Particle deposition in a CT-scanned human lung airway

The particle deposition in a computerized tomography (CT)-scanned human lung was numerically investigated. The five-generation airway is extracted from the trachea to segmental bronchi of a 60-year-old Chinese male patient. Computations were carried out in the flow rate range of 210–630 ml/s (Reynolds number range of 1000–3000) and particle size of 2–10 μm (Stokes number range of 0.0007–0.049). To count the effect of laryngeal jet on trachea inlet, the trachea was extended and modified to simulate the larynx, consequently the inlet velocity profile is biased towards the rear wall. The laryngeal jet-induced turbulence was simulated using low Reynolds number (LRN) κ–ω turbulent model. Particle deposition patterns, deposition efficiency and deposition factor were studied in detail. The turbulent flow has significant effect on the particle deposition, and the present deposition factor is compared well with the available data.     

Numerical investigation of the three-dimensional flow in a human lung model

The flow field at inspiration and expiration in the upper human airways consisting of the trachea down to the sixth generation of the bronchial tree is numerically simulated. The three-dimensional steady flow at a hydraulic diameter-based Reynolds number Re(D)=1250 is computed via a lattice-Boltzmann method (LBM). The simulation is validated by the experimental data based on particle-image velocimetry (PIV) measurements. The good agreement between numerical and experimental results is evidenced by comparing velocity contours and distributions in a defined reference plane. The results show the LBM to be an accurate tool to numerically predict flow structures in the human lung. Using an automatic Cartesian grid generator, the overall process time from meshing to a steady-state solution is <12h. Moreover, the numerical simulation allows a closer analysis of the secondary flow structures than in the experimental investigation. The three-dimensional streamline patterns reveal some insight on the air exchange mechanism at inspiration and expiration. At inspiration, the slower near-wall tracheal flow enters through the right principal bronchus into the right upper lobar bronchus. The bulk mass flux in the trachea is nearly evenly distributed over the left upper, center and lower lobar bronchi and the right center and lower bronchi. At expiration, the air from the right upper lobar bronchus enters the right center of the trachea and displaces the airflow from the lower and center right bronchi such that the tracheal positions of the streamlines at inspiration and expiration are switched. The flow in the left bronchi does not show this kind of switching. The findings emphasize the impact of the asymmetry of the lung geometry on the respiratory air exchange mechanism.     

A numerical calculation of flow in a curved tube model of the left main coronary artery

The flow pattern in the left main coronary artery has been calculated using an idealized geometry and by numerically solving the full Navier-Stokes equations for a Newtonian fluid. Two different forms for the entrance velocity profile were used, one a time-varying, flat profile and the other a time-varying, less flat velocity profile. The results obtained demonstrate the presence of secondary motions for conditions simulating flow in the left main coronary artery, with maximum secondary flow velocities being on the order of three to four percent of the maximum axial velocity. This secondary flow phenomenon has an important influence on the wall shear stress distribution, in spite of the fact that there is virtually no alteration in the axial velocity profile. The maximum ratio of the outer wall shear stress to that on the inner wall is 1.4 at a Reynolds number of Re = 270, and it increases with increasing Reynolds number, reaching a value of 1.7 at Re = 810. Although there are significant differences in the results in the immediate vicinity of the inlet for the two different forms of the entrance velocity profile used, this difference does not persist far into the tube. Independent of the choice of the entrance velocity profile, it appears that there will be significant secondary flow effects on the wall shear stress.     

Flow measurements in a human femoral artery model with reverse lumen curvature

Flow visualization and wall pressure measurements were made in a smooth reverse curvature model that conformed to the gentle "s" shape of a left femoral artery angiogram of a patient in a clinical trial. Observed lesion localization at the inner (lesser) curvatures appeared to be associated with secondary flows in the wall vicinity directed toward the inner curvatures that tended to reverse direction in the flow entering the reverse curvature region. Moderate flow resistance increases of about 20 percent above the Poiseuille flow relation were found at the higher physiological Reynolds numbers Re above about 600-700 and thus Dean numbers for steady flow. For pulsatile flow simulation, flow resistances did not increase up to the largest Re of 470 tested. Apparently, the large variations in velocity during the cardiac cycle disrupted the stronger secondary flow patterns observed at the higher Reynolds numbers for steady flow.     

Combined MR imaging and numerical simulation of flow in realistic arterial bypass graft models

We report methods for (a) transforming a three-dimensional geometry acquired by magnetic resonance angiography (MRA) in vivo, or by imaging a model cast, into a computational surface representation, (b) use of this to construct a three dimensional numerical grid for computational fluid dynamic (CFD) studies, and (c) use of the surface representation to produce a stereo-lithographic replica of the real detailed geometry, at a scale convenient for detailed magnetic resonance imaging (MRI) flow studies. This is applied to assess the local flow field in realistic geometry arterial bypass grafts. Results from a parallel numerical simulation and MRI measurement of flow in an aorto-coronary bypass graft with various inlet flow conditions demonstrate the strong influence of the graft inlet waveform on the perianastomotic flow field. A sinusoidal and a multi harmonic coronary flow waveform both with a mean Reynolds number (Re) of 100 and a Womersley parameter of 2.7 were applied at the graft inlet. A weak axial flow separation region just distal to the toe was found in sinusoidal flow near end deceleration (Re = 25). At the same location and approximately the same point in the cycle (Re = 30) but in coronary flow, the axial flow separation was stronger and more spatially pronounced. No axial flow separation occurred in steady flow for Re = 100. Numerical predictions indicate a region in the vicinity of the suture line (where there is a local narrowing of the graft) with a wall shear magnitude in excess of five times that associated with fully developed flow at the graft inlet.     

Effect of the larynx on oscillatory flow in the central airways: a model study

Measurements were made of the effect of the larynx on the oscillatory flow profiles in a 3:1 scale model of the human central airways. A fixed glottic aperture corresponding to the shape and size at midinspiration was used. Oscillatory airflows at peak Reynolds numbers, similar to those obtained during spontaneous breathing and panting, were studied. The flow distribution to the five lobar bronchi was maintained by distally placed linear resistors. A hot-wire anemometer probe was used to measure the local velocity along two perpendicular diameters at six stations distributed through the model. Near the proximal end of the trachea, the flat velocity profiles at the beginning of the flow cycle peaked at maximum flow because of the jet created by the glottic aperture. This peaked structure was conserved during the latter half of the inspiratory cycle. Close to the carina, the jet had almost dissipated and the entry conditions into the main bronchi corresponded to those in the absence of the laryngeal model. The effect of the glottic aperture on the mean velocity was not felt beyond the carina, and the characteristic skewed profiles seen in oscillatory flows, in the absence of the larynx, were present in the main and lobar bronchi.     

Velocity profiles in central airways with endotracheal intubation: a model study

Steady inspiratory velocity profiles were measured at two flow rates in a 3:1 scale model of the human central airways in the presence of five modes of endotracheal intubation. The presence of an orifice or a short endotracheal tube had no significant effect on the velocity profiles distal to the carina. Long endotracheal tubes change the profiles in both main bronchi. A significant peak occurred in the frontal plane near the walls, and the maximum velocity in the airway was almost identical to the endotracheal tube center-line velocity. The flow impinging on the medial wall of the main bronchus was redirected up around the anterior and posterior walls yielding bipeak velocity profiles in the sagittal plane. A tube placed eccentrically in the trachea over the right main bronchus did not alter the velocity profiles in the left main bronchus, suggesting a redirection of flow over the carina into the left lung. An endobronchial tube at the mouth of the right main bronchus did change the shape of the velocity profiles in the left main bronchus. In the left upper lobar bronchus the presence of trachea intubation had no effect on the velocity profiles. However, in the right upper lobar bronchus, the long endotracheal tube flattened the velocity profiles from the strongly skewed ones seen in the absence of the endotracheal inserts. These results not only are relevant to distribution of ventilation and aerosol particle deposition, but also have strong implications in intrapulmonary gas mixing, especially when high-frequency low tidal-volume ventilation is involved.     

Effect of geometric variations on pressure loss for a model bifurcation of the human lung airway

Characteristics of pressure loss (ΔP) in human lung airways were numerically investigated using a realistic model bifurcation. Flow equations were numerically solved for the steady inspiratory condition with the tube length, the branching angle and flow velocity being varied over a wide range. In general, the ΔP coefficient K showed a power-law dependence on Reynolds number (Re) and length-to-diameter ratio with a different exponent for Re≥100 than for Re<100. The effect of different branching angles on pressure loss was very weak in the smooth-branching airways.     

Transverse images of the human thoracic trachea during forced expiration

The thoracic trachea and the proximal portion of the major bronchi were imaged in five normal volunteers during a forced expiration maneuver using a cine-computer-tomography system. Sixteen images of two contiguous slices were obtained in less than 1 is while expiratory flow was recorded at the mouth. The area of the thoracic trachea decreased rapidly as flow rate rose to its maximum and the wave of collapse propagated distally. The compressive narrowing of both the pars membranacea and the ventrolateral wall was asymmetric. A contact area appeared between the posterior and the left lateral walls. In one subject the trachea was imaged during the entire maneuver with a lower scan frequency. By 725 ms after the beginning of the forced expiration, the area had first decreased to 15% of its initial value and then reincreased to 46% of its initial value. It stayed constant for the remainder of the maneuver. The measured maximum air velocity was greater than the estimated local wave velocity.     

Numerical simulation of steady flow in a model of the aortic bifurcation.

The governing equations of steady flow of an incompressible viscous fluid through a 3-D model of the aortic bifurcation are solved with the finite element method. The effect of Reynolds number on the flow was studied for a range including the physiological values (200 < or = Re < or = 1600). The symmetrical bifurcation, with a branch angle of 70 degrees and an area ratio of 0.8, includes a tapered transition zone. Secondary flows induced by the tube curvature are observed in the daughter tubes. Transverse currents in the transition zone are generated by the combined effect of diverging and converging walls. Flow separation depends on both the Reynolds number and the inlet wall shear.     

Numerical investigation of inspiratory airflow in a realistic model of the human tracheobronchial airways and a comparison with experimental results

In this article, the results of numerical simulations using computational fluid dynamics (CFD) and a comparison with experiments performed with phase Doppler anemometry are presented. The simulations and experiments were conducted in a realistic model of the human airways, which comprised the throat, trachea and tracheobronchial tree up to the fourth generation. A full inspiration/expiration breathing cycle was used with tidal volumes 0.5 and 1 L, which correspond to a sedentary regime and deep breath, respectively. The length of the entire breathing cycle was 4 s, with inspiration and expiration each lasting 2 s. As a boundary condition for the CFD simulations, experimentally obtained flow rate distribution in 10 terminal airways was used with zero pressure resistance at the throat inlet. CCM+ CFD code (Adapco) was used with an SST k-\(\upomega \) low-Reynolds Number RANS model. The total number of polyhedral control volumes was 2.6 million with a time step of 0.001 s. Comparisons were made at several points in eight cross sections selected according to experiments in the trachea and the left and right bronchi. The results agree well with experiments involving the oscillation (temporal relocation) of flow structures in the majority of the cross sections and individual local positions. Velocity field simulation in several cross sections shows a very unstable flow field, which originates in the tracheal laryngeal jet and propagates far downstream with the formation of separation zones in both left and right airways. The RANS simulation agrees with the experiments in almost all the cross sections and shows unstable local flow structures and a quantitatively acceptable solution for the time-averaged flow field.     

Comparison of axisymmetric and three-dimensional models for gas uptake in a single bifurcation during steady expiration

Reactive gas uptake is predicted and compared in a single bifurcation at steady expiratory flow in terms of Sherwood number using an axisymmetric single-path model (ASPM) and a three-dimensional computational fluid dynamics model (CFDM). ASPM is validated in a two-generation geometry by comparing the average gas-phase mass transfer coefficients with the experimental values. ASPM predicted mass transfer coefficients within 20% of the experimental values. The flow and concentration variables in the ASPM were solved using Galerkin finite element method and in the CFDM using commercial finite element software FIDAP. The simulations were performed for reactive gas flowing at Reynolds numbers ranging from 60 to 350 in both symmetric bifurcation for three bifurcation angles, 30 deg, 70 deg, and 90 deg, and in an asymmetric bifurcation. The numerical models compared with each other qualitatively but quantitatively they were within 0.4-8% due to nonfully developed flow in the parent branch predicted by the CFDM. The radially averaged concentration variation along the axial location matched qualitatively between the CFDM and ASPM but quantitatively they were within 32% due to differences in the flow field. ASPM predictions compared well with the CFDM predictions for an asymmetric bifurcation. These results validate the simplified ASPM and the complex CFDM. ASPM predicts higher Sherwood number with a flat velocity inlet profile compared to a parabolic inlet velocity profile. Sherwood number increases with the inlet average velocity, wall mass transfer coefficient, and bifurcation angle since the boundary layer grows slower in the parent and daughter branches.     

Multilaboratory particle image velocimetry analysis of the FDA benchmark nozzle model to support validation of computational fluid dynamics simulations

This study is part of a FDA-sponsored project to evaluate the use and limitations of computational fluid dynamics (CFD) in assessing blood flow parameters related to medical device safety. In an interlaboratory study, fluid velocities and pressures were measured in a nozzle model to provide experimental validation for a companion round-robin CFD study. The simple benchmark nozzle model, which mimicked the flow fields in several medical devices, consisted of a gradual flow constriction, a narrow throat region, and a sudden expansion region where a fluid jet exited the center of the nozzle with recirculation zones near the model walls. Measurements of mean velocity and turbulent flow quantities were made in the benchmark device at three independent laboratories using particle image velocimetry (PIV). Flow measurements were performed over a range of nozzle throat Reynolds numbers (Re(throat)) from 500 to 6500, covering the laminar, transitional, and turbulent flow regimes. A standard operating procedure was developed for performing experiments under controlled temperature and flow conditions and for minimizing systematic errors during PIV image acquisition and processing. For laminar (Re(throat)=500) and turbulent flow conditions (Re(throat)≥3500), the velocities measured by the three laboratories were similar with an interlaboratory uncertainty of ～10% at most of the locations. However, for the transitional flow case (Re(throat)=2000), the uncertainty in the size and the velocity of the jet at the nozzle exit increased to ～60% and was very sensitive to the flow conditions. An error analysis showed that by minimizing the variability in the experimental parameters such as flow rate and fluid viscosity to less than 5% and by matching the inlet turbulence level between the laboratories, the uncertainties in the velocities of the transitional flow case could be reduced to ～15%. The experimental procedure and flow results from this interlaboratory study (available at http://fdacfd.nci.nih.gov) will be useful in validating CFD simulations of the benchmark nozzle model and in performing PIV studies on other medical device models.     

Importance of flow division on transition to turbulence within an arteriovenous graft

Transitional blood flow in an arteriovenous graft under various conditions of flow division was examined through direct numerical simulation. This junction consists of an inlet vessel (prosthetic graft) connected to a host vessel (vein) at an acute angle (21.6 degrees ). Inlet Reynolds numbers, based on mean velocity and graft inlet diameter, ranged from 800 to 1400. Various flow divisions between the two ends of the host vessel (i.e., the proximal venous segment, PVS, and distal venous segment, DVS) were considered (PVS:DVS ratios of 100:0, 85:15, 70:30 and 115:(15)). The numerical technique employed the spectral element method which is a high-order discretization ideally suited to the simulation of transitional flows in complex domains. High velocity and pressure fluctuations were observed for the PVS:DVS=70:30 and 85:15 cases and absent from the 100:0 and 115:(15) cases; the results indicate the importance of flow division on the development of turbulence in this junction. Transition to turbulence was observed at Reynolds numbers as low as 1000 and 800 under flow divisions of 85:15 and 70:30, respectively, significantly lower than the critical value of 2100. The frequency spectra of velocity fluctuations indicated a significant intensity within the frequency range of approximately 300Hz downstream of the junction. An adverse pressure gradient developed in the PVS when graft inflow divided into opposite directions in the junction. This pressure gradient had a destabilizing effect on the flow and enhanced transition to turbulence in the PVS. These findings suggest that measurements of in vivo flow rates at the inlet and outlets are critical for the accurate prediction of arteriovenous hemodynamics. A potential clinical application of these results might be to close off the DVS during graft construction to ensure a 100:0 flow division.     

Role of tracheal and bronchial circulation in respiratory heat exchange

Due to their anatomic configuration, the vessels supplying the central airways may be ideally suited for regulation of respiratory heat loss. We have measured blood flow to the trachea, bronchi, and lung parenchyma in 10 anesthetized supine open-chest dogs. They were hyperventilated (frequency, 40; tidal volume 30-35 ml/kg) for 30 min or 1) warm humidified air, 2) cold (-20 degrees C dry air, and 3) warm humidified air. End-tidal CO2 was kept constant by adding CO2 to the inspired ventilator line. Five minutes before the end of each period of hyperventilation, measurements of vascular pressures (pulmonary arterial, left atrial, and systemic), cardiac output (CO), arterial blood gases, and inspired, expired, and tracheal gas temperatures were made. Then, using a modification of the reference flow technique, 113Sn-, 153Gd-, and 103Ru-labeled microspheres were injected into the left atrium to make separate measurements of airway blood flow at each intervention. After the last measurements had been made, the dogs were killed and the lungs, including the trachea, were excised. Blood flow to the trachea, bronchi, and lung parenchyma was calculated. Results showed that there was no change in parenchymal blood flow, but there was an increase in tracheal and bronchial blood flow in all dogs (P less than 0.01) from 4.48 +/- 0.69 ml/min (0.22 +/- 0.01% CO) during warm air hyperventilation to 7.06 +/- 0.97 ml/min (0.37 +/- 0.05% CO) during cold air hyperventilation.     

Low Reynolds number equi-bifurcation flow in a two-dimensional channel

The fluid flow in some physiological vessels such as the blood flow in blood vessels and the air flow through bronchi and bronchioles in the lungs undergoes a large number of bifurcations. The understanding of the bifurcation flow is of importance for a better comprehension of its effect in the blood and the air circulatory systems of the living body. The Reynolds number of flow in large blood vessels and bronchi is high and fluid inertia plays a dominant role in the bifurcation flow in such vessels. In small caliber blood vessels such as arterioles and capillaries, and bronchioles, the Reynolds number of flow is quite low and the effect of fluid inertia is negligible compared to the pressure and shear forces. In order to have a quantitative understanding of the bifurcation flow at low Reynolds numbers, the low Reynolds number equi-bifurcation flow in a two-dimensional channel at zero bifurcation angle is studied based on the Stokes approximation. The solution of the problem is posed as an infinite series, where the truncated version is used in numerical calculations. The results of this analysis is discussed in connection with the bifurcation flow of blood in small caliber blood vessels and that of the air in bronchioles in the lung.     

A numerical simulation of steady flow fields in a bypass tube.

Steady flow in a complete by-pass tube was simulated numerically. The study was to consider a complete flow field, which included both the by-pass and the host tubes. The changes of the hemodynamics were investigated with three parameters: the inlet flow Reynolds number (Re), anastomotic angle (alpha) and the position of the occlusion in the host tube. The baseline flow field was set up with Re=200, alpha=45 degrees and the centered position of occlusion. The parametric study was then conducted on combination of Re=100, 200, 400, alpha=35 degrees, 45 degrees, 60 degrees, 75 degrees, 90 degrees and three occlusion positions: left, center and right. It was found that in the baseline case, large slow/recirculation flows could be seen in the host tube both upstream and downstream of the occlusion. The separation points were on the opposite walls to the junctions. Recirculation zones were also found near the toe and in the proximal outer wall of the by-pass tube. Their sizes were about one diameter of the tube or smaller. In some cases, pairing vortices could be seen in the host tube upstream of the occlusion. The shear rate distribution associated with the flow fields was presented. The flow pattern obtained was agreeable to those observed experimentally by other investigators. The difference of the flow fields between a complete bypass and simple anastomosis was discussed. The present numerical code provides a preliminary simulation/design tool for bypass graft flows.     

The effect of Reynolds number on the propulsive efficiency of a biomorphic pulsed-jet underwater vehicle

The effect of Reynolds number on the propulsive efficiency of pulsed-jet propulsion was studied experimentally on a self-propelled, pulsed-jet underwater vehicle, dubbed Robosquid due to the similarity of its propulsion system with squid. Robosquid was tested for jet slug length-to-diameter ratios (L/D) in the range 2-6 and dimensionless frequency (St(L)) in the range 0.2-0.6 in a glycerin-water mixture. Digital particle image velocimetry was used for measuring the impulse and energy of jet pulses from the velocity and vorticity fields of the jet flow to calculate the pulsed-jet propulsive efficiency, and compare it with an equivalent steady jet system. Robosquid's Reynolds number (Re) based on average vehicle velocity and vehicle diameter ranged between 37 and 60. The current results for propulsive efficiency were compared to the previously published results in water where Re ranged between 1300 and 2700. The results showed that the average propulsive efficiency decreased by 26% as the average Re decreased from 2000 to 50 while the ratio of pulsed-jet to steady jet efficiency (η(P)/η(P, ss)) increased up to 0.15 (26%) as the Re decreased over the same range and for similar pulsing conditions. The improved η(P)/η(P, ss) at lower Re suggests that pulsed-jet propulsion can be used as an efficient propulsion system for millimeter-scale propulsion applications. The Re = 37-60 conditions in the present investigation, showed a reduced dependence of η(P) and η(P)/η(P, ss)on L/D compared to higher Re results. This may be due to the lack of clearly observed vortex ring pinch-off as L/D increased for this Re regime.     

Computational Analysis of Micron-particle Deposition in a Human Triple Bifurcation Airway Model

Steady laminar axisymmetric inhalation flow and wall deposition of micron-size particles in representative triple bifurcation airways have been simulated using a commercial finite-volume code with user-enhanced programs. Assuming spherical non-interacting particles (3 μm≤ d p ≤7 μm), various inlet Reynolds numbers (Re=500-2000) and Stokes numbers (St=0.02-0.23) were considered. The resulting particle deposition patterns were analyzed and then summarized in terms of deposition efficiencies, i.e. DE=DE(Re,St) Surprisingly high DE-values occur at relatively low Reynolds numbers (e.g., Re=500 ) in the third bifurcation. The quantitative results are of interest to researchers either conducting health risk assessment studies for inhaled particulate pollutants or analyzing drug aerosol inhalation and deposition at desired lung target sites.