Computational simulations for aortic coarctation: representative results from a sampling of patients

A Novel Diastolic Doppler Index Less Affected by Aortic Arch Anomalies Co-existing with Coarctation

Severity assessment for coarctation of the aorta (CoA) is challenging due to concomitant morphological anomalies (complex CoA) and inaccurate Doppler-based indices. Promising diagnostic performance has been reported for the continuous flow pressure gradient (CFPG), but it has not been studied in complex CoA. Our objective was to characterize the effect of complex CoA and associated hemodynamics on CFPG in a clinical cohort. Retrospective analysis identified discrete juxtaductal (n = 25) and complex CoA (n = 43; transverse arch and/or isthmus hypoplasia) patients with arm-leg systolic blood pressure gradients (BPG) within 24 h of echocardiography for comparison to BPG by conventional Doppler indices (simplified Bernoulli equation and modified forms correcting for proximal kinetic energy and/or recovered pressure). Results were interpreted using the current CoA guideline (BPG ≥ 20 mmHg) to compare diagnostic performance indicators including receiver operating characteristic curves, sensitivity, specificity, and diagnostic accuracy, among others. Echocardiography Z-scored aortic diameters were applied with computational simulations from a preclinical CoA model to understand aspects of the CFPG driving performance differences. Diagnostic performance was substantially reduced from discrete to complex CoA for conventional Doppler indices calculated from patient data, and by hypoplasia and/or long segment stenosis in simulations. In contrast, diagnostic indicators for the CFPG only modestly dropped for complex vs discrete CoA. Simulations revealed differences in performance due to inclusion of the Doppler velocity index and diastolic pressure half-time in the CFPG calculation. CFPG is less affected by aortic arch anomalies co-existing with CoA when compared to conventional Doppler indices.

Non-invasive Estimation of Pressure Drop Across Aortic Coarctations: Validation of 0D and 3D Computational Models with In Vivo Measurements

Blood pressure gradient ( Δ P ) across an aortic coarctation (CoA) is an important measurement to diagnose CoA severity and gauge treatment efficacy. Invasive cardiac catheterization is currently the gold-standard method for measuring blood pressure. The objective of this study was to evaluate the accuracy of Δ P estimates derived non-invasively using patient-specific 0D and 3D deformable wall simulations. Medical imaging and routine clinical measurements were used to create patient-specific models of patients with CoA (N = 17). 0D simulations were performed first and used to tune boundary conditions and initialize 3D simulations. Δ P across the CoA estimated using both 0D and 3D simulations were compared to invasive catheter-based pressure measurements for validation. The 0D simulations were extremely efficient ( ∼ 15 s computation time) compared to 3D simulations ( ∼ 30 h computation time on a cluster). However, the 0D Δ P estimates, unsurprisingly, had larger mean errors when compared to catheterization than 3D estimates (12.1 ± 9.9 mmHg vs 5.3 ± 5.4 mmHg). In particular, the 0D model performance degraded in cases where the CoA was adjacent to a bifurcation. The 0D model classified patients with severe CoA requiring intervention (defined as Δ P ≥ 20 mmHg) with 76% accuracy and 3D simulations improved this to 88%. Overall, a combined approach, using 0D models to efficiently tune and launch 3D models, offers the best combination of speed and accuracy for non-invasive classification of CoA severity.

Convergence of Phase-Averaged, Transitional Flow in an Abdominal Aortic Aneurysmal Model

Abdominal aortic aneurysm can exhibit transitional flow characteristics in laminar flow regimes. To report transitional flow characteristics, we examined the convergence of phase-averaged solutions by executing blood flow simulations of a patient-specific abdominal aortic aneurysmal model for 257 cardiac cycles with periodic, pulsatile boundary conditions. The phase-averaged solutions were computed by averaging the solutions over various numbers of cardiac cycles and compared against the ones averaged over 124 cycles. The phase-averaged solutions reported small differences when they were averaged over a large number of cardiac cycles. The instantaneous solutions, however, failed to exhibit fluctuations reported in the phase-averaged solutions. To study transitional blood flows in the aneurysmal region, we need to report phase-averaged solutions as they exhibit nonperiodic, disturbed flow characteristics. Additionally, when reporting phase-averaged solutions, it is preferred to compute an average over a large number of cardiac cycles to be able to represent flow structures of the converged phase-averaged solutions.

Consistency of the continuous flow pressure gradient despite aortic arch anomalies co-existing with coarctation

Aims

Severity assessment for coarctation of the aorta (CoA) is challenging due to concomitant morphological anomalies (complex CoA) and inaccurate Doppler-based indices. Promising diagnostic performance has been reported for the continuous flow pressure gradient (CFPG), but it has not been studied in complex CoA. Our objective was to characterize the effect of complex CoA and associated hemodynamics on CFPG in a clinical cohort.

Methods and Results

Retrospective analysis identified discrete juxtaductal (n=25) and complex CoA (n=43; transverse arch and/or isthmus hypoplasia) patients with arm-leg systolic blood pressure gradients (BPG) within 24 hours of echocardiography for comparison to BPG by conventional Doppler indices (simplified Bernoulli equation and modified forms correcting for proximal kinetic energy and/or recovered pressure). Results were interpreted using the current CoA guideline (BPG ≥20 mmHg) to compare diagnostic performance indicators including receiver operating characteristic curves, sensitivity, specificity, and diagnostic accuracy, among others. Echocardiography Z-scored aortic diameters were applied with computational stimulations from a preclinical CoA model to understand aspects of the CFPG driving performance differences.Diagnostic performance was substantially reduced from discrete to complex CoA for conventional Doppler indices calculated from patient data, and by hypoplasia and/or long segment stenosis in simulations. In contrast, diagnostic indicators for the CFPG only modestly dropped for complex vs discrete CoA. Simulations revealed differences in performance due to inclusion of the Doppler velocity index and diastolic pressure half-time in the CFPG calculation.

Conclusion

CFPG is less affected by aortic arch anomalies co-existing with CoA when compared to conventional Doppler indices.

Non-invasive estimation of pressure drop across aortic coarctations: validation of 0D and 3D computational models with in vivo measurements

Purpose

Blood pressure gradient (Δ P ) across an aortic coarctation (CoA) is an important measurement to diagnose CoA severity and gauge treatment efficacy. Invasive cardiac catheterization is currently the gold-standard method for measuring blood pressure. The objective of this study was to evaluate the accuracy of Δ P estimates derived non-invasively using patient-specific 0 D and 3 D deformable wall simulations.

Methods

Medical imaging and routine clinical measurements were used to create patient-specific models of patients with CoA (N = 17 ). 0 D simulations were performed first and used to tune boundary conditions and initialize 3 D simulations. Δ P across the CoA estimated using both 0 D and 3 D simulations were compared to invasive catheter-based pressure measurements for validation.

Results

The 0 D simulations were extremely efficient (~15 secs computation time) compared to 3 D simulations (~30 hrs computation time on a cluster). However, the 0 D Δ P estimates, unsurprisingly, had larger mean errors when compared to catheterization than 3 D estimates (12.1 ± 9.9 mmHg vs 5.3 ± 5.4 mmHg). In particular, the 0 D model performance degraded in cases where the CoA was adjacent to a bifurcation. The 0 D model classified patients with severe CoA requiring intervention (defined as Δ P ≥ 20 mmHg) with 76% accuracy and 3 D simulations improved this to 88%.

Conclusion

Overall, a combined approach, using 0 D models to efficiently tune and launch 3 D models, offers the best combination of speed and accuracy for non-invasive classification of CoA severity.

Irregular anatomical features can alter hemodynamics in Takayasu arteritis

Objective

Takayasu arteritis (TA) is a difficult disease to deal with because there are neither reliable clinical signs, laboratory biomarkers, nor a single noninvasive imaging technique that can be used for early diagnosis and disease activity monitoring. Knowledge of aortic hemodynamics in TA is lacking. This study aimed to fill this gap by assessing hemodynamics in patients with TA using image-based computational fluid dynamics (CFD) simulations.

Methods

Eleven patients with TA were included in the present study. Patient-specific geometries were reconstructed from either clinical aortic computed tomography angiography or magnetic resonance angiography studies and coupled with physiological boundary conditions for CFD simulations. Key anatomical and hemodynamic parameters were compared with a control group consisting of 18 age- and sex-matched adults without TA who had healthy aortas.

Results

Compared with controls, patients with TA had significantly higher aortic velocities (0.9 m/s [0.7, 1.1 m/s] vs 0.6 m/s [0.5, 0.7 m/s]; P = .002), maximum time-averaged wall shear stress (14.2 Pa [9.8, 20.9 Pa] vs 8.0 Pa [6.2, 10.3 Pa]; P = .004), and maximum pressure drops between the ascending and descending aorta (36.9 mm Hg [29.0, 49.3 mm Hg] vs 28.5 mm Hg [25.8, 31.5 mm Hg]; P = .004). These significant hemodynamic alterations in patients with TA might result from abnormal anatomical features including smaller arch diameter (20.0 mm [13.8, 23.3 mm] vs 25.2 mm [23.3, 26.8 mm]; P = .003), supra-aortic branch diameters (21.9 mm [18.5, 24.6 mm] vs 25.7 mm [24.3, 28.3 mm]; P = .003) and descending aorta diameter (14.7 mm [12.2, 16.8 mm] vs 22.5 mm [19.8, 24.0 mm]; P < .001).

Conclusions

CFD analysis reveals hemodynamic changes in the aorta of patients with TA. The applicability of CFD technique coupled with standard imaging assessments in predicting disease progression of such patients will be explored in future studies. Future large cohort study with outcome correlation is also warranted.

Clinical Relevance

Based on patient-specific computational fluid dynamics simulations, the present retrospective study revealed significant difference in aortic hemodynamics between the patients with and without Takayasu arteritis (TA). To the best of our knowledge, this study is the first to evaluate hemodynamic conditions within TA, demonstrating the potential of computational flow modeling in capturing abnormal hemodynamic forces, such as high wall shear stress, resulted from irregular morphological changes. In the future, assessing the hemodynamic parameters within patients with TA during the prestenotic period, together with longitudinal computational fluid dynamics studies may allow better monitoring and management of TA.

Temporal evolution of mechanical stimuli from vascular remodeling in response to the severity and duration of aortic coarctation in a preclinical model

Coarctation of the aorta (CoA) is one of the most common congenital cardiovascular diseases. CoA patients frequently undergo surgical repair, but hypertension (HTN) is still common. The current treatment guideline has revealed irreversible changes in structure and function, yet revised severity guidelines have not been proposed. Our objective was to quantify temporal alterations in mechanical stimuli and changes in arterial geometry in response to the range of CoA severities and durations (i.e. age of treatment) seen clinically. Rabbits were exposed to CoA resulting in peak-to-peak blood pressure gradient (BPGpp) severities of ≤ 10, 10-20, and ≥ 20 mmHg for a duration of ~ 1, 3, or 20 weeks using permanent, dissolvable, and rapidly dissolvable sutures. Elastic moduli and thickness were estimated from imaging and longitudinal fluid-structure interaction (FSI) simulations were conducted at different ages using geometries and boundary conditions from experimentally measured data. Mechanical stimuli were characterized including blood flow velocity patterns, wall tension, and radial strain. Experimental results show vascular alternations including thickening and stiffening proximal to the coarctation with increasing severity and/or duration of CoA. FSI simulations indicate wall tension in the proximal region increases markedly with coarctation severity. Importantly, even mild CoA induced stimuli for remodeling that exceeds values seen in adulthood if not treated early and using a BPGpp lower than the current clinical threshold. The findings are aligned with observations from other species and provide some guidance for the values of mechanical stimuli that could be used to predict the likelihood of HTN in human patients with CoA.

In-silico investigations of haemodynamic parameters for a blunt thoracic aortic injury case

Accounting for 1.5% of thoracic trauma, blunt thoracic aortic injury (BTAI) is a rare disease with a high mortality rate that nowadays is treated mostly via thoracic endovascular aortic repair (TEVAR). Personalised computational models based on fluid-solid interaction (FSI) principals not only support clinical researchers in studying virtual therapy response, but also are capable of predicting eventual outcomes. The present work studies the variation of key haemodynamic parameters in a clinical case of BTAI after successful TEVAR, using a two-way FSI model. The three-dimensional (3D) patient-specific geometries of the patient were coupled with three-element Windkessel model for both prior and post intervention cases, forcing a correct prediction of blood flow over each section. Results showed significant improvement in velocity and pressure distribution after stenting. High oscillatory, low magnitude shear (HOLMES) regions require careful examination in future follow-ups, since thrombus formation was confirmed in some previously clinically reported cases of BTAI treated with TEVAR. The strength of swirling flows along aorta was also damped after stent deployment. Highlighting the importance of haemodynamic parameters in case-specific therapies. In future studies, compromising motion of aortic wall due to excessive cost of FSI simulations can be considered and should be based on the objectives of studies to achieve a more clinical-friendly patient-specific CFD model.

Beyond CFD: Emerging methodologies for predictive simulation in cardiovascular health and disease

Physics-based computational models of the cardiovascular system are increasingly used to simulate hemodynamics, tissue mechanics, and physiology in evolving healthy and diseased states. While predictive models using computational fluid dynamics (CFD) originated primarily for use in surgical planning, their application now extends well beyond this purpose. In this review, we describe an increasingly wide range of modeling applications aimed at uncovering fundamental mechanisms of disease progression and development, performing model-guided design, and generating testable hypotheses to drive targeted experiments. Increasingly, models are incorporating multiple physical processes spanning a wide range of time and length scales in the heart and vasculature. With these expanded capabilities, clinical adoption of patient-specific modeling in congenital and acquired cardiovascular disease is also increasing, impacting clinical care and treatment decisions in complex congenital heart disease, coronary artery disease, vascular surgery, pulmonary artery disease, and medical device design. In support of these efforts, we discuss recent advances in modeling methodology, which are most impactful when driven by clinical needs. We describe pivotal recent developments in image processing, fluid-structure interaction, modeling under uncertainty, and reduced order modeling to enable simulations in clinically relevant timeframes. In all these areas, we argue that traditional CFD alone is insufficient to tackle increasingly complex clinical and biological problems across scales and systems. Rather, CFD should be coupled with appropriate multiscale biological, physical, and physiological models needed to produce comprehensive, impactful models of mechanobiological systems and complex clinical scenarios. With this perspective, we finally outline open problems and future challenges in the field.

A workflow for viewing biomedical computational fluid dynamics results and corresponding data within virtual and augmented reality environments

Researchers conducting computational fluid dynamics (CFD) modeling can spend weeks obtaining imaging data, determining boundary conditions, running simulations and post-processing files. However, results are typically viewed on a 2D display and often at one point in time thus reducing the dynamic and inherently three-dimensional data to a static image. Results from different pathologic states or cases are rarely compared in real-time, and supplementary data are seldom included. Therefore, only a fraction of CFD results are typically studied in detail, and associations between mechanical stimuli and biological response may be overlooked. Virtual and augmented reality facilitate stereoscopic viewing that may foster extraction of more information from CFD results by taking advantage of improved depth cues, as well as custom content development and interactivity, all within an immersive approach. Our objective was to develop a straightforward, semi-automated workflow for enhanced viewing of CFD results and associated data in an immersive virtual environment (IVE). The workflow supports common CFD software and has been successfully completed by novice users in about an hour, demonstrating its ease of use. Moreover, its utility is demonstrated across clinical research areas and IVE platforms spanning a range of cost and development considerations. We are optimistic that this advancement, which decreases and simplifies the steps to facilitate more widespread use of immersive CFD viewing, will foster more efficient collaboration between engineers and clinicians. Initial clinical feedback is presented, and instructional videos, manuals, templates and sample data are provided online to facilitate adoption by the community.

Automated generation of 0D and 1D reduced-order models of patient-specific blood flow

Three-dimensional (3D) cardiovascular fluid dynamics simulations typically require hours to days of computing time on a high-performance computing cluster. One-dimensional (1D) and lumped-parameter zero-dimensional (0D) models show great promise for accurately predicting blood bulk flow and pressure waveforms with only a fraction of the cost. They can also accelerate uncertainty quantification, optimization, and design parameterization studies. Despite several prior studies generating 1D and 0D models and comparing them to 3D solutions, these were typically limited to either 1D or 0D and a singular category of vascular anatomies. This work proposes a fully automated and openly available framework to generate and simulate 1D and 0D models from 3D patient-specific geometries, automatically detecting vessel junctions and stenosis segments. Our only input is the 3D geometry; we do not use any prior knowledge from 3D simulations. All computational tools presented in this work are implemented in the open-source software platform SimVascular. We demonstrate the reduced-order approximation quality against rigid-wall 3D solutions in a comprehensive comparison with N = 72 publicly available models from various anatomies, vessel types, and disease conditions. Relative average approximation errors of flows and pressures typically ranged from 1% to 10% for both 1D and 0D models, measured at the outlets of terminal vessel branches. In general, 0D model errors were only slightly higher than 1D model errors despite requiring only a third of the 1D runtime. Automatically generated ROMs can significantly speed up model development and shift the computational load from high-performance machines to personal computers.

Computational Assessment of Hemodynamic Significance in Patients With Intramural Anomalous Aortic Origin of the Coronary Artery Using Virtually Derived Fractional Flow Reserve and Downstream Microvascular Resistance

Anomalous aortic origin of a coronary artery (AAOCA) is the second most common cause of sudden cardiac death in young athletes. One of the hypothesized mechanisms of ischemia in these patients is the lateral compression of the anomalous artery with an intramural or interarterial course. The presence of a narrowing in the anomalous artery will cause physiologic changes in downstream resistance that should be included for computational assessment of possible clinical ramifications. In this study, we created different compression levels, i.e., proximal narrowing, in the intramural course of a representative patient model and calculated hyperemic stenosis resistance (HSR) as well as virtual fractional flow reserve (vFFR). Models also included the effect of the distal hyperemic microvascular resistance (HMR) on vFFR. Our results agreed with similar FFR studies indicating that FFR is increased with increasing HMR and that different compression levels could have similar FFR depending on the HMR. For example, vFFR at HSR: 1.0-1.3 and HMR: 2.30 mmHg/cm/s is 0.68 and close to vFFR at HSR: 0.6-0.7 and HMR: 1.6 mmHg/cm/s, which is 0.7. The current findings suggest that functional assessment of anomalous coronary arteries through FFR should consider the vascular resistance distal to the narrowing in addition to the impact of a proximal narrowing and provides computational approaches for implementation of these important considerations.

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.

Multiscale modelling of Potts shunt as a potential palliative treatment for suprasystemic idiopathic pulmonary artery hypertension: a paediatric case study

Potts shunt (PS) was suggested as palliation for patients with suprasystemic pulmonary arterial hypertension (PAH) and right ventricular (RV) failure. PS, however, can result in poorly understood mortality. Here, a patient-specific geometrical multiscale model of PAH physiology and PS is developed for a paediatric PAH patient with stent-based PS. In the model, 7.6mm-diameter PS produces near-equalisation of the aortic and PA pressures and [Formula: see text] (oxygenated vs deoxygenated blood flow) ratio of 0.72 associated with a 16% decrease of left ventricular (LV) output and 18% increase of RV output. The flow from LV to aortic arch branches increases by 16%, while LV contribution to the lower body flow decreases by 29%. Total flow in the descending aorta (DAo) increases by 18% due to RV contribution through the PS with flow into the distal PA branches decreasing. PS induces 18% increase of RV work due to its larger stroke volume pumped against lower afterload. Nonetheless, larger RV work does not lead to increased RV end-diastolic volume. Three-dimensional flow assessment demonstrates the PS jet impinging with a high velocity and wall shear stress on the opposite DAo wall with the most of the shunt flow being diverted to the DAo. Increasing the PS diameter from 5mm up to 10mm results in a nearly linear increase in post-operative shunt flow and a nearly linear decrease in shunt pressure-drop. In conclusion, this model reasonably represents patient-specific haemodynamics pre- and post-creation of the PS, providing insights into physiology of this complex condition, and presents a predictive tool that could be useful for clinical decision-making regarding suitability for PS in PAH patients with drug-resistant suprasystemic PAH.

Hemodynamic effects of stent-graft introducer sheath during thoracic endovascular aortic repair

Thoracic endovascular aortic repair (TEVAR) has become the standard treatment of a variety of aortic pathologies. The objective of this study is to evaluate the hemodynamic effects of stent-graft introducer sheath during TEVAR. Three idealized representative diseased aortas were designed: aortic aneurysm, coarctation of the aorta, and aortic dissection. Computational fluid dynamics studies were performed in the above idealized aortic geometries. An introducer sheath routinely used in the clinic was virtually placed into diseased aortas. Comparative analysis was carried out to evaluate the hemodynamic effects of the introducer sheath. Results show that the blood flow to the supra-aortic branches would increase above 9% due to the obstruction of the introducer sheath. The region exposed to high endothelial cell activation potential (ECAP) expands in the scenarios of coarctation of the aorta and aortic dissection, which indicates that the probability of thrombus formation may increase during TEVAR. The pressure magnitude in peak systole shows an obvious rise, and a similar phenomenon is not observed in early diastole. The blood viscosity in the aortic arch and descending aorta is remarkably altered by the introducer sheath. The uneven viscosity distribution confirms the necessity of using non-Newtonian models, and high-viscosity region with high ECAP further promotes thrombosis. Our results highlight the hemodynamic effects of stent-graft introducer sheath during TEVAR, which may associate with perioperative complications.

A Pilot Study Characterizing Flow Patterns in the Thoracic Aorta of Patients With Connective Tissue Disease: Comparison to Age- and Gender-Matched Controls via Fluid Structure Interaction

Prior computational and imaging studies described changes in flow patterns for patients with Marfan syndrome, but studies are lacking for related populations. This pilot study addresses this void by characterizing wall shear stress (WSS) indices for patients with Loeys-Dietz and undifferentiated connective tissue diseases. Using aortic valve-based velocity profiles from magnetic resonance imaging as input to patient-specific fluid structure interaction (FSI) models, we determined local flow patterns throughout the aorta for four patients with various connective tissue diseases (Loeys-Dietz with the native aorta, connective tissue disease of unclear etiology with native aorta in female and male patients, and an untreated patient with Marfan syndrome, as well as twin patients with Marfan syndrome who underwent valve-sparing root replacement). FSI simulations used physiological boundary conditions and material properties to replicate available measurements. Time-averaged WSS (TAWSS) and oscillatory shear index (OSI) results are presented with localized comparison to age- and gender-matched control participants. Ascending aortic dimensions were greater in almost all patients with connective tissue diseases relative to their respective control. Differences in TAWSS and OSI were driven by local morphological differences and cardiac output. For example, the model for one twin had a more pronounced proximal descending aorta in the vicinity of the ductus ligamentum that impacted WSS indices relative to the other. We are optimistic that the results of this study can serve as a foundation for larger future studies on the connective tissue disorders presented in this article.

Isolating the Effect of Arch Architecture on Aortic Hemodynamics Late After Coarctation Repair: A Computational Study

Objectives

Effective management of aortic coarctation (CoA) affects long-term cardiovascular outcomes. Full appreciation of CoA hemodynamics is important. This study aimed to analyze the relationship between aortic shape and hemodynamic parameters by means of computational simulations, purposely isolating the morphological variable.

Methods

Computational simulations were run in three aortic models. MRI-derived aortic geometries were generated using a statistical shape modeling methodology. Starting from n = 108 patients, the mean aortic configuration was derived in patients without CoA (n = 37, "no-CoA"), with surgically repaired CoA (n = 58, "r-CoA") and with unrepaired CoA (n = 13, "CoA"). As such, the aortic models represented average configurations for each scenario. Key hemodynamic parameters (i.e., pressure drop, aortic velocity, vorticity, wall shear stress WSS, and length and number of strong flow separations in the descending aorta) were measured in the three models at three time points (peak systole, end systole, end diastole).

Results

Comparing no-CoA and CoA revealed substantial differences in all hemodynamic parameters. However, simulations revealed significant increases in vorticity at the site of CoA repair, higher WSS in the descending aorta and a 12% increase in power loss, in r-CoA compared to no-CoA, despite no clinically significant narrowing (CoA index >0.8) in the r-CoA model.

Conclusions

Small alterations in aortic morphology impact on key hemodynamic indices. This may contribute to explaining phenomena such as persistent hypertension in the absence of any clinically significant narrowing. Whilst cardiovascular events in these patients may be related to hypertension, the role of arch geometry may be a contributory factor.

Applications of computational fluid dynamics to congenital heart diseases: a practical review for cardiovascular professionals

INTRODUCTION

The increased survival rate of patients with congenital heart disease (CHD) has made it likely that 70%-95% of infants with CHDs surviving into adulthood often require careful follow-up and (repeat) interventions. Patients with CHDs often have abnormal blood flow patterns, due to both primary cardiac defect and the consequent surgical or endovascular repair.

AREA COVERED

Computational fluid dynamics (CFD) alone or coupled with advanced imaging tools can assess blood flow patterns of CHDs to both understand their pathophysiology and anticipate the results of surgical or interventional repair.

EXPERT OPINION

CFD is a mathematical technique that quantifies and describes the characteristics of fluid flow using the laws of physics. Through dedicated software based on virtual reconstruction and simulation and patients' real data coming from computed tomography, magnetic resonance imaging, and 3/4 D-ultrasound, reconstruction of models of circulation of most CHD can be accomplished. CFD can provide insights about the pathophysiology of coronary artery anomalies, interatrial shunts, coarctation of the aorta and aortic bicuspid valve, tetralogy of Fallot and univentricular heart, with the capability in some cases of simulating different types of surgical or interventional repair and tailoring the treatment on the basis of these findings.

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.

Aorta size mismatch predicts decreased exercise capacity in patients with successfully repaired coarctation of the aorta

OBJECTIVE

Coarctation of the aorta (CoA) is associated with decreased exercise capacity despite successful repair with no residual stenosis; however, the hemodynamic mechanism remains unknown. This study aims to correlate aortic arch geometry with exercise capacity in patients with successfully repaired CoA and explain hemodynamic changes using 3-dimensional-printed aorta models in a mock circulatory flow loop.

METHODS

A retrospective chart review identified patients with CoA repair who had cardiac magnetic resonance imaging and an exercise stress test. Measurements included aorta diameters, arch height to diameter ratio, left ventricular function, and percent descending aorta (%DAo) flow. Each aorta was printed 3-dimensionally for the flow loop. Flow and pressure were measured at the ascending aorta (AAo) and DAo during simulated rest and exercise. Measurements were correlated with percent predicted peak oxygen consumption (VO2 max).

RESULTS

Fifteen patients (mean age 26.8 ± 8.6 years) had a VO2 max between 47% and 126% predicted (mean 92 ± 20%) with normal left ventricular function. DAo diameter and %DAo flow positively correlated with VO2 (P = .007 and P = .04, respectively). AAo to DAo diameter ratio (DAAo/DDAo) negatively correlated with VO2 (P < .001). From flow loop simulations, the ratio of %DAo flow in exercise to rest negatively correlated with VO2 (P = .02) and positively correlated with DAAo/DDAo (P < .01).

CONCLUSIONS

This study suggests aorta size mismatch (DAAo/DDAo) is a novel, clinically important measurement predicting exercise capacity in patients with successful CoA repair, likely due to increased resistance and altered flow distribution. Aorta size mismatch and %DAo flow are targets for further clinical evaluation in repaired CoA.

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.

Correlation of Computational Instantaneous Wave-Free Ratio With Fractional Flow Reserve for Intermediate Multivessel Coronary Disease

This study computationally assesses the accuracy of an instantaneous wave-free ratio (iFR) threshold range compared to standard modalities such as fractional flow reserve (FFR) and coronary flow reserve (CFR) for multiple intermediate lesions near the left main (LM) coronary bifurcation. iFR is an adenosine-independent index encouraged for assessment of coronary artery disease (CAD), but different thresholds are debated. This becomes particularly challenging in cases of multivessel disease when sensitivity to downstream lesions is unclear. Idealized LM coronary arteries with 34 different intermediate stenoses were created and categorized (Medina) as single and multiple lesion groups. Computational fluid dynamics modeling was performed with physiologic boundary conditions using an open-source software (simvascular1) to solve the time-dependent Navier-Stokes equations. A strong linear relationship between iFR and FFR was observed among studied models, indicating computational iFR values of 0.92 and 0.93 are statistically equivalent to an FFR of 0.80 in single and multiple lesion groups, respectively. At the clinical FFR value (i.e., 0.8), a triple-lesion group had smaller CFR compared to the single and double lesion groups (e.g., triple = 3.077 versus single = 3.133 and double = 3.132). In general, the effect of additional intermediate downstream lesions (minimum lumen area > 3 mm2) was not statistically significant for iFR and CFR. A computational iFR of 0.92 best predicts an FFR of 0.80 and may be recommended as threshold criteria for computational assessment of LM stenosis following additional validation using patient-specific models.

The Hemodynamics of Patent Ductus Arteriosus in Patients after Central Shunt Operation

A central shunt (CS) was an important surgery of systemic-to-pulmonary shunt (SPS) for the treatment of complex congenital heart diseases with decreased pulmonary blood flow (CCHDs-DPBF). There was no clear conclusion on how to deal with unclosed patent ductus arteriosus (PDA) during CS surgery. This study expanded the knowledge base on PDA by exploring the influence of the closing process of the PDA on the hemodynamic parameters for the CS model. The initial three-dimensional (3D) geometry was reconstructed based on the patient's computed tomography (CT) data. Then, a CS configuration with three typical pulmonary artery (PA) dysplasia structures and different sizes of PDA was established. The three-element windkessel (3WK) multiscale coupling model was used to define boundary conditions for transient simulation through computational fluid dynamics (CFD). The results showed that the larger size of PDA led to a greater systemic-to-pulmonary shunt ratio (Q _S/A), and the flow ratio of the left pulmonary artery (LPA) to right pulmonary artery (RPA) (Q _L/R) was more close to 1, while both the proportion of high wall shear stress (WSS) areas and power loss decreased. The case of PDA nonclosure demonstrates that the aortic oxygen saturation (Sao₂) increased, while the systemic oxygen delivery (Do₂) decreased. In general, for the CS model with three typical PA dysplasia, the changing trends of hemodynamic parameters during the spontaneous closing process of PDA were roughly identical, and nonclosure of PDA had a series of hemodynamic advantages, but a larger PDA may cause excessive PA perfusion and was not conducive to reducing cyanosis symptoms.

Image-Based Computational Model Predicts Dobutamine-Induced Hemodynamic Changes in Patients With Aortic Coarctation

BACKGROUND

Pharmacological stress testing can help to uncover pathological hemodynamic conditions and is, therefore, used in the clinical routine to assess patients with structural heart diseases such as aortic coarctation with borderline indication for treatment. The aim of this study was to develop and test a reduced-order model predicting dobutamine stress induced pressure gradients across the coarctation.

METHODS

The reduced-order model was developed based on n=21 imaging data sets of patients with aortic coarctation and a meta-analysis of subjects undergoing dobutamine stress testing. Within an independent test cohort of n=21 patients with aortic coarctation, the results of the model were compared with dobutamine stress testing during catheterization.

RESULTS

In n=19 patients responding to dobutamine stress testing, pressure gradients across the coarctation during dobutamine stress increased from 15.7±5.1 to 33.6±10.3 mm Hg (paired t test, P<0.001). The model-predicted pressure gradients agreed with catheter measurements with a mean difference of -2.2 mm Hg and a limit of agreement of ±11.16 mm Hg according to Bland-Altman analysis. Significant equivalence between catheter-measured and simulated pressure gradients during stress was found within the study cohort (two 1-sided tests of equivalence with a noninferiority margin of 5.0 mm Hg, 33.6±10.33 versus 31.5±11.15 mm Hg, P=0.021).

CONCLUSIONS

The developed reduced-order model can instantly predict dobutamine-induced hemodynamic changes with accuracy equivalent to heart catheterization in patients with aortic coarctation. The method is easy to use, available as a web-based calculator, and provides a promising alternative to conventional stress testing in the clinical routine. Registration: URL: https://www.clinicaltrials.gov. Unique identifier: NCT02591940.

High Wall Shear Stress can Predict Wall Degradation in Ascending Aortic Aneurysms: An Integrated Biomechanics Study

Background: Blood flow patterns can alter material properties of ascending thoracic aortic aneurysms (ATAA) via vascular wall remodeling. This study examines the relationship between wall shear stress (WSS) obtained from image-based computational modelling with tissue-derived mechanical and microstructural properties of the ATAA wall using segmental analysis. Methods: Ten patients undergoing surgery for ATAA were recruited. Exclusions: bicuspid aortopathy, connective tissue disease. All patients had pre-operative 4-dimensional flow magnetic resonance imaging (4D-MRI), allowing for patient-specific computational fluid dynamics (CFD) analysis and anatomically precise WSS mapping of ATAA regions (6-12 segments per patient). ATAA samples were obtained from surgery and subjected to region-specific tensile and peel testing (matched to WSS segments). Computational pathology was used to characterize elastin/collagen abundance and smooth muscle cell (SMC) count. Results: Elevated values of WSS were predictive of: reduced wall thickness [coef -0.0489, 95% CI (-0.0905, -0.00727), p = 0.022] and dissection energy function (longitudinal) [-15,0, 95% CI (-33.00, -2.98), p = 0.048]. High WSS values also predicted higher ultimate tensile strength [coef 0.136, 95% CI (0 0.001, 0.270), p = 0.048]. Additionally, elevated WSS also predicted a reduction in elastin levels [coef -0.276, 95% (CI -0.531, -0.020), p = 0.035] and lower SMC count ([oef -6.19, 95% CI (-11.41, -0.98), p = 0.021]. WSS was found to have no effect on collagen abundance or circumferential mechanical properties. Conclusions: Our study suggests an association between elevated WSS values and aortic wall degradation in ATAA disease. Further studies might help identify threshold values to predict acute aortic events.

Validation and Diagnostic Performance of a CFD-Based Non-invasive Method for the Diagnosis of Aortic Coarctation

Purpose: The clinical diagnosis of aorta coarctation (CoA) constitutes a challenge, which is usually tackled by applying the peak systolic pressure gradient (PSPG) method. Recent advances in computational fluid dynamics (CFD) have suggested that multi-detector computed tomography angiography (MDCTA)-based CFD can serve as a non-invasive PSPG measurement. The aim of this study was to validate a new CFD method that does not require any medical examination data other than MDCTA images for the diagnosis of CoA.

Materials and methods: Our study included 65 pediatric patients (38 with CoA, and 27 without CoA). All patients underwent cardiac catheterization to confirm if they were suffering from CoA or any other congenital heart disease (CHD). A series of boundary conditions were specified and the simulated results were combined to obtain a stenosis pressure-flow curve. Subsequently, we built a prediction model and evaluated its predictive performance by considering the AUC of the ROC by 5-fold cross-validation.

Results: The proposed MDCTA-based CFD method exhibited a good predictive performance in both the training and test sets (average AUC: 0.948 vs. 0.958; average accuracies: 0.881 vs. 0.877). It also had a higher predictive accuracy compared with the non-invasive criteria presented in the European Society of Cardiology (ESC) guidelines (average accuracies: 0.877 vs. 0.539).

Conclusion: The new non-invasive CFD-based method presented in this work is a promising approach for the accurate diagnosis of CoA, and will likely benefit clinical decision-making.

A Distributed Lumped Parameter Model of Blood Flow

We propose a distributed lumped parameter (DLP) modeling framework to efficiently compute blood flow and pressure in vascular domains. This is achieved by developing analytical expressions describing expected energy losses along vascular segments, including from viscous dissipation, unsteadiness, flow separation, vessel curvature and vessel bifurcations. We apply this methodology to solve for unsteady blood flow and pressure in a variety of complex 3D image-based vascular geometries, which are typically approached using computational fluid dynamics (CFD) simulations. The proposed DLP framework demonstrated consistent agreement with CFD simulations in terms of flow rate and pressure distribution, with mean errors less than 7% over a broad range of hemodynamic conditions and vascular geometries. The computational cost of the DLP framework is orders of magnitude lower than the computational cost of CFD, which opens new possibilities for hemodynamics modeling in timely decision support scenarios, and a multitude of applications of imaged-based modeling that require ensembles of numerical simulations.

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.

Patient-Specific Numerical Analysis of Coronary Flow in Children With Intramural Anomalous Aortic Origin of Coronary Arteries

Unroofing surgery for anomalous aortic origin of a coronary artery (AAOCA) alters coronary anatomy by opening the intramural segment so that the anomalous coronary orifice arises perpendicularly from appropriate aortic sinus. Computational fluid dynamics modeling (CFD) allows for quantification of hemodynamics linked to morbidity such as wall shear stress (WSS), relative to patient-specific features like the angle of origin (AO). We hypothesize that CFD will reveal abnormal WSS indices in unroofed arteries that are related to AO. Six AAOCA patients (3 left, 3 right) status post unroofing (median = 13.5 years, range 9-17) underwent cardiac magnetic resonance imaging. CFD models were created from pre (n = 2) and postunroofing (n = 6) cardiac magnetic resonance imaging data, for the anomalous and contralateral normally-arising arteries. Downstream vasculature was represented by lumped parameter networks. Time-averaged WSS (TAWSS) and oscillatory shear index (OSI) were quantified relative to AO and measured hemodynamics. TAWSS was elevated along the outer wall of the normally-arising left vs right coronary arteries, as well as along unroofed left vs right coronary arteries (n = 6/group). No significant differences were noted when comparing unroofed and same-sided normally-arising coronaries. TAWSS was reduced after unroofing (eg, 276 ± 28 dyne/cm² vs 91 ± 15 dyne/cm²; n = 2/group). Models with more acute preoperative AO indicated lower TAWSS at the proximity of ostium. Differences in OSI were not significant. Different flow patterns exist natively between right and left coronary arteries. Unroofing may normalize TAWSS but with variance related to the AO. This study suggests CFD may help stratify risk in AAOCA.

Accelerating massively parallel hemodynamic models of coarctation of the aorta using neural networks

Comorbidities such as anemia or hypertension and physiological factors related to exertion can influence a patient’s hemodynamics and increase the severity of many cardiovascular diseases. Observing and quantifying associations between these factors and hemodynamics can be difficult due to the multitude of co-existing conditions and blood flow parameters in real patient data. Machine learning-driven, physics-based simulations provide a means to understand how potentially correlated conditions may affect a particular patient. Here, we use a combination of machine learning and massively parallel computing to predict the effects of physiological factors on hemodynamics in patients with coarctation of the aorta. We first validated blood flow simulations against in vitro measurements in 3D-printed phantoms representing the patient’s vasculature. We then investigated the effects of varying the degree of stenosis, blood flow rate, and viscosity on two diagnostic metrics – pressure gradient across the stenosis (ΔP) and wall shear stress (WSS) - by performing the largest simulation study to date of coarctation of the aorta (over 70 million compute hours). Using machine learning models trained on data from the simulations and validated on two independent datasets, we developed a framework to identify the minimal training set required to build a predictive model on a per-patient basis. We then used this model to accurately predict ΔP (mean absolute error within 1.18 mmHg) and WSS (mean absolute error within 0.99 Pa) for patients with this disease.

Towards non-invasive computational-mechanics and imaging-based diagnostic framework for personalized cardiology for coarctation

Coarctation of the aorta (COA) is a congenital narrowing of the proximal descending aorta. Although accurate and early diagnosis of COA hinges on blood flow quantification, proper diagnostic methods for COA are still lacking because fluid-dynamics methods that can be used for accurate flow quantification are not well developed yet. Most importantly, COA and the heart interact with each other and because the heart resides in a complex vascular network that imposes boundary conditions on its function, accurate diagnosis relies on quantifications of the global hemodynamics (heart-function metrics) as well as the local hemodynamics (detailed information of the blood flow dynamics in COA). In this study, to enable the development of new non-invasive methods that can quantify local and global hemodynamics for COA diagnosis, we developed an innovative fast computational-mechanics and imaging-based framework that uses Lattice Boltzmann method and lumped-parameter modeling that only need routine non-invasive clinical patient data. We used clinical data of patients with COA to validate the proposed framework and to demonstrate its abilities to provide new diagnostic analyses not possible with conventional diagnostic methods. We validated this framework against clinical cardiac catheterization data, calculations using the conventional finite-volume method and clinical Doppler echocardiographic measurements. The diagnostic information, that the framework can provide, is vitally needed to improve clinical outcomes, to assess patient risk and to plan treatment.

Prediction of post-stenting biomechanics in coarcted aortas: A pilot finite element study

Endovascular stenting has recently become a standard treatment for native coarctation of the aorta (CoA) in children and young adults, given the efficacy in relieving vessel obstruction with a low incidence of adverse events. Yet, despite the short-term success of the technique, late hypertension remains an endemic risk. To assess the impact of the percutaneous procedure on the aortic wall biomechanics, we designed a novel finite element (FE) protocol for the simulation of endovascular stenting in three patient-specific CoA anatomies, developing a remeshing procedure that allows for coping with different CoA severities. Our FE protocol was able to yield numerical results on stent distortions and stresses, as well as on changes in aortic wall stresses and distensibility. These results were consistent with intraprocedural in-vivo evidences and with previous findings from the literature, and they suggest that our numerical approach could be used to understand the role of patient specific anatomical features (CoA severity and arch type) on the post-stenting aortic biomechanics. If soundly validated on a vast cohort of patients, our approach could support patient selection for the procedure.

A protocol for automated a posteriori adaptive meshing with SimVascular: a test case

OBJECTIVE

Operational details regarding the use of the adaptive meshing (AM) algorithm available in the SimVascular package are scarce despite its application in several studies. Lacking these details, novice users of the AM algorithm may experience undesirable outcomes post-adaptation such as increases in mesh error metrics, unpredictable increases in mesh size, and losses in geometric fidelity. Here we present a test case using our proposed iterative protocol that will help prevent these undesirable outcomes and enhance the utility of the AM algorithm. We present three trials (conservative, moderate, and aggressive settings) applied to a scenario modelling a Fontan junction with a patient-specific geometry and physiologically realistic boundary conditions.

RESULTS

In all three trials, an overall reduction in mesh error metrics is observed (range 47%-86%). The increase in the number of elements through each adaptation never exceeded the mesh size of the pre-adaptation mesh by one order of magnitude. In all three trials, the protocol resulted in consistent, repeatable improvements in mesh error metrics, no losses of geometric fidelity and steady increments in the number of elements in the mesh. Our proposed protocol prevented the aforementioned undesirable outcomes and can potentially save new users considerable effort and computing resources.

Phase-contrast magnetic resonance imaging and computational fluid dynamics assessment of thoracic aorta blood flow: a literature review

The death rate from thoracic aortic disease is on the rise and represents a growing global health concern as patients are often asymptomatic before acute events, which have devastating effects on health-related quality of life. Biomechanical factors have been found to play a major role in the development of both acquired and congenital aortic diseases. However, much is still unknown and translational benefits of this knowledge are yet to be seen. Phase-contrast cardiovascular magnetic resonance imaging of thoracic aortic blood flow has emerged as an exceptionally powerful non-invasive tool enabling visualization of complex flow patterns, and calculation of variables such as wall shear stress. This has led to multiple new findings in the areas of phenotype-dependent bicuspid valve flow patterns, thoracic aortic aneurysm formation and aortic prosthesis performance assessment. Phase-contrast cardiovascular magnetic resonance imaging has also been used in conjunction with computational fluid modelling techniques to produce even more sophisticated analyses, by allowing the calculation of haemodynamic variables with exceptional temporal and spatial resolution. Translationally, these technologies may potentially play a major role in the emergence of precision medicine and patient-specific treatments in patients with aortic disease. This clinically focused review will provide a systematic overview of key insights from published studies to date.

Subject-specific simulation for non-invasive assessment of aortic coarctation: Towards a translational approach

We present a multi-scale CFD-based study conducted in a cohort of 11 patients with coarctation of the aorta (CoA). The study explores the potential for implementation of a workflow using non-invasive routinely collected medical imaging data and clinical measurements to provide a more detailed insight into local aortic haemodynamics in order to support clinical decision making. Our approach is multi-scale, using a reduced-order model (1D/0D) and an optimization process for the personalization of patient-specific boundary conditions and aortic vessel wall parameters from non-invasive measurements, to inform a more complex model (3D/0D) representing 3D aortic patient-specific anatomy. The reliability of the modelling approach is investigated by comparing 3D/0D model pressure drop estimation with measured peak gradients recorded during diagnostic cardiac catheterization and 2D PC-MRI flow rate measurements in the descending aorta. The current study demonstrated that the proposed approach requires low levels of user interaction, making it suitable for the clinical setting. The agreement between computed blood pressure drop and catheter measurements is 10  ±  8 mmHg at the coarctation site. The comparison between CFD derived and catheter measured pressure gradients indicated that the model has to be improved, suggesting the use of time varying pressure waveforms to further optimize the tuning process and modelling assumptions.

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.

Human genotyping and an experimental model reveal NPR-C as a possible contributor to morbidity in coarctation of the aorta

Coarctation of the aorta (CoA) is a common congenital cardiovascular (CV) defect characterized by a stenosis of the descending thoracic aorta. Treatment exists, but many patients develop hypertension (HTN). Identifying the cause of HTN is challenging because of patient variability (e.g., age, follow-up duration, severity) and concurrent CV abnormalities. Our objective was to conduct RNA sequencing of aortic tissue from humans with CoA to identify a candidate gene for mechanistic studies of arterial dysfunction in a rabbit model of CoA devoid of the variability seen with humans. We present the first known evidence of natriuretic peptide receptor C (NPR-C; aka NPR3) downregulation in human aortic sections subjected to high blood pressure (BP) from CoA versus normal BP regions (validated to PCR). These changes in NPR-C, a gene associated with BP and proliferation, were replicated in the rabbit model of CoA. Artery segments from this model were used with human aortic endothelial cells to reveal the functional relevance of altered NPR-C activity. Results showed decreased intracellular calcium ([Ca²⁺]_i) activity to C-type natriuretic peptide (CNP). Normal relaxation induced by CNP and atrial natriuretic peptide was impaired for aortic segments exposed to elevated BP from CoA. Inhibition of NPR-C (M372049) also impaired aortic relaxation and [Ca²⁺]_i activity. Genotyping of NPR-C variants predicted to be damaging revealed that rs146301345 was enriched in our CoA patients, but sample size limited association with HTN. These results may ultimately be used to tailor treatment for CoA based on mechanical stimuli, genotyping, and/or changes in arterial function.

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.

Patient-specific non-invasive estimation of pressure gradient across aortic coarctation using magnetic resonance imaging

BACKGROUND

Non-invasive estimation of the pressure gradient in aortic coarctation has much clinical importance in assisting the diagnosis and treatment of the disease. Previous researchers applied computational fluid dynamics for the prediction of the pressure gradient in aortic coarctation. The accuracy of the prediction was satisfactory but the procedure was time-consuming and resource-demanding.

METHOD

In this research a magnetic resonance imaging (MRI)-based non-invasive modeling procedure is implemented to predict the pressure gradient in 14 patient cases of aortic coarctation. Multi-cycle patient flow and pressure data are processed to produce the flow and pressure conditions in the patient cases. Bernoulli equation-based friction loss model combined with the inertial effect of the blood flow in the vessel segments are applied to model the pressure gradient in the aortic coarctation. The model-predicted pressure gradient data are then compared with the catheter in vivo measurement data for validation.

RESULTS

The MRI-based model prediction technique produces results that are consistent with those from the catheter measurement, based on the criteria of both the cycle-averaged instantaneous pressure gradient and the peak-to-peak pressure gradient.

CONCLUSION

This study suggests that the MRI-based non-invasive modeling procedure has much potential to be applied in clinical practice for the prediction of the pressure gradient in aortic coarctation patients.

Computational fluid dynamics in the numerical simulation analysis of end-to-side anastomosis for coarctation of the aorta

Background

Based on CT image data, a computational fluid dynamics (CFD) model of the aortic arch was established. We aimed to investigate the hemodynamic features associated with end-to-side anastomosis (ESA) surgery for coarctation of the aorta (CoA) by CFD model.

Methods

The data of enhanced CT two-dimensional medical images obtained through clinical practice were processed using medical image post-processing software. The three-dimensional model of the aortic arch was obtained through the geometric model and boundary condition. This was subsequently transformed into a CAD model, which can be used for simulation calculation.

Results

The CFD model accurately reflected the shape of the aortic arch, and produced the hemodynamic results before and after ESA for CoA.

Conclusions

The CFD model provides a virtual execution platform for the scientific research of aortic arch disease and will be helpful to evaluate the operation plan, even to determine the best surgical procedure. Hemodynamic analysis may be helpful to evaluate the therapeutic effects of other aortic diseases.

Computing the ankle-brachial index with parallel computational fluid dynamics

The ankle-brachial index (ABI), a ratio of arterial blood pressure in the ankles and upper arms, is used to diagnose and monitor circulatory conditions such as coarctation of the aorta and peripheral artery disease. Computational simulations of the ABI can potentially determine the parameters that produce an ABI indicative of ischemia or other abnormalities in blood flow. However, 0- and 1-D computational methods are limited in describing a 3-D patient-derived geometry. Thus, we present a massively parallel framework for computational fluid dynamics (CFD) simulations in the full arterial system. Using the lattice Boltzmann method to solve the Navier-Stokes equations, we employ highly parallelized and scalable methods to generate the simulation domain and efficiently distribute the computational load among processors. For the first time, we compute an ABI with 3-D CFD. In this proof-of-concept study, we investigate the dependence of ABI on the presence of stenoses, or narrowed regions of the arteries, by directly modifying the arterial geometry. As a result, our framework enables the computation a hemodynamic factor characterizing flow at the scale of the full arterial system, in a manner that is extensible to patient-specific imaging data and holds potential for treatment planning.

Comparison between a generalized Newtonian model and a network-type multiscale model for hemodynamic behavior in the aortic arch: Validation with 4D MRI data for a case study

Blood is a complex fluid in which the presence of the various constituents leads to significant changes in its rheological properties. Thus, an appropriate non-Newtonian model is advisable; and we choose a Modified version of the rheological model of Phan-Thien and Tanner (MPTT). The different parameters of this model, derived from the rheology of polymers, allow characterization of the non-Newtonian nature of blood, taking into account the behavior of red blood cells in plasma. Using the MPTT model that we implemented in the open access software OpenFOAM, numerical simulations have been performed on blood flow in the thoracic aorta for a healthy patient. We started from a patient-specific model which was constructed from medical images. Exiting flow boundary conditions have been developped, based on a 3-element Windkessel model to approximate physiological conditions. The parameters of the Windkessel model were calibrated with in vivo measurements of flow rate and pressure. The influence of the selected viscosity of red blood cells on the flow and wall shear stress (WSS) was investigated. Results obtained from this model were compared to those of the Newtonian model, and to those of a generalized Newtonian model, as well as to in vivo dynamic data from 4D MRI during a cardiac cycle. Upon evaluating the results, the MPTT model shows better agreement with the MRI data during the systolic and diastolic phases than the Newtonian or generalized Newtonian model, which confirms our interest in using a complex viscoelastic model.

Clinical validation and assessment of aortic hemodynamics using computational fluid dynamics simulations from computed tomography angiography

Background

Hemodynamic information including peak systolic pressure (PSP) and peak systolic velocity (PSV) carry an important role in evaluation and diagnosis of congenital heart disease (CHD). Since MDCTA cannot evaluate hemodynamic information directly, the aim of this study is to provide a noninvasive method based on a computational fluid dynamics (CFD) model, derived from multi-detector computed tomography angiography (MDCTA) raw data, to analyze the aortic hemodynamics in infants with CHD, and validate these results against echocardiography and cardiac catheter measurements.

Methods

This study included 25 patients (17 males, and 8 females; a median age of 2 years, range: 4 months–4 years) with CHD. All patients underwent both transthoracic echocardiography (TTE) and MDCTA within 2 weeks prior to cardiac catheterization. CFD models were created from MDCTA raw data. Boundary conditions were confirmed by lumped parameter model and transthoracic echocardiography (TTE). Peak systolic velocity derived from CFD models (PSV_CFD) was compared to TTE measurements (PSV_TTE), while the peak systolic pressure derived from CFD (PSP_CFD) was compared to catheterization (PSP_CC). Regions with low and high peak systolic wall shear stress (PSWSS) were also evaluated.

Results

PSV_CFD and PSP_CFD showed good agreements between PSV_TTE (r = 0.968, p < 0.001; mean bias = − 7.68 cm/s) and PSP_CC (r = 0.918, p < 0.001; mean bias = 1.405 mmHg). Regions with low and high PSWSS) can also be visualized. Skewing of velocity or helical blood flow was also observed at aortic arch in patients.

Conclusions

Our result demonstrated that CFD scheme based on MDCTA raw data is an accurate and convenient method in obtaining the velocity and pressure from aorta and displaying the distribution of PSWSS and flow pattern of aorta. The preliminary results from our study demonstrate the capability in combining clinical imaging data and novel CFD tools in infants with CHD and provide a noninvasive approach for diagnose of CHD such as coarctation of aorta in future.

An Outflow Boundary Condition Model for Noninvasive Prediction of Fractional Flow Reserve in Diseased Coronary Arteries

This paper reports on a new boundary condition formulation to model the total coronary myocardial flow and resistance characteristics of the myocardial vascular bed for any specific patient when considered for noninvasive diagnosis of ischemia. The developed boundary condition model gives an implicit representation of the downstream truncated coronary bed. Further, it is based on incorporating patient-specific physiological parameters that can be noninvasively extracted to account for blood flow demand to the myocardium at rest and hyperemic conditions. The model is coupled to a steady three-dimensional (3D) collocated pressure-based finite volume flow solver and used to characterize the “functional significance” of a patient diseased coronary artery segment without the need for predicting the hemodynamics of the entire arterial system. Predictions generated with this boundary condition provide a deep understanding of the inherent challenges behind noninvasive image-based diagnostic techniques when applied to human diseased coronary arteries. The overall numerical method and formulated boundary condition model are validated via two computational-based procedures and benchmarked with available measured data. The newly developed boundary condition is used via a designed computational methodology to (a) confirm the need for incorporating patient-specific physiological parameters when modeling the downstream coronary resistance, (b) explain the discrepancies presented in the literature between measured and computed fractional flow reserve (FFRCT), and (c) discuss the current limitations and future challenges in shifting to noninvasive assessment of ischemia.

On the choice of outlet boundary conditions for patient-specific analysis of aortic flow using computational fluid dynamics

Boundary conditions (BCs) are an essential part in computational fluid dynamics (CFD) simulations of blood flow in large arteries. Although several studies have investigated the influence of BCs on predicted flow patterns and hemodynamic wall parameters in various arterial models, there is a lack of comprehensive assessment of outlet BCs for patient-specific analysis of aortic flow. In this study, five different sets of outlet BCs were tested and compared using a subject-specific model of a normal aorta. Phase-contrast magnetic resonance imaging (PC-MRI) was performed on the same subject and velocity profiles extracted from the in vivo measurements were used as the inlet boundary condition. Computational results obtained with different outlet BCs were assessed in terms of their agreement with the PC-MRI velocity data and key hemodynamic parameters, such as pressure and flow waveforms and wall shear stress related indices. Our results showed that the best overall performance was achieved by using a well-tuned three-element Windkessel model at all model outlets, which not only gave a good agreement with in vivo flow data, but also produced physiological pressure waveforms and values. On the other hand, opening outlet BCs with zero pressure at multiple outlets failed to reproduce any physiologically relevant flow and pressure features.

Systems Analysis of Thrombus Formation

The systems analysis of thrombosis seeks to quantitatively predict blood function in a given vascular wall and hemodynamic context. Relevant to both venous and arterial thrombosis, a Blood Systems Biology approach should provide metrics for rate and molecular mechanisms of clot growth, thrombotic risk, pharmacological response, and utility of new therapeutic targets. As a rapidly created multicellular aggregate with a polymerized fibrin matrix, blood clots result from hundreds of unique reactions within and around platelets propagating in space and time under hemodynamic conditions. Coronary artery thrombosis is dominated by atherosclerotic plaque rupture, complex pulsatile flows through stenotic regions producing high wall shear stresses, and plaque-derived tissue factor driving thrombin production. In contrast, venous thrombosis is dominated by stasis or depressed flows, endothelial inflammation, white blood cell-derived tissue factor, and ample red blood cell incorporation. By imaging vessels, patient-specific assessment using computational fluid dynamics provides an estimate of local hemodynamics and fractional flow reserve. High-dimensional ex vivo phenotyping of platelet and coagulation can now power multiscale computer simulations at the subcellular to cellular to whole vessel scale of heart attacks or strokes. In addition, an integrated systems biology approach can rank safety and efficacy metrics of various pharmacological interventions or clinical trial designs.

Personalized blood flow computations: A hierarchical parameter estimation framework for tuning boundary conditions

We propose a hierarchical parameter estimation framework for performing patient-specific hemodynamic computations in arterial models, which use structured tree boundary conditions. A calibration problem is formulated at each stage of the hierarchical framework, which seeks the fixed point solution of a nonlinear system of equations. Common hemodynamic properties, like resistance and compliance, are estimated at the first stage in order to match the objectives given by clinical measurements of pressure and/or flow rate. The second stage estimates the parameters of the structured trees so as to match the values of the hemodynamic properties determined at the first stage. A key feature of the proposed method is that to ensure a large range of variation, two different structured tree parameters are personalized for each hemodynamic property. First, the second stage of the parameter estimation framework is evaluated based on the properties of the outlet boundary conditions in a full body arterial model: the calibration method converges for all structured trees in less than 10 iterations. Next, the proposed framework is successfully evaluated on a patient-specific aortic model with coarctation: only six iterations are required for the computational model to be in close agreement with the clinical measurements used as objectives, and overall, there is a good agreement between the measured and computed quantities. Copyright © 2016 John Wiley & Sons, Ltd.

Partial hepatectomy hemodynamics changes: Experimental data explained by closed-loop lumped modeling

The liver function may be degraded after partial liver ablation surgery. Adverse liver hemodynamics have been shown to be associated to liver failure. The link between these hemodynamics changes and ablation size is however poorly understood. This article proposes to explain with a closed-loop lumped model the hemodynamics changes observed during twelve surgeries in pigs. The portal venous tree is modeled with a pressure-dependent variable resistor. The variables measured, before liver ablation, are used to tune the model parameters. Then, the liver partial ablation is simulated with the model and the simulated pressures and flows are compared with post-operative measurements. Fluid infusion and blood losses occur during the surgery. The closed-loop model presented accounts for these blood volume changes. Moreover, the impact of blood volume changes and the liver lobe mass estimations on the simulated variables is studied. The typical increase of portal pressure, increase of liver pressure loss, slight decrease of portal flow and major decrease in arterial flow are quantitatively captured by the model for a 75% hepatectomy. It appears that the 75% decrease in hepatic arterial flow can be explained by the resistance increase induced by the surgery, and that no hepatic arterial buffer response (HABR) mechanism is needed to account for this change. The different post-operative states, observed in experiments, are reproduced with the proposed model. Thus, an explanation for inter-subjects post-operative variability is proposed. The presented framework can easily be adapted to other species circulations and to different pathologies for clinical hepatic applications.