheterization and CFD correlated significantly for both pre- and posttreatment measurements (pre: r = 0.98, p = 0.00; post: r = 0.87, p = 0.00). The pretreatment bias was -0.5 ± 3.33 mmHg (95% confidence interval -2.55 to 1.47 mmHg). CFD predicted a reduction of the peak systolic pressure drop after treatment that ranged from 17.6 ± 5.56 mmHg to 6.7 ± 5.58 mmHg. The posttreatment bias was 3.0 ± 2.91 mmHg (95% CI -1.74 to 5.43 mmHg).

CONCLUSION

Peak systolic pressure drops can be reliably calculated using MRI-based CFD in a clinical setting. Therefore, CFD might be an attractive noninvasive alternative to diagnostic catheterization.