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

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.

Sensitivity of hostile hemodynamics to aneurysm geometry via unsupervised shape interpolation

BACKGROUND AND OBJECTIVE

Vessel geometry and hemodynamics are intrinsically linked, whereby geometry determines hemodynamics, and hemodynamics influence vascular remodeling. Both have been used for testing clinical outcomes, but geometry/morphology generally has less uncertainty than hemodynamics derived from medical image-based computational fluid dynamics (CFD). To provide clinical utility, CFD-based hemodynamic parameters must be robust to modeling errors and/or uncertainties, but must also provide useful information not more-easily extracted from shape alone. The objective of this study was to methodically assess the response of hemodynamic parameters to gradual changes in shape created using an unsupervised 3D shape interpolation method.

METHODS

We trained the neural network NeuroMorph on 3 patient-derived intracranial aneurysm surfaces (labelled A, B, C), and then generated 3 distinct morph sequences (A→B, B→C, C→A) each containing 10 interpolated surfaces. From high-fidelity CFD simulation of these, we calculated a variety of common reduced hemodynamic parameters, including many previously associated with aneurysm rupture, and analyzed their responses to changes in shape, and their correlations.

RESULTS

The interpolated surfaces demonstrate complex, gradual changes in branch angles, vessel diameters, and aneurysm morphology. CFD simulation showed gradual changes in aneurysm jetting characteristics and wall-shear stress (WSS) patterns, but demonstrated a range of responses from the reduced hemodynamic parameters. Spatially and temporally averaged parameters including time-averaged WSS, time-averaged velocity, and low-shear area (LSA) showed low variation across all morph sequences, while parameters of flow complexity such as oscillatory shear, spectral broadening, and spectral bandedness indices showed high variation between slightly-altered neighboring surfaces. Correlation analysis revealed a great deal of mutual information with easier-to-measure shape-based parameters.

CONCLUSIONS

In the absence of large clinical datasets, unsupervised shape interpolation provides an ideal laboratory for exploring the delicate balance between robustness and sensitivity of nominal hemodynamic predictors of aneurysm rupture. Parameters like time-averaged WSS and LSA that are highly "robust" may, as a result, be effectively redundant to morphological predictors, whereas more sensitive parameters may be too uncertain for practical clinical use. Understanding these sensitivities may help identify parameters that are capable of providing added value to rupture risk assessment.

Segmentation of the aorta in systolic phase from 4D flow MRI: multi-atlas vs. deep learning

OBJECTIVE

In the management of the aortic aneurysm, 4D flow magnetic resonance Imaging provides valuable information for the computation of new biomarkers using computational fluid dynamics (CFD). However, accurate segmentation of the aorta is required. Thus, our objective is to evaluate the performance of two automatic segmentation methods on the calculation of aortic wall pressure.

METHODS

Automatic segmentation of the aorta was performed with methods based on deep learning and multi-atlas using the systolic phase in the 4D flow MRI magnitude image of 36 patients. Using mesh morphing, isotopological meshes were generated, and CFD was performed to calculate the aortic wall pressure. Node-to-node comparisons of the pressure results were made to identify the most robust automatic method respect to the pressures obtained with a manually segmented model.

RESULTS

Deep learning approach presented the best segmentation performance with a mean Dice similarity coefficient and a mean Hausdorff distance (HD) equal to 0.92+/- 0.02 and 21.02+/- 24.20 mm, respectively. At the global level HD is affected by the performance in the abdominal aorta. Locally, this distance decreases to 9.41+/- 3.45 and 5.82+/- 6.23 for the ascending and descending thoracic aorta, respectively. Moreover, with respect to the pressures from the manual segmentations, the differences in the pressures computed from deep learning were lower than those computed from multi-atlas method.

CONCLUSION

To reduce biases in the calculation of aortic wall pressure, accurate segmentation is needed, particularly in regions with high blood flow velocities. Thus, the deep learning segmen-tation method should be preferred.

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.

Reducing Geometric Uncertainty in Computational Hemodynamics by Deep Learning-Assisted Parallel-Chain MCMC

Computational hemodynamic modeling has been widely used in cardiovascular research and healthcare. However, the reliability of model predictions is largely dependent on the uncertainties of modeling parameters and boundary conditions, which should be carefully quantified and further reduced with available measurements. In this work, we focus on propagating and reducing the uncertainty of vascular geometries within a Bayesian framework. A novel deep learning (DL)-assisted parallel Markov chain Monte Carlo (MCMC) method is presented to enable efficient Bayesian posterior sampling and geometric uncertainty reduction. A DL model is built to approximate the geometry-to-hemodynamic map, which is trained actively using online data collected from parallel MCMC chains and utilized for early rejection of unlikely proposals to facilitate convergence with less expensive full-order model evaluations. Numerical studies on two-dimensional aortic flows are conducted to demonstrate the effectiveness and merit of the proposed method.

Inverse problems in blood flow modeling: A review

Mathematical and computational modeling of the cardiovascular system is increasingly providing non-invasive alternatives to traditional invasive clinical procedures. Moreover, it has the potential for generating additional diagnostic markers. In blood flow computations, the personalization of spatially distributed (i.e., 3D) models is a key step which relies on the formulation and numerical solution of inverse problems using clinical data, typically medical images for measuring both anatomy and function of the vasculature. In the last years, the development and application of inverse methods has rapidly expanded most likely due to the increased availability of data in clinical centers and the growing interest of modelers and clinicians in collaborating. Therefore, this work aims to provide a wide and comparative overview of literature within the last decade. We review the current state of the art of inverse problems in blood flows, focusing on studies considering fully dimensional fluid and fluid-solid models. The relevant physical models and hemodynamic measurement techniques are introduced, followed by a survey of mathematical data assimilation approaches used to solve different kinds of inverse problems, namely state and parameter estimation. An exhaustive discussion of the literature of the last decade is presented, structured by types of problems, models and available data.

Machine Learning for Cardiovascular Biomechanics Modeling: Challenges and Beyond

Recent progress in machine learning (ML), together with advanced computational power, have provided new research opportunities in cardiovascular modeling. While classifying patient outcomes and medical image segmentation with ML have already shown significant promising results, ML for the prediction of biomechanics such as blood flow or tissue dynamics is in its infancy. This perspective article discusses some of the challenges in using ML for replacing well-established physics-based models in cardiovascular biomechanics. Specifically, we discuss the large landscape of input features in 3D patient-specific modeling as well as the high-dimensional output space of field variables that vary in space and time. We argue that the end purpose of such ML models needs to be clearly defined and the tradeoff between the loss in accuracy and the gained speedup carefully interpreted in the context of translational modeling. We also discuss several exciting venues where ML could be strategically used to augment traditional physics-based modeling in cardiovascular biomechanics. In these applications, ML is not replacing physics-based modeling, but providing opportunities to solve ill-defined problems, improve measurement data quality, enable a solution to computationally expensive problems, and interpret complex spatiotemporal data by extracting hidden patterns. In summary, we suggest a strategic integration of ML in cardiovascular biomechanics modeling where the ML model is not the end goal but rather a tool to facilitate enhanced modeling.

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.

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.

Reducing Morbidity and Mortality in Patients With Coarctation Requires Systematic Differentiation of Impacts of Mixed Valvular Disease on Coarctation Hemodynamics

Background Despite ongoing advances in surgical techniques for coarctation of the aorta (COA) repair, the long-term results are not always benign. Associated mixed valvular diseases (various combinations of aortic and mitral valvular pathologies) are responsible for considerable postoperative morbidity and mortality. We investigated the impact of COA and mixed valvular diseases on hemodynamics. Methods and Results We developed a patient-specific computational framework. Our results demonstrate that mixed valvular diseases interact with COA fluid dynamics and contribute to speed up the progression of the disease by amplifying the irregular flow patterns downstream of COA (local) and exacerbating the left ventricular function (global) (N=26). Velocity downstream of COA with aortic regurgitation alone was increased, and the situation got worse when COA and aortic regurgitation coexisted with mitral regurgitation (COA with normal valves: 5.27 m/s, COA with only aortic regurgitation: 8.8 m/s, COA with aortic and mitral regurgitation: 9.36 m/s; patient 2). Workload in these patients was increased because of the presence of aortic stenosis alone, aortic regurgitation alone, mitral regurgitation alone, and when they coexisted (COA with normal valves: 1.0617 J; COA with only aortic stenosis: 1.225 J; COA with only aortic regurgitation: 1.6512 J; COA with only mitral regurgitation: 1.3599 J; patient 1). Conclusions Not only the severity of COA, but also the presence and the severity of mixed valvular disease should be considered in the evaluation of risks in patients. The results suggest that more aggressive surgical approaches may be required, because regularly chosen current surgical techniques may not be optimal for such patients.

Effects of a Short-Term Left Ventricular Assist Device on Hemodynamics in a Heart Failure Patient-Specific Aorta Model: A CFD Study

Patients with heart failure (HF) or undergoing cardiogenic shock and percutaneous coronary intervention require short-term cardiac support. Short-term cardiac support using a left ventricular assist device (LVAD) alters the pressure and flows of the vasculature by enhancing perfusion and improving the hemodynamic performance for the HF patients. However, due to the position of the inflow and outflow of the LVAD, the local hemodynamics within the aorta is altered with the LVAD support. Specifically, blood velocity, wall shear stress, and pressure difference are altered within the aorta. In this study, computational fluid dynamics (CFD) was used to elucidate the effects of a short-term LVAD for hemodynamic performance in a patient-specific aorta model. The three-dimensional (3D) geometric models of a patient-specific aorta and a short-term LVAD, Impella CP, were created. Velocity, wall shear stress, and pressure difference in the patient-specific aorta model with the Impella CP assistance were calculated and compared with the baseline values of the aorta without Impella CP support. Impella CP support augmented cardiac output, blood velocity, wall shear stress, and pressure difference in the aorta. The proposed CFD study could analyze the quantitative changes in the important hemodynamic parameters while considering the effects of Impella CP, and provide a scientific basis for further predicting and assessing the effects of these hemodynamic signals on the aorta.

CTA-Based Non-invasive Estimation of Pressure Gradients Across a CoA: a Validation Against Cardiac Catheterisation

Non-invasive estimation of pressure gradients across a coarctation of the aorta (CoA) can reduce the need for diagnostic cardiac catheterisation. We aimed to validate two novel computational strategies-target-value approaching (TVA) and target-value fixing (TVF)-together with unrefined Doppler estimates, and to compare their diagnostic performance in identifying critical pressure drops for 40 patients. Compared to catheterisation, no statistically significant difference was demonstrated with TVA (P = 0.086), in contrast to TVF (P = 0.005) and unrefined Doppler echocardiography (P < 0.001). TVA manifested the strongest correlation with catheterisation (r = 0.93), compared to TVF (r = 0.83) and echocardiography (r = 0.67) (all P < 0.001). In discriminating pressure gradients greater than 20 mmHg, TVA, TVF, and echocardiography had respective sensitivities of 0.92, 0.88, and 0.80; specificities of 0.93, 0.80, and 0.73; and AUCs of 0.96, 0.89, and 0.80. The TVA strategy may serve as an effective and easily implemented approach to be used in clinical management of patients with CoA. Graphical Abstract Central illustration. Pressure gradients estimated using Doppler echocardiography and two novel computational strategies (TVA and TVF) were compared with cardiac catheterisation for 40 patients. TVA and TVF utilised the CTA images to obtain the CoA anatomy and Doppler echocardiography velocimetry to obtain velocity data for the assignment of CFD boundary conditions.

Application of physics-based flow models in cardiovascular medicine: Current practices and challenges

Personalized physics-based flow models are becoming increasingly important in cardiovascular medicine. They are a powerful complement to traditional methods of clinical decision-making and offer a wealth of physiological information beyond conventional anatomic viewing using medical imaging data. These models have been used to identify key hemodynamic biomarkers, such as pressure gradient and wall shear stress, which are associated with determining the functional severity of cardiovascular diseases. Importantly, simulation-driven diagnostics can help researchers understand the complex interplay between geometric and fluid dynamic parameters, which can ultimately improve patient outcomes and treatment planning. The possibility to compute and predict diagnostic variables and hemodynamics biomarkers can therefore play a pivotal role in reducing adverse treatment outcomes and accelerate development of novel strategies for cardiovascular disease management.

Modeling and Reducing the Effect of Geometric Uncertainties in Intracranial Aneurysms with Polynomial Chaos Expansion, Data Decomposition, and 4D-Flow MRI

PURPOSE

Variations in the vessel radius of segmented surfaces of intracranial aneurysms significantly influence the fluid velocities given by computer simulations. It is important to generate models that capture the effect of these variations in order to have a better interpretation of the numerically predicted hemodynamics. Also, it is highly relevant to develop methods that combine experimental observations with uncertainty modeling to get a closer approximation to the blood flow behavior.

METHODS

This work applies polynomial chaos expansion to model the effect of geometric uncertainties on the simulated fluid velocities of intracranial aneurysms. The radius of the vessel is defined as the uncertainty variable. Proper orthogonal decomposition is applied to characterize the solution space of fluid velocities. Next, a process of projecting the 4D-Flow MRI velocities on the basis vectors followed by coefficient mapping using generalized dynamic mode decomposition enables the merging of 4D-Flow MRI with the uncertainty propagated fluid velocities.

RESULTS

Polynomial chaos expansion propagates the fluid velocities with an error of 2% in velocity magnitude relative to computer simulations. Also, the bifurcation region (or impingement location) shows a standard deviation of 0.17 m/s (since an available reported variance in the vessel radius is adopted to model the uncertainty, the expected standard deviation may be different). Numerical phantom experiments indicate that the proposed approach reconstructs the fluid velocities with 0.3% relative error in presence of geometric uncertainties.

CONCLUSION

Polynomial chaos expansion is an effective approach to propagate the effect of the uncertainty variable in the blood flow velocities of intracranial aneurysms. Merging 4D-Flow MRI and uncertainty propagated fluid velocities leads to more realistic flow trends relative to ignoring the uncertainty in the vessel radius.

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.

User-dependent variability in mitral valve segmentation and its impact on CFD-computed hemodynamic parameters

PURPOSE

While novel tools for segmentation of the mitral valve are often based on automatic image processing, they mostly require manual interaction by a proficient user. Those segmentations are essential for numerical support of mitral valve treatment using computational fluid dynamics, where the reconstructed geometry is incorporated into a simulation domain. To quantify the uncertainty and reliability of hemodynamic simulations, it is crucial to examine the influence of user-dependent variability in valve segmentation.

METHODS

Previously, the inter-user variability of landmarks in mitral valve segmentation was investigated. Here, the inter-user variability of geometric parameters of the mitral valve, projected orifice area (OA) and projected annulus area (AA), is investigated for 10 mitral valve geometries, each segmented by three users. Furthermore, the propagation of those variations into numerically calculated hemodynamics, i.e., the blood flow velocity, was investigated.

RESULTS

Among the three geometric valve parameters, AA was least user-dependent. Almost all deviations to the mean were below 10%. Larger variations were observed for OA. Variations observed for the numerically calculated hemodynamics were in the same order of magnitude as those of geometric parameters. No correlation between variation of geometric parameters and variation of calculated hemodynamic parameters was found.

CONCLUSION

Errors introduced due to the user-dependency were of the same size as the variations of calculated hemodynamics. The variation was thereby of the same scale as deviations in clinical measurements of blood flow velocity using Doppler echocardiography. Since no correlation between geometric and hemodynamic uncertainty was found, further investigation of the complex relationship between anatomy, leaflet shape and flow is necessary.