Deep learning based assessment of hemodynamics in the coarctation of the aorta: comparison of bidirectional recurrent and convolutional neural networks.

The utilization of numerical methods, such as computational fluid dynamics (CFD), has been widely established for modeling patient-specific hemodynamics based on medical imaging data. Hemodynamics assessment plays a crucial role in treatment decisions for the coarctation of the aorta (CoA), a congenital heart disease, with the pressure drop (PD) being a crucial biomarker for CoA treatment decisions. However, implementing CFD methods in the clinical environment remains challenging due to their computational cost and the requirement for expert knowledge. This study proposes a deep learning approach to mitigate the computational need and produce fast results. Building upon a previous proof-of-concept study, we compared the effects of two different artificial neural network (ANN) architectures trained on data with different dimensionalities, both capable of predicting hemodynamic parameters in CoA patients: a one-dimensional bidirectional recurrent neural network (1D BRNN) and a three-dimensional convolutional neural network (3D CNN). The performance was evaluated by median point-wise root mean square error (RMSE) for pressures along the centerline in 18 test cases, which were not included in a training cohort. We found that the 3D CNN (median RMSE of 3.23 mmHg) outperforms the 1D BRNN (median RMSE of 4.25 mmHg). In contrast, the 1D BRNN is more precise in PD prediction, with a lower standard deviation of the error (±7.03 mmHg) compared to the 3D CNN (±8.91 mmHg). The differences between both ANNs are not statistically significant, suggesting that compressing the 3D aorta hemodynamics into a 1D centerline representation does not result in the loss of valuable information when training ANN models. Additionally, we evaluated the utility of the synthetic geometries of the aortas with CoA generated by using a statistical shape model (SSM), as well as the impact of aortic arch geometry (gothic arch shape) on the model's training. The results show that incorporating a synthetic cohort obtained through the SSM of the clinical cohort does not significantly increase the model's accuracy, indicating that the synthetic cohort generation might be oversimplified. Furthermore, our study reveals that selecting training cases based on aortic arch shape (gothic versus non-gothic) does not improve ANN performance for test cases sharing the same shape.

In-silico enhanced animal study of pulmonary artery pressure sensors: assessing hemodynamics using computational fluid dynamics.

To assess whether in-silico models can be used to predict the risk of thrombus formation in pulmonary artery pressure sensors (PAPS), a chronic animal study using pigs was conducted. Computed tomography (CT) data was acquired before and immediately after implantation, as well as one and three months after the implantation. Devices were implanted into 10 pigs, each one in the left and right pulmonary artery (PA), to reduce the required number of animal experiments. The implantation procedure aimed at facilitating optimal and non-optimal positioning of the devices to increase chances of thrombus formation. Eight devices were positioned non-optimally. Three devices were positioned in the main PA instead of the left and right PA. Pre-interventional PA geometries were reconstructed from the respective CT images, and the devices were virtually implanted at the exact sites and orientations indicated by the follow-up CT after one month. Transient intra-arterial hemodynamics were calculated using computational fluid dynamics. Volume flow rates were modelled specifically matching the animals body weights. Wall shear stresses (WSS) and oscillatory shear indices (OSI) before and after device implantation were compared. Simulations revealed no relevant changes in any investigated hemodynamic parameters due to device implantation. Even in cases, where devices were implanted in a non-optimal manner, no marked differences in hemodynamic parameters compared to devices implanted in an optimal position were found. Before implantation time and surface-averaged WSS was 2.35±0.47 Pa, whereas OSI was 0.08±0.17, respectively. Areas affected by low WSS magnitudes were 2.5±2.7 cm2, whereas the areas affected by high OSI were 18.1±6.3 cm2. After device implantation, WSS and OSI were 2.45±0.49 Pa and 0.08±0.16, respectively. Surface areas affected by low WSS and high OSI were 2.9±2.7 cm2, and 18.4±6.1 cm2, respectively. This in-silico study indicates that no clinically relevant differences in intra-arterial hemodynamics are occurring after device implantation, even at non-optimal positioning of the sensor. Simultaneously, no embolic events were observed, suggesting that the risk for thrombus formation after device implantation is low and independent of the sensor position.

Modelling blood flow in patients with heart valve disease using deep learning: A computationally efficient method to expand diagnostic capabilities in clinical routine.

Introduction: The computational modelling of blood flow is known to provide vital hemodynamic parameters for diagnosis and treatment-support for patients with valvular heart disease. However, most diagnosis/treatment-support solutions based on flow modelling proposed utilize time- and resource-intensive computational fluid dynamics (CFD) and are therefore difficult to implement into clinical practice. In contrast, deep learning (DL) algorithms provide results quickly with little need for computational power. Thus, modelling blood flow with DL instead of CFD may substantially enhances the usability of flow modelling-based diagnosis/treatment support in clinical routine. In this study, we propose a DL-based approach to compute pressure and wall-shear-stress (WSS) in the aorta and aortic valve of patients with aortic stenosis (AS). Methods: A total of 103 individual surface models of the aorta and aortic valve were constructed from computed tomography data of AS patients. Based on these surface models, a total of 267 patient-specific, steady-state CFD simulations of aortic flow under various flow rates were performed. Using this simulation data, an artificial neural network (ANN) was trained to compute spatially resolved pressure and WSS using a centerline-based representation. An unseen test subset of 23 cases was used to compare both methods. Results: ANN and CFD-based computations agreed well with a median relative difference between both methods of 6.0% for pressure and 4.9% for wall-shear-stress. Demonstrating the ability of DL to compute clinically relevant hemodynamic parameters for AS patients, this work presents a possible solution to facilitate the introduction of modelling-based treatment support into clinical practice.

Virtual treatment planning in three patients with univentricular physiology using computational fluid dynamics-Pitfalls and strategies.

Background: Uneven hepatic venous blood flow distribution (HFD) to the pulmonary arteries is hypothesized to be responsible for the development of intrapulmonary arteriovenous malformations (PAVM) in patients with univentricular physiology. Thus, achieving uniform distribution of hepatic blood flow is considered favorable. However, no established method for the prediction of the post-interventional hemodynamics currently exists. Computational fluid dynamics (CFD) offers the possibility to quantify HFD in patient-specific anatomies before and after virtual treatment. In this study, we evaluated the potential benefit of CFD-assisted treatment planning. Materials and methods: Three patients with total cavopulmonary connection (TCPC) and PAVM underwent cardiovascular magnetic resonance imaging (CMR) and computed tomography imaging (CT). Based on this imaging data, the patient-specific anatomy was reconstructed. These patients were considered for surgery or catheter-based intervention aiming at hepatic blood flow re-routing. CFD simulations were then performed for the untreated state as well as for different surgical and interventional treatment options. These treatment options were applied as suggested by treating cardiologists and congenital heart surgeons with longstanding experience in interventional and surgical treatment of patients with univentricular physiology. HFD was quantified for all simulations to identify the most viable treatment decision regarding redistribution of hepatic blood flow. Results: For all three patients, the complex TCPC anatomy could be reconstructed. However, due to the presence of metallic stent implants, hybrid models generated from CT as well as CMR data were required. Numerical simulation of pre-interventional HFD agreed well with angiographic assessment and physiologic considerations. One treatment option resulting in improvement of HFD was identified for each patient. In one patient follow-up data after treatment was available. Here, the virtual treatment simulation and the CMR flow measurements differed by 15%. Conclusion: The combination of modern computational methods as well as imaging methods for assessment of patient-specific anatomy and flow might allow to optimize patient-specific therapy planning in patients with pronounced hepatic flow mismatch and PAVM. In this study, we demonstrate that these methods can also be applied in patients with complex univentricular physiology and extensive prior interventions. However, in those cases, hybrid approaches utilizing information of different image modalities may be required.

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

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

Computed Tomography-Based Assessment of Transvalvular Pressure Gradient in Aortic Stenosis.

Background: In patients with aortic stenosis, computed tomography (CT) provides important information about cardiovascular anatomy for treatment planning but is limited in determining relevant hemodynamic parameters such as the transvalvular pressure gradient (TPG). Purpose: In the present study, we aimed to validate a reduced-order model method for assessing TPG in aortic stenosis using CT data. Methods: TPGCT was calculated using a reduced-order model requiring the patient-specific peak-systolic aortic flow rate (Q) and the aortic valve area (AVA). AVA was determined by segmentation of the aortic valve leaflets, whereas Q was quantified based on volumetric assessment of the left ventricle. For validation, invasively measured TPGcatheter was calculated from pressure measurements in the left ventricle and the ascending aorta. Altogether, 84 data sets of patients with aortic stenosis were used to compare TPGCT against TPGcatheter. Results: TPGcatheter and TPGCT were 50.6 ± 28.0 and 48.0 ± 26 mmHg, respectively (p = 0.56). A Bland-Altman analysis revealed good agreement between both methods with a mean difference in TPG of 2.6 mmHg and a standard deviation of 19.3 mmHg. Both methods showed good correlation with r = 0.72 (p < 0.001). Conclusions: The presented CT-based method allows assessment of TPG in patients with aortic stenosis, extending the current capabilities of cardiac CT for diagnosis and treatment planning.

Surgical Aortic Valve Replacement: Are We Able to Improve Hemodynamic Outcome?

Aortic valve replacement (AVR) does not usually restore physiological flow profiles. Complex flow profiles are associated with aorta dilatation, ventricle remodeling, aneurysms, and development of atherosclerosis. All these affect long-term morbidity and often require reoperations. In this pilot study, we aim to investigate an ability to optimize the real surgical AVR procedure toward flow profile associated with healthy persons. Four cases of surgical AVR (two with biological and two with mechanical valve prosthesis) with available post-treatment cardiac magnetic resonance imaging (MRI), including four-dimensional flow MRI and showing abnormal complex post-treatment hemodynamics, were investigated. All cases feature complex hemodynamic outcomes associated with valve-jet eccentricity and strong secondary flow characterized by helical flow and recirculation regions. A commercial computational fluid dynamics solver was used to simulate peak systolic hemodynamics of the real post-treatment outcome using patient-specific MRI measured boundary conditions. Then, an attempt to optimize hemodynamic outcome by modifying valve size and orientation as well as ascending aorta size reduction was made. Pressure drop, wall shear stress, secondary flow degree, helicity, maximal velocity, and turbulent kinetic energy were evaluated to characterize the AVR hemodynamic outcome. The proposed optimization strategy was successful in three of four cases investigated. Although no single parameter was identified as the sole predictor for a successful flow optimization, downsizing of the ascending aorta in combination with the valve orientation was the most effective optimization approach. Simulations promise to become an effective tool to predict hemodynamic outcome. The translation of these tools requires, however, studies with a larger cohort of patients followed by a prospective clinical validation study.

Hodge decomposition of wall shear stress vector fields characterizing biological flows.

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

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

PURPOSE: Numerical assessment of the pressure drop across an aortic coarctation using CFD is a promising approach to replace invasive catheter-based measurements. The aim of this study was to investigate and quantify the uncertainty of numerical calculation of the pressure drop introduced during two essential steps of medical image processing: segmentation of the patient-specific geometry and measurement of patient-specific flow rates from 4D-flow-MRI. METHODS: Based on the baseline segmentation, geometries with different stenosis diameters were generated for a sample of ten patients. The pressure drop generated by these geometries was calculated for different volume flow rates using computational fluid dynamics. Based on these simulations, a second order polynomial fit was calculated. Based on these polynomial fits an uncertainty of pressure drop calculation was quantified. RESULTS: The calculated pressure drop values varied strongly between the patients. In four patients, pressure drops above and below the clinical threshold of 20 mmHg were found. The median standard deviation of the pressure drop was 2.3 mmHg. The sensitivity of the pressure drop toward changes in the volume flow rate or the stenosis geometry varied between patients. CONCLUSION: The uncertainty of numerical pressure drop calculation introduced by uncertainties during image segmentation and measurement of volume flow rates was comparable to the uncertainty of pressure drop measurements using invasive catheterization. However, in some patients this uncertainty would have led to different treatment decision. Therefore, patient-specific uncertainty assessment might help to better understand the reliability of a numerically calculated biomarker as the pressure drop across an aortic coarctation.

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

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

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

PURPOSE: To reduce the need for diagnostic catheterization and optimize treatment in a variety of congenital heart diseases, magnetic resonance imaging (MRI)-based computational fluid dynamics (CFD) is proposed. However, data about the accuracy of CFD in a clinical context are still sparse. To fill this gap, this study compares MRI-based CFD to catheterization in the coarctation of aorta (CoA) setting. MATERIALS AND METHODS: Thirteen patients with CoA were investigated by routine MRI prior to catheterization. 3D whole-heart MRI was used to reconstruct geometries and 4D flow-sensitive phase-contrast MRI was used to acquire flows. Peak systolic flows were simulated using the program FLUENT. RESULTS: Peak systolic pressure drops in CoA measured by catheterization and CFD correlated significantly for both pre- and posttreatment measurements (pre: r = 0.98, p = 0.00; post: r = 0.87, p = 0.00). The pretreatment bias was -0.5 ± 3.33 mmHg (95% confidence interval -2.55 to 1.47 mmHg). CFD predicted a reduction of the peak systolic pressure drop after treatment that ranged from 17.6 ± 5.56 mmHg to 6.7 ± 5.58 mmHg. The posttreatment bias was 3.0 ± 2.91 mmHg (95% CI -1.74 to 5.43 mmHg). CONCLUSION: Peak systolic pressure drops can be reliably calculated using MRI-based CFD in a clinical setting. Therefore, CFD might be an attractive noninvasive alternative to diagnostic catheterization.