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Gas exchange in human lungs is established by several flow mechanisms. In the present study, the features of gas displacement in the distal bronchioles of a human lung are investigated by both numerical calculation and experimental observation with particle image velocimetry. The effect of respiration frequency is considered, such as high frequency oscillatory ventilation. By comparing the obtained results, it has been found that the redistribution of gas is attributed to irreversible flow, which is remarkable in higher frequencies oscillation with even lower tidal volumes. Owing to the continuous driving, a time-averaged net flow was induced and intensified by the oscillation. Thus, the gas in the centre region penetrated the deeper region and the outer gas was evacuated to the upper region. Consequently, this streaming contributes to prompt gas replacement. Furthermore, we analysed the effect of the respiration wave form to consider the flow acceleration. From this inspection, it was found that the enhanced inertial force tends to encourage the irreversible flow.

Air flow in lungs exhibits various flow patterns, in terms of frequency and tidal volume, involving normal breath and artificial respiration. For example, during rest breathing in a healthy lung, the tissue expansion during the inspiration phase causes negative pressures in the peripheral airspaces, i.e. there is a pressure gradient between the alveolar air and the environment. On the other hand, exhalation is a passive process that is achieved through recoil of the lung and the chest wall by reducing the lung volume. The motion establishes a positive alveolar pressure; hence, a positive pressure gradient evacuates the air from the lung [

A schematic of human respiration system is shown in

sacs 23 times as demonstrated in

Research concerning human respiration system plays an important role in biology, physiology, fluid mechanics, and pharmacology. In the recent research into fluid mechanics, there are several research subjects to be considered regarding lung airflow, e.g. turbulence, airway resistance, interaction between the lung geometry and airflow, the influence of the upper airways and peripheral airways on flow, high-frequency oscillatory ventilation, shear stress, and airway expansion and deformation. In the present study, we focus on the irreversible flow within peripheral airways when high frequency oscillatory ventilation (HFOV) is adopted. HFOV is a unique approach as one of techniques regarding artificial ventilation, which oscillates the gas much faster and shallower than our rest breathings or conventional ventilations.

HFOV causes the change in flow regimes as the convective regime extends more deeply into the small airways. Hence, the airflow becomes complex and turbulent in each airway. Airway flow is dominated by different factors depending on the generation number, i.e. inertia forces and convections are more dominant in the upper area. However, intermediate lung region and peripherals, viscous forces and molecular diffusions are more crucial. Chang HK summarized several effective mechanisms of HFOV, i.e. turbulence, Taylor dispersion, asymmetric velocity profile, pendelluft flow, coaxial flow, and molecular diffusion [

HFOV has attracted considerable research interest because of its peculiar working pattern, which is very different from conventional ventilations or our normal breathing, and effect on ventilation as well. Recently, with the development of numerical calculation and experiment techniques, more detailed and subtle airflows by HFOV have been discovered. Tanaka et al. found that the secondary flow contribution was remarkable in the left main stem bronchus when compared to the right main stem bronchus [

The influence of asymmetric airway compliances on redistribution of gas particles during the HFOV has been numerically investigated by Hirahara et al. [

The studies mentioned above mainly demonstrate airflows within particular airways. Many of them focused on the complicated flow mechanism in the upper lung airways, except for the small peripheral airways. Additionally, an interest of HFOV is that the tidal volume is usually lower than the dead space of a conducting region. This fact indicates that the fresh air can barely enter or is not delivered directly to the respiratory region. However, HFOV is still effective as a prompt ventilation system and is widely used in the clinical field. In addition, there may be progressive patterns to push fresh gas deeper into the distal region to overcome the shortage of tidal volume. From those aspects, the present work focuses on the flow features at the transition zone about G18, i.e. between the conducting and respiratory airways, in order to survey how fresh air enters this deep region where tidal volume cannot directly reach.

We have preliminary calculated the values of the Reynolds number (Re), the Peclet number (Pe), and the Womersley (Wo) number for every generation according to the geometrical sizes based on Weibel’s model and oscillatory velocity under HFOV (sinusoidal, 10 Hz, 15 Hz, and 20 Hz, and a 150 mL tidal volume) and rest breathing (sinusoidal, 0.2 Hz with a 500 mL tidal volume) [

Haselton and Scherer experimentally investigated oscillatory flow in branching airways where the diffusion coefficient was negligible under an extremely low Reynolds number. In their report, a bulk exchange of aerosol across the reference origin was confirmed while the total flow was zero. Despite their study being conducted in a branching airway whose internal diameter was larger than the trachea, the resultant mechanism was expected to act throughout the whole respiratory tract [

Moreover, considering the effect of inertial force, we hypothesize that if the inertia force of gas is somehow enhanced, the gas will be thrust more deeply into the downstream airways and more turbulence will be induced in the upper airways. This fact may benefit gas exchange; therefore, the ventilation efficiency will consequently be improved. In order to strengthen the inertia force, an available approach is to feed the gas with a shock-like velocity profile while maintaining the tidal volume unchanged. Accordingly, four gas-feeding patterns, i.e. sinusoidal respiration (SIN), steep inspiration (SI), steep expiration (SE), and steep inspiration and expiration (SIE) will be applied and analysed numerically to verify the hypothesis.

In this study, numerical calculation and particle image velocimetry (PIV) measurements are carried out for 1) revealing the gas replacement mechanism in peripheral lung airways (G18-G20) under HFOV application, and evaluating its significance to respiration by comparing with conventional ventilation (CV) or normal breathing; and 2) demonstrating the dislocation of fluid parcels in peripheral lung region caused by steep gas feeding patterns in order to estimate its influence on ventilation efficiency. Here, it is necessary to remember that molecular diffusion was neglected in order to inspect the influence of flow convection in the present survey.

Research of gas flow in lung airways is extremely complex due to the intricate anatomical structure, various breathing conditions, and different physiological features of individual, etc. The anatomical lung models developed by Weibel [

he termed the generated branch numbers as orders. Weibel’s model is considered more suitable for this study due to its symmetry and representativeness, and it is helpful to obtain more general flow features by neglecting the irregular and over-complex airway geometry.

A numerical model consisting of mother-daughter-granddaughter branches from G18 to G20 is shown schematically in

The numerical model has been meshed into 489,362 polyhedral cells with 10 progressive sub-prism layers. The typical mesh size is 2 × 10^{−}^{5} m over all regions. In this survey, a 3-generations airway model is adopted for investigation; however, we will not discuss the flow within the granddaughter airway. The influence of the granddaughters’ asymmetry on airflow in a branch model has been investigated by Soni et al. [

Three important non-dimensional parameters that reflect flow characteristics are Reynolds number Re, Womersley number Wo, and Peclet number Pe, i.e.

where U, R, υ, ω, and α indicate cross sectional mean velocity, airway radius, kinematic viscosity, angular frequency, and molecular diffusivity, respectively.

The simulation and post-processing were implemented with Star-ccm+®, which is based on the FVM (finite volume method) algorithm. The governing equations for the present problems are represented in the ordinal Navier-Stokes and continuum equations.

where,

Moreover, the method fresh air enters the peripheral lung region is expected to be clarified for better understanding the flow mechanisms in a peripheral lung under a HFOV application. The volume of fluid (VOF) method is considered a proper technique that traces the interface of fluids in lattices without moving the computational grid. Normally, a VOF scheme is used to distinguish different species of fluid, whereas in this case, VOF is adopted to clearly determine the net flow through the deformation of the interface between same species. VOF resolves the gas replacement with a free- surface condition on the free boundary. In the calculation, a nominal function with a value between 0 and 1 is used to indicate which part of the cell is filled with fluid. It belongs to the class of Eulerian multiphase model, and was firstly brought forward on paper by Hirt and Nichols [

As depicted in _{P}) is estimated as the volume of the fresh gas that enters the deeper region. The volume varies with time; hence, the penetration volume is a time-dependent variable that also represents the intensity of the bulk flow. The volume of net flow (V_{nf}) indicates the amount of fresh gas that has been left in the following deeper region after a certain cycles of oscillation. V_{nf} is a time-averaged value and reflects the strength of steady streaming. Furthermore, if the area near the bifurcation is divided into 4 fluids as shown in

and dislocations among them will be observed more precisely. Meanwhile, the Lagrangian tracing technique (

The inlet located at the top of G18 inhales and discharges air flow as a velocity boundary. The four outlets at the bottom of G20, on the other hand, were assigned as the pressure boundaries. Now, we consider the boundary condition for the inlet in cylindrical coordinates. Here, the z direction is assumed as the pipe axis. The governing equation of axial oscillatory flow is presented in Equation (6), where u_{z}, t, ρ, G, υ, and r denote velocity in the z direction, time, fluid density, pressure gradient, kinematic viscosity and radial distance, respectively.

If we supply the pressure oscillation, the pressure term is represented by the following relation.

where, K is the acceleration amplitude per unit mass; ω denotes the angular frequency. Then, the solution of Equation (6) can be obtained as

where J_{0} is the 0th order of Bessel function; i represents the imaginary number. R is the inner radius of the channel. By approximation for a small Womersley number (

where u_{c} is the velocity amplitude of central axis in oscillatory Poiseuille flow at the inlet. In this way, the tidal volume and oscillation frequency can be regulated by changing the values of u_{c} and ω. For instance, Equation (10) guarantees 50 mL tidal volume for sinusoidal oscillation with different frequencies, where R = 2.5 × 10^{−}^{4} (m) indicates the radius of G18 airway.

Next, as stated before, a pulsated flow velocity was assigned for inlet boundary to inspect the influence of enhanced inertial force. Here, four different inlet velocity waveforms including sinusoidal (SIN), steep inspiration (SI), steep expiration (SE), and steep inspiration and expiration (SIE) under the same frequency of 10 Hz and tidal volume of 50 mL are configured for the inlet boundary. The u_{c} is specified in different shapes of waveform as shown in

Type | Time range (s) | a | b | c |
---|---|---|---|---|

SI | 0 < t ≤ 0.0297 | 0.23825513 | 0.008 | 0.003 |

0.0297 < t ≤ 0.1 | −0.0796739 | 0.05 | 0.009 | |

SE | 0 < t ≤ 0.0703 | 0.0796739 | 0.0203 | 0.009 |

0.0703 < t ≤ 0.1 | −0.23825513 | 0.0783 | 0.003 | |

SIE | 0 < t ≤ 0.05 | 0.23825513 | 0.008 | 0.003 |

0.05 < t ≤ 0.1 | −0.23825513 | 0.058 | 0.003 |

SIN

(11)

Steep velocities

For the four outlets at the bottom, the gas pressure is assigned as the boundary condition by Java coding in Star CCM+, which consists of lung compliance C, laminar resistance in the airway R_{j} and volumetric flow rate in the bronchi for a given generation q as demonstrated in Equation (13). The lung compliance C is defined as the ratio of volume difference ΔV to pressure difference ΔP. Rigid wall is selected for the peripheral wall as boundary condition.

where the suffix i indicates the generation number of interest, and j is an index from i + 1 to the terminal.

As illustrated in Figures 10-12, a doubly bifurcated airway model from G18 to G20 has been fabricated and prepared for PIV measurement based on the anatomical dimensions of Weibel’s model. The airways are cut out from a black anodized aluminium plate, and the widths of G18, G19, and G20 are 500 μm, 450 μm and 400 μm, respectively. The thickness of the plate is 500 μm. The length of G19 is 1.2 mm along the centre line, G18 and G20 are long enough for the flow to fully develop. The angles of upper and lower junctions are 70˚ and 60˚, respectively.

The fresh air is supplied from a HFOV device to the airway model via a buffer tank which simulates the lung space above G18 (dead space) and serves as a particle reservoir. For the outlets at the bottom, four identical compliances are achieved by using truncated elastic tubes whose compliances are all approximately 1.92 × 10^{−6} mL/Pa. A

CMOS camera (XS-5, 1280 pixels × 1024 pixels resolution, IDT) and a micro lens (VQ-Z50, KEYENCE) are used for image acquisition, a double-pulsed Nd-YAG laser (Solo Ⅲ PIV 15, 532 nm wave length, 50 mJ intensity, New Wave Research) was adopted to illuminate the airway channels at an angle of 30˚ from the top, as illustrated in

The experiment commenced immediately after the particles were fed into the device. Then, 100 pairs of phase-locked images were subsequently obtained for each delay. Thus, the ensemble velocity can be calculated from the acquired data. The phase-locked data were obtained by means of shifting the trigger signal by 1/16T. Both the Womersley number and Reynolds number were less than 10 under this condition, which implies the airflow does not include high order turbulence. The velocity fields were obtained as ensemble phase lock sampling. The images acquisition period was set as 1/16T. After acquiring all the particle images and calibration plate (grid size 0.1 mm) image, a PIV software (pro VISION, IDT) was used for velocity reconstruction. The interrogation size was set at 64 pixels × 64 pixels to guarantee more than 10 particles inside, and the mesh size was set as 16 pixels × 16 pixels.

We assume the pattern of CV is identical to our rest breathing (sinusoidal oscillation, 0.2 Hz with 500 mL tidal volume), while the HFOV was adopted using a 10 Hz frequency and 50 mL tidal volume. The flow is laminar and parabolic quasi-steady within the interrogation region for both CV and HFOV. However, obvious differences between these two schemes have been verified. The CV takes 5 seconds for one-cycle oscillation, in contrast, the HFOV accomplishes 50 cycles of oscillation in the same duration.

can even pass through G20 during respiration, but after the extensive stretching and contracting, almost all the particles return to the vicinity of original locations as illustrated in the last instance. Therefore, bulk flow is considered as the main mechanism for gas delivery, and the time averaged streaming is not obvious in CV.

In a similar way, the movement of particles at different instants are demonstrated in

In the VOF scheme, as mentioned above, the effect of molecular diffusion was neglected to discuss the convective effect. XZ plane is selected as the observation plane.

is similar to what

On the other hand, in the case of HFOV as illustrated in

the core gas moves faster than the peripheral gas in the airways, and the peak value is approximately 0.08 m/s in both phases. The magnitude is higher than the numerical result of 0.061 m/s. This fact may be caused by a difference in the inlet boundary conditions between the calculations and experiment.

Similar to the numerical calculations, the oscillated gas flows up and down symmetrically for all phases of the experiment. The particle displacements are obtained by integrating the individual particle velocity in a cycle, as shown in

The penetration volume V_{P}, has been calculated using the VOF technique as demonstrated in _{nf} directly reflects the intensity of the net flow of fresh gas; therefore, it could act as a criterion for ventilation efficiency of HFOV. Here, we adopt the calculation scheme as shown in _{nf} = 3.98 × 10^{−}^{5} ml) for deeper generations after the one-cycle oscillation. In contrast, although HFOV oscillates a much smaller amount of gas, the flow leaves more and was stretched for fresh gas (V_{nf} = 4.67 × 10^{−}^{5} ml) in the deeper regions after an identical duration. Moreover, HFOV rearranges the gas in a

more orderly fashion as shown in Figures 14-18. _{T} is the volume of air displaced between inhalation and exhalation at trachea, while local tidal volume indicates the volume of air displaced between inhalation and exhalation at G18.

Based on the obtained results, HFOV thrusts the core gas downwards and the peripheral gas upwards much more than CV. Here, the net flow indicates a time-averaged value that the new air penetrates. Hence, it does not involve simultaneous flows in opposite directions as in coaxial counter-flows or out-of-phase flows [

Although the volume of net flow in one distal bifurcation is small under HFOV, it may take place in every dichotomous lung branch, hence, the large number of branches boost the significance of the net flow. For example, the number of G18 airways is on the order of approximately 2^{18} in a healthy lung, so the total amount of V_{nf} becomes reasonably considerable. Consequently, the answer to our initial question is provided; the net flow of steady streaming works to overcome the tidal-volume shortage of HFOV and delivers fresh air to the respiratory lung region. Steady streaming is hereby deemed as an important contributor to the effect of HFOV.

The net flows caused by steep velocities will be illustrated for comparing ventilation efficiency of steep gas-feeding in HFOV. The boundary conditions, except for the inlet, are identical to the previous HFOV calculations.

Conventional Ventilation | HFOV | |
---|---|---|

f (Frequency) | 0.2 Hz | 10 Hz |

V_{T} (Tidal Volume) | 500 ml | 50 ml |

Local T_{V} | 500 ml/2^{18} | 50 ml/2^{18} |

V_{nf} (Volume of net flow) | 3.98 × 10^{−}^{5} ml | 4.7 × 10^{−}^{5} ml |

Fresh gas movement | shallow | deep |

especially the SIE, produces the strongest net flow, thereby delivers more fresh gas downwards and sharpens the interface more than the other patterns.

_{G}_{18}), as shown in _{G}_{18} = 0.00023 mL. At the end of a three cycle oscillation, the steep gas-feeding uplifts V_{nf}, especially SIE that boosts V_{nf} by 223% compared to SIN, which is generally used in current HFOV. Additionally, SI and SE improve V_{nf} by 134% and 126%, respectively. These numerical investigations indicate that the enhanced inertia force is capable

of accelerating the gas, i.e. the rapid accelerated operation pushes fresh gas into the deep lung region and improves the ventilation efficiency of current HFOV.

In order to clarify the effect of the steepening gas feeding pattern, a discussion of the particle trajectory during the respiration is provided. As demonstrated in

HFOV drives the core gas downwards and evacuates the peripheral gas upwards in distal lung airways much more apparently and neatly than CV does after oscillations. The occurrence of time-averaged net flow has been investigated and confirmed by means of PIV measurement and numerical calculations. The net flow can be considered as an integrated result of asymmetric velocity profiles; therefore, it may further be affected by the non-uniformity of airway geometry. The steady streaming conceived in the net flow contributes gas replacement as one of the factors even though HFOV is operated with a small tidal-volume. Although the volume of net flow is quite low in a single bifurcation at the peripheral lung region, the total amount becomes considerable because of the enormous number of bifurcations in this region as well as the cumulative effect along the stem. Additionally, steady streaming is expected to act throughout the whole respiratory tract since it progresses when the gas is oscillated with high frequency. Consequently, steady streaming is considered as a significant contributor to the efficiency of HFOV. Therefore, a steep gas-feeding scheme enhances the irreversibility of the oscillatory flow and increases the streaming effects.

Han, B. and Hirahara, H. (2016) Effect of Gas Oscillation-In- duced Irreversible Flow in Transitional Bronchioles of Human Lung. Journal of Flow Control, Measurement & Visualization, 4, 171-193. http://dx.doi.org/10.4236/jfcmv.2016.44015

C: Compliance [m^{3}/Pa]

f: Frequency [Hz]

G: Pressure gradient [Pa/m]

J_{0}: 0^{th} order of Bessel function

K: Acceleration amplitude per unit mass [m/s^{2}/kg]

p: Pressure [Pa]

Pe: Peclet number

q: Flow rate [m^{3}/s]

r: radial position [m]

R: Radius of airway [m]

Re: Reynolds number

R_{j}: airway resistance [Pa∙s/m^{3}]

u: Velocity in x-direction [m/s]

U: cross sectional mean velocity [m/s]

v: Velocity in y-direction [m/s]

V: Volume [m^{3}]

V: Velocity [m/s]

w: Velocity in z-direction [m/s]

Wo: Womersley number

α: molecular diffusivity [m^{2}/s]

ρ: Gas density [kg/m^{3}]

υ: Kinematic viscosity [m^{2}/s]

ω: Angular frequency [rad/s]

c: at the central axis

G: Generation

i: ith generation of lung

j: jth generation of lung

P: Penetration

T: Tidal

z: z-direction