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

Literature Survey for In-Vivo Reynolds and Womersley Numbers of Various Arteries and Implications for Compliant In-Vitro Modelling

PURPOSE

In-vitro modelling can be used to investigate haemodynamics of arterial geometry and stent implants. However, in-vitro model fidelity relies on precise matching of in-vivo conditions. In pulsatile flow, velocity distribution and wall shear stress depend on compliance, and the Reynolds and Womersley numbers. However, matching such values may lead to unachievable tolerances in phantom fabrication.

METHODS

Published Reynolds and Womersley numbers for 14 major arteries in the human body were determined via a literature search. Preference was given to in-vivo publications but in-vitro and in-silico values were presented when in-vivo values were not found. Subsequently ascending aorta and carotid artery case studies were presented to highlight the limitations dynamic matching would apply to phantom fabrication.

RESULTS

Seven studies reported the in-vivo Reynolds and Womersley numbers for the aorta and two for the carotid artery. However, only one study each reported in-vivo numbers for the remaining ten arteries. No in-vivo data could be found for the femoral, superior mesenteric and renal arteries. Thus, information derived in-vitro and in-silico were provided instead. The ascending aorta and carotid artery models required scaling to 1.5× and 3× life-scale, respectively, to achieve dimensional tolerance restrictions. Modelling the ascending aorta with the comparatively high viscosity water/glycerine solution will lead to high pump power demands. However, all the working fluids considered could be dynamically matched with low pump demand for the carotid model.

CONCLUSION

This paper compiles available human haemodynamic information, and highlights the paucity of information for some arteries. It also provides a method for optimal in-vitro experimental configuration.

Medical-Surgical Implications of Branching Variation of Human Aortic Arch Known as Bovine Aortic Arch (BAA)

(1) Background: The aortic arch (AA) branching model is challenging, considering the multiple anatomical variations documented in existing research. The bovine aortic arch (BAA) is the most prevalent anatomical variation among these. This variant of AA branching has long been considered a nonsymptomatic malformation, having been discovered incidentally during imaging investigations for other causes. However, more recent studies have demonstrated that BAA shows a frequent association with coarctation of the aorta (CoA), thoracic aortic disease (TAD), and stroke. At the same time, given the current context of increasing activity in the fields of interventional and surgical procedures in the aorta and its branches, it is very important to know the medical-surgical implications of this anatomical variant. (2) Methods: We conducted a comprehensive review using PubMed and Embase, focusing specifically on randomized trials and cohort analyses that examined the medical-surgical implications of BAA. We assessed information related to studied groups, medical procedures, and study outcomes. Initially, we identified 8454 studies, and after rigorous evaluation, we narrowed down our review to 25 articles. (3) Discussions: The intervention consisted of assessing the risks associated with BAA through different imaging investigation methods such as computer tomographic angiography (CTA), magnetic resonance imaging (MRI), or ultrasonography (US). The following results were evaluated: the prevalence of the BAA, the importance of imaging investigations in establishing the diagnosis and the therapeutic management and monitoring the evolution of patients with the BAA, the association of the BAA with CoA, TAD, and stroke, and the potential risks of interventional treatment in patients with the BAA. (4) Conclusions: The prevalence of the BAA differs both between different ethnic groups and between genders. Advanced imaging methods such as CTA and 4D flow MRI allow detailed descriptions of supra-aortic vascular anatomy and information about blood flow velocities, direction, and turbulence in the AA. US remains an easy and valuable imaging investigation, with the potential to detect and correctly diagnose the BAA and its hemodynamic implications. Anatomical variations in the AA are associated with increased rates of TAD, CoA, and stroke, necessitating early diagnosis and increased supervision of patients with such incidentally observed abnormalities. In addition, there is a need to further develop and refine the surgical techniques used and personalize them to the individual characteristics of patients with the BAA.

Computational fluid dynamics in cardiac surgery and perfusion: A review

Cardiovascular diseases persist as a leading cause of mortality and morbidity, despite significant advances in diagnostic and surgical approaches. Computational Fluid Dynamics (CFD) represents a branch of fluid mechanics widely used in industrial engineering but is increasingly applied to the cardiovascular system. This review delves into the transformative potential for simulating cardiac surgery procedures and perfusion systems, providing an in-depth examination of the state-of-the-art in cardiovascular CFD modeling. The study first describes the rationale for CFD modeling and later focuses on the latest advances in heart valve surgery, transcatheter heart valve replacement, aortic aneurysms, and extracorporeal membrane oxygenation. The review underscores the role of CFD in better understanding physiopathology and its clinical relevance, as well as the profound impact of hemodynamic stimuli on patient outcomes. By integrating computational methods with advanced imaging techniques, CFD establishes a quantitative framework for understanding the intricacies of the cardiac field, providing valuable insights into disease progression and treatment strategies. As technology advances, the evolving synergy between computational simulations and clinical interventions is poised to revolutionize cardiovascular care. This collaboration sets the stage for more personalized and effective therapeutic strategies. With its potential to enhance our understanding of cardiac pathologies, CFD stands as a promising tool for improving patient outcomes in the dynamic landscape of cardiovascular medicine.

Hemodynamic predictors of negative false lumen remodeling after frozen elephant trunk for acute aortic dissection

OBJECTIVE

We evaluated the blood flow within the downstream aortic false lumen after frozen elephant trunk repair for acute aortic dissection and identified hemodynamic predictors of false lumen expansion and negative false lumen remodeling using four-dimensional flow magnetic resonance imaging.

METHODS

Thirty-one patients (Stanford type A, n = 28; Stanford type B, n = 3) with patent false lumen who underwent frozen elephant trunk procedures for acute aortic dissection were included in this observational study. Each patient underwent computed tomography during the follow-up period and four-dimensional flow magnetic resonance imaging within 3 postoperative months. The false lumen volumetric expansion rate was calculated using computed tomography data. The direction and the rate of flow in the lower descending aortic false lumen were analyzed. Negative false lumen remodeling was defined as a volumetric increase of > 10% from the baseline volume.

RESULTS

Negative false lumen remodeling had developed in 6 of the 31 patients during the observation period. Most of the false lumen flows were biphasic during systole. The range between peak and nadir flow rates was associated with the false lumen volumetric expansion rate (β coefficient = 6.77; p < 0.01, R2 = 0.43).

CONCLUSIONS

The range between peak and nadir flow rates may serve as a hemodynamic predictor of negative false lumen remodeling, enabling further treatment for patients at risk of expansion in the downstream aorta.

Quantitative evaluation of pulmonary hypertension using 4D flow MRI: A retrospective study

Background

Pulmonary hypertension (PH) is a severe vascular disorder that may affect 50 % of patients with heart failure. Currently, right-sided heart catheterization is required to definitively diagnose PH. However, this method is invasive and thus may not be appropriate for repeated, long-term monitoring of PH patients. This retrospective study's aim was to evaluate whether 4D flow magnetic resonance imaging (MRI) can be used to quantitively measure flow parameters to identify patients with PH.

Methods

The study cohort included 97 patients recruited from a single institution and divided into three groups based on echocardiographic estimate of pulmonary artery systolic pressure (PASP): normal group with PASP<36 mmHg, borderline PH group with PASP of 37-50 mmHg, and PH group with PASP>50 mmHg. 4D flow MRI was used to quantitively assess blood flow and velocity, regurgitation, wall shear stress (WSS) and kinetic energy in the pulmonary artery trunk, right main pulmonary artery, and left pulmonary artery. Two experienced radiologists independently analyzed the MR images, blinded to clinical details.

Results

We found a significant difference in WSS in the pulmonary artery trunk, right main pulmonary artery and left main pulmonary artery among the three patient groups. We also found significant differences in the kinetic energy and average through velocity in the pulmonary artery trunk and right main pulmonary artery, and significant differences in the flow rate in the right main pulmonary artery.

Conclusion

These data suggest that 4D flow MRI can quantitate pulmonary artery flow parameters and distinguish between patients with and without PH.

Virtual Planning and Patient-Specific Graft Design for Aortic Repairs

PURPOSE

Patients presenting with coarctation of the aorta (CoA) may also suffer from co-existing transverse arch hypoplasia (TAH). Depending on the risks associated with the surgery and the severity of TAH, clinicians may decide to repair only CoA, and monitor the TAH to see if it improves as the patient grows. While acutely successful, eventually hemodynamics may become suboptimal if TAH is left untreated. The objective of this work aims to develop a patient-specific surgical planning framework for predicting and assessing postoperative outcomes of simple CoA repair and comprehensive repair of CoA and TAH.

METHODS

The surgical planning framework consisted of virtual clamp placement, stenosis resection, and design and optimization of patient-specific aortic grafts that involved geometrical modeling of the graft and computational fluid dynamics (CFD) simulation for evaluating various surgical plans. Time-dependent CFD simulations were performed using Windkessel boundary conditions at the outlets that were obtained from patient-specific non-invasive pressure and flow data to predict hemodynamics before and after the virtual repairs. We applied the proposed framework to investigate optimal repairs for six patients (n = 6) diagnosed with both CoA and TAH. Design optimization was performed by creating a combination of a tubular graft and a waterslide patch to reconstruct the aortic arch. The surfaces of the designed graft were parameterized to optimize the shape.

RESULTS

Peak systolic pressure drop (PSPD) and time-averaged wall shear stress (TAWSS) were used as performance metrics to evaluate surgical outcomes of various graft designs and implantation. The average PSPD improvements were 28% and 44% after the isolated CoA repair and comprehensive repair, respectively. Maximum values of TAWSS were decreased by 60% after CoA repair and further improved by 22% after the comprehensive repair. The oscillatory shear index was calculated and the values were confirmed to be in the normal range after the repairs.

CONCLUSION

The results showed that the comprehensive repair outperforms the simple CoA repair and may be more advantageous in the long term in some patients. We demonstrated that the surgical planning and patient-specific flow simulations could potentially affect the selection and outcomes of aorta repairs.

A 3D scaling law for supravalvular aortic stenosis suited for stethoscopic auscultations

In this study a frequency scaling law for 3D anatomically representative supravalvular aortic stenosis (SVAS) cases is proposed. The law is uncovered for stethoscopy's preferred auscultation range (70-120 Hz). LES simulations are performed on the CFD solver Fluent, leveraging Simulia's Living Heart Human Model (LHHM), modified to feature hourglass stenoses that range between 30 to 80 percent (mild to severe) in addition to the descending aorta. For physiological hemodynamic boundary conditions the Windkessel model is implemented via a UDF subroutine. The flow-generated acoustic signal is then extracted using the FW-H model and analyzed using FFT. A preferred receiver location that matches clinical practice is confirmed (right intercostal space) and a correlation between the degree of stenosis and a corresponding acoustic frequency is obtained. Five clinical auscultation signals are tested against the scaling law, with the findings interpreted in relation to the NHS classification of stenosis and to the assessments of experienced cardiologists. The scaling law is thus shown to succeed as a potential quantitative decision-support tool for clinicians, enabling them to reliably interpret stethoscopic auscultations for all degrees of stenosis, which is especially useful for moderate degrees of SVAS. Computational investigation of more complex stenotic cases would enhance the clinical relevance of this proposed scaling law, and will be explored in future research.

Differences in blood flow dynamics between balloon- and self-expandable valves in patients with aortic stenosis undergoing transcatheter aortic valve replacement

BACKGROUND

The differences in pre- and early post-procedural blood flow dynamics between the two major types of bioprosthetic valves, the balloon-expandable valve (BEV) and self-expandable valve (SEV), in patients with aortic stenosis (AS) undergoing transcatheter aortic valve replacement (TAVR), have not been investigated. We aimed to investigate the differences in blood flow dynamics between the BEV and SEV using four-dimensional flow cardiovascular magnetic resonance (4D flow CMR).

METHODS

We prospectively examined 98 consecutive patients with severe AS who underwent TAVR between May 2018 and November 2021 (58 BEV and 40 SEV) after excluding those without CMR because of a contraindication, inadequate imaging from the analyses, or patients' refusal. CMR was performed in all participants before (median interval, 22 [interquartile range (IQR) 4-39] days) and after (median interval, 6 [IQR 3-6] days) TAVR. We compared the changes in blood flow patterns, wall shear stress (WSS), and energy loss (EL) in the ascending aorta (AAo) between the BEV and SEV using 4D flow CMR.

RESULTS

The absolute reductions in helical flow and flow eccentricity were significantly higher in the SEV group compared in the BEV group after TAVR (BEV: - 0.22 ± 0.86 vs. SEV: - 0.85 ± 0.80, P < 0.001 and BEV: - 0.11 ± 0.79 vs. SEV: - 0.50 ± 0.88, P = 0.037, respectively); there were no significant differences in vortical flow between the groups. The absolute reduction of average WSS was significantly higher in the SEV group compared to the BEV group after TAVR (BEV: - 0.6 [- 2.1 to 0.5] Pa vs. SEV: - 1.8 [- 3.5 to - 0.8] Pa, P = 0.006). The systolic EL in the AAo significantly decreased after TAVR in both the groups, while the absolute reduction was comparable between the groups.

CONCLUSIONS

Helical flow, flow eccentricity, and average WSS in the AAo were significantly decreased after SEV implantation compared to BEV implantation, providing functional insights for valve selection in patients with AS undergoing TAVR. Our findings offer valuable insights into blood flow dynamics, aiding in the selection of valves for patients with AS undergoing TAVR. Further larger-scale studies are warranted to confirm the prognostic significance of hemodynamic changes in these patients.

A CFD-FFT approach to hemoacoustics that enables degree of stenosis prediction from stethoscopic signals

In this paper, we identify a new (acoustic) frequency-stenosis relation whose frequencies lie within the recommended auscultation threshold of stethoscopy (< 120 Hz). We show that this relation can be used to extend the application of phonoangiography (quantifying the degree of stenosis from bruits) to widely accessible stethoscopes. The relation is successfully identified from an analysis restricted to the acoustic signature of the von Karman vortex street, which we automatically single out by means of a metric we propose that is based on an area-weighted average of the Q-criterion for the post-stenotic region. Specifically, we perform CFD simulations on internal flow geometries that represent stenotic blood vessels of different severities. We then extract their emitted acoustic signals using the Ffowcs Williams-Hawkings equation, which we subtract from a clean signal (stenosis free) at the same heart rate. Next, we transform this differential signal to the frequency domain and carefully classify its acoustic signatures per six (stenosis-)invariant flow phases of a cardiac cycle that are newly identified in this paper. We then automatically restrict our acoustic analysis to the sounds emitted by the von Karman vortex street (phase 4) by means of our Q-criterion-based metric. Our analysis of its acoustic signature reveals a strong linear relationship between the degree of stenosis and its dominant frequency, which differs considerably from the break frequency and the heart rate (known dominant frequencies in the literature). Applying our new relation to available stethoscopic data, we find that its predictions are consistent with clinical assessment. Our finding of this linear correlation is also unlike prevalent scaling laws in the literature, which feature a small exponent (i.e., low stenosis percentage sensitivity over much of the clinical range). They hence can only distinguish mild, moderate, and severe cases. Conversely, our linear law can identify variations in the degree of stenosis sensitively and accurately for the full clinical range, thus significantly improving the utility of the relevant scaling laws... Future research will investigate incorporating the vibroacoustic role of adjacent organs to expand the clinical applicability of our findings. Extending our approach to more complex 3D stenotic morphologies and including the vibroacoustic role of surrounding organs will be explored in future research to advance the clinical reach of our findings.

Pulmonary artery blood flow dynamics in chronic thromboembolic pulmonary hypertension

Chronic thromboembolic pulmonary hypertension is caused by incomplete resolution and organization of thrombi. Blood flow dynamics are involved in thrombus formation; however, only a few studies have reported on pulmonary artery blood flow dynamics in patients with chronic thromboembolic pulmonary hypertension. Furthermore, the effects of treatment interventions on pulmonary artery blood flow dynamics are not fully understood. The aim of the study was to evaluate pulmonary artery blood flow dynamics in patients with chronic thromboembolic pulmonary hypertension before and after pulmonary endarterectomy and balloon pulmonary angioplasty, using computational fluid dynamics. We analyzed patient-specific pulmonary artery models of 10 patients with chronic thromboembolic pulmonary hypertension and three controls using computational fluid dynamics. In patients with chronic thromboembolic pulmonary hypertension, flow velocity and wall shear stress in the pulmonary arteries were significantly decreased, and the oscillatory shear index and blood stagnation volume were significantly increased than in controls. Pulmonary endarterectomy induced redistribution of pulmonary blood flow and improved blood flow dynamics in the pulmonary artery. Balloon pulmonary angioplasty improved pulmonary blood flow disturbance, decreased blood flow stagnation, and increased wall shear stress, leading to vasodilatation of the distal portion of the pulmonary artery following balloon pulmonary angioplasty treatment.

Influence of aortic valve morphology on vortical structures and wall shear stress

The aim of this paper is to assess the association between valve morphology and vortical structures quantitatively and to highlight the influence of valve morphology/orientation on aorta's susceptibility to shear stress, both proximal and distal. Four-dimensional phase-contrast magnetic resonance imaging (4D PCMRI) data of 6 subjects, 3 with tricuspid aortic valve (TAV) and 3 with functionally bicuspid aortic values (BAV) with right-left coronary leaflet fusion, were processed and analyzed for vorticity and wall shear stress trends. Computational fluid dynamics (CFD) has been used with moving TAV and BAV valve designs in patient-specific aortae to compare with in vivo shear stress data. Vorticity from 4D PCMRI data about the aortic centerline demonstrated that TAVs had a higher number of vortical flow structures than BAVs at peak systole. Coalescing of flow structures was shown to be possible in the arch region of all subjects. Wall shear stress (WSS) distribution from CFD results at the aortic root is predominantly symmetric for TAVs but highly asymmetric for BAVs with the region opposite the raphe (fusion location of underdeveloped leaflets) being subjected to higher WSS. Asymmetry in the size and number of leaflets in BAVs and TAVs significantly influence vortical structures and WSS in the proximal aorta for all valve types and distal aorta for certain valve orientations of BAV. Analysis of vortical structures using 4D PCMRI data (on the left side) and wall shear stress data using CFD (on the right side).

Modeling Flow in an In Vitro Anatomical Cerebrovascular Model with Experimental Validation

Acute ischemic stroke (AIS) is a leading cause of mortality that occurs when an embolus becomes lodged in the cerebral vasculature and obstructs blood flow in the brain. The severity of AIS is determined by the location and how extensively emboli become lodged, which are dictated in large part by the cerebral flow and the dynamics of embolus migration which are difficult to measure in vivo in AIS patients. Computational fluid dynamics (CFD) can be used to predict the patient-specific hemodynamics and embolus migration and lodging in the cerebral vasculature to better understand the underlying mechanics of AIS. To be relied upon, however, the computational simulations must be verified and validated. In this study, a realistic in vitro experimental model and a corresponding computational model of the cerebral vasculature are established that can be used to investigate flow and embolus migration and lodging in the brain. First, the in vitro anatomical model is described, including how the flow distribution in the model is tuned to match physiological measurements from the literature. Measurements of pressure and flow rate for both normal and stroke conditions were acquired and corresponding CFD simulations were performed and compared with the experiments to validate the flow predictions. Overall, the CFD simulations were in relatively close agreement with the experiments, to within ±7% of the mean experimental data with many of the CFD predictions within the uncertainty of the experimental measurement. This work provides an in vitro benchmark data set for flow in a realistic cerebrovascular model and is a first step towards validating a computational model of AIS.

Modeling flow in an in vitro anatomical cerebrovascular model with experimental validation

Acute ischemic stroke (AIS) is a leading cause of mortality that occurs when an embolus becomes lodged in the cerebral vasculature and obstructs blood flow in the brain. The severity of AIS is determined by the location and how extensively emboli become lodged, which are dictated in large part by the cerebral flow and the dynamics of embolus migration which are difficult to measure in vivo in AIS patients. Computational fluid dynamics (CFD) can be used to predict the patient-specific hemodynamics and embolus migration and lodging in the cerebral vasculature to better understand the underlying mechanics of AIS. To be relied upon, however, the computational simulations must be verified and validated. In this study, a realistic in vitro experimental model and a corresponding computational model of the cerebral vasculature are established that can be used to investigate flow and embolus migration and lodging in the brain. First, the in vitro anatomical model is described, including how the flow distribution in the model is tuned to match physiological measurements from the literature. Measurements of pressure and flow rate for both normal and stroke conditions were acquired and corresponding CFD simulations were performed and compared with the experiments to validate the flow predictions. Overall, the CFD simulations were in relatively close agreement with the experiments, to within ±7% of the mean experimental data with many of the CFD predictions within the uncertainty of the experimental measurement. This work provides an in vitro benchmark data set for flow in a realistic cerebrovascular model and is a first step towards validating a computational model of AIS.

Accelerated sequences of 4D flow MRI using GRAPPA and compressed sensing: A comparison against conventional MRI and computational fluid dynamics

PURPOSE

To evaluate hemodynamic markers obtained by accelerated GRAPPA (R = 2, 3, 4) and compressed sensing (R = 7.6) 4D flow MRI sequences under complex flow conditions.

METHODS

The accelerated 4D flow MRI scans were performed on a pulsatile flow phantom, along with a nonaccelerated fully sampled k-space acquisition. Computational fluid dynamics simulations based on the experimentally measured flow fields were conducted for additional comparison. Voxel-wise comparisons (Bland-Altman analysis, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics> <mml:mrow><mml:msub><mml:mi>L</mml:mi> <mml:mn>2</mml:mn></mml:msub> </mml:mrow> <mml:annotation>$$ {L}_2 $$</mml:annotation></mml:semantics> </mml:math> -norm metric), as well as nonderived quantities (velocity profiles, flow rates, and peak velocities), were used to compare the velocity fields obtained from the different modalities.

RESULTS

4D flow acquisitions and computational fluid dynamics depicted similar hemodynamic patterns. Voxel-wise comparisons between the MRI scans highlighted larger discrepancies at the voxels located near the phantom's boundary walls. A trend for all MR scans to overestimate velocity profiles and peak velocities as compared to computational fluid dynamics was noticed in regions associated with high velocity or acceleration. However, good agreement for the flow rates was observed, and eddy-current correction appeared essential for consistency of the flow rates measurements with respect to the principle of mass conservation.

CONCLUSION

GRAPPA (R = 2, 3) and highly accelerated compressed sensing showed good agreement with the fully sampled acquisition. Yet, all 4D flow MRI scans were hampered by artifacts inherent to the phase-contrast acquisition procedure. Computational fluid dynamics simulations are an interesting tool to assess these differences but are sensitive to modeling parameters.

Hemodynamics in a three-dimensional printed aortic model: a comparison of four-dimensional phase-contrast magnetic resonance and image-based computational fluid dynamics

OBJECTIVE

This study aims to compare an electrocardiogram (ECG)-gated four-dimensional (4D) phase-contrast (PC) magnetic resonance imaging (MRI) technique and computational fluid dynamics (CFD) using variables controlled in a laboratory environment to minimize bias factors.

MATERIALS AND METHODS

Data from 4D PC-MRI were compared with computational fluid dynamics using steady and pulsatile flows at various inlet velocities. Anatomically realistic models for a normal aorta, a penetrating atherosclerotic ulcer, and an abdominal aortic aneurysm were constructed using a three-dimensional printer.

RESULTS

For the normal aorta model, the errors in the peak and the average velocities were within 5%. The peak velocities of the penetrating atherosclerotic ulcer and the abdominal aortic aneurysm models displayed a more extensive range of differences because of the high-speed and vortical fluid flows generated by the shape of the blood vessel. However, the average velocities revealed only relatively minor differences.

CONCLUSIONS

This study compared the characteristics of PC-MRI and CFD through a phantom study that only included controllable experimental parameters. Based on these results, 4D PC-MRI and CFD are powerful tools for analyzing blood flow patterns in vivo. However, there is room for future developments to improve velocity measurement accuracy.

Synthesis of patient-specific multipoint 4D flow MRI data of turbulent aortic flow downstream of stenotic valves

We propose to synthesize patient-specific 4D flow MRI datasets of turbulent flow paired with ground truth flow data to support training of inference methods. Turbulent blood flow is computed based on the Navier-Stokes equations with moving domains using realistic boundary conditions for aortic shapes, wall displacements and inlet velocities obtained from patient data. From the simulated flow, synthetic multipoint 4D flow MRI data is generated with user-defined spatiotemporal resolutions and reconstructed with a Bayesian approach to compute time-varying velocity and turbulence maps. For MRI data synthesis, a fixed hypothetical scan time budget is assumed and accordingly, changes to spatial resolution and time averaging result in corresponding scaling of signal-to-noise ratios (SNR). In this work, we focused on aortic stenotic flow and quantification of turbulent kinetic energy (TKE). Our results show that for spatial resolutions of 1.5 and 2.5 mm and time averaging of 5 ms as encountered in 4D flow MRI in practice, peak total turbulent kinetic energy downstream of a 50, 75 and 90% stenosis is overestimated by as much as 23, 15 and 14% (1.5 mm) and 38, 24 and 23% (2.5 mm), demonstrating the importance of paired ground truth and 4D flow MRI data for assessing accuracy and precision of turbulent flow inference using 4D flow MRI exams.

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

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

Computational fluid dynamics investigation on aortic hemodynamics in double aortic arch before and after ligation surgery

Double aortic arch (DAA) malformation is one of the reasons for symptomatic vascular rings, the hemodynamics of which is still poorly understood. This study aims to investigate the blood flow characteristics in patient-specific double aortic arches using computational fluid dynamics (CFD). Seven cases of infantile patients with DAA were collected and their computed tomography images were used to reconstruct 3D computational models. A modified Carreau model was used to consider the non-Newtonian effect of blood and a three-element Windkessel model taking the effect of the age of patients into account was applied to reproduce physiological pressure waveforms. Numerical results show that blood flow distribution and energy loss of DAA depends on relative sizes of the two aortic arches and their angles with the ascending aorta. Ligation of either aortic arch increases the energy loss of blood in the DAA, leading to the increase in cardiac workload. Generally, the rising rate of energy loss before and after the surgery is almost linear with the area ratio between the aortic arch without ligation and the ascending aorta.

Enhanced 4D Flow MRI-Based CFD with Adaptive Mesh Refinement for Flow Dynamics Assessment in Coarctation of the Aorta

4D Flow MRI is a diagnostic tool that can visualize and quantify patient-specific hemodynamics and help interventionalists optimize treatment strategies for repairing coarctation of the aorta (COA). Despite recent developments in 4D Flow MRI, shortcomings include phase-offset errors, limited spatiotemporal resolution, aliasing, inaccuracies due to slow aneurysmal flows, and distortion of images due to metallic artifact from vascular stents. To address these limitations, we developed a framework utilizing Computational Fluid Dynamics (CFD) with Adaptive Mesh Refinement (AMR) that enhances 4D Flow MRI visualization/quantification. We applied this framework to five pediatric patients with COA, providing in-vivo and in-silico datasets, pre- and post-intervention. These two data sets were compared and showed that CFD flow rates were within 9.6% of 4D Flow MRI, which is within a clinically acceptable range. CFD simulated slow aneurysmal flow, which MRI failed to capture due to high relative velocity encoding (Venc). CFD successfully predicted in-stent blood flow, which was not visible in the in-vivo data due to susceptibility artifact. AMR improved spatial resolution by factors of 101 to 103 and temporal resolution four-fold. This computational framework has strong potential to optimize visualization/quantification of aneurysmal and in-stent flows, improve spatiotemporal resolution, and assess hemodynamic efficiency post-COA treatment.

Hemolytic anemia caused by an excessively kinked prosthetic graft after total arch replacement detected by 4-dimensional flow magnetic resonance imaging: A case report

RATIONALE

Hemolytic anemia is a rare postoperative complication of aortic surgery, which may be caused by an excessively kinked graft that causes abnormal blood flow. It has been reported that 4-dimensional flow magnetic resonance imaging (4D flow MRI) can identify abnormal flow. Herein, we report the guidance of 4D flow MRI in performing the revision procedure for a patient with hemolytic anemia by evaluating abnormal blood flow based on this method.

PATIENT CONCERNS

A 70-year-old woman presented with dizziness and fatigue. She had undergone total arch replacement with a frozen elephant trunk 5 years prior. We diagnosed hemolytic anemia caused by a kinked graft after total arch replacement.

DIAGNOSIS

Although computed tomography findings revealed 3 lesions of the kinked graft at the ascending portion and cervical branches, 4D flow MRI findings showed that only the kinked graft at the ascending portion caused hemolytic anemia due to an elevated viscous energy loss around it.

INTERVENTION

We performed surgery to remove the kinked section instead of revision surgery consisting of total arch replacement.

OUTCOMES

The patient's postoperative course was uneventful and there were no complications. Postoperative enhanced computed tomography findings showed that the repaired graft had an adequate length and smoothly curved shape. The 4D flow MRI findings revealed smooth flow in the ascending portion and decreased viscous energy loss.

LESSONS

Based on the 4D flow MRI findings, we adopted a less invasive approach, repairing only the ascending portion of the graft, instead of performing revision surgery comprising total arch replacement.

Blood flow analysis with computational fluid dynamics and 4D-flow MRI for vascular diseases

Both computational fluid dynamics (CFD) and time-resolved, three-dimensional, phase-contrast, magnetic resonance imaging (4D-flow MRI) enable visualization of time-varying blood flow structures and quantification of blood flow in vascular diseases. However, they are totally different. CFD is a method to calculate blood flow by solving the governing equations of fluid mechanics, so the obtained flow field is somewhat virtual. On the other hand, 4D-flow MRI measures blood flow in vivo, thus the flow is real. Recently, with the development and enhancement of computers, medical imaging techniques, and related software, blood flow analysis has become more accessible to clinicians and its usefulness in vascular diseases has been demonstrated. In this review, we have outlined the methods and characteristics of CFD and 4D-flow MRI, respectively. We have discussed the differences in the characteristics between both methods; reviewed the milestones achieved by blood flow analysis in various vascular diseases; and discussed the usefulness, challenges, and limitations of blood flow analysis. We have discussed the difficulties and limitations of current blood flow analysis. We have also discussed our views on future directions.

Impact of extra-anatomical bypass on coarctation fluid dynamics using patient-specific lumped parameter and Lattice Boltzmann modeling

Accurate hemodynamic analysis is not only crucial for successful diagnosis of coarctation of the aorta (COA), but intervention decisions also rely on the hemodynamics assessment in both pre and post intervention states to minimize patient risks. Despite ongoing advances in surgical techniques for COA treatments, the impacts of extra-anatomic bypass grafting, a surgical technique to treat COA, on the aorta are not always benign. Our objective was to investigate the impact of bypass grafting on aortic hemodynamics. We investigated the impact of bypass grafting on aortic hemodynamics using a patient-specific computational-mechanics framework in three patients with COA who underwent bypass grafting. Our results describe that bypass grafting improved some hemodynamic metrics while worsened the others: (1) Doppler pressure gradient improved (decreased) in all patients; (2) Bypass graft did not reduce the flow rate substantially through the COA; (3) Systemic arterial compliance increased in patients #1 and 3 and didn't change (improve) in patient 3; (4) Hypertension got worse in all patients; (5) The flow velocity magnitude improved (reduced) in patient 2 and 3 but did not improve significantly in patient 1; (6) There were elevated velocity magnitude, persistence of vortical flow structure, elevated turbulence characteristics, and elevated wall shear stress at the bypass graft junctions in all patients. We concluded that bypass graft may lead to pseudoaneurysm formation and potential aortic rupture as well as intimal hyperplasia due to the persistent abnormal and irregular aortic hemodynamics in some patients. Moreover, post-intervention, exposures of endothelial cells to high shear stress may lead to arterial remodeling, aneurysm, and rupture.

Component quantification of aortic blood flow energy loss using computational fluid-structure interaction hemodynamics

BACKGROUND AND OBJECTIVES

The aorta serves as the main tube of the human blood circulation system. Energy loss (EL) occurs when blood flows through the aorta and there may be a potential correlation between EL and aortic diseases. However, the components of blood flow EL are still not fully understood. This study aims to quantitatively reveal the EL components in healthy and diseased aortas.

METHODS

We construct an idealized healthy aorta and three idealized representative diseased aortas: aortic aneurysm, coarctation of the aorta, and aortic dissection. Computational hemodynamic studies are carried out by using the fluid-structure interaction simulation framework.

RESULTS

Four kinds of EL components: viscous friction, turbulence dissipation, wall deformation, and local lesion are firstly acquired in healthy and diseased aortas based on the high-resolution blood flow information. Viscous friction contributes most to the EL (45.69%-57.22%). EL caused by the deformation of the aortic wall ranks second (15.18%-33.12%). The proportions of turbulence dissipation and local lesion depend on individual geometric characteristics. Besides, the buffering efficiency of the healthy and diseased aorta is about 80%.

CONCLUSIONS

This study quantitatively reports the components of blood flow EL in healthy and diseased aortas, the finding may provide novel insights into the pathogenesis of aortic diseases.

Medical Image-Based Computational Fluid Dynamics and Fluid-Structure Interaction Analysis in Vascular Diseases

Hemodynamic factors, induced by pulsatile blood flow, play a crucial role in vascular health and diseases, such as the initiation and progression of atherosclerosis. Computational fluid dynamics, finite element analysis, and fluid-structure interaction simulations have been widely used to quantify detailed hemodynamic forces based on vascular images commonly obtained from computed tomography angiography, magnetic resonance imaging, ultrasound, and optical coherence tomography. In this review, we focus on methods for obtaining accurate hemodynamic factors that regulate the structure and function of vascular endothelial and smooth muscle cells. We describe the multiple steps and recent advances in a typical patient-specific simulation pipeline, including medical imaging, image processing, spatial discretization to generate computational mesh, setting up boundary conditions and solver parameters, visualization and extraction of hemodynamic factors, and statistical analysis. These steps have not been standardized and thus have unavoidable uncertainties that should be thoroughly evaluated. We also discuss the recent development of combining patient-specific models with machine-learning methods to obtain hemodynamic factors faster and cheaper than conventional methods. These critical advances widen the use of biomechanical simulation tools in the research and potential personalized care of vascular diseases.

Hemodynamic Parameters for Cardiovascular System in 4D Flow MRI: Mathematical Definition and Clinical Applications

Blood flow imaging becomes an emerging trend in cardiology with the recent progress in computer technology. It not only visualizes colorful flow velocity streamlines but also quantifies the mechanical stress on cardiovascular structures; thus, it can provide the detailed inspections of the pathophysiology of diseases and predict the prognosis of cardiovascular functions. Clinical applications include the comprehensive assessment of hemodynamics and cardiac functions in echocardiography vector flow mapping (VFM), 4D flow MRI, and surgical planning as a simulation medicine in computational fluid dynamics (CFD).For evaluation of the hemodynamics, novel mathematically derived parameters obtained using measured velocity distributions are essential. Among them, the traditional and typical parameters are wall shear stress (WSS) and its related parameters. These parameters indicate the mechanical damages to endothelial cells, resulting in degenerative intimal change in vascular diseases. Apart from WSS, there are abundant parameters that describe the strength of the vortical and/or helical flow patterns. For instance, vorticity, enstrophy, and circulation indicate the rotating flow strength or power of 2D vortical flows. In addition, helicity, which is defined as the cross-linking number of the vortex filaments, indicates the 3D helical flow strength and adequately describes the turbulent flow in the aortic root in cases with complicated anatomies. For the description of turbulence caused by the diseased flow, there exist two types of parameters based on completely different concepts, namely: energy loss (EL) and turbulent kinetic energy (TKE). EL is the dissipated energy with blood viscosity and evaluates the cardiac workload related to the prognosis of heart failure. TKE describes the fluctuation in kinetic energy during turbulence, which describes the severity of the diseases that cause jet flow. These parameters are based on intuitive and clear physiological concepts, and are suitable for in vivo flow measurements using inner velocity profiles.

Does the Pulsatile Non-uniform Flow Matter in MR Flowmetry?

3D cine phase-contrast (4D flow) MRI is a sequence with great potential for non-invasive time-resolved 3D flowmetry at arbitrary vessel sections in various blood vessels. However, it is not widely known that the flowmetry with 4D flow MRI is vulnerable to pulsatile and non-uniform flow. Due to the limited spatial and temporal resolutions, averaging within the 3D voxel is occurring during the flowmetry. A simple solution is to avoid setting the measurement plane in the area where non-uniform flow is dominant, which is possible with an aid of streamline depictions generated by computational fluid dynamics (CFD) or 4D flow MRI data. Unlike 4D flow MRI, flowmetry in CFD simulation can use higher spatial and temporal resolution depending on computer performance; therefore, it is robust to fluctuating non-uniform flow. However, the performance of CFD simulations might be limited due to inlet conditions with low temporal resolution. Difficulty applying complex blood flow such as reflection flow from periphery may also limit accurate simulation. Caution should be taken when comparing the result of CFD simulation to that of 4D flow measurement.

WSSNet: Aortic Wall Shear Stress Estimation Using Deep Learning on 4D Flow MRI

Wall shear stress (WSS) is an important contributor to vessel wall remodeling and atherosclerosis. However, image-based WSS estimation from 4D Flow MRI underestimates true WSS values, and the accuracy is dependent on spatial resolution, which is limited in 4D Flow MRI. To address this, we present a deep learning algorithm (WSSNet) to estimate WSS trained on aortic computational fluid dynamics (CFD) simulations. The 3D CFD velocity and coordinate point clouds were resampled into a 2D template of 48 × 93 points at two inward distances (randomly varied from 0.3 to 2.0 mm) from the vessel surface (“velocity sheets”). The algorithm was trained on 37 patient-specific geometries and velocity sheets. Results from 6 validation and test cases showed high accuracy against CFD WSS (mean absolute error 0.55 ± 0.60 Pa, relative error 4.34 ± 4.14%, 0.92 ± 0.05 Pearson correlation) and noisy synthetic 4D Flow MRI at 2.4 mm resolution (mean absolute error 0.99 ± 0.91 Pa, relative error 7.13 ± 6.27%, and 0.79 ± 0.10 Pearson correlation). Furthermore, the method was applied on in vivo 4D Flow MRI cases, effectively estimating WSS from standard clinical images. Compared with the existing parabolic fitting method, WSSNet estimates showed 2–3 × higher values, closer to CFD, and a Pearson correlation of 0.68 ± 0.12. This approach, considering both geometric and velocity information from the image, is capable of estimating spatiotemporal WSS with varying image resolution, and is more accurate than existing methods while still preserving the correct WSS pattern distribution.

On the Role and Effects of Uncertainties in Cardiovascular in silico Analyses

The assessment of cardiovascular hemodynamics with computational techniques is establishing its fundamental contribution within the world of modern clinics. Great research interest was focused on the aortic vessel. The study of aortic flow, pressure, and stresses is at the basis of the understanding of complex pathologies such as aneurysms. Nevertheless, the computational approaches are still affected by sources of errors and uncertainties. These phenomena occur at different levels of the computational analysis, and they also strongly depend on the type of approach adopted. With the current study, the effect of error sources was characterized for an aortic case. In particular, the geometry of a patient-specific aorta structure was segmented at different phases of a cardiac cycle to be adopted in a computational analysis. Different levels of surface smoothing were imposed to define their influence on the numerical results. After this, three different simulation methods were imposed on the same geometry: a rigid wall computational fluid dynamics (CFD), a moving-wall CFD based on radial basis functions (RBF) CFD, and a fluid-structure interaction (FSI) simulation. The differences of the implemented methods were defined in terms of wall shear stress (WSS) analysis. In particular, for all the cases reported, the systolic WSS and the time-averaged WSS (TAWSS) were defined.

Retrograde flow in aortic isthmus in normal and fetal heart disease by principal component analysis and computational fluid dynamics

OBJECTIVES

Reverse flow Retrograde flow (RF) of blood in the aortic isthmus can be observed in different types of fetal heart disease (FHD), including abnormalities in heart structure and function. This study sought to investigate the relationship between RF and blood flow parameters, and develop a computational fluid dynamics (CFD) model to understand the mechanisms underlying this observation.

MATERIAL AND METHODS

A total of 281 fetuses (gestational age [GA] 26.6±.3 weeks) with FHD and 2803 normal fetuses (GA: 26.1±.1 weeks) by fetal echocardiography collected from May 2016 to December 2018. Principal component analysis (PCA) was performed to find the relationship and the CFD model reconstructed from 3D/4D spatio-temporal image correlation (STIC) images to simulate hemodynamics.

RESULTS

There was a significant difference in the percentages of RF between the study (80/201 (39%)) and control (29/2803 (1%)) groups (p < 0.05). The RF occur when the aorta flow rate (left heart) is reduced to 60% by CFD stimulation. Pearson correlation analysis showed significant correlations between flow rate and wall shear stress(WSS) (r = .883, p = 0.047) variables at the AI.

CONCLUSION

Volumetric flow rate of AO or left heart was the main component of the cause of RF. The hemodynamics of the cardiovascular system have highly complex behavior hinge on the turbulent nature of circulating blood flow.

Evaluation and verification of patient-specific modelling of type B aortic dissection

Quantitative assessment of the complex hemodynamic environment in type B aortic dissection (TBAD) through computational fluid dynamics (CFD) simulations can provide detailed insights into the disease and its progression. As imaging and computational technologies have advanced, methodologies have been developed to increase the accuracy and physiological relevance of CFD simulations. This study presents a patient-specific workflow to simulate blood flow in TBAD, utilising the maximum amount of in vivo data available in the form of CT images, 4D-flow MRI and invasive Doppler-wire pressure measurements, to implement the recommended current best practice methodologies in terms of patient-specific geometry and boundary conditions. The study aimed to evaluate and verify this workflow through detailed qualitative and quantitative comparisons of the CFD and in vivo data. Based on data acquired from five TBAD patients, a range of essential model inputs was obtained, including inlet flow waveforms and 3-element Windkessel model parameters, which can be utilised in further studies where in vivo flow data is not available. Local and global analysis showed good consistency between CFD results and 4D-MRI data, with the maximum velocity in the primary entry tear differing by up to 0.3 m/s, and 80% of the analysed regions achieving moderate or strong correlations between the predicted and in vivo velocities. CFD predicted pressures were generally well matched to the Doppler-wire measurements, with some deviation in peak systolic values. Overall, this study presents a validated comprehensive workflow with extensive data for CFD simulation of TBAD.

Evaluation of Computational Methodologies for Accurate Prediction of Wall Shear Stress and Turbulence Parameters in a Patient-Specific Aorta

Background: Recent studies suggest that blood flow in main arteries is intrinsically disturbed, even under healthy conditions. Despite this, many computational fluid dynamics (CFD) analyses of aortic haemodynamics make the assumption of laminar flow, and best practices surrounding appropriate modelling choices are lacking. This study aims to address this gap by evaluating different modelling and post-processing approaches in simulations of a patient-specific aorta. Methods: Magnetic resonance imaging (MRI) and 4D flow MRI from a patient with aortic valve stenosis were used to reconstruct the aortic geometry and derive patient-specific inlet and outlet boundary conditions. Three different computational approaches were considered based on assumed laminar or assumed disturbed flow states including low-resolution laminar (LR-Laminar), high-resolution laminar (HR-Laminar) and large-eddy simulation (LES). Each simulation was ran for 30 cardiac cycles and post-processing was conducted on either the final cardiac cycle, or using a phase-averaged approach which utilised all 30 simulated cycles. Model capabilities were evaluated in terms of mean and turbulence-based parameters. Results: All simulation types, regardless of post-processing approach could correctly predict velocity values and flow patterns throughout the aorta. Lower resolution simulations could not accurately predict gradient-derived parameters including wall shear stress and viscous energy loss (largest differences up to 44.6% and 130.3%, respectively), although phase-averaging these parameters improved predictions. The HR-Laminar simulation produced more comparable results to LES with largest differences in wall shear stress and viscous energy loss parameters up to 5.1% and 11.6%, respectively. Laminar-based parameters were better estimated than turbulence-based parameters. Conclusion: Our findings suggest that well-resolved laminar simulations can accurately predict many laminar-based parameters in disturbed flows, but there is no clear benefit to running a HR-Laminar simulation over an LES simulation based on their comparable computational cost. Additionally, post-processing "typical" laminar simulation results with a phase-averaged approach is a simple and cost-effective way to improve accuracy of lower-resolution simulation results.

Alcohol septal ablation markedly reduces energy loss in hypertrophic cardiomyopathy with left ventricular outflow tract obstruction: A four-dimensional flow cardiac magnetic resonance study

Background

Functional follow-up modalities of hypertrophic cardiomyopathy (HCM) with left ventricular (LV) outflow tract obstruction (LVOTO) subjected to alcohol septal ablation (ASA) are limited.

Methods

This retrospective cohort study included patients of HCM with LVOTO who underwent ASA and four-dimensional (4D) flow cardiac magnetic resonance imaging (MRI) both before and after ASA. We analyzed energy loss in one cardiac cycle within the three-chamber plane of the LV and aortic root, and compared between pre- and post-ASA measurements.

Results

Of the 26 included patients, 10 (39%) were male, and median age was 71 (interquartile range 58–78) years. ASA significantly reduced not only LVOT pressure gradient (70 [19–50] to 9 [3–16], P < 0.001), but also energy loss during one cardiac cycle within the three-chamber plane of the LV and aortic root (80 [65–99] to 56 [45–70], P < 0.001). A linear association was observed between the reductions of energy loss and pressure gradient (R² = 0.58, P < 0.001).

Conclusions

ASA significantly reduced energy loss within the LV and aortic root as quantified by 4D flow MRI, reflecting the decreased cardiac workload. This approach is a promising candidate for serial functional follow-up in patients undergoing ASA.

A novel MRI-based data fusion methodology for efficient, personalised, compliant simulations of aortic haemodynamics

We present a novel, cost-efficient methodology to simulate aortic haemodynamics in a patient-specific, compliant aorta using an MRI data fusion process. Based on a previously-developed Moving Boundary Method, this technique circumvents the high computational cost and numerous structural modelling assumptions required by traditional Fluid-Structure Interaction techniques. Without the need for Computed Tomography (CT) data, the MRI images required to construct the simulation can be obtained during a single imaging session. Black Blood MR Angiography and 2D Cine-MRI data were used to reconstruct the luminal geometry and calibrate wall movement specifically to each region of the aorta. 4D-Flow MRI and non-invasive pressure measurements informed patient-specific inlet and outlet boundary conditions. Luminal area closely matched 2D Cine-MRI measurements with a mean error of less than 4.6% across the cardiac cycle, while physiological pressure and flow distributions were simulated to within 3.3% of patient-specific targets. Moderate agreement with 4D-Flow MRI velocity data was observed. Despite lower peak velocity, an equivalent rigid-wall simulation predicted a mean Time-Averaged Wall Shear Stress (TAWSS) 13% higher than the compliant simulation. The agreement observed between compliant simulation results and MRI data is testament to the accuracy and efficiency of this MRI-based simulation technique.

In vitro pulsatile flow study in compliant and rigid ascending aorta phantoms by stereo particle image velocimetry

The aorta is a high risk region for cardiovascular disease (CVD). Haemodynamic patterns leading to CVD are not well established despite numerous experimental and numerical studies. Most overlook effects of arterial compliance and pulsatile flow. However, rigid wall assumptions can lead to overestimation of wall shear stress; a key CVD determinant. This work investigates the effect of compliance on aortic arch haemodynamics experiencing pulsatility. Rigid and compliant phantoms of the arch and brachiocephalic branch (BCA) were manufactured. Stereoscopic particle image velocimetry was used to observe velocity fields. Higher velocity magnitude was observed in the rigid BCA during acceleration. However, during deceleration, the compliant phantom experienced higher velocity. During deceleration, a low velocity region initiated and increased in size in the BCA of both phantoms with irregular shape in the compliant. At mid-deceleration, considerably larger recirculation was observed under compliance compared to rigid. Another recirculation region formed and increased in size on the inner wall of the arch in the compliant during late deceleration, but not rigid. The recirculation regions witnessed identify as high risk areas for atherosclerosis formation by a previous ex-vivo study. The results demonstrate necessity of compliance and pulsatility in haemodynamic studies to obtain highly relevant clinical outcomes.

Optimization of 4D flow MRI velocity field in the aorta with divergence-free smoothing

Divergence-free smoothing with wall treatment (DFS_wt) method is proposed for processing with four-dimensional (4D) flow magnetic resonance imaging (MRI) data of blood flows to enhance the quality of flow field with physical constraints. The new method satisfies the no-slip wall boundary condition and applies wall function of velocity profile for better estimating the velocity gradient in the near-wall region, and consequently improved wall shear stress (WSS) calculation against the issue of coarse resolution of 4D flow MRI. In the first testing case, blood flow field obtained from 4D flow MRI is well smoothed by DFS_wt method. A great consistency is observed between the post-processed 4D flow MRI data and the computational fluid dynamics (CFD) data in the interested velocity field. WSS has an apparent improvement due to the proposed near-wall treatment with special wall function comparing to the result from original 4D flow MRI data or the DFS-processed data with no wall function. The other five cases also show the same performance that smoothed velocity field and improved WSS estimation are achieved on 4D flow MRI data optimized by DFS_wt. The improvements will benefit the study of hemodynamics regarding the determination of location or the potential possibility of lesions.

Altered hemodynamics by 4D flow cardiovascular magnetic resonance predict exercise intolerance in repaired coarctation of the aorta: an in vitro study

BACKGROUND

Coarctation of the aorta (CoA) is associated with decreased exercise capacity despite successful repair. Altered flow patterns have been identified due to abnormal aortic arch geometry. Our previous work demonstrated aorta size mismatch to be associated with exercise intolerance in this population. In this study, we studied aortic flow patterns during simulations of exercise in repaired CoA using 4D flow cardiovascular magnetic resonance (CMR) using aortic replicas connected to an in vitro flow pump and correlated findings with exercise stress test results to identify biomarkers of exercise intolerance.

METHODS

Patients with CoA repair were retrospectively analyzed after CMR and exercise stress test. Each aorta was manually segmented and 3D printed. Pressure gradient measurements from ascending aorta (AAo) to descending aorta (DAo) and 4D flow CMR were performed during simulations of rest and exercise using a mock circulatory flow loop. Changes in wall shear stress (WSS) and secondary flow formation (vorticity and helicity) from rest to exercise were quantified, as well as estimated DAo Reynolds number. Parameters were correlated with percent predicted peak oxygen consumption (VO2max) and aorta size mismatch (DAAo/DDAo).

RESULTS

Fifteen patients were identified (VO2max 47 to 126% predicted). Pressure gradient did not correlate with VO2max at rest or exercise. VO2max correlated positively with the change in peak vorticity (R = 0.55, p = 0.03), peak helicity (R = 0.54, p = 0.04), peak WSS in the AAo (R = 0.68, p = 0.005) and negatively with peak WSS in the DAo (R = - 0.57, p = 0.03) from rest to exercise. DAAo/DDAo correlated strongly with change in vorticity (R = - 0.38, p = 0.01), helicity (R = - 0.66, p = 0.007), and WSS in the AAo (R = - 0.73, p = 0.002) and DAo (R = 0.58, p = 0.02). Estimated DAo Reynolds number negatively correlated with VO2max for exercise (R = - 0.59, p = 0.02), but not rest (R = - 0.28, p = 0.31). Visualization of streamline patterns demonstrated more secondary flow formation in aortic arches with better exercise capacity, larger DAo, and lower Reynolds number.

CONCLUSIONS

There are important associations between secondary flow characteristics and exercise capacity in repaired CoA that are not captured by traditional pressure gradient, likely due to increased turbulence and inefficient flow. These 4D flow CMR parameters are a target of investigation to identify optimal aortic arch geometry and improve long term clinical outcomes after CoA repair.

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.

Analysis of Turbulence Effects in a Patient-Specific Aorta with Aortic Valve Stenosis

Blood flow in the aorta is often assumed laminar, however aortic valve pathologies may induce transition to turbulence and our understanding of turbulence effects is incomplete. The aim of the study was to provide a detailed analysis of turbulence effects in aortic valve stenosis (AVS).

METHODS

Large-eddy simulation (LES) of flow through a patient-specific aorta with AVS was conducted. Magnetic resonance imaging (MRI) was performed and used for geometric reconstruction and patient-specific boundary conditions. Computed velocity field was compared with 4D flow MRI to check qualitative and quantitative consistency. The effect of turbulence was evaluated in terms of fluctuating kinetic energy, turbulence-related wall shear stress (WSS) and energy loss.

RESULTS

Our analysis suggested that turbulence was induced by a combination of a high velocity jet impinging on the arterial wall and a dilated ascending aorta which provided sufficient space for turbulence to develop. Turbulent WSS contributed to 40% of the total WSS in the ascending aorta and 38% in the entire aorta. Viscous and turbulent irreversible energy losses accounted for 3.9 and 2.7% of the total stroke work, respectively.

CONCLUSIONS

This study demonstrates the importance of turbulence in assessing aortic haemodynamics in a patient with AVS. Neglecting the turbulent contribution to WSS could potentially result in a significant underestimation of the total WSS. Further work is warranted to extend the analysis to more AVS cases and patients with other aortic valve diseases.

Estimating the Haemodynamic Streamline Vena Contracta as the Effective Orifice Area Measured from Reconstructed Multislice Phase-contrast MR Images for Patients with Moderately Accelerated Aortic Stenosis

PURPOSE

In aortic stenosis (AS), the discrepancy between moderately accelerated flow and effective orifice area (EOA) continues to pose a challenge. We developed a method of measuring the vena contracta area as hemodynamic EOA using cardiac MRI focusing on AS patients with a moderately accelerated flow to solve the problem that AS severity can currently be determined only by echocardiography.

METHODS

We investigated 40 patients with a peak transvalvular velocity > 3.0 m/s on transthoracic echocardiography (TTE). The patients were divided into highly accelerated and moderately accelerated AS groups according to whether or not the peak transvalvular velocity was ≥ 4.0 m/s. From the multislice 2D cine phase-contrast MRI data, the cross-sectional area of the vena contracta of the reconstructed streamline in the Valsalva sinus was defined as MRI-EOAs. Patient symptoms and echocardiography data, including EOA (defined as TTE-EOA), were derived from the continuity equation using TTE.

RESULTS

All participants in the highly accelerated AS group (n = 19) showed a peak velocity ≥ 4.0 m/s in MRI. Eleven patients in the moderately accelerated AS group (n = 21) had a TTE-EOA < 1.00 cm². In the moderately accelerated AS group, MRI-EOAs demonstrated a strong correlation with TTE-EOAs (r = 0.76, P < 0.01). Meanwhile, in the highly accelerated AS group, MRI-EOAs demonstrated positivity but a moderate correlation with TTE-EOAs (r = 0.63, P = 0.004). MRI-EOAs were overestimated compared to TTE-EOAs. In terms of the moderately accelerated AS group, the best cut-off value for MRI-EOAs was < 1.23 cm², compatible with TTE-EOAs < 1.00 cm², with an excellent prediction of the New York Heart Association classification ≥ III (sensitivity 87.5%, specificity 76.9%).

CONCLUSION

MRI-EOAs may be an alternative to conventional echocardiography for patients with moderately accelerated AS, especially those with discordant echocardiographic parameters.

Blood flow dynamics with four-dimensional flow cardiovascular magnetic resonance in patients with aortic stenosis before and after transcatheter aortic valve replacement

BACKGROUND

Pre- and post-procedural hemodynamic changes which could affect adverse outcomes in aortic stenosis (AS) patients who undergo transcatheter aortic valve replacement (TAVR) have not been well investigated. Four-dimensional (4D) flow cardiovascular magnetic resonance (CMR) enables accurate analysis of blood flow dynamics such as flow velocity, flow pattern, wall shear stress (WSS), and energy loss (EL). We sought to examine the changes in blood flow dynamics of patients with severe AS who underwent TAVR.

METHODS

We examined 32 consecutive severe AS patients who underwent TAVR between May 2018 and June 2019 (17 men, 82 ± 5 years, median left ventricular ejection fraction 61%, 6 self-expanding valve), after excluding those without CMR because of a contraindication or inadequate imaging from the analyses. We analyzed blood flow patterns, WSS and EL in the ascending aorta (AAo), and those changes before and after TAVR using 4D flow CMR.

RESULTS

After TAVR, semi-quantified helical flow in the AAo was significantly decreased (1.4 ± 0.6 vs. 1.9 ± 0.8, P = 0.002), whereas vortical flow and eccentricity showed no significant changes. WSS along the ascending aortic circumference was significantly decreased in the left (P = 0.038) and left anterior (P = 0.033) wall at the basal level, right posterior (P = 0.011) and left (P = 0.010) wall at the middle level, and right (P = 0.012), left posterior (P = 0.019) and left anterior (P = 0.028) wall at the upper level. EL in the AAo was significantly decreased (15.6 [10.8-25.1 vs. 25.8 [18.6-36.2]] mW, P = 0.012). Furthermore, a significant negative correlation was observed between EL and effective orifice area index after TAVR (r = - 0.38, P = 0.034).

CONCLUSIONS

In severe AS patients undergoing TAVR, 4D flow CMR demonstrates that TAVR improves blood flow dynamics, especially when a larger effective orifice area index is obtained.

Clinical Applications of 4D Flow MR Imaging in Aortic Valvular and Congenital Heart Disease

4D flow MRI allows time-resolved 3D velocity-encoded phase-contrast imaging for 3D visualization and quantification of aortic and intracardiac flow. Radiologists should be familiar with the principles of 4D flow MRI and methods for evaluating blood flow qualitatively and quantitatively. The most substantial benefits of 4D flow MRI are that it enables the simultaneous comprehensive assessment of different vessels, and that retrospective analysis can be achieved in all vessels in any direction in the field of view, which is especially beneficial for patients with complicated congenital heart disease (CHD). For aortic valvular diseases, new parameters such as wall shear stress and energy loss may provide new prognostic values for 4D flow MRI. In this review, we introduce the clinical applications of 4D flow MRI for the visualization of blood flow and quantification of hemodynamic metrics in the setting of aortic valvular disease and CHD, including intracardiac shunt and coronary artery anomaly.

Circulation derived from 4D flow MRI correlates with right ventricular dysfunction in patients with tetralogy of Fallot

We used 4D-flow MRI to investigate circulation, an area integral of vorticity, in the main pulmonary artery (MPA) as a new hemodynamic parameter for assessing patients with a repaired Tetralogy of Fallot (TOF). We evaluated the relationship between circulation, right ventricular (RV) function and the pulmonary regurgitant fraction (PRF). Twenty patients with a repaired TOF underwent cardiac MRI. Flow-sensitive 3D-gradient sequences were used to obtain 4D-flow images. Vortex formation in the MPA was visualized, with short-axis and longitudinal vorticities calculated by software specialized for 4D flow. The RV indexed end-diastolic/end-systolic volumes (RVEDVi/RVESVi) and RV ejection fraction (RVEF) were measured by cine MRI. The PR fraction (PRF) and MPA area were measured by 2D phase-contrast MRI. Spearman ρ values were determined to assess the relationships between circulation, RV function, and PRF. Vortex formation in the MPA occurred in 15 of 20 patients (75%). The longitudinal circulation (11.7 ± 5.1 m²/s) was correlated with the RVEF (ρ = − 0.85, p = 0.0002), RVEDVi (ρ = 0.62, p = 0.03), and RVESVi (ρ = 0.76, p = 0.003) after adjusting for the MPA size. The short-axis circulation (9.4 ± 3.4 m²/s) in the proximal MPA was positively correlated with the MPA area (ρ = 0.61, p = 0.004). The relationships between the PRF and circulation or RV function were not significant. Increased longitudinal circulation in the MPA, as demonstrated by circulation analysis using 4D flow MRI, was related to RV dysfunction in patients with a repaired TOF.

Go with the flow: modeling unique biological flows in engineered in vitro platforms

Interest in recapitulating in vivo phenomena in vitro using organ-on-a-chip technology has grown rapidly and with it, attention to the types of fluid flow experienced in the body has followed suit. These platforms offer distinct advantages over in vivo models with regards to human relevance, cost, and control of inputs (e.g., controlled manipulation of biomechanical cues from fluid perfusion). Given the critical role biophysical forces play in several tissues and organs, it is therefore imperative that engineered in vitro platforms capture the complex, unique flow profiles experienced in the body that are intimately tied with organ function. In this review, we outline the complex and unique flow regimes experienced by three different organ systems: blood vasculature, lymphatic vasculature, and the intestinal system. We highlight current state-of-the-art platforms that strive to replicate physiological flows within engineered tissues while introducing potential limitations in current approaches.

Aortic aneurysms and dissections: Unmet needs from physicians and engineers perspectives

The treatment of aortic disease is complex, requiring cardiothoracic and vascular surgeons to make pre-, post- and intraoperative decisions directly influencing patient survival and well-being. Despite tremendous advancement in vascular surgery and endovascular techniques in the last two decades, along with the abundance of research in the field, many unmet needs and unanswered questions remain. Tight collaboration between engineers and physicians is a keystone in translating new tools, techniques, and devices into practice. Here, we have gathered our perspective, as physicians and engineers, in several pressing issues associated with the diagnosis and treatment of aortic aneurysms and dissection, referring to the current knowledge and practice, signifying unmet needs as well as future directions.

CFD validation using in-vitro MRI velocity data - Methods for data matching and CFD error quantification

Predicting blood flow velocities in patient-specific geometries with Computational Fluid Dynamics (CFD) can provide additional data for diagnosis and treatment planning but the solution can be inaccurate. Therefore, it is crucial to understand the simulation errors and calibrate the numerical model. In-vitro velocity-encoded MRI is a versatile tool to validate CFD. The comparison between CFD and in-vitro MRI velocity data, and the analysis of the simulation error are the objectives of this study. A three-step routine is presented to validate medical CFD data. First, a properly scaled model of the patient-specific geometry is fabricated to achieve high relative resolution in the MRI experiment. Second, the measured flow geometry is matched with the CFD data using one of two algorithms, Coherent Point Drift and Iterative Closest Point. The aligned data sets are then interpolated onto a common grid to enable a point-to-point comparison. Third, the global and local deviations between CFD and MRI velocity data are calculated using different algorithms to reliably estimate the simulation error. The routine is successfully tested with a patient-specific model of a cerebral aneurysm. In conclusion, the methods presented here provide a framework for CFD validation using in-vitro MRI velocity data.

Computerized virtual surgery based on computational fluid dynamics simulation for planning coronary revascularization with aortic root replacement in adult congenital heart disease: a case report

A 38-year-old woman presented with exertional dyspnea and chest compression. She had undergone repair of congenital supravalvular aortic stenosis at 8 years of age. Contrast-enhanced computed tomography showed re-stenosis in the ascending aorta, bilateral coronary arterial aneurysm, and a highly thickened left ventricular wall. Release of stenosis was necessary to avoid left ventricular functional deterioration; however, it could cause demand–supply mismatch in coronary flow due to substantial left ventricular hypertrophy. Sufficient statistical evidence was not available in this situation; therefore, computerized virtual surgery based on computational fluid dynamics (CFD) was performed to predict the postoperative hemodynamics. Consequently, root replacement with in situ Carrel patch coronary reconstruction was considered a better option than coronary artery graft bypass in the left-side coronary flow supply. The patient underwent root replacement with in situ Carrel patch coronary reconstruction as planned based on CFD without any complication and was discharged 15 days postoperatively.

Computational fluid dynamics simulations of flow distribution and graft designs in apicoaortic bypass

OBJECTIVE

Apicoaortic bypass has double outlets and its graft design is similar to that of a left ventricular assist device (LVAD). The left ventricular apex to the descending aorta (LV-DsAo) bypass is widely used in apicoaortic bypass. In contrast, the left ventricular apex to the ascending aorta (LV-AsAo) bypass is standard in LVAD surgery. This study aimed to evaluate the graft designs of apicoaortic bypass and their effects on flow distribution and energy loss (EL).

METHODS

A simulation study using computational fluid dynamics was performed on the geometry and hemodynamics data obtained from a 30-year-old patient who underwent a LV-DsAo bypass. The ratio of the cardiac output (CO) through the ascending aorta (AsAo) and apicoaortic conduit was set at 50:50, 30:70, and 10:90. Regional blood flow (RBF) and EL were calculated for the different distribution ratios. As an alternative to the LV-DsAo bypass, a virtual LV-AsAo bypass surgery was performed, and each parameter was compared with that of the LV-DsAo bypass.

RESULTS

At a distribution ratio of 50:50, the RBF to the head and EL were 16.4% of the total CO and 62.0 mW in the LV-DsAo bypass, and 32.3% and 81.5 mW in the LV-AsAo bypass, respectively. The RBF to the head decreased with the CO through the AsAo in the LV-DsAo bypass, but it was constant in the LV-AsAo bypass. The EL increased inversely with the CO through the AsAo in both graft designs.

CONCLUSION

The regional blood flow distribution was different, but the trend of the EL which increased inversely with the CO through the AsAo was similar between the LV-DsAo and LV-AsAo bypasses.

Patient-Specific Bicuspid Aortic Valve Biomechanics: A Magnetic Resonance Imaging Integrated Fluid-Structure Interaction Approach

Congenital bicuspid aortic valve (BAV) consists of two fused cusps and represents a major risk factor for calcific valvular stenosis. Herein, a fully coupled fluid-structure interaction (FSI) BAV model was developed from patient-specific magnetic resonance imaging (MRI) and compared against in vivo 4-dimensional flow MRI (4D Flow). FSI simulation compared well with 4D Flow, confirming direction and magnitude of the flow jet impinging onto the aortic wall as well as location and extension of secondary flows and vortices developing at systole: the systolic flow jet originating from an elliptical 1.6 cm² orifice reached a peak velocity of 252.2 cm/s, 0.6% lower than 4D Flow, progressively impinging on the ascending aorta convexity. The FSI model predicted a peak flow rate of 22.4 L/min, 6.7% higher than 4D Flow, and provided BAV leaflets mechanical and flow-induced shear stresses, not directly attainable from MRI. At systole, the ventricular side of the non-fused leaflet revealed the highest wall shear stress (WSS) average magnitude, up to 14.6 Pa along the free margin, with WSS progressively decreasing towards the belly. During diastole, the aortic side of the fused leaflet exhibited the highest diastolic maximum principal stress, up to 322 kPa within the attachment region. Systematic comparison with ground-truth non-invasive MRI can improve the computational model ability to reproduce native BAV hemodynamics and biomechanical response more realistically, and shed light on their role in BAV patients' risk for developing complications; this approach may further contribute to the validation of advanced FSI simulations designed to assess BAV biomechanics.

Towards improving the accuracy of aortic transvalvular pressure gradients: rethinking Bernoulli

The transvalvular pressure gradient (TPG) is commonly estimated using the Bernoulli equation. However, the method is known to be inaccurate. Therefore, an adjusted Bernoulli model for accurate TPG assessment was developed and evaluated. Numerical simulations were used to calculate TPG_CFD in patient-specific geometries of aortic stenosis as ground truth. Geometries, aortic valve areas (AVA), and flow rates were derived from computed tomography scans. Simulations were divided in a training data set (135 cases) and a test data set (36 cases). The training data was used to fit an adjusted Bernoulli model as a function of AVA and flow rate. The model-predicted TPG_Model was evaluated using the test data set and also compared against the common Bernoulli equation (TPG_B). TPG_B and TPG_Model both correlated well with TPG_CFD (r > 0.94), but significantly overestimated it. The average difference between TPG_Model and TPG_CFD was much lower: 3.3 mmHg vs. 17.3 mmHg between TPG_B and TPG_CFD. Also, the standard error of estimate was lower for the adjusted model: SEE_Model = 5.3 mmHg vs. SEE_B = 22.3 mmHg. The adjusted model's performance was more accurate than that of the conventional Bernoulli equation. The model might help to improve non-invasive assessment of TPG. Graphical abstract Processing pipeline for the definition of an adjusted Bernoulli model for the assessment of transvalvular pressure gradient. Using CT image data, the patient specific geometry of the stenosed AVs were reconstructed. Using this segmentation, the AVA as well as the volume flow rate was calculated and used for model definition. This novel model was compared against classical approaches on a test data set, which was not used for the model definition.