A turbulence model for pulsatile arterial flows

The relationship between aerodynamic characteristics of the upper airway and severity of obstructive sleep apnea in adults

OBJECTIVE

To investigate the relationship between aerodynamic characteristics of the upper airway and severity of obstructive sleep apnea (OSA) in adults.

METHODS

Ninety-seven adult OSA patients underwent polysomnography and cone beam computed tomography (CBCT). The anatomical and aerodynamic characteristics were measured based on CBCT images and computational fluid dynamics modelling of the upper airway.

RESULTS

After controlling for patients' gender, age, and body mass index (BMI), the maximum velocity during inspiration (In-Vmax) led to the largest increase in the explanatory power of apnea-hypopnea index (AHI) variation. The In-Vmax was closely correlated with the minimum axial area, and their relationship was represented by an inversely proportional fitted curve.

CONCLUSIONS

The In-Vmax was the most relevant to OSA severity, and it could be used to assist in recognizing severe OSA patients and as a primary variable to evaluate treatment outcomes of OSA. The In-Vmax was closely related to the most constricted area of the upper airway.

Effects of vertical control on anatomic and aerodynamic characteristics of the oropharyngeal airway during premolar extraction treatment of Class II hyperdivergent nonsevere crowding malocclusion

INTRODUCTION

This study aimed to analyze the effects of premolar extraction treatment with vertical control on changes in the anatomy and aerodynamics of the oropharynx in Class II hyperdivergent malocclusion with nonsevere crowding.

METHODS

Thirty-nine patients with Class II hyperdivergent malocclusion were enrolled consecutively. All the participants underwent 4 premolar extractions. The high-pull J-hook and mini-implants were used to provide vertical control. Cone-beam computed tomography was performed before and after treatment. The participants were divided into a decreased lower vertical facial height group (n = 23) and an increased lower vertical facial height group (n = 16) on the basis of superimposition. The aerodynamic characteristics, including airway resistance (inspiration, R_in; expiration, R_ex) and maximum velocity (inspiration, Vmax_in; expiration, Vmax_ex) at inspiration and expiration, were calculated using computational fluid dynamics. Anatomic characteristics, including volume and cross-sectional area (CSA_min), were measured using the Dolphin Imaging software (Dolphin Imaging and Management Solutions, Chatsworth, Calif).

RESULTS

After treatment, the median volume and CSA_min increased by 2357 mm³ and 43 mm², respectively, and median R_in and Vmax_ex decreased by 0.15 Pa/L/min and 0.24 m×s^-1, respectively, in decreased lower vertical facial height group. In contrast, the median CSA_min decreased by 9.5 mm² in the increased lower vertical facial height group. All the changes were statistically significant (all P <0.05). Significant differences in volume, CSA_min, R_in, and Vmax_ex were observed between the 2 groups.

CONCLUSIONS

Vertical control might improve the anatomic and aerodynamic characteristics of the oropharyngeal airway during premolar extraction treatment of Class II hyperdivergent malocclusion with nonsevere crowding.

A fluid-structure interaction model accounting arterial vessels as a key part of the blood-flow engine for the analysis of cardiovascular diseases

According to the classical Windkessel model, the heart is the only power source for blood flow, while the arterial system is assumed to be an elastic chamber that acts as a channel and buffer for blood circulation. In this paper we show that in addition to the power provided by the heart for blood circulation, strain energy stored in deformed arterial vessels in vivo can be transformed into mechanical work to propel blood flow. A quantitative relationship between the strain energy increment and functional (systolic, diastolic, mean and pulse blood pressure) and structural (stiffness, diameter and wall thickness) parameters of the aorta is described. In addition, details of blood flow across the aorta remain unclear due to changes in functional and other physiological parameters. Based on the arterial strain energy and fluid-structure interaction theory, the relationship between physiological parameters and blood supply to organs was studied, and a corresponding mathematical model was developed. The findings provided a new understanding about blood-flow circulation, that is, cardiac output allows blood to enter the aorta at an initial rate, and then strain energy stored in the elastic arteries pushes blood toward distal organs and tissues. Organ blood supply is a key factor in cardio-cerebrovascular diseases (CCVD), which are caused by changes in blood supply in combination with multiple physiological parameters. Also, some physiological parameters are affected by changes in blood supply, and vice versa. The model can explain the pathophysiological mechanisms of chronic diseases such as CCVD and hypertension among others, and the results are in good agreement with epidemiological studies of CCVD.

Comparison of anatomic and aerodynamic characteristics of the upper airway among edentulous mild, moderate, and severe obstructive sleep apnea in older adults

STUDY OBJECTIVES

First, to compare the upper airway's anatomic and aerodynamic characteristics of the edentulous older adults who experience mild, moderate, and severe obstructive sleep apnea (OSA). Second, to examine the correlation between the severity of OSA and the anatomic and aerodynamic characteristic(s) of the upper airway in these edentulous individuals.

METHODS

NewTom5G cone beam computed tomography scans of 58 edentulous individuals with mild, moderate, and severe OSA were included in this analysis. 1) Computational models of the upper airway were reconstructed based on cone beam computed tomography images and the anatomical and aerodynamic characteristics of the upper airway were examined by an observer blind to OSA severity. 2) Pearson correlation analysis was used to determine the correlation between apnea-hypopnea index and the anatomic and aerodynamic characteristics of the upper airway.

RESULTS

Compared with edentulous patients with mild and moderate OSA, those with severe OSA have a more hourglass-shaped upper airway. The severity of OSA, namely, apnea-hypopnea index, was significantly correlated with the length, shape, and minimum cross-sectional area of the upper airway. During inspiration, the mean velocity of the airflow within the upper airway of the edentulous patients with severe OSA was higher than that of patients with mild and moderate OSA. During both inspiration and expiration, apnea-hypopnea index was found to be significantly correlated with maximum velocity (P = .05) and airway resistance (P = .024, 0.038).

CONCLUSIONS

The edentulous patients with severe OSA have a more hourglass-shaped upper airway. The findings also suggest that, during inspiration, the airflow travels faster in edentulous patients with severe OSA than in those with mild or moderate OSA.

CLINICAL TRIAL REGISTRATION

Registry: ClinicalTrials.gov; Name: The Effect of Nocturnal Wear of Dentures on Sleep and Oral Health Related Quality of Life; URL: https://clinicaltrials.gov/ct2/show/NCT01868295; Identifier: NCT01868295.

CITATION

Chen H, Elham E, Li Y, et al. Comparison of anatomic and aerodynamic characteristics of the upper airway among edentulous mild, moderate, and severe obstructive sleep apnea in older adults. J Clin Sleep Med. 2022;18(3):759-768.

Patient-specific Computational Hemodynamic Analysis for Interrupted Aortic Arch in an Adult: Implications for Aortic Dissection Initiation

The guideline for the treatment of interrupted aortic arch (IAA) in adults has not been established although most centers tend to propose surgery. There is no clear evidence for the preferred selection of surgical repair versus conservatively medical treatment for the uncertain effects of both treatments. However, reports of sporadic aortic dissection (AD) of descending aorta (DAo) in IAA in adults before surgery drew our attention. It is quite perplexing because there seems to be no risk factors for the development of AD at DAo such as long-term uncontrolled hypertension, atherosclerosis, aortic aneurysm or genetic disorder. In this paper, we carried out the numerical investigation on the hemodynamics in a patient-specific IAA model, which was reconstructed from computed tomography images. Hemodynamic parameters including the flow pattern, pressure distribution, and wall shear stress (WSS) indicators were obtained. The simulation revealed that the jet flows from the collateral arteries (CAs) induced risk hemodynamic forces on the lumen wall including high time-averaged wall shear stress (TAWSS), high pressure and rapid change of WSS direction throughout the cardiac cycle. Moreover, it is found that only a jet flow which circumferentially washes out the aortic wall might cause tears on the wall. It is concluded that the specific geometrical features of the extensive major CAs might result in the risky hemodynamics leading to the initiation and development of AD in this particular IAA patient. CFD analysis in IAA can provide a clinical reference, and the results should be further studied in depth in the future.

Analyses of aerodynamic characteristics of the oropharynx applying CBCT: obstructive sleep apnea patients versus control subjects

OBJECTIVES

To determine the most relevant aerodynamic characteristic of the oropharynx related to the collapse of the upper airway in obstructive sleep apnea (OSA) patients; and to determine the correlation between the most relevant aerodynamic characteristic(s) of the oropharynx and anatomical characteristics of the oropharynx in OSA patients.

METHODS

31 mild to moderate OSA patients (mean ± SD age = 43.5 ± 9.7 years) and 13 control subjects (mean ± SD age = 48.5 ± 16.2 years) were included in this prospective study. The diagnosis of OSA patients was based on an overnight polysomnographic recording. To exclude the presence of OSA in the control subjects, they were asked to fill out a validated questionnaire to determine the risk of OSA. NewTom5G cone beam CT (CBCT) scans were obtained from both OSA patients and control subjects. Computational models of the oropharynx were reconstructed based on CBCT images. The aerodynamic characteristics of the oropharynx were calculated based on these computational models. Pearson correlation analysis was used to analyse the correlation between the most relevant aerodynamic characteristic(s) and anatomical characteristics of the oropharynx in OSA patients.

RESULTS

Compared with controls, the airway resistance during expiration (R_ex) of the OSA patients was significantly higher (p = 0.04). There was a significant negative correlation between R_ex and the minimum cross-sectional area (CSA_min) of the oropharynx (r = -0.41, p = 0.02), and between R_ex and the volume of the oropharynx (r = -0.48, p = 0.01) in OSA patients. After excluding an outlier, there is only significant correlation between R_ex and the CSA_min of the oropharynx (r = -0.45, p = 0.01).

CONCLUSIONS

Within the limitations of this study, we concluded that the most relevant aerodynamic characteristic of the oropharynx in the collapse of the upper airway in OSA patients is R_ex. Therefore, the repetitive collapse of the upper airway in OSA patients may be explained by a high R_ex, which is related to the CSA_min of the oropharynx.

Transitional Flow in a Cylindrical Flow Chamber for Studies at the Cellular Level

Fluid shear stress is an important regulator of vascular and endothelial cell (EC) functions. Its effect is dependent not only on magnitude but also on flow type. Although laminar flow predominates in the vasculature, transitional flow can occur and is thought to play a role in vascular diseases. While a great deal is known about the mechanisms and signaling cascades through which laminar shear stress regulates cells, little is known on how transitional shear stress regulates cells. To better understand the response of endothelial cells to transitional shear stress, a novel cylindrical flow chamber was designed to expose endothelial cells to a transitional flow environment similar to that found in vivo. The velocity profiles within the transitional flow chamber at Reynolds numbers 2200 and 3000 were measured using laser Doppler anemometry (LDA). At both Reynolds numbers, the velocity profiles are blunt (non-parabolic) with fluctuations larger than 5% of the velocity at the center of the pipe indicating the flows are transitional. Based on near wall velocity measurements and well established data for flow at these Reynolds numbers, the wall shear stress was estimated to be 3–4 and 5–6 dynes/cm² for Reynolds number 2200 and 3000, respectively. In contrast to laminar shear stress, no cell alignment was observed under transitional shear stress at both Reynolds numbers. However, transitional shear stress at the higher Reynolds number caused cell elongation similar to that of laminar shear stress at 3 dynes/cm². The fluctuating component of the wall shear stress may be responsible for these differences. The transitional flow chamber will facilitate cellular studies to identify the mechanisms through which transitional shear stress alters EC biology, which will assist in the development of vascular therapeutic treatments.

Experimental and numerical study on the hemodynamics of stenosed carotid bifurcation

Numerical simulation is performed to demonstrate that hemodynamic factors are significant determinants for the development of a vascular pathology. Experimental measurements by particle image velocimetry are carried out to validate the credibility of the computational approach. We present a study for determining complex flow structures using the case of an anatomically realistic carotid bifurcation model that is reconstructed from medical imaging. A transparent silicone replica of the artery is developed for in-vitro flow measurement. The dynamic behaviours of blood through the vascular structure based on the numerical and experimental approaches show good agreement.

Feasibility of in vivo measurement of carotid wall shear rate using spiral Fourier velocity encoded MRI

Arterial wall shear stress is widely believed to influence the formation and growth of atherosclerotic plaque; however, there is currently no gold standard for its in vivo measurement. The use of phase contrast MRI has proved to be challenging due to partial-volume effects and inadequate signal-to-noise ratio at the high spatial resolutions that are required. This work evaluates the use of spiral Fourier velocity encoded MRI as a rapid method for assessing wall shear rate in the carotid arteries. Wall shear rate is calculated from velocity histograms in voxels spanning the blood/vessel wall interface, using a method developed by Frayne and Rutt (Magn Reson Med 1995;34:378-387). This study (i) demonstrates the accuracy of the velocity histograms measured by spiral Fourier velocity encoding in a pulsatile carotid flow phantom compared with high-resolution two-dimensional Fourier transform phase contrast, (ii) demonstrates the accuracy of Fourier velocity encoding-based shear rate measurements in a numerical phantom designed using a computational fluid dynamics simulation of carotid flow, and (iii) demonstrates in vivo measurement of regional wall shear rate and oscillatory shear index in the carotid arteries of healthy volunteers at 3 T.

Development and verification of a high-fidelity computational fluid dynamics model of canine nasal airflow

The canine nasal cavity contains a complex airway labyrinth, dedicated to respiratory air conditioning, filtering of inspired contaminants, and olfaction. The small and contorted anatomical structure of the nasal turbinates has, to date, precluded a proper study of nasal airflow in the dog. This study describes the development of a high-fidelity computational fluid dynamics (CFD) model of the canine nasal airway from a three-dimensional reconstruction of high-resolution magnetic resonance imaging scans of the canine anatomy. Unstructured hexahedral grids are generated, with large grid sizes ((10-100) x 10(6) computational cells) required to capture the details of the nasal airways. High-fidelity CFD solutions of the nasal airflow for steady inspiration and expiration are computed over a range of physiological airflow rates. A rigorous grid refinement study is performed, which also illustrates a methodology for verification of CFD calculations on complex unstructured grids in tortuous airways. In general, the qualitative characteristics of the computed solutions for the different grid resolutions are fairly well preserved. However, quantitative results such as the overall pressure drop and even the regional distribution of airflow in the nasal cavity are moderately grid dependent. These quantities tend to converge monotonically with grid refinement. Lastly, transient computations of canine sniffing were carried out as part of a time-step study, demonstrating that high temporal accuracy is achievable using small time steps consisting of 160 steps per sniff period. Here we demonstrate that acceptable numerical accuracy (between approximately 1% and 15%) is achievable with practical levels of grid resolution (approximately 100 x 10(6) computational cells). Given the popularity of CFD as a tool for studying flow in the upper airways of humans and animals, based on this work we recommend the necessity of a grid dependence study and quantification of numerical error when presenting CFD results in complicated airways.

Direct numerical simulation of transitional flow in a stenosed carotid bifurcation

The blood flow dynamics of a stenosed, subject-specific, carotid bifurcation were numerically simulated using the spectral element method. Pulsatile inlet conditions were based on in vivo color Doppler ultrasound measurements of blood velocity. The results demonstrated the transitional or weakly turbulent state of the blood flow, which featured rapid velocity and pressure fluctuations in the post-stenotic region of the internal carotid artery (ICA) during systole and laminar flow during diastole. High-frequency vortex shedding was greatest downstream of the stenosis during the deceleration phase of systole. Velocity fluctuations had a frequency within the audible range of 100-300Hz. Instantaneous wall shear stress (WSS) within the stenosis was relatively high during systole ( approximately 25-45Pa) compared to that in a healthy carotid. In addition, high spatial gradients of WSS were present due to flow separation on the inner wall. Oscillatory flow reversal and low pressure were observed distal to the stenosis in the ICA. This study predicts the complex flow field, the turbulence levels and the distribution of the biomechanical stresses present in vivo within a stenosed carotid artery.

Computational representation and hemodynamic characterization of in vivo acquired severe stenotic renal artery geometries using turbulence modeling

The present study reports on computational fluid dynamics in the case of severe renal artery stenosis (RAS). An anatomically realistic model of a renal artery was reconstructed from CT scans, and used to conduct CFD simulations of blood flow across RAS. The recently developed shear stress transport (SST) turbulence model was pivotally applied in the simulation of blood flow in the region of interest. Blood flow was studied in vivo under the presence of RAS and subsequently in simulated cases before the development of RAS, and after endovascular stent implantation. The pressure gradients in the RAS case were many orders of magnitude larger than in the healthy case. The presence of RAS increased flow resistance, which led to considerably lower blood flow rates. A simulated stent in place of the RAS decreased the flow resistance at levels proportional to, and even lower than, the simulated healthy case without the RAS. The wall shear stresses, differential pressure profiles, and net forces exerted on the surface of the atherosclerotic plaque at peak pulse were shown to be of relevant high distinctiveness, so as to be considered potential indicators of hemodynamically significant RAS.

Turbulence modeling in three-dimensional stenosed arterial bifurcations

Under normal healthy conditions, blood flow in the carotid artery bifurcation is laminar. However, in the presence of a stenosis, the flow can become turbulent at the higher Reynolds numbers during systole. There is growing consensus that the transitional k-omega model is the best suited Reynolds averaged turbulence model for such flows. Further confirmation of this opinion is presented here by a comparison with the RNG k-epsilon model for the flow through a straight, nonbifurcating tube. Unlike similar validation studies elsewhere, no assumptions are made about the inlet profile since the full length of the experimental tube is simulated. Additionally, variations in the inflow turbulence quantities are shown to have no noticeable affect on downstream turbulence intensity, turbulent viscosity, or velocity in the k-epsilon model, whereas the velocity profiles in the transitional k-omega model show some differences due to large variations in the downstream turbulence quantities. Following this validation study, the transitional k-omega model is applied in a three-dimensional parametrically defined computer model of the carotid artery bifurcation in which the sinus bulb is manipulated to produce mild, moderate, and severe stenosis. The parametric geometry definition facilitates a powerful means for investigating the effect of local shape variation while keeping the global shape fixed. While turbulence levels are generally low in all cases considered, the mild stenosis model produces higher levels of turbulent viscosity and this is linked to relatively high values of turbulent kinetic energy and low values of the specific dissipation rate. The severe stenosis model displays stronger recirculation in the flow field with higher values of vorticity, helicity, and negative wall shear stress. The mild and moderate stenosis configurations produce similar lower levels of vorticity and helicity.