Microflows in two-generation alveolar cells at an acinar bifurcation

Abstract

The alveolus is a basic functional unit of the human respiratory system, and the airflow in the alveoli plays an important role in determining the transport and deposition of particulate matter, which is crucial for inhaled disease diagnosis and drug delivery. In the present study, taking advantage of the precise control ability of the microfluidic technique, a rhythmically expanding alveolar chip with multiple alveoli in two generations is designed and both the geometric and kinematic similarities are matched with the real human respiration system. With the help of a micro-PIV measurement system, the microflow patterns inside each alveolus can be studied. The observed vortex and radial flow patterns and the discovery of stagnant saddle points are similar to those captured in our previous platform with only one alveolus [Lv et al., Lab Chip 20, 2394–2402 (2020)]. However, the interactions between multiple alveoli also uncover new phenomena, such as the finding of stagnant saddle points in non-vortex flow patterns and significant differences in the flow pattern around the points between the time of T/4 and 3T/4. The obtained results could enrich the understanding of microflow in a whole alveolar tree with multiple generations.

I. INTRODUCTION

The proportion of urban populations suffering from respiratory diseases is increasing, and harmful particles, such as PM2.5, are a constant threat to human health. The air and particles inhaled through the mouth and nose gradually move into the alveoli, which are the basic respiratory functional units with complex internal flow (Tsuda et al., 2008). The flow pattern plays an important role in the transport path and deposition location of aerosol particles in the alveoli (Tsuda et al., 1995). To cope with various respiratory diseases, there is an urgent need to gain an in-depth understanding of the air flow characteristics in the alveoli to provide the necessary theoretical basis for disease diagnosis and targeted inhalation therapy (Ciloglu et al., 2017; Monjezi et al., 2017; and Shachar-Berman et al., 2019).

Most of the research studies on the airflow characteristics in the pulmonary alveolar system are still based on numerical simulations due to the difficulty of establishing realistic physical models (Haber et al., 2000; Haber et al., 2010; Henry et al., 2012; Henry and Tsuda, 2010,2016; Hofemeier and Sznitman, 2014; Sznitman et al., 2007; Tsuda et al., 1994; and Tsuda et al., 1996). A complete human alveolar airway model was developed, and bifurcated units were constructed to represent the 16–23 generations (Kolanjiyil and Kleinstreuer, 2019). The alveolar flow patterns from proximal to distal during a cycle of expiratory and inspiratory phases were obtained by numerical simulation analysis. The flow pattern of the lungs suffering from emphysema can vary due to diseases such as COPD (COPD refers to a group of diseases that cause airflow blockage and breathing-related problems. It includes emphysema and chronic bronchitis). Based on the numerical simulations to model six generations of airways (polyhedral shaped alveolar units), Oakes' group found that in the alveoli with emphysema, the flow lines are smoother due to the absence of alveolar wall spacing (Oakes et al., 2016). Sznitman et al. similarly modeled a multi-generation airway tree using polyhedral shaped alveolar units for spatially tightly arranged filling and found that the flow ratio was an important factor directly affecting the alveolar flow field across generations (Sznitman et al., 2009). The Reynolds number of the flow in the alveoli is low (much less than 1) and the conventional view is that this flow is a fully reversible Stokes flow (Cinkotai, 1974). However, Tsuda et al. predicted the existence of chaotic flow in the alveoli marked by stagnant saddle points through numerical simulations (Henry et al., 2002; Tsuda et al., 1995; and Tsuda et al., 2002), revealing the irreversibility of the flow in the alveoli.

In addition, Hofemeier and Sznitman conducted an in-depth numerical study of the local deposition sites and convection-diffusion interactions of ultrafine particles in multi-generational acinar networks with anisotropic expansion (Hofemeier and Sznitman, 2015; and Hofemeier and Sznitman, 2016). It is noteworthy that the above models were based on space-filling geometrical polyhedral ones, while morphometrically realistic sub-acinar units with larger scale were recently derived (Hofemeier et al., 2018; and Koullapis et al., 2020). Hofemeier et al. designed a morphometrically faithful model to capture more details of human acinar morphometry, which gave a high-resolution and 3D spatial–temporal data on aerosol transport and deposition (Hofemeier et al., 2018). Furthermore, in the latest study, Koullapis et al. utilized a previously established deep lung (DLM) 3D model to investigate the effects of breathing profile, breath-hold, and gravity orientation in the deep airway (Koullapis et al., 2020).

On the other hand, many experimental platforms have also been built to study the air flow pattern in the alveoli, including in vivo lung tests in mice (Butler and Tsuda, 2005; and Tsuda et al., 2002), scale-up (Berg and Robinson, 2011; Berg et al., 2010; Chhabra and Prasad, 2011; Sera et al., 2021; Tippe and Tsuda, 2000), and real-size models (Dong et al., 2021; Fishler et al., 2015; Fishler et al., 2013; Fishler et al., 2017; and Lv et al., 2020). In recent years, the booming development of microfluidics has offered new possibilities to study the microflow in the alveoli with better similarity in both geometry and dynamics. Fishler et al. (2013) developed a pulmonary alveolar system on a microfluidic chip to capture the transition of alveolar flow patterns from vortex-like to radial flow with an increasing number of alveolar ductal generation. A subsequent article also designed a platform of acinus-on-a-chip for flow field and particle deposition studies (Fishler et al., 2015), while these studies did not take into account the variation of alveolar tube dimensions across generations. Based on the microfluidic technique and precisely controlling the chamber pressure and liquid flow rate, our group was able to develop a rhythmically expanding alveolar chip with dynamic similarity matched with the real case (Lv et al., 2020). The stagnant saddle points were experimentally detected in a single alveolus for the first time. However, the detailed interactions between multiple alveoli and the effects of them on the microflow patterns and stagnant saddle points detection still remain unknown. The present work tries to extend the study of an alveolar chip with only one alveolus to the one with multiple alveoli. Therefore, a rhythmically expanding alveolar chip with multiple alveoli in two generations is designed and both the geometry and kinetic similarities are matched with a real human respiration system. A micro-PIV measurement system is applied to detect the details of microflow patterns inside each alveolus.

II. METHODOLOGY

A. Two-generation alveolar chip model

Figure 1 illustrates a two-dimensional design of a two-generation alveolar chip, and the structure is designed according to the classical dichotomous tree model of the pulmonary alveolar system (Weibel et al., 2005), consisting of an alveolar duct with a rectangular cross section, an alveolus of a partial cylinder, and a rectangular chamber surrounding the alveolus. Although alveoli are generally considered to be spherical (Haefelibleuer and Weibel, 1988), the spherical alveoli model with the same size and expansion effect as the real one cannot be produced due to the limitation of micro- and nanoprocessing. So, this approximate two-dimensional or quasi-three-dimensional structural design is adopted, which has been demonstrated to be reasonable in previous studies (Lv et al., 2020).

FIG. 1.

Schematic of the (a) two-generation alveolar chip structure, (b) two-layer chip construction consisting of PDMS upper layer and glass lower layer, (c) two-dimensional channel of the alveolar chip, and (d) entire experimental measurement platform. Note that the photo of a fabricated chip is also shown in (a).

To avoid the invariation of initial flow conditions, the fluid would pass a sufficient entrance length in a buffer pipe with a fully developed pattern before flowing through the alveolar opening area. At this moment, part of the fluid in the channel flows into or out of the alveoli with the expansion and contraction movement of the alveoli. As the flow exchange occurs, a specific flow pattern is formed in the alveoli. When the fluid flows from one generation to the next, it splits into two branches at the Y-shaped bifurcation between the two generations, and each bundle continues to repeat the above motion. Due to the difference in flow rate and expansion rate (Dong et al., 2020), alveoli located at different generations would display different flow patterns. The alveolar chip consists of two layers, of which the upper layer contains microchannels, a structure formed by soft lithography and PDMS(Polydimethylsiloxane, called PDMS or dimethicone, is a polymer widely used for the fabrication and prototyping of microfluidic chips). casting, and the lower layer is a thin glass sheet for sealing. These two layers are bonded together to form the complete chip, as shown in Fig. 1(b).

The pulmonary bronchial network in the human body is physiologically divided into 23 generations, and the alveoli attached to the alveolar ducts start to appear from the 15th generation. Starting with the alveoli of the 15th generation up to the penultimate (22nd) generation of alveoli, the alveolar ducts of each generation divide into two finer branched ends in a Y-shape (Haefelibleuer and Weibel, 1988; and Weibel et al., 2005), and our two-generation alveolar model is designed based on this structure. The alveolus geometry shown in Fig. 1(c) is designed according to the anatomical dimensions of the last generation (23rd generation) of human alveoli. In the present study, although the same alveolus geometry is applied for different generations, the flow rate and expansion amplitude are precisely controlled to represent the specific flow conditions at each generation. The alveolar tube height (i.e., channel height), tube width, wall thickness, and alveolus radius are set as 240, 240, 45, and 225 μm, respectively. The main reason of assigning a wall thickness larger than the real situation is to increase the durability of the alveolar chip during repeated expansion and contraction movements.

B. Geometry and dynamic similarity

A complete respiratory cycle consists of two phases: inhalation and exhalation of air. In a calm breathing state, the amount of gas entering the alveoli during each breath is about 70% of the total inhalation volume in adults, i.e., 350 ml, and a respiratory cycle is about 4 s (Dong et al., 2021; Fishler et al., 2017; van Ertbruggen et al., 2008; Weibel et al., 2005; and Zhang et al., 2022). Based on the volume of air inhaled and the total number of alveoli on the bifurcated structures of the pulmonary glandular alveolar system, our previous studies have calculated the theoretical flow rate in the alveolar ducts for each generation (Lv et al., 2020). The flow rate through a breathing cycle is modeled as a sinusoidal function, and the peak values at each generation are shown in Table I. The parameter settings of the alveolar flow experiments for generations 19–22 involved in this study refer to the data in this table.

TABLE I.

Air flow parameters in an alveolus at different generations [adapted from ^Lv et al. (2020)].

Gen. i	19	20	21	22	23
The peak value of ductal flow rate Qmax (μl/s)	0.50	0.26	0.13	0.06	0.02
Ratio of alveolar to ductal flow rate λ (%)	0.13	0.27	0.63	1.41	4.25

To model the respiratory flow in a real human body by means of fluid motion in an alveolar chip, the two states of motion must be matched in terms of geometric similarity and dynamic similarity. Two-generation alveolar chips are designed to follow the anatomical dimensions of human alveoli to achieve geometric similarity, and the two fundamental dimensionless parameters affecting fluid motion within the alveoli, i.e., Reynolds number Re and Womersley number Wo, were matched in the chip to the real conditions in the human body, achieving dynamic similarity. The equations for calculating Re and Wo are as follows:

$$Re={\displaystyle \frac{UD}{\nu },}$$ (1)

$$Wo=D\sqrt{{\displaystyle \frac{\omega }{\nu }}},$$ (2)

where U is the characteristic velocity, i.e., the velocity of the fluid in the alveolar duct, D is the characteristic length, i.e., the diameter of the alveolar duct, ω = 2π/T, T is the respiratory period, and v is the kinematic viscosity.

To match these two dimensionless numbers, a glycerol solution of 68% by volume with the same viscosity as moist air was chosen as the working fluid (ν_o = 1.65 × 10⁻⁵ m²/s for the former and ν_air = 1.67 × 10⁻⁵ m²/s for the latter) and the values of Re and Wo in real human alveoli were used to calculate U and ω in the equations to guide the setting of our experimental parameters. The 500 nm red polystyrene fluorescent microspheres were mixed well into the glycerol solution at a volume ratio of 30:1 for flow visualization, and fluid motion in the chip could be observed and photographed at every moment by the micro-PIV system.

According to previous studies (Tsuda et al., 1995), the flow ratio λ = Q_a/Q_d is the decisive parameter affecting the alveolar flow pattern. Q_d is the alveolar duct flow rate, which approximately obeys a sinusoidal curve variation and is generally defined by the flow function $Q_{\mathrm{d}}=Q_{\max }\sin \left(\frac{2\pi t}{T}\right)$, and Q_max is the peak value of Q_d at the moment T/2 during the respiratory cycle. Q_a is the flow rate into the alveoli from the alveolar duct and it is also a time-dependent sinusoidal variable $Q_{\mathrm{a}}=Q_{\mathrm{a},\max }\cdot \sin (2\pi t/T)$.In addition, the magnitude of Q_a reflects the volume change of the alveoli during expansion and contraction movements, so the rate of alveolar expansion is also a function of time.

C. Experimental setup

The experimental system used in this study refers to the one applied by Lv et al. (2020), which consists of two main parts: a respiratory control system and a micro-PIV visualization system. As shown in Fig. 1(d), the experimental equipment includes a microscope, a laser, a precision syringe pump, PIV software and hardware, a synchronizer, etc. Combining the schematic shown in Fig. 1(c), the fluid flows in position 1, flows through the previous generation of alveoli and then splits evenly into two bundles of fluid at position 2, enters the next generation of alveolar tubes, and after repeating a similar motion as the previous generation, exits from positions 3 and 4, respectively. Positions 5, 6, and 7 are connected to the same pressure chamber, and this pressure chamber is connected to the air feeder on the syringe pump via a catheter. While the gas in the chamber is being pumped, the pressure in the chamber changes, thus controlling the expansion and contraction of all alveoli simultaneously.

The micro-PIV system consists of a CCD camera (specifications of the 630 091 PowerView 4MP-HS camera, TSI), a double pulsed Nd-YAG laser (Vlite-135, Beamtech), a microscope (IX73, Olympus) with a 40× objective, a synchronizer, and a computer. The camera has a resolution of 2048 × 2048 pixels, with a pixel size of 7.4 × 7.4 μm². The spatial resolution of PIV is defined by the interrogation window (i.e., 64 × 64 pixels), which corresponds to 11.84 μm × 11.84 μm² (Lv et al., 2020; Meinhart et al., 1999; and Santiago et al., 1998). It should be noted that the value of time interval δt in the timing settings of the PIV software needs to be adjusted according to the velocity of the fluorescent fluid movement. Considering that there are significant differences in the magnitude of the flow velocity in the alveolar ducts of different generations, the corresponding values of δt are different, which in any case need to satisfy the criteria reported by Boillot and Prasad (Boillot and Prasad, 1996). Based on the summary of previous studies, the flow with typical characteristics at T/4 and 3T/4 moments was focused on in this study, and in these two moments, we can capture the saddle point phenomenon and study the flow details in it. The camera takes pictures of the two peak moments of respiratory flow, T/4 and 3T/4, and obtains a set of two frames for each capture. The flow field was calculated from each pair of images captured by the intercorrelation algorithm of the software package Insight 4G, and the measurements were repeated for each alveolus for about 70 cycles. The overall average velocity field was obtained by combining dozens of data sets, and, finally, the velocity distribution contours and streamlines were processed using Tecplot software. It is worthy to note that although both geometric and dynamic similarities were matched in the present experimental setting, it is still a two-dimensional model with a uniform thickness, not a three-dimensional one as the real human alveoli. This limitation may make us miss some details of complex and new 3D alveolar flow patterns.

III. RESULTS AND DISCUSSION

A. Flow patterns in the alveoli

Considering the specific flow conditions at different generations of the alveoli, to match the dynamic similarity, the following parameters were set for the 19–20th generations: a liquid flow rate of Q_max = 0.5 μl/s at the tube inlet of the chip channel, a free pressure end at the outlet, a respiratory period of T = 2.4 s, and a gas flow rate of Q_p,max= −480 μl/s in the pressure chamber to achieve an alveolar expansion ratio of α = 13%. As a comparison, those for the 21st–22nd generations were set as: Q_d= 0.13 μl/s, T = 3 s, Q_p= −600 μl/s, and α = 16%. The observed microflow patterns in the 19th and 20th generations and 21st and 22nd generations are presented in Figs. 2(a) and 2(b), respectively.

FIG. 2.

The observed microflow patterns in the alveoli at (a) 19–20th generation and (b) 21st–22nd generation at T/4.

It can be found that the alveolar flow pattern of the 19th generation is dominated by vortex flow. The center of the vortex does not coincide with the geometric center of the alveoli and is slightly offset from the flow inlet of the alveolar chip. When the fluid in the alveolar ducts flows from the 19th generation to the 20th generation, it enters the two alveolar ducts of the 20th generation at the bifurcation of the Y-shaped structure, and the flow rate of each branch is reduced to one-half of the original one. The flow is synchronized with the respiratory movement of the alveoli. Alveolar flow patterns in the 20th generation do not change substantially compared to the 19th generation, but the vortex flow zone is reduced and morphologically it appears to be “compressed,” with the vortex center further away from the geometric center and also closer to the fluid inlet side of the alveolar chip, which is consistent with the phenomenon with a single alveolus on the chip (Lv et al., 2020).

The alveolar flow field in the 21st generation has both vortex flow and radial flow regions, which differ from the characteristics of the 19th and 20th generations. The vortex region is much smaller than the radial flow region, and the vortex center is located close to the alveolar wall at the inlet end of the alveolar duct flow. As can be observed, the entire alveolar flow field is dominated by the radial flow. When it comes to the 22nd generation, only radial flow is present in the alveolar flow field, and vortex flow disappeared completely. This is because of that the vortex center of the alveolar flow field is very close to the wall in the 21st generation, and the shear-driven vortex flow is gradually replaced by the pressure differential-driven (alveolar expansion and contraction motion) radial flow due to the further reduction of the alveolar ductal flow velocity in the 22nd generation.

B. Analysis of flow velocity distribution

The flow fields in the four alveoli located at the different positions of the 19th generation display similar characteristics, all of which are vortex flow dominated flow patterns, as shown in Fig. 2(a)(1)–(4). For the four alveoli, the velocity components of 200 sample points on the line where the vortex center of the swirling flow was located were taken out along the direction parallel to the x-coordinate axis for analysis, and the velocity distribution curves were plotted in Fig. 3.

FIG. 4.

(a) The contour of the flow field and (b) velocity distribution of the first alveolus in the 21st generation. (c) The x-direction and (d) y-direction velocity distribution of the four alveoli in the 21st generation.

FIG. 3.

The x-direction (left) and y-direction (right) velocity distribution of the 19th generation on the line across the vortex center.

It was also found that the velocity distribution of different alveoli showed the same trend, but the peak velocity of the left two alveoli was significantly higher than that of the right two alveoli. Since the alveoli on the left side were located closer to the inlet, the fluid in the alveolar duct was passing through the left alveoli first and then the right alveoli. As the alveoli in the forward position inhaled a certain amount of fluid during expansion, it led to a decrease in the instantaneous flow rate for the alveoli at the backward position. Due to the symmetry in position between the upper and lower alveoli, the velocity component V in the y-direction shows an approximate symmetry across the position of y = 0. In contrast, the flow velocity distribution pattern of alveoli at two locations on the same side of the alveolar cavity shows a consistent trend.

The corresponding flow patterns and velocity distributions on the 21st generation are shown in Fig. 4. Different from the 19th generation, where the vortex flow pattern dominates, the radial flow pattern plays a significant role in the 21st generation as observed in Fig. 4(a). The distribution curves of the velocity components U along the x-direction in the alveolar flow field of the 21st generation tend to overlap, as illustrated in Fig. 4(c). It is notable that there is no significant drop in the peak velocity here, as in the 19th generation, which is mainly because of the different flow patterns that dominate in these two flow fields. The vortex-like flow pattern that dominates the 19th generation flow field is formed by the shear force action of the high-speed fluid movement in the alveolar duct, and the interval where the peak velocity appears corresponds to the region near the vortex center of the flow field. However, as the flow rate decreases in the 21st generation, the vortex flow pattern is concentrated only in the region near the alveolar wall, and the peak velocity occurs near the geometric center. The velocity component V mainly reflects the velocity of the fluid flowing into the alveoli during alveolar expansion, which is smaller in magnitude relative to the velocity component U. Similar to that of the 19th generation, the velocity component V in the y-direction shows an approximate symmetry across the position of y = 0.

C. Detection of the stagnant saddle points

Figure 5 shows a partial magnification of the saddle point phenomenon appearing in the 21st generation, where (A) and (B) correspond to the T/4 and 3T/4 moments of the respiratory cycle, respectively, i.e., the moments of maximum instantaneous flow rate during the inspiratory and expiratory phases (Fishler et al., 2013; and Lv et al., 2020).

FIG. 5.

The contours of flow filed with stagnant saddle points detected in the four alveoli of the 21st generation at the (a) T/4 moment and (b) 3T/4 moment of a breathing cycle.

Comparing the saddle point phenomena in Fig. 5 for different alveoli and at different moments, it can be found that the common feature is that the saddle points appear in the narrow region sandwiched between the vortex center of the flow field and the alveolar wall. The positions are very close to the alveolar wall surface, which is consistent with the previous findings in the flow field study of a single alveolus (Lv et al., 2020). Not only in the vortex flow but saddle points in non-vortex flow, i.e., radial flow as shown in Fig. 5(b), were also captured. In the flow field at the moment of 3T/4, the swirling flow pattern close to the alveolar wall does not appear, but there is still a saddle point phenomenon similar to that at the T/4 moment. Due to the existence of saddle points near the vortex center, the fluorescent particle motion around them becomes chaotic, resulting in the flow details of the two originally mutually inverted moments (T/4 and 3T/4 moments) not being identical, and the vortex flow during the expiratory phase has shifted slightly. Although the new saddle point phenomenon cannot help us completely reveal the nature of the chaotic phenomenon for the time being, and more abundant data are needed to deeply understand the chaotic flow, the findings in this experiment can provide new references for follow-up research.

IV. CONCLUSIONS

A microfluidics based alveolar chip containing multiple alveoli was designed and fabricated in the present study to investigate the air flow pattern in each alveolus and the interactions between them. To guarantee the flow conditions close to the real respiration process, both geometry and kinetic similarities were well matched according to different alveolus generations. The flow fields observed by the micro-PIV system and the following velocity distribution analysis were studied to discover the microflow details. The dominant vortex flow in the 19th generation would evolve to a radial one in the 21st generation as the flow rate and flow ratio change. Compared to the observation shown in a single alveolus model (Lv et al., 2020), the microflow in each alveolus of a multiple alveoli model displays similar patterns and shift trend of vortex center, while the velocity amplitude would differ. The flow fields in each alveolus at the moment of T/4 and 3T/4 of a breathing cycle present a large discrepancy when the interaction between multiple alveoli and chaotic flow effect is considered. Furthermore, as a new finding, stagnant saddle points were also detected in radial flow regions and not only in the vortex flow regions observed in previous studies. The experimental methods developed in the present study and obtained results could provide a reference for future studies to gain a deeper understanding of microflow in a whole alveolar tissue.

AUTHOR DECLARATIONS

Conflict of Interest

The authors have no conflicts to disclose.

Author Contributions

Yue Yang and Weitao Bai have contributed equally to this work.

Author Contributions

Yue Yang: Conceptualization (equal); Formal analysis (equal); Methodology (equal); Writing – original draft (equal); Writing – review & editing (equal); Contribution (equal). Weitao Bai: Formal analysis (equal); Investigation (equal); Methodology (equal); Writing – original draft (equal); Contribution (equal). Jun Dong: Formal analysis (equal); Methodology (equal); Writing – original draft (equal). Huimin Lv: Methodology (equal); Writing – original draft (equal). Yonggang Zhu: Conceptualization (lead); Funding acquisition (lead); Methodology (lead); Resources (lead); Supervision (lead); Writing – review & editing (equal).

DATA AVAILABILITY

The data that support the findings of this study are available within the article.