The effect of torus tubarius size on upper airway aerodynamics in children: a computational fluid dynamics study

PURPOSE

Some children with sleep-disordered breathing (SDB) continue to experience symptoms after adenotonsillectomy. One possible cause is the excessive size of the torus tubarius.

METHODS

In this study, the relationship between torus tubarius size and surgical outcome in 24 children with SDB who underwent adenotonsillectomy was retrospectively analyzed based on cone beam computed tomography (CBCT) imaging measurements and medical records. A computational fluid dynamics (CFD) approach was used to quantitatively compare the effects of different torus tubarius sizes on upper airway (UA) aerodynamics in children.

RESULTS

The percentage of UA area occupied by the torus tubarius (TTA%) was significantly different between the excellent and poor groups (10.4 ± 3.58% vs. 17.71 ± 4.7%, p < 0.001). The results of CFD simulation showed that the mean airflow velocity, wall shear stress (WSS) and pressure drop (ΔP) in the nasopharynx significantly increased when the TTA% was > 15%.

CONCLUSION

Our study confirmed the effect of round pillow size on the aerodynamics of the UA in children. When the TTA% exceeds 15%, it causes change in aerodynamics, which may affect the outcome of children with SDB.

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.

Generation of synthetic aortic valve stenosis geometries for in silico trials

In silico trials are a promising way to increase the efficiency of the development, and the time to market of cardiovascular implantable devices. The development of transcatheter aortic valve implantation (TAVI) devices, could benefit from in silico trials to overcome frequently occurring complications such as paravalvular leakage and conduction problems. To be able to perform in silico TAVI trials virtual cohorts of TAVI patients are required. In a virtual cohort, individual patients are represented by computer models that usually require patient-specific aortic valve geometries. This study aimed to develop a virtual cohort generator that generates anatomically plausible, synthetic aortic valve stenosis geometries for in silico TAVI trials and allows for the selection of specific anatomical features that influence the occurrence of complications. To build the generator, a combination of non-parametrical statistical shape modeling and sampling from a copula distribution was used. The developed virtual cohort generator successfully generated synthetic aortic valve stenosis geometries that are comparable with a real cohort, and therefore, are considered as being anatomically plausible. Furthermore, we were able to select specific anatomical features with a sensitivity of around 90%. The virtual cohort generator has the potential to be used by TAVI manufacturers to test their devices. Future work will involve including calcifications to the synthetic geometries, and applying high-fidelity fluid-structure-interaction models to perform in silico trials.

Numerical investigation of nanoparticle deposition in the olfactory region among pediatric nasal airways with adenoid hypertrophy

To understand inhaled nanoparticle transport and deposition characteristics in pediatric nasal airways with adenoid hypertrophy (AH), with a specific emphasis on the olfactory region, virtual nanoparticle inhalation studies were conducted on anatomically accurate child nasal airway models. The computational fluid-particle dynamics (CFPD) method was employed, and numerical simulations were performed to compare the airflow and nanoparticle deposition patterns between nasal airways with nasopharyngeal obstruction before adenoidectomy and healthy nasal airways after virtual adenoidectomy. The influence of different inhalation rates and exhalation phase on olfactory regional nanoparticle deposition features was systematically analyzed. We found that nasopharyngeal obstruction resulted in significant uneven airflow distribution in the nasal cavity. The deposited nanoparticles were concentrated in the middle meatus, septum, inferior meatus and nasal vestibule. The deposition efficiency (DE) in the olfactory region decreases with increasing nanoparticle size (1-10 nm) during inhalation. After adenoidectomy, the pediatric olfactory region DE increased significantly while nasopharynx DE dramatically decreased. When the inhalation rate decreased, the deposition pattern in the olfactory region significantly altered, exhibiting an initial rise followed by a subsequent decline, reaching peak deposition at 2 nm. During exhalation, the pediatric olfactory region DE was substantially lower than during inhalation, and the olfactory region DE in the pre-operative models were found to be significantly higher than that of the post-operative models. In conclusions, ventilation and particle deposition in the olfactory region were significantly improved in post-operative models. Inhalation rate and exhalation process can significantly affect nanoparticle deposition in the olfactory region.

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.

Assessing the impact of turbulent kinetic energy boundary conditions on turbulent flow simulations using computational fluid dynamics

Computational fluid dynamics has been widely used to study hemodynamics, but accurately determining boundary conditions for turbulent blood flow remains challenging. This study aims to investigate the effect of patient-specific turbulence boundary conditions on the accuracy of turbulent flow simulation. Using a stenosis model with 50% severity in diameter, the post-stenosis turbulence flow region was simulated with different planes to obtain inlet boundary conditions and simulate downstream flows. The errors of simulated flow fields obtained with turbulence kinetic energy (TKE) boundary data and arbitrary turbulence intensity were compared. Additionally, the study tested various TKE data resolutions and noise levels to simulate experimental environments. The mean absolute error of velocity and TKE was investigated with various turbulence intensities and TKE mapping. While voxel size and signal-to-noise ratio of the TKE data affected the results, simulation with SNR > 5 and voxel size < 10% resulted in better accuracy than simulations with turbulence intensities. The simulation with appropriate TKE boundary data resulted in a more accurate velocity and turbulence field than those with arbitrary turbulence intensity boundary conditions. The study demonstrated the potential improvement of turbulent blood flow simulation with patient-specific turbulence boundary conditions, which can be obtained from recent measurement techniques.

Effect of different degrees of adenoid hypertrophy on pediatric upper airway aerodynamics: a computational fluid dynamics study

To improve the diagnostic accuracy of adenoid hypertrophy (AH) in children and prevent further complications in time, it is important to study and quantify the effects of different degrees of AH on pediatric upper airway (UA) aerodynamics. In this study, based on computed tomography (CT) scans of a child with AH, UA models with different degrees of obstruction (adenoidal-nasopharyngeal (AN) ratio of 0.9, 0.8, 0.7, and 0.6) and no obstruction (AN ratio of 0.5) were constructed through virtual surgery to quantitatively analyze the aerodynamic characteristics of UA with different degrees of obstruction in terms of the peak velocity, pressure drop (△P), and maximum wall shear stress (WSS). We found that two obvious whirlpools are formed in the anterior upper part of the pediatric nasal cavity and in the oropharynx, which is caused by the sudden increase in the nasal cross-section area, resulting in local flow separation and counterflow. In addition, when the AN ratio was ≥ 0.7, the airflow velocity peaked at the protruding area in the nasopharynx, with an increase 1.1-2.7 times greater than that in the nasal valve area; the △P in the nasopharynx was significantly increased, with an increase 1.1-6.8 times greater than that in the nasal cavity; and the maximum WSS of the posterior wall of the nasopharynx was 1.1-4.4 times larger than that of the nasal cavity. The results showed that the size of the adenoid plays an important role in the patency of the pediatric UA.

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.

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.

Fluid-structure interaction modeling of compliant aortic valves using the lattice Boltzmann CFD and FEM methods

The lattice Boltzmann method (LBM) has been increasingly used as a stand-alone CFD solver in various biomechanical applications. This study proposes a new fluid-structure interaction (FSI) co-modeling framework for the hemodynamic-structural analysis of compliant aortic valves. Toward that goal, two commercial software packages are integrated using the lattice Boltzmann (LBM) and finite element (FE) methods. The suitability of the LBM-FE hemodynamic FSI is examined in modeling healthy tricuspid and bicuspid aortic valves (TAV and BAV), respectively. In addition, a multi-scale structural approach that has been employed explicitly recognizes the heterogeneous leaflet tissues and differentiates between the collagen fiber network (CFN) embedded within the elastin matrix of the leaflets. The CFN multi-scale tissue model is inspired by monitoring the distribution of the collagen in 15 porcine leaflets. Different simulations have been examined, and structural stresses and resulting hemodynamics are analyzed. We found that LBM-FE FSI approach can produce good predictions for the flow and structural behaviors of TAV and BAV and correlates well with those reported in the literature. The multi-scale heterogeneous CFN tissue structural model enhances our understanding of the mechanical roles of the CFN and the elastin matrix behaviors. The importance of LBM-FE FSI also emerges in its ability to resolve local hemodynamic and structural behaviors. In particular, the diastolic fluctuating velocity phenomenon near the leaflets is explicitly predicted, providing vital information on the flow transient nature. The full closure of the contacting leaflets in BAV is also demonstrated. Accordingly, good structural kinematics and deformations are captured for the entire cardiac cycle.

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.

Aerodynamic characteristics in upper airways among orthodontic patients and its association with adenoid nasopharyngeal ratios in lateral cephalograms

BACKGROUND

Adenoid hypertrophy among orthodontic patients may be detected in lateral cephalograms. The study investigates the aerodynamic characteristics within the upper airway (UA) by means of computational fluid dynamics (CFD) simulation. Furthermore, airflow features are compared between subgroups according to the adenoidal nasopharyngeal (AN) ratios.

METHODS

This retrospective study included thirty-five patients aged 9-15 years having both lateral cephalogram and cone beam computed tomography (CBCT) imaging that covered the UA region. The cases were divided into two subgroups according to the AN ratios measured on the lateral cephalograms: Group 1 with an AN ratio < 0.6 and Group 2 with an AN ratio ≥ 0.6. Based on the CBCT images, segmented UA models were created and the aerodynamic characteristics at inspiration and expiration were simulated by the CFD method for the two groups. The studied aerodynamic parameters were pressure drop (ΔP), maximum midsagittal velocity (V_ms), maximum wall shear stress (P_ws), and minimum wall static pressure (P_w).

RESULTS

The maximum V_ms exhibits nearly 30% increases in Group 2 at both inspiration (p = 0.013) and expiration (p = 0.045) compared to Group 1. For the other aerodynamic parameters such as ΔP, the maximum P_ws, and minimum P_w, no significant difference is found between the two groups.

CONCLUSIONS

The maximum V_ms seems to be the most sensitive aerodynamic parameter for the groups of cases. An AN ratio of more than 0.6 measured on a lateral cephalogram may associate with a noticeably increased maximum V_ms, which could assist clinicians in estimating the airflow features in the UA.

Numerical analysis of stenoses severity and aortic wall mechanics in patients with supravalvular aortic stenosis

Supravalvular aortic stenosis (SVAS) is an aortic malformation characterized by a narrowing of the ascending aorta, resulting in abnormal hemodynamics and pressure drop across the stenosed region. It has been observed that the pressure drops measured from Doppler ultrasound exams often tend to be higher than those obtained from invasive cardiac catheterization. These misleadingly elevated pressure measurements may drive the decision to refer patients for surgical treatment prematurely. Considering this strong clinical association, the purpose of this work is to develop a computational modeling approach using a two-way coupled fluid-structure interaction methodology to determine an accurate prediction of trans-stenotic pressure drop and to further highlight the discrepancy between the SVAS assessment methods. Blood is modeled using Navier-Stokes equations while the aortic wall is simulated by a composite poroelastic structure to represent the three main layers of the arterial wall. The relationship between aortic wall elasticity and the blood flow conditions is examined in varying levels of stenosis, ranging from mild to severe degrees of vessel diameter narrowing. A substantial overestimation of the traditional Doppler pressure drop measurement is observed, especially for severe stenosis levels. The simulation results indicate that elasticity of the aortic wall has a relatively little effect on trans-stenotic pressure drop for the range of mild to moderate SVAS cases, but predicted to have a profound effect for severe SVAS cases. Moreover, significant sensitivity to the pressure drop across the SVAS region from stenosis severity is observed.

Modeling of aortic valve stenosis using fluid-structure interaction method

BACKGROUND AND OBJECTIVES

Fluid structure interaction (FSI) is defined as interaction of the structures with contacting fluids. The aortic valve experiences the interaction with blood flow in systolic phase. In this study, we have tried to predict the hemodynamics of blood flow through a normal and stenotic aortic valve in two relaxation and exercise conditions using a three-dimensional FSI method.

METHODS

The aorta valve was modeled as a three-dimensional geometry including a normal model and two others with 25% and 50% stenosis. The geometry of the aortic valve was extracted from CT images and the models were generated by MMIMCS software and then they were implemented in ANSYS software. The pulsatile flow rate was used for all cases and the numerical simulations were conducted based on a time-dependent domain.

RESULTS

The obtained results including the velocity, pressure, and shear stress contours in different systolic time sequences were explained and discussed. The maximum blood flow velocity in relaxation phase was obtained 1.62 m/s (normal valve), 3.78 m/s (25% stenosed valve), and 4.73 m/s (50% stenosed valve). In exercise condition, the maximum velocities are 2.86, 4.32, and 5.42 m/s respectively. The maximum blood pressure in relaxation phase was calculated 111.45 mmHg (normal), 148.66 mmHg (25% stenosed), and 164.21 mmHg (50% stenosed). However, the calculated values in exercise situation were 129.57, 163.58, and 191.26 mmHg.The validation of the predicted results was also conducted using existing literature.

CONCLUSIONS

We believe that such model are useful tools for biomechanical experts. The further studies should be done using experimental data and the data are implemented on the boundary conditions for better comparison of the results.

Hemodynamic Modeling of Biological Aortic Valve Replacement Using Preoperative Data Only

Objectives: Prediction of aortic hemodynamics after aortic valve replacement (AVR) could help optimize treatment planning and improve outcomes. This study aims to demonstrate an approach to predict postoperative maximum velocity, maximum pressure gradient, secondary flow degree (SFD), and normalized flow displacement (NFD) in patients receiving biological AVR.

Methods: Virtual AVR was performed for 10 patients, who received actual AVR with a biological prosthesis. The virtual AVRs used only preoperative anatomical and 4D flow MRI data. Subsequently, computational fluid dynamics (CFD) simulations were performed and the abovementioned hemodynamic parameters compared between postoperative 4D flow MRI data and CFD results.

Results: For maximum velocities and pressure gradients, postoperative 4D flow MRI data and CFD results were strongly correlated (R² = 0.75 and R² = 0.81) with low root mean square error (0.21 m/s and 3.8 mmHg). SFD and NFD were moderately and weakly correlated at R² = 0.44 and R² = 0.20, respectively. Flow visualization through streamlines indicates good qualitative agreement between 4D flow MRI data and CFD results in most cases.

Conclusion: The approach presented here seems suitable to estimate postoperative maximum velocity and pressure gradient in patients receiving biological AVR, using only preoperative MRI data. The workflow can be performed in a reasonable time frame and offers a method to estimate postoperative valve prosthesis performance and to identify patients at risk of patient-prosthesis mismatch preoperatively. Novel parameters, such as SFD and NFD, appear to be more sensitive, and estimation seems harder. Further workflow optimization and validation of results seems warranted.

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.

Computational fluid dynamics: a primer for congenital heart disease clinicians

Computational fluid dynamics has become an important tool for studying blood flow dynamics. As an in-silico collection of methods, computational fluid dynamics is noninvasive and provides numerical values for the most important parameters of blood flow, such as velocity and pressure that are crucial in hemodynamic studies. In this primer, we briefly explain the basic theory and workflow of the two most commonly applied computational fluid dynamics techniques used in the congenital heart disease literature: the finite element method and the finite volume method. We define important terminology and include specific examples of how using these methods can answer important clinical questions in congenital cardiac surgery planning and perioperative patient management.

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.