Boundary Conditions by Schwarz-Christoffel Mapping in Anatomically Accurate Hemodynamics

Influence of Pulsatility and Inflow Waveforms on Tracheal Airflow Dynamics in Healthy Older Adults

Tracheal collapsibility is a dynamic process altering local airflow dynamics. Patient-specific simulation is a powerful technique to explore the physiological and pathological characteristics of human airways. One of the key considerations in implementing airway computations is choosing the right inlet boundary conditions that can act as a surrogate model for understanding realistic airflow simulations. To this end, we numerically examine airflow patterns under the influence of different profiles, i.e., flat, parabolic, and Womersley, and compare these with a realistic inlet obtained from experiments. Simulations are performed in ten patient-specific cases with normal and rapid breathing rates during the inhalation phase of the respiration cycle. At normal breathing, velocity and vorticity contours reveal primary flow structures on the sagittal plane that impart strength to cross-plane vortices. Rapid breathing, however, encounters small recirculation zones. Quantitative flow metrics are evaluated using time-averaged wall shear stress (TAWSS) and oscillatory shear index (OSI). Overall, the flow metrics encountered in a real velocity profile are in close agreement with parabolic and Womersley profiles for normal conditions, however, the Womersley inlet alone conforms to a realistic profile under rapid breathing conditions.

Analysis of Inlet Velocity Profiles in Numerical Assessment of Fontan Hemodynamics

Computational fluid dynamic (CFD) simulations are widely utilized to assess Fontan hemodynamics that are related to long-term complications. No previous studies have systemically investigated the effects of using different inlet velocity profiles in Fontan simulations. This study implements real, patient-specific velocity profiles for numerical assessment of Fontan hemodynamics using CFD simulations. Four additional, artificial velocity profiles were used for comparison: (1) flat, (2) parabolic, (3) Womersley, and (4) parabolic with inlet extensions [to develop flow before entering the total cavopulmonary connection (TCPC)]. The differences arising from the five velocity profiles, as well as discrepancies between the real and each of the artificial velocity profiles, were quantified by examining clinically important metrics in TCPC hemodynamics: power loss (PL), viscous dissipation rate (VDR), hepatic flow distribution, and regions of low wall shear stress. Statistically significant differences were observed in PL and VDR between simulations using real and flat velocity profiles, but differences between those using real velocity profiles and the other three artificial profiles did not reach statistical significance. These conclusions suggest that the artificial velocity profiles (2)-(4) are acceptable surrogates for real velocity profiles in Fontan simulations, but parabolic profiles are recommended because of their low computational demands and prevalent applicability.

Optimal B-spline Mapping of Flow Imaging Data for Imposing Patient-specific Velocity Profiles in Computational Hemodynamics

OBJECTIVE

We propose a novel method to map patient-specific blood velocity profiles obtained from imaging data such as 2D flow MRI or 3D colour Doppler ultrasound) to geometric vascular models suitable to perform CFD simulations of haemodynamics. We describe the implementation and utilisation of the method within an open-source computational hemodynamics simulation software (CRIMSON).

METHODS

The proposed method establishes point-wise correspondences between the contour of a fixed geometric model and time-varying contours containing the velocity image data, from which a continuous, smooth and cyclic deformation field is calculated. Our methodology is validated using synthetic data, and demonstrated using two different in-vivo aortic velocity datasets: a healthy subject with normal tricuspid valve and a patient with bicuspid aortic valve.

RESULTS

We compare our method with the state-of-the-art Schwarz-Christoffel method, in terms of preservation of velocities and execution time. Our method is as accurate as the Schwarz-Christoffel method, while being over 8 times faster.

CONCLUSIONS

Our mapping method can accurately preserve either the flow rate or the velocity field through the surface, and can cope with inconsistencies in motion and contour shape.

SIGNIFICANCE

The proposed method and its integration into the CRIMSON software enable a streamlined approach towards incorporating more patient-specific data in blood flow simulations.

Impact of Patient-Specific Inflow Velocity Profile on Hemodynamics of the Thoracic Aorta

Computational fluid dynamics (CFD) provides a noninvasive method to functionally assess aortic hemodynamics. The thoracic aorta has an anatomically complex inlet comprising of the aortic valve and root, which is highly prone to different morphologies and pathologies. We investigated the effect of using patient-specific (PS) inflow velocity profiles compared to idealized profiles based on the patient's flow waveform. A healthy 31 yo with a normally functioning tricuspid aortic valve (subject A), and a 52 yo with a bicuspid aortic valve (BAV), aortic valvular stenosis, and dilated ascending aorta (subject B) were studied. Subjects underwent MR angiography to image and reconstruct three-dimensional (3D) geometric models of the thoracic aorta. Flow-magnetic resonance imaging (MRI) was acquired above the aortic valve and used to extract the patient-specific velocity profiles. Subject B's eccentric asymmetrical inflow profile led to highly complex velocity patterns, which were not replicated by the idealized velocity profiles. Despite having identical flow rates, the idealized inflow profiles displayed significantly different peak and radial velocities. Subject A's results showed some similarity between PS and parabolic inflow profiles; however, other parameters such as Flowasymmetry were significantly different. Idealized inflow velocity profiles significantly alter velocity patterns and produce inaccurate hemodynamic assessments in the thoracic aorta. The complex structure of the aortic valve and its predisposition to pathological change means the inflow into the thoracic aorta can be highly variable. CFD analysis of the thoracic aorta needs to utilize fully PS inflow boundary conditions in order to produce truly meaningful results.

Computational Fluid Dynamics Modeling of the Human Pulmonary Arteries with Experimental Validation

Pulmonary hypertension (PH) is a chronic progressive disease characterized by elevated pulmonary arterial pressure, caused by an increase in pulmonary arterial impedance. Computational fluid dynamics (CFD) can be used to identify metrics representative of the stage of PH disease. However, experimental validation of CFD models is often not pursued due to the geometric complexity of the model or uncertainties in the reproduction of the required flow conditions. The goal of this work is to validate experimentally a CFD model of a pulmonary artery phantom using a particle image velocimetry (PIV) technique. Rapid prototyping was used for the construction of the patient-specific pulmonary geometry, derived from chest computed tomography angiography images. CFD simulations were performed with the pulmonary model with a Reynolds number matching those of the experiments. Flow rates, the velocity field, and shear stress distributions obtained with the CFD simulations were compared to their counterparts from the PIV flow visualization experiments. Computationally predicted flow rates were within 1% of the experimental measurements for three of the four branches of the CFD model. The mean velocities in four transversal planes of study were within 5.9 to 13.1% of the experimental mean velocities. Shear stresses were qualitatively similar between the two methods with some discrepancies in the regions of high velocity gradients. The fluid flow differences between the CFD model and the PIV phantom are attributed to experimental inaccuracies and the relative compliance of the phantom. This comparative analysis yielded valuable information on the accuracy of CFD predicted hemodynamics in pulmonary circulation models.

The role of wall shear stress in the assessment of right ventricle hydraulic workload

Pulmonary hypertension (PH) is a devastating disease affecting approximately 15-50 people per million, with a higher incidence in women. PH mortality is mostly attributed to right ventricle (RV) failure, which results from RV hypotrophy due to an overburdened hydraulic workload. The objective of this study is to correlate wall shear stress (WSS) with hemodynamic metrics that are generally accepted as clinical indicators of RV workload and are well correlated with disease outcome. Retrospective right heart catheterization data for 20 PH patients were analyzed to derive pulmonary vascular resistance (PVR), arterial compliance (C), and an index of wave reflections (Γ). Patient-specific contrast-enhanced computed tomography chest images were used to reconstruct the individual pulmonary arterial trees up to the seventh generation. Computational fluid dynamics analyses simulating blood flow at peak systole were conducted for each vascular model to calculate WSS distributions on the endothelial surface of the pulmonary arteries. WSS was found to be decreased proportionally with elevated PVR and reduced C. Spatially averaged WSS (SAWSS) was positively correlated with PVR (R (2) = 0.66), C (R (2) = 0.73), and Γ (R (2) = 0.5) and also showed promising preliminary correlations with RV geometric characteristics. Evaluating WSS at random cross sections in the proximal vasculature (main, right, and left pulmonary arteries), the type of data that can be acquired from phase-contrast magnetic resonance imaging, did not reveal the same correlations. In conclusion, we found that WSS has the potential to be a viable and clinically useful noninvasive metric of PH disease progression and RV health. Future work should be focused on evaluating whether SAWSS has prognostic value in the management of PH and whether it can be used as a rapid reactivity assessment tool, which would aid in selection of appropriate therapies.

Considerations for numerical modeling of the pulmonary circulation--a review with a focus on pulmonary hypertension

Both in academic research and in clinical settings, virtual simulation of the cardiovascular system can be used to rapidly assess complex multivariable interactions between blood vessels, blood flow, and the heart. Moreover, metrics that can only be predicted with computational simulations (e.g., mechanical wall stress, oscillatory shear index, etc.) can be used to assess disease progression, for presurgical planning, and for interventional outcomes. Because the pulmonary vasculature is susceptible to a wide range of pathologies that directly impact and are affected by the hemodynamics (e.g., pulmonary hypertension), the ability to develop numerical models of pulmonary blood flow can be invaluable to the clinical scientist. Pulmonary hypertension is a devastating disease that can directly benefit from computational hemodynamics when used for diagnosis and basic research. In the present work, we provide a clinical overview of pulmonary hypertension with a focus on the hemodynamics, current treatments, and their limitations. Even with a rich history in computational modeling of the human circulation, hemodynamics in the pulmonary vasculature remains largely unexplored. Thus, we review the tasks involved in developing a computational model of pulmonary blood flow, namely vasculature reconstruction, meshing, and boundary conditions. We also address how inconsistencies between models can result in drastically different flow solutions and suggest avenues for future research opportunities. In its current state, the interpretation of this modeling technology can be subjective in a research environment and impractical for clinical practice. Therefore, considerations must be taken into account to make modeling reliable and reproducible in a laboratory setting and amenable to the vascular clinic. Finally, we discuss relevant existing models and how they have been used to gain insight into cardiopulmonary physiology and pathology.