Estimation of valvular resistance of segmented aortic valves using computational fluid dynamics

An intelligent aortic valve model for complete cardiac cycle

The aortic valve (AV) is crucial for cardiovascular (CV) hemodynamic, impacting cardiac output (CO) and left ventricular volumetric flow rate (LVQ). Its nonlinear behavior challenges standard LVQ prediction methods as well as CO one. This study presents a novel approach for modeling the AV in the CV system, offering an improved method for estimating crucial parameters like LVQ across various AV conditions, including aortic stenosis (AS). The model, based on AV channel length during the entire cardiac phase, introduces a time-varying AV resistance (TV-AVR) parameterized by the pressure ratio across the AV and LVQ, enabling the simulation of both healthy and AS-related conditions. To validate this model, in vitro measurements are compared using a hybrid mock circulatory loop device. An unconventional use of a convolutional neural network (CNN) corrects the model's estimates, eliminating the need for labeled datasets. This approach, incorporating real-time learning and transforming 1-D CV signals into 2-D tensors, significantly improves the accuracy of LVQ measurements, achieving an error rate of less than 3.41 ± 4.84% for CO in healthy conditions and 2.83 ± 1.35% in AS cases-a 33.13% enhancement over linear diode models. These results underscore the potential of this approach for enhancing the diagnosis, prediction, and treatment of AV diseases. The key contributions of the proposed method encompass nonlinear TV-AVR estimation, investigation of transient CV responses, prediction of instantaneous CO, development of a flexible framework for noninvasive measurements integration, and the introduction of an adjustable resistance model using an extended Kalman filter (EKF) and CNN combination, all without requiring labeled data.

Quantification of functional hemodynamics in aortic valve disease using cardiac computed tomography angiography

BACKGROUND AND OBJECTIVE

Cardiac computed tomography angiography (CTA) is the preferred modality for preoperative planning in aortic valve stenosis. However, it cannot provide essential functional hemodynamic data, specifically the mean transvalvular pressure gradient (MPG). This study aims to introduce a computational fluid dynamics (CFD) approach for MPG quantification using cardiac CTA, enhancing its diagnostic value.

METHODS

Twenty patients underwent echocardiography, cardiac CTA, and invasive catheterization for pressure measurements. Cardiac CTA employed retrospective electrocardiographic gating to capture multi-phase data throughout the cardiac cycle. We segmented the region of interest based on mid-systolic phase cardiac CTA images. Then, we computed the average flow velocity into the aorta as the inlet boundary condition, using variations in end-diastolic and end-systolic left ventricular volume. Finally, we conducted CFD simulations using a steady-state model to obtain pressure distribution within the computational domain, allowing for the derivation of MPG.

RESULTS

The mean value of MPG, measured via invasive catheterization (MPGInv), echocardiography (MPGEcho), and cardiac CTA (MPGCT), were 51.3 ± 28.4 mmHg, 44.8 ± 19.5 mmHg, and 55.8 ± 25.6 mmHg, respectively. In comparison to MPGInv, MPGCT exhibited a higher correlation of 0.91, surpassing that of MPGEcho, which was 0.82. Moreover, the limits of agreement for MPGCT ranged from -27.7 to 18.7, outperforming MPGEcho, which ranged from -40.1 to 18.0.

CONCLUSIONS

The proposed method based on cardiac CTA enables the evaluation of MPG for aortic valve stenosis patients. In future clinical practice, a single cardiac CTA examination can comprehensively assess both the anatomical and functional hemodynamic aspects of aortic valve disease.

Potential Clinical Usefulness of Post-Valvular Contrast Densities to Determine the Severity of Aortic Valve Stenosis Using Computed Tomography

BACKGROUND

Different methods are established for the changes in aortic valve stenosis with cardiac computed tomography angiography (CCTA), but the effect of the grade of stenosis on contrast densities around the valve has not been investigated.

AIMS/METHODS

Using the information from flow dynamics in cases of increased velocity through narrowed lumen, the hypothesis was formed that flow changes can alter the contrast densities in stenotic post-valvular regions, and the density changes might correlate with the grade of stenosis. Forty patients with severe aortic stenosis and fifteen with a normal aortic valve were enrolled. With echocardiography, the peak/mean transvalvular gradients, peak transvalvular velocity, and aortic valve opening area were obtained. With CCTA, densities 4-5 mm above the aortic valve; at the junction of the left, right, and noncoronary cusp to the annulus; at the middle level of the left, right, and noncoronary sinuses of Valsalva in the center and the lateral points; at the sinotubular junction; and 4 cm from the sinotubular junction at the midline were measured. First, a comparison of the densities between the normal and stenotic valve was performed, and then possible correlations between echocardiography and CCTA values were investigated in the stenotic group.

RESULTS

In all CCTA regions, significantly lower-density values were detected among stenotic valve patients compared to the normal aortic valve population. Additionally, in both groups, higher densities were measured in the peri-jet regions than in the lateral ones. Furthermore, a good correlation was found between the aortic valve opening area and the densities in almost all perivalvular areas. With regard to the densities at the junction of the non-coronary leaflet to the fibrotic annulus and at the most lateral point of the right sinus of Valsalva, a high level of correlation was found between all echocardiography and CCTA parameters. Lastly, with receiver operating characteristic curve measurements, area under the curve values were between 0.857 and 0.930.

CONCLUSION

Certain CCTA density values, especially 4-5mm above the valve opening, can serve as auxiliary information to echocardiography when the severity of aortic valve stenosis is unclear.

Hemodynamic Effects of Subaortic Stenosis on Blood Flow Characteristics of a Mechanical Heart Valve Based on OpenFOAM Simulation

Subaortic stenosis (SAS) is a common congenital heart disease that can cause significant morbidity and mortality if not treated promptly. Patients with heart valve disease are prone to complications after replacement surgery, and the existence of SAS can accelerates disease progression, so timely diagnosis and treatment are required. However, the effects of subaortic stenosis on mechanical heart valves (MHV) are unknown. This study aimed to investigate flow characteristics in the presence of subaortic stenosis and computationally quantify the effects on the hemodynamics of MHV. Through the numerical simulation method, the flow characteristics and related parameters in the presence of SAS can be more intuitively observed. Based on its structure, there are three types of SAS: Tunnel-type SAS (TSS); Fibromuscular annulus SAS (FSS); Discrete SAS (DSS). The first numerical simulation study on different types of SAS found that there are obvious differences among them. Among them, the tunnel-type SAS formed a separated vortex structure on the tunnel-type narrow surface, which exhibits higher wall shear force at a low obstacle percentage. However, discrete SAS showed obvious differences when there was a high percentage of obstacles, forming high peak flow, high wall shear stress, and a high-intensity complex vortex. The presence of all three types of SAS results in the formation of high-velocity jets and complex vortices in front of the MHV, leading to increased shear stress and stagnation time. These hemodynamic changes significantly increase the risk of MHV dysfunction and the development of complications. Despite differences between the three types of SAS, the resultant effects on MHV hemodynamics are consistent. Therefore, early surgical intervention is warranted in SAS patients with implanted MHV.

A parametric geometry model of the aortic valve for subject-specific blood flow simulations using a resistive approach

Cardiac valves simulation is one of the most complex tasks in cardiovascular modeling. Fluid-structure interaction is not only highly computationally demanding but also requires knowledge of the mechanical properties of the tissue. Therefore, an alternative is to include valves as resistive flow obstacles, prescribing the geometry (and its possible changes) in a simple way, but, at the same time, with a geometry complex enough to reproduce both healthy and pathological configurations. In this work, we present a generalized parametric model of the aortic valve to obtain patient-specific geometries that can be included into blood flow simulations using a resistive immersed implicit surface (RIIS) approach. Numerical tests are presented for geometry generation and flow simulations in aortic stenosis patients whose parameters are extracted from ECG-gated CT images.

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

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

The impact of shape uncertainty on aortic-valve pressure-drop computations

Patient-specific image-based computational fluid dynamics (CFD) is widely adopted in the cardiovascular research community to study hemodynamics, and will become increasingly important for personalized medicine. However, segmentation of the flow domain is not exact and geometric uncertainty can be expected which propagates through the computational model, leading to uncertainty in model output. Seventy-four aortic-valves were segmented from computed tomography images at peak systole. Statistical shape modeling was used to obtain an approximate parameterization of the original segmentations. This parameterization was used to train a meta-model that related the first five shape mode coefficients and flowrate to the CFD-computed transvalvular pressure-drop. Consequently, shape uncertainty in the order of 0.5 and 1.0 mm was emulated by introducing uncertainty in the shape mode coefficients. A global variance-based sensitivity analysis was performed to quantify output uncertainty and to determine relative importance of the shape modes. The first shape mode captured the opening/closing behavior of the valve and uncertainty in this mode coefficient accounted for more than 90% of the output variance. However, sensitivity to shape uncertainty is patient-specific, and the relative importance of the fourth shape mode coefficient tended to increase with increases in valvular area. These results show that geometric uncertainty in the order of image voxel size may lead to substantial uncertainty in CFD-computed transvalvular pressure-drops. Moreover, this illustrates that it is essential to assess the impact of geometric uncertainty on model output, and that this should be thoroughly quantified for applications that wish to use image-based CFD models.

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: TPG_CT 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 TPG_catheter 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 TPG_CT against TPG_catheter.

Results: TPG_catheter and TPG_CT 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.

Quantifying the unknown impact of segmentation uncertainty on image-based simulations

Image-based simulation, the use of 3D images to calculate physical quantities, relies on image segmentation for geometry creation. However, this process introduces image segmentation uncertainty because different segmentation tools (both manual and machine-learning-based) will each produce a unique and valid segmentation. First, we demonstrate that these variations propagate into the physics simulations, compromising the resulting physics quantities. Second, we propose a general framework for rapidly quantifying segmentation uncertainty. Through the creation and sampling of segmentation uncertainty probability maps, we systematically and objectively create uncertainty distributions of the physics quantities. We show that physics quantity uncertainty distributions can follow a Normal distribution, but, in more complicated physics simulations, the resulting uncertainty distribution can be surprisingly nontrivial. We establish that bounding segmentation uncertainty can fail in these nontrivial situations. While our work does not eliminate segmentation uncertainty, it improves simulation credibility by making visible the previously unrecognized segmentation uncertainty plaguing image-based simulation.

The EurValve model execution environment

The goal of this paper is to present a dedicated high-performance computing (HPC) infrastructure which is used in the development of a so-called reduced-order model (ROM) for simulating the outcomes of interventional procedures which are contemplated in the treatment of valvular heart conditions. Following a brief introduction to the problem, the paper presents the design of a model execution environment, in which representative cases can be simulated and the parameters of the ROM fine-tuned to enable subsequent deployment of a decision support system without further need for HPC. The presentation of the system is followed by information concerning its use in processing specific patient cases in the context of the EurValve international collaboration.

Computational Assessment of Valvular Dysfunction in Discrete Subaortic Stenosis: A Parametric Study

PURPOSE

Discrete subaortic stenosis (DSS) is a left-ventricular outflow tract (LVOT) obstruction caused by a membranous lesion. DSS is associated with steep aortoseptal angles (AoSAs) and is a risk factor for aortic regurgitation (AR). However, the etiology of AR secondary to DSS remains unknown. This study aimed at quantifying computationally the impact of AoSA steepening and DSS on aortic valve (AV) hemodynamics and AR.

METHODS

An LV geometry reconstructed from cine-MRI data was connected to an AV geometry to generate a unified 2D LV-AV model. Six geometrical variants were considered: unobstructed (CTRL) and DSS-obstructed LVOT (DSS), each reflecting three AoSA variations (110°, 120°, 130°). Fluid-structure interaction simulations were run to compute LVOT flow, AV leaflet dynamics, and regurgitant fraction (RF).

RESULTS

AoSA steepening and DSS generated vortex dynamics alterations and stenotic flow conditions. While the CTRL-110° model generated the highest degree of leaflet opening asymmetry, DSS preferentially altered superior leaflet kinematics, and caused leaflet-dependent alterations in systolic fluttering. LVOT steepening and DSS subjected the leaflets to increasing WSS overloads (up to 94% increase in temporal shear magnitude), while DSS also increased WSS bidirectionality on the inferior leaflet belly (+ 0.30-point in oscillatory shear index). Although AoSA steepening and DSS increased diastolic transvalvular backflow, regurgitant fractions (RF < 7%) remained below the threshold defining clinical mild AR.

CONCLUSIONS

The mechanical interactions between AV leaflets and LVOT steepening/DSS hemodynamic derangements do not cause AR. However, the leaflet WSS abnormalities predicted in those anatomies provide new support to a mechanobiological etiology of AR secondary to DSS.

Combining statistical shape modeling, CFD, and meta-modeling to approximate the patient-specific pressure-drop across the aortic valve in real-time

BACKGROUND

Advances in medical imaging, segmentation techniques, and high performance computing have stimulated the use of complex, patient-specific, three-dimensional Computational Fluid Dynamics (CFD) simulations. Patient-specific, CFD-compatible geometries of the aortic valve are readily obtained. CFD can then be used to obtain the patient-specific pressure-flow relationship of the aortic valve. However, such CFD simulations are computationally expensive, and real-time alternatives are desired.

AIM

The aim of this work is to evaluate the performance of a meta-model with respect to high-fidelity, three-dimensional CFD simulations of the aortic valve.

METHODS

Principal component analysis was used to build a statistical shape model (SSM) from a population of 74 iso-topological meshes of the aortic valve. Synthetic meshes were created with the SSM, and steady-state CFD simulations at flow-rates between 50 and 650 mL/s were performed to build a meta-model. The meta-model related the statistical shape variance, and flow-rate to the pressure-drop.

RESULTS

Even though the first three shape modes account for only 46% of shape variance, the features relevant for the pressure-drop seem to be captured. The three-mode shape-model approximates the pressure-drop with an average error of 8.8% to 10.6% for aortic valves with a geometric orifice area below 150 mm² . The proposed methodology was least accurate for aortic valve areas above 150 mm² . Further reduction to a meta-model introduces an additional 3% error.

CONCLUSIONS

Statistical shape modeling can be used to capture shape variation of the aortic valve. Meta-models trained by SSM-based CFD simulations can provide an estimate of the pressure-flow relationship in real-time.

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

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