Respiratory fluid mechanics

Mechanical ventilation energy analysis: Recruitment focuses injurious power in the ventilated lung

The progression of acute respiratory distress syndrome (ARDS) from its onset due to disease or trauma to either recovery or death is poorly understood. Currently, there are no generally accepted treatments aside from supportive care using mechanical ventilation. However, this can lead to ventilator-induced lung injury (VILI), which contributes to a 30 to 40% mortality rate. In this study, we develop and demonstrate a technique to quantify forms of energy transport and dissipation during mechanical ventilation to directly evaluate their relationship to VILI. A porcine ARDS model was used, with ventilation parameters independently controlling lung overdistension and alveolar/airway recruitment/derecruitment (RD). Hourly measurements of airflow, tracheal and esophageal pressures, respiratory system impedance, and oxygen transport were taken for six hours following lung injury to track energy transfer and lung function. The final degree of injury was assessed histologically. Total and dissipated energies were quantified from lung pressure-volume relationships and subdivided into contributions from airflow, tissue viscoelasticity, and RD. Only RD correlated with physiologic recovery. Despite accounting for a very small fraction (2 to 5%) of the total energy dissipation, RD is damaging because it occurs quickly over a very small area. We estimate power intensity of RD energy dissipation to be 100 W/m2, equivalent to 10% of the Sun's luminance at the Earth's surface. Minimizing repetitive RD events may thus be crucial for mitigating VILI.

Prediction of shear stress imposed on alveolar epithelium of healthy and diseased lungs

Lung alveoli are modeled as spherical caps, lined internally by a thin surfactant-laden liquid film, and the periodic wall shear stress exerted along the epithelium during small-amplitude radial oscillations of their wall is computed. A novel set of boundary conditions, applied at the rim, reveals the dominant role of Marangoni stresses. These stresses develop along the air/liquid interface due to spatial gradients of interfacial surfactant concentration and are transported to the wall by the action of viscosity. The effect of a variety of geometric and functional characteristics, including rim interstitial thickness, alveolar opening angle and liquid film thickness and viscosity, is interrogated, and the results are discussed in relation to the onset and evolution of acute and chronic lung diseases, such as asthmatic attacks, pulmonary emphysema and pulmonary fibrosis.

Liquid plug propagation in computer-controlled microfluidic airway-on-a-chip with semi-circular microchannels

This paper introduces a two-inlet, one-outlet lung-on-a-chip device with semi-circular cross-section microchannels and computer-controlled fluidic switching that enables a broader systematic investigation of liquid plug dynamics in a manner relevant to the distal airways. A leak-proof bonding protocol for micro-milled devices facilitates channel bonding and culture of confluent primary small airway epithelial cells. Production of liquid plugs with computer-controlled inlet channel valving and just one outlet allows more stable long-term plug generation and propagation compared to previous designs. The system also captures both plug speed and length as well as pressure drop concurrently. In one demonstration, the system reproducibly generates surfactant-containing liquid plugs, a challenging process due to lower surface tension that makes the plug formation less stable. The addition of surfactant decreases the pressure required to initiate plug propagation, a potentially significant effect in diseases where surfactant in the airways is absent or dysfunctional. Next, the device recapitulates the effect of increasing fluid viscosity, a challenging analysis due to higher resistance of viscous fluids that makes plug formation and propagation more difficult particularly in airway-relevant length scales. Experimental results show that increased fluid viscosity decreases plug propagation speed for a given air flow rate. These findings are supplemented by computational modeling of viscous plug propagation that demonstrates increased plug propagation time, increased maximum wall shear stress, and greater pressure differentials in more viscous conditions of plug propagation. These results match physiology as mucus viscosity is increased in various obstructive lung diseases where it is known that respiratory mechanics can be compromised due to mucus plugging of the distal airways. Finally, experiments evaluate the effect of channel geometry on primary human small airway epithelial cell injury in this lung-on-a-chip. There is more injury in the middle of the channel relative to the edges highlighting the role of channel shape, a physiologically relevant parameter as airway cross-sectional geometry can also be non-circular. In sum, this paper describes a system that pushes the device limits with regards to the types of liquid plugs that can be stably generated for studies of distal airway fluid mechanical injury.

Integrating mechanical cues with engineered platforms to explore cardiopulmonary development and disease

Mechanical forces provide critical biological signals to cells during healthy and aberrant organ development as well as during disease processes in adults. Within the cardiopulmonary system, mechanical forces, such as shear, compressive, and tensile forces, act across various length scales, and dysregulated forces are often a leading cause of disease initiation and progression such as in bronchopulmonary dysplasia and cardiomyopathies. Engineered in vitro models have supported studies of mechanical forces in a number of tissue and disease-specific contexts, thus enabling new mechanistic insights into cardiopulmonary development and disease. This review first provides fundamental examples where mechanical forces operate at multiple length scales to ensure precise lung and heart function. Next, we survey recent engineering platforms and tools that have provided new means to probe and modulate mechanical forces across in vitro and in vivo settings. Finally, the potential for interdisciplinary collaborations to inform novel therapeutic approaches for a number of cardiopulmonary diseases are discussed.

Liquid plug propagation in computer-controlled microfluidic airway-on-a-chip with semi-circular microchannels

This paper introduces a two-inlet, one-outlet lung-on-a-chip device with semi-circular cross-section microchannels and computer-controlled fluidic switching that enables a broader systematic investigation of liquid plug dynamics in a manner relevant to the distal airways. A leak-proof bonding protocol for micro-milled devices facilitates channel bonding and culture of confluent primary small airway epithelial cells. Production of liquid plugs with computer-controlled inlet channel valving and just one outlet allows more stable long-term plug generation and propagation compared to previous designs. The system also captures both plug speed and length as well as pressure drop concurrently. In one demonstration, the system reproducibly generates surfactant-containing liquid plugs, a challenging process due to lower surface tension that makes the plug formation less stable. The addition of surfactant decreases the pressure required to initiate plug propagation, a potentially significant effect in diseases where surfactant in the airways is absent or dysfunctional. Next, the device recapitulates the effect of increasing fluid viscosity, a challenging analysis due to higher resistance of viscous fluids that makes plug formation and propagation more difficult particularly in airway-relevant length scales. Experimental results show that increased fluid viscosity decreases plug propagation speed for a given air flow rate. These findings are supplemented by computational modeling of viscous plug propagation that demonstrate increased plug propagation time, increased maximum wall shear stress, and greater pressure differentials in more viscous conditions of plug propagation. These results match physiology as mucus viscosity is increased in various obstructive lung diseases where it is known that respiratory mechanics can be compromised due to mucus plugging of the distal airways. Finally, experiments evaluate the effect of channel geometry on primary human small airway epithelial cell injury in this lung-on-a-chip. There is more injury in the middle of the channel relative to the edges highlighting the role of channel shape, a physiologically relevant parameter as airway cross-sectional geometry can also be non-circular. In sum, this paper describes a system that pushes the device limits with regards to the types of liquid plugs that can be stably generated for studies of distal airway fluid mechanical injury.

Pulmonary Pharmacokinetics of Polymer Lung Surfactants Following Pharyngeal Administration in Mice

We have recently discovered that pulmonary administration of nanoparticles (micelles) formed by amphiphilic poly(styrene-block-ethylene glycol) (PS-PEG) block copolymers has the potential to treat a lung disorder involving lung surfactant (LS) dysfunction (called acute respiratory distress syndrome (ARDS)), as PS-PEG nanoparticles are capable of reducing the surface tension of alveolar fluid, while they are resistant to deactivation caused by plasma proteins/inflammation products unlike natural LS. Herein, we report studies of the clearance pathways and kinetics of PS-PEG nanoparticles from the lung, which are essential for designing further preclinical IND-enabling studies. Using fluorescently labeled PS-PEG nanoparticles, we found that, following pharyngeal aspiration in mice, the retention of these nanoparticles in the lungs extends over 2 weeks, while their transport into other (secondary) organs is relatively insignificant. An analysis based on a multicompartmental pharmacokinetic model suggests a biphasic mechanism involving a fast mucociliary escalator process through the conducting airways and much slower alveolar clearance processes by the action of macrophages and also via direct translocation into the circulation. An excessive dose of PS-PEG nanoparticles led to prolonged retention in the lungs due to saturation of the alveolar clearance capacity.

Revisiting Airflow and Aerosol Transport Phenomena in the Deep Lungs with Microfluidics

The dynamics of respiratory airflows and the associated transport mechanisms of inhaled aerosols characteristic of the deep regions of the lungs are of broad interest in assessing both respiratory health risks and inhalation therapy outcomes. In the present review, we present a comprehensive discussion of our current understanding of airflow and aerosol transport phenomena that take place within the unique and complex anatomical environment of the deep lungs, characterized by submillimeter 3D alveolated airspaces and nominally slow resident airflows, known as low-Reynolds-number flows. We exemplify the advances brought forward by experimental efforts, in conjunction with numerical simulations, to revisit past mechanistic theories of respiratory airflow and particle transport in the distal acinar regions. Most significantly, we highlight how microfluidic-based platforms spanning the past decade have accelerated opportunities to deliver anatomically inspired in vitro solutions that capture with sufficient realism and accuracy the leading mechanisms governing both respiratory airflow and aerosol transport at true scale. Despite ongoing challenges and limitations with microfabrication techniques, the efforts witnessed in recent years have provided previously unattainable in vitro quantifications on the local transport properties in the deep pulmonary acinar airways. These may ultimately provide new opportunities to explore improved strategies of inhaled drug delivery to the deep acinar regions by investigating further the mechanistic interactions between airborne particulate carriers and respiratory airflows at the pulmonary microscales.

Translating nanoparticle dosimetry from conventional in vitro systems to occupational inhalation exposures

As encouraged by Toxicity Testing in the 21st Century, researchers increasingly apply high-throughput in vitro approaches to identify and characterize nanoparticle hazards, including conventional aqueous cell culture systems to assess respiratory hazards. Translating nanoparticle dose from conventional toxicity testing systems to relevant human exposures remains a major challenge for assessing occupational risk of nanoparticle exposures. Here, we explored existing computational tools and data available to translate nanoparticle dose metrics from cellular test systems to inhalation exposures of silver nanoparticles in humans. We used the Multiple-Path Particle Dosimetry (MPPD) Model to predict nanoparticle deposition of humans exposed to 20 and 110 nm silver nanoparticles at 0.9 μg/m3 over an 8 h period, the proposed National Institute of Occupational Safety and Health (NIOSH) recommended exposure limit (REL). MPPD predicts 8.1 and 3.7 μg of silver deposited in an 8 h period for 20 and 110 nm nanoparticles, respectively, with 20 nm particles displaying nearly 11-fold higher total surface area deposited. Peak deposited nanoparticle concentrations occurred more proximal in the pulmonary tract compared to mass deposition patterns (generation 4 vs. generations 20-21, respectively) due to regional differences in lung lining fluid volumes. Assuming 0.4% nanoparticle dissolution by mass measured in previous studies predicted peak concentrations of silver ions in cells of 1.06 and 0.89 μg/mL for 20 and 110 nm particles, respectively. Both predicted concentrations are below the measured toxic threshold of 1.7 μg/mL of silver ions in cells from in vitro assessments. Assuming 4% dissolution by mass predicted 10-fold higher silver concentrations in tissues, peaking at 10.6 and 8.9 μg/mL, for 20 and 110 nm nanoparticles respectively, exceeding the observed in vitro toxic threshold and highlighting the importance and sensitivity of dissolution rates. Overall, this approach offers a framework for extrapolating nanotoxicity results from in vitro cell culture systems to human exposures. Aligning appropriate dose metrics from in vitro and in vivo hazard characterizations and human pulmonary doses from occupational exposures are critical components for successful nanoparticle risk assessment and worker protection providing guidance for designing future in vitro studies aimed at relevant human exposures.

A guideline to limit indoor airborne transmission of COVID-19

The current revival of the American economy is being predicated on social distancing, specifically the Six-Foot Rule, a guideline that offers little protection from pathogen-bearing aerosol droplets sufficiently small to be continuously mixed through an indoor space. The importance of airborne transmission of COVID-19 is now widely recognized. While tools for risk assessment have recently been developed, no safety guideline has been proposed to protect against it. We here build on models of airborne disease transmission in order to derive an indoor safety guideline that would impose an upper bound on the "cumulative exposure time," the product of the number of occupants and their time in an enclosed space. We demonstrate how this bound depends on the rates of ventilation and air filtration, dimensions of the room, breathing rate, respiratory activity and face mask use of its occupants, and infectiousness of the respiratory aerosols. By synthesizing available data from the best-characterized indoor spreading events with respiratory drop size distributions, we estimate an infectious dose on the order of 10 aerosol-borne virions. The new virus (severe acute respiratory syndrome coronavirus 2 [SARS-CoV-2]) is thus inferred to be an order of magnitude more infectious than its forerunner (SARS-CoV), consistent with the pandemic status achieved by COVID-19. Case studies are presented for classrooms and nursing homes, and a spreadsheet and online app are provided to facilitate use of our guideline. Implications for contact tracing and quarantining are considered, and appropriate caveats enumerated. Particular consideration is given to respiratory jets, which may substantially elevate risk when face masks are not worn.

A guideline to limit indoor airborne transmission of COVID-19

The current revival of the American economy is being predicated on social distancing, specifically the Six-Foot Rule, a guideline that offers little protection from pathogen-bearing aerosol droplets sufficiently small to be continuously mixed through an indoor space. The importance of airborne transmission of COVID-19 is now widely recognized. While tools for risk assessment have recently been developed, no safety guideline has been proposed to protect against it. We here build on models of airborne disease transmission in order to derive an indoor safety guideline that would impose an upper bound on the "cumulative exposure time," the product of the number of occupants and their time in an enclosed space. We demonstrate how this bound depends on the rates of ventilation and air filtration, dimensions of the room, breathing rate, respiratory activity and face mask use of its occupants, and infectiousness of the respiratory aerosols. By synthesizing available data from the best-characterized indoor spreading events with respiratory drop size distributions, we estimate an infectious dose on the order of 10 aerosol-borne virions. The new virus (severe acute respiratory syndrome coronavirus 2 [SARS-CoV-2]) is thus inferred to be an order of magnitude more infectious than its forerunner (SARS-CoV), consistent with the pandemic status achieved by COVID-19. Case studies are presented for classrooms and nursing homes, and a spreadsheet and online app are provided to facilitate use of our guideline. Implications for contact tracing and quarantining are considered, and appropriate caveats enumerated. Particular consideration is given to respiratory jets, which may substantially elevate risk when face masks are not worn.

The effect of viscoelasticity in an airway closure model

The closure of a human lung airway is modeled as a pipe coated internally with a liquid that takes into account the viscoelastic properties of mucus. For a thick enough coating, the Plateau-Rayleigh instability blocks the airway by the creation of a liquid plug, and the pre-closure phase is dominated by the Newtonian behavior of the liquid. Our previous study with a Newtonian-liquid model demonstrated that the bifrontal plug growth consequent to airway closure induces a high level of stress and stress gradients on the airway wall, which is large enough to damage the epithelial cells, causing sub-lethal or lethal responses. In this study, we explore the effect of the viscoelastic properties of mucus by means of the Oldroyd-B and FENE-CR model. Viscoelasticity is shown to be very relevant in the post-coalescence process, introducing a second peak of the wall shear stresses. This second peak is related to an elastic instability due to the presence of the polymeric extra stresses. For high-enough Weissenberg and Laplace numbers, this second shear stress peak is as severe as the first one. Consequently, a second lethal or sub-lethal response of the epithelial cells is induced.

Towards homogenization of liquid plug distribution in reconstructed 3D upper airways of the preterm infant

Liquid plug therapies are commonly instilled in premature babies suffering from infant respiratory distress syndrome (IRDS) by a procedure called surfactant replacement therapy (SRT) in which a surfactant-laden bolus is instilled endotracheally in the neonatal lungs, dramatically reducing mortality and morbidity in neonatal populations. Since data are frequently limited, the optimal method for surfactant delivery has yet to be established towards more standardized guidelines. Here, we explore the dynamics of liquid plug transport using an anatomically-relevant, true-scale in vitro 3D model of the upper airways of a premature infant. We quantify the initial plug's distribution as a function of two underlying parameters that can be clinically controlled; namely, the injection flow rate and the viscosity of the administered fluid. By extracting a homogeneity index (HI), our in vitro results underline how the combination of both high fluid viscosity and injection flow rates may be advantageous in improving homogeneous dispersion. Such outcomes are anticipated to help refine future SRT administration guidelines towards more uniform distribution using more anatomically-realistic 3D in vitro models at true scale of the preterm neonate.

A dynamical overview of droplets in the transmission of respiratory infectious diseases

The outbreak of the coronavirus disease has drawn public attention to the transmission of infectious pathogens, and as major carriers of those pathogens, respiratory droplets play an important role in the process of transmission. This Review describes respiratory droplets from a physical and mechanical perspective, especially their correlation with the transmission of infectious pathogens. It covers the important aspects of (i) the generation and expulsion of droplets during respiratory activities, (ii) the transport and evolution of respiratory droplets in the ambient environment, and (iii) the inhalation and deposition of droplets in the human respiratory tract. State-of-the-art experimental, computational, and theoretical models and results are presented, and the corresponding knowledge gaps are identified. This Review stresses the multidisciplinary nature of its subject and appeals for collaboration among different fields to fight the present pandemic.

An experimental study of respiratory aerosol transport in phantom lung bronchioles

The transport and deposition of micrometer-sized particles in the lung is the primary mechanism for the spread of aerosol borne diseases such as corona virus disease-19 (COVID-19). Considering the current situation, modeling the transport and deposition of drops in human lung bronchioles is of utmost importance to determine their consequences on human health. The current study reports experimental observations on deposition in micro-capillaries, representing distal lung bronchioles, over a wide range of Re that imitates the particle dynamics in the entire lung. The experiment investigated deposition in tubes of diameter ranging from 0.3 mm to 2 mm and over a wide range of Reynolds number (10-2 ⩽ Re ⩽ 103). The range of the tube diameter and Re used in this study is motivated by the dimensions of lung airways and typical breathing flow rates. The aerosol fluid was loaded with boron doped carbon quantum dots as fluorophores. An aerosol plume was generated from this mixture fluid using an ultrasonic nebulizer, producing droplets with 6.5 µm as a mean diameter and over a narrow distribution of sizes. The amount of aerosol deposited on the tube walls was measured using a spectrofluorometer. The experimental results show that dimensionless deposition (δ) varies inversely with the bronchiole aspect ratio (L ¯ ), with the effect of the Reynolds number (Re) being significant only at lowL ¯ . δ also increased with increasing dimensionless bronchiole diameter (D ¯ ), but it is invariant with the particle size based Reynolds number. We show that δ L ¯ ∼ R e - 2 for 10-2 ⩽ Re ⩽ 1, which is typical of a diffusion dominated regime. For Re ⩾ 1, in the impaction dominated regime, δ L ¯ is shown to be independent of Re. We also show a crossover regime where sedimentation becomes important. The experimental results conclude that lower breathing frequency and higher breath hold time could significantly increase the chances of getting infected with COVID-19 in crowded places.

A new wrinkle on liquid sheets: Turning the mechanism of viscous bubble collapse upside down

Viscous bubbles are prevalent in both natural and industrial settings. Their rupture and collapse may be accompanied by features typically associated with elastic sheets, including the development of radial wrinkles. Previous investigators concluded that the film weight is responsible for both the film collapse and wrinkling instability. Conversely, we show here experimentally that gravity plays a negligible role: The same collapse and wrinkling arise independently of the bubble's orientation. We found that surface tension drives the collapse and initiates a dynamic buckling instability. Because the film weight is irrelevant, our results suggest that wrinkling may likewise accompany the breakup of relatively small-scale, curved viscous and viscoelastic films, including those in the respiratory tract responsible for aerosol production from exhalation events.

Stability of gravity-driven free-surface flow past a deformable solid: The role of depth-dependent modulus

The linear stability of a Newtonian liquid layer flowing down an inclined plane lined with a deformable linear elastic solid characterized by a continuously varying modulus is analyzed in this study. A low-wave-number asymptotic analysis is performed to obtain an analytical expression for the complex wavespeed which shows striking similarity with the earlier results of Sahu and Shankar [Sahu and Shankar, Phys. Rev. E 94, 013111 (2016)10.1103/PhysRevE.94.013111] for gravity-driven flow of Newtonian fluid past a solid bilayer having constant shear modulus (in each layer) lined on a rigid inclined plane. This shows that a deformable solid layer having a continuously varying shear modulus can be treated as a generalization of a system having multiple solid layers of constant shear modulus. Also, in the low-wave-number limit, we show that the stability of the free surface is governed by the value of effective shear modulus G_{eff}, and not by the detailed spatial variation of the modulus. Here the effective shear modulus (H/G_{eff}=∫_{1}^{1+H}1/[E_{0}+E[over ¯](z)]dz, where [E_{0}+E[over ¯](z)] represents the modulus gradient function) characterizes the overall modulus of the elastic solid, which is obtained by treating the continuous variation to be the limit of the arrangement of solid layers of infinitesimal thickness (each having a constant shear modulus) in a series. At finite wave numbers, we show that the free-surface and the liquid-solid interface become unstable as we increase the value of Γ, where Γ indicates the ratio of viscous stresses in the fluid to elastic stresses in the solid. When the system is analysed for different types of spatial modulus variations, we find results similar to those of Gkanis and Kumar [Gkanis and Kumar, Phys. Rev. E 73, 026307 (2006)10.1103/PhysRevE.73.026307], i.e., when we have two different configurations of the shear modulus function that have the same spatially averaged modulus, but have different values at the interface, the system is more stable for the configuration having higher shear modulus at the liquid-solid interface. In a similar manner, when we examined systems having the same shear modulus at the liquid-solid interface and same average modulus, the more stable case is the one which has a higher value of shear modulus just below the interface. Thus the use of deformable solids with a depth-dependent modulus potentially offers more control in the passive manipulation of the instabilities.

In situ-Like Aerosol Inhalation Exposure for Cytotoxicity Assessment Using Airway-on-Chips Platforms

Lung exposure to inhaled particulate matter (PM) is known to injure the airway epithelium via inflammation, a phenomenon linked to increased levels of global morbidity and mortality. To evaluate physiological outcomes following PM exposure and concurrently circumvent the use of animal experiments, in vitro approaches have typically relied on traditional assays with plates or well inserts. Yet, these manifest drawbacks including the inability to capture physiological inhalation conditions and aerosol deposition characteristics relative to in vivo human conditions. Here, we present a novel airway-on-chip exposure platform that emulates the epithelium of human bronchial airways with critical cellular barrier functions at an air-liquid interface (ALI). As a proof-of-concept for in vitro lung cytotoxicity testing, we recapitulate a well-characterized cell apoptosis pathway, induced through exposure to 2 μm airborne particles coated with αVR1 antibody that leads to significant loss in cell viability across the recapitulated airway epithelium. Notably, our in vitro inhalation assays enable simultaneous aerosol exposure across multiple airway chips integrated within a larger bronchial airway tree model, under physiological respiratory airflow conditions. Our findings underscore in situ-like aerosol deposition outcomes where patterns depend on respiratory flows across the airway tree geometry and gravitational orientation, as corroborated by concurrent numerical simulations. Our airway-on-chips not only highlight the prospect of realistic in vitro exposure assays in recapitulating characteristic local in vivo deposition outcomes, such platforms open opportunities toward advanced in vitro exposure assays for preclinical cytotoxicity and drug screening applications.

Nucleation of Capillary Bridges and Bubbles in Nanoconfined CO2

Using molecular simulation, we examine the capillary condensation and the capillary evaporation of CO₂ in cylindrical nanopores. More specifically, we employ the recently developed μV T-S method to determine the microscopic mechanism associated with these processes and the corresponding free energy profiles. We calculate the free energy barrier for capillary condensation and identify that the key step consists in the nucleation of a liquid bridge of a critical size. Similarly, the free energy maximum found for the capillary evaporation process is found to correspond to the nucleation of a vapor bubble of a critical size. In addition, we assess the impact of the strength of the wall-fluid on the height of the free energy barrier and on the critical size of liquid bridges (condensation process) and vapor bubbles (evaporation process). We observe that the height of the free energy barrier increases with the strength of the wall-fluid interactions. Finally, we build a theoretical model, based on capillary theory, to rationalize our findings. In particular, the simulation results reveal a linear scaling of the free energy barrier with the critical size, in excellent agreement with the theoretical predictions.

Liquid plug formation in an airway closure model

The closure of a human lung airway is modeled as an instability of a two-phase flow in a pipe coated internally with a Newtonian liquid. For a thick enough coating, the Plateau-Rayleigh instability creates a liquid plug which blocks the airway, halting distal gas exchange. Owing to a bi-frontal plug growth, this airway closure flow induces high stress levels on the wall, which is the location of airway epithelial cells. A parametric numerical study is carried out simulating relevant conditions for human lungs, either in ordinary or pathological situations. Our simulations can represent the physical process from pre- to post-coalescence phases. Previous studies have been limited to pre-coalescence only. The topological change during coalescence induces a high level of stress and stress gradients on the epithelial cells, which are large enough to damage them, causing sub-lethal or lethal responses. We find that post-coalescence wall stresses can be in the range of 300% to 600% greater than pre-coalescence values, so introduce a new important source of mechanical perturbation to the cells.

Effects of surfactant on propagation and rupture of a liquid plug in a tube

Surfactant-laden liquid plug propagation and rupture occurring in lower lung airways are studied computationally using a front-tracking method. The plug is driven by an applied constant pressure in a rigid axisymmetric tube whose inner surface is coated by a thin liquid film. The evolution equations of the interfacial and bulk surfactant concentrations coupled with the incompressible Navier-Stokes equations are solved in the front-tracking framework. The numerical method is first validated for a surfactant-free case and the results are found to be in good agreement with the earlier simulations of Fujioka et al. (2008) and Hassan et al. (2011). Then extensive simulations are performed to investigate the effects of surfactant on the mechanical stresses that could be injurious to epithelial cells such as pressure and shear stress. It is found that the liquid plug ruptures violently to induce large pressure and shear stress on airway walls and even a tiny amount of surfactant significantly reduces the pressure and shear stress and thus improves cell survivability. However, addition of surfactant also delays the plug rupture and thus airway reopening.

A Three-Dimensional Model of Human Lung Airway Tree to Study Therapeutics Delivery in the Lungs

Surfactant instillation into the lungs is used to treat several respiratory disorders such as neonatal respiratory distress syndrome (NRDS). The success of the treatments significantly depends on the uniformity of distribution of the instilled surfactant in airways. This is challenging to directly evaluate due to the inaccessibility of lung airways and great difficulty with imaging them. To tackle this problem, we developed a 3D physical model of human lung airway tree. Using a defined set of principles, we first generated computational models of eight generations of neonates' tracheobronchial tree comprising the conducting zone airways. Similar to native lungs, these models contained continuously-branching airways that rotated in the 3D space and reduced in size with increase in the generation number. Then, we used additive manufacturing to generate physical airway tree models that precisely replicated the computational designs. We demonstrated the utility of the physical models to study surfactant delivery in the lungs and showed the effect of orientation of the airway tree in the gravitational field on the distribution of instilled surfactant between the left and right lungs and within each lung. Our 3D lung airway tree model offers a novel tool for quantitative studies of therapeutics delivery.

Engineered Airway Models to Study Liquid Plug Splitting at Bifurcations: Effects of Orientation and Airway Size

Delivery of biological fluids, such as surfactant solutions, into lungs is a major strategy to treat respiratory disorders including respiratory distress syndrome that is caused by insufficient or dysfunctional natural lung surfactant. The instilled solution forms liquid plugs in lung airways. The plugs propagate downstream in airways by inspired air or ventilation, continuously split at airway bifurcations to smaller daughter plugs, simultaneously lose mass from their trailing menisci, and eventually rupture. A uniform distribution of the instilled biofluid in lung airways is expected to increase the treatments success. The uniformity of distribution of instilled liquid in the lungs greatly depends on the splitting of liquid plugs between daughter airways, especially in the first few generations from which airways of different lobes of lungs emerge. To mechanistically understand this process, we developed a bioengineering approach to computationally design three-dimensional bifurcating airway models using morphometric data of human lungs, fabricate physical models, and examine dynamics of liquid plug splitting. We found that orientation of bifurcating airways has a major effect on the splitting of liquid plugs between daughter airways. Changing the relative gravitational orientation of daughter tubes with respect to the horizontal plane caused a more asymmetric splitting of liquid plugs. Increasing the propagation speed of plugs partially counteracted this effect. Using airway models of smaller dimensions reduced the asymmetry of plug splitting. This work provides a step toward developing delivery strategies for uniform distribution of therapeutic fluids in the lungs.

Biomimetics of the pulmonary environment in vitro: A microfluidics perspective

The entire luminal surface of the lungs is populated with a complex yet confluent, uninterrupted airway epithelium in conjunction with an extracellular liquid lining layer that creates the air-liquid interface (ALI), a critical feature of healthy lungs. Motivated by lung disease modelling, cytotoxicity studies, and drug delivery assessments amongst other, in vitro setups have been traditionally conducted using macroscopic cultures of isolated airway cells under submerged conditions or instead using transwell inserts with permeable membranes to model the ALI architecture. Yet, such strategies continue to fall short of delivering a sufficiently realistic physiological in vitro airway environment that cohesively integrates at true-scale three essential pillars: morphological constraints (i.e., airway anatomy), physiological conditions (e.g., respiratory airflows), and biological functionality (e.g., cellular makeup). With the advent of microfluidic lung-on-chips, there have been tremendous efforts towards designing biomimetic airway models of the epithelial barrier, including the ALI, and leveraging such in vitro scaffolds as a gateway for pulmonary disease modelling and drug screening assays. Here, we review in vitro platforms mimicking the pulmonary environment and identify ongoing challenges in reconstituting accurate biological airway barriers that still widely prevent microfluidic systems from delivering mainstream assays for the end-user, as compared to macroscale in vitro cell cultures. We further discuss existing hurdles in scaling up current lung-on-chip designs, from single airway models to more physiologically realistic airway environments that are anticipated to deliver increasingly meaningful whole-organ functions, with an outlook on translational and precision medicine.

Analytical solutions for the profile of two-dimensional droplets with finite-length precursor films

By means of the lubrication approximation we obtain the full family of static bidimensional profiles of a liquid resting on a substrate under partial-wetting conditions imposed by a disjoining-conjoining pressure. We show that for a set of quite general disjoining-conjoining pressure potentials, the free surface can adopt only five nontrivial static patterns; in particular, we find solutions when the height goes to zero which describe satisfactorily the complete free surface for a finite amount of fluid deposited on a substrate. To test the extension of the applicability of our solutions, we compare them with those obtained when the lubrication approximations are not employed and under conditions where the lubrication hypothesis are not strictly valid, and also with axisymmetric solutions. For a given disjoining-conjoining potential, we report a new analytical solution that accounts for all the five possible solutions.

Numerical simulations of targeted delivery of magnetic drug aerosols in the human upper and central respiratory system: a validation study

In the present study, we investigate the concept of the targeted delivery of pharmaceutical drug aerosols in an anatomically realistic geometry of the human upper and central respiratory system. The geometry considered extends from the mouth inlet to the eighth generation of the bronchial bifurcations and is identical to the phantom model used in the experimental studies of Banko et al. (2015 Exp. Fluids56, 1-12 (doi:10.1007/s00348-015-1966-y)). In our computer simulations, we combine the transitional Reynolds-averaged Navier-Stokes (RANS) and the wall-resolved large eddy simulation (LES) methods for the air phase with the Lagrangian approach for the particulate (aerosol) phase. We validated simulations against recently obtained magnetic resonance velocimetry measurements of Banko et al. (2015 Exp. Fluids56, 1-12. (doi:10.1007/s00348-015-1966-y)) that provide a full three-dimensional mean velocity field for steady inspiratory conditions. Both approaches produced good agreement with experiments, and the transitional RANS approach is selected for the multiphase simulations of aerosols transport, because of significantly lower computational costs. The local and total deposition efficiency are calculated for different classes of pharmaceutical particles (in the 0.1 μm≤d_p≤10 μm range) without and with a paramagnetic core (the shell-core particles). For the latter, an external magnetic field is imposed. The source of the imposed magnetic field was placed in the proximity of the first bronchial bifurcation. We demonstrated that both total and local depositions of aerosols at targeted locations can be significantly increased by an applied magnetization force. This finding confirms the possible potential for further advancement of the magnetic drug targeting technique for more efficient treatments for respiratory diseases.

Controlled delivery and minimally invasive imaging of stem cells in the lung

Intratracheal delivery of stem cells into injured or diseased lungs can provide a variety of therapeutic and immunomodulatory effects for the treatment of acute lung injury and chronic lung disease. While the efficacy of this approach depends on delivering the proper cell dosage into the target region of the airway, tracking and analysis of the cells have been challenging, largely due to the limited understanding of cell transport and lack of suitable cell monitoring techniques. We report on the transport and deposition of intratracheally delivered stem cells as well as strategies to modulate the number of cells (e.g., dose), topographic distribution, and region-specific delivery in small (rodent) and large (porcine and human) lungs. We also developed minimally invasive imaging techniques for real-time monitoring of intratracheally delivered cells. We propose that this approach can facilitate the implementation of patient-specific cells and lead to enhanced clinical outcomes in the treatment of lung disease with cell-based therapies.

Stability of viscous film flow coating the interior of a vertical tube with a porous wall

The stability of the gravity-driven flow of a viscous film coating the inside of a tube with a porous wall is studied theoretically. We used Darcy's law to describe the motion of fluids in a porous medium. The Beaver-Joseph condition is used to describe the discontinuity of velocity at the porous-fluid interface. We derived an evolution equation for the film thickness using a long-wave approximation. The effect of velocity slip at the porous wall is identified by a parameter β. We examine the effect of β on the temporal stability, the absolute-convective instability (AI-CI), and the nonlinear evolution of the interface deformation. The results of the temporal stability reveal that the effect of velocity slip at the porous wall is destabilizing. The parameter β plays an important role in determining the AI-CI behavior and the nonlinear evolution of the interface. The presence of the porous wall promotes the absolute instability and the formation of the plug in the tube.

Dynamics of liquid plugs in prewetted capillary tubes: from acceleration and rupture to deceleration and airway obstruction

The dynamics of individual liquid plugs pushed at a constant pressure head inside prewetted cylindrical capillary tubes is investigated experimentally and theoretically. It is shown that, depending on the thickness of the prewetting film and the magnitude of the pressure head, the plugs can either experience a continuous acceleration leading to a dramatic decrease of their size and eventually their rupture or conversely, a progressive deceleration associated with their growth and an exacerbation of the airway obstruction. These behaviors are quantitatively reproduced using a simple nonlinear model [Baudoin et al., Proc. Natl. Acad. Sci. U. S. A., 2013, 110, 859] adapted here for cylindrical channels. Furthermore, an analytical criterion for the transition between these two regimes is derived and successfully compared with extensive experimental data. The potential implications of this work for pulmonary obstructive diseases are discussed.

Stabilization of carbon dioxide (CO2) bubbles in micrometer-diameter aqueous droplets and the formation of hollow microparticles

We report an approach to stabilize carbon dioxide (CO2) gas bubbles encapsulated in micrometer-diameter aqueous drops when water in the aqueous drops is evaporated. CO2-in-water-in-oil double emulsion drops are generated using microfluidic approaches and evaporation is conducted in the presence of sodium dodecyl sulfate (SDS), poly(vinyl alcohol) (PVA) and/or graphene oxide (GO) particles dispersed in the aqueous phase of the double emulsion drops. We examine the roles of the bubble-to-drop size ratio, PVA and GO concentration in the stabilization of CO2 bubbles upon water evaporation and show that thin-shell particles with encapsulated CO2 bubbles can be obtained under optimized conditions. The developed approach offers a new strategy to study CO2 dissolution and stability on the microscale and the synthesis of novel gas-core microparticles.

Rapid retraction of microvolume aqueous plugs traveling in a wettable capillary

We report a transport behavior-specifically, rapid retraction movement-of small (∼μL) deionized water plugs traveling in series within a small wettable tubular geometry. In this study, two water plugs separated by a certain distance in a dry cylindrical glass capillary were moved by positive pressure airflow applied at the tube inlet. As the plugs travel, a thin aqueous film is generated between the plugs as a result of the leading plug's aqueous deposition onto the inner surface of the tube. The leading plug continuously loses volume by film deposition onto the surface and eventually ruptures. Then, the lagging plug quickly travels the distance initially separating the two plugs (plug retraction). Our studies show that the rapid retraction of the lagging plug is caused by surface tension in addition to the positive pressure applied. Furthermore, the plug retraction speed is strongly affected by tube radius and the distance between the plugs.

Pulmonary fluid flow challenges for experimental and mathematical modeling

Modeling the flow of fluid in the lungs, even under baseline healthy conditions, presents many challenges. The complex rheology of the fluids, interaction between fluids and structures, and complicated multi-scale geometry all add to the complexity of the problem. We provide a brief overview of approaches used to model three aspects of pulmonary fluid and flow: the surfactant layer in the deep branches of the lung, the mucus layer in the upper airway branches, and closure/reopening of the airway. We discuss models of each aspect, the potential to capture biological and therapeutic information, and open questions worthy of further investigation. We hope to promote multi-disciplinary collaboration by providing insights into mathematical descriptions of fluid-mechanics in the lung and the kinds of predictions these models can make.

Instability of viscous flow over a deformable two-layered gel: experiments and theory

The instability of the flow of a viscous fluid past a soft, two-layered gel is probed using experiments, and the observations are compared with results from a linear stability analysis. The experimental system consists of the rotating top plate of a rheometer and its stationary bottom plate on which the two-layer gel is placed. When the flow between the top plate and the two-layer gel is viscometric (i.e., laminar), the viscosity obtained from the rheometer is a measure of the material property of the fluid. However, after a critical shear stress, there is a sudden increase in apparent viscosity, indicating that the flow has undergone an instability due to the deformable nature of the two-layer gel. Experiments are carried out to quantify how the critical value of fluid shear stress required to destabilize the flow varies as a function of ratio of solid to fluid layer thickness, and the ratio of the shear moduli of the two gels. A linear stability analysis is carried out for plane Couette flow of a Newtonian fluid past the two-layered gel, by assuming the two solid layers to be elastic neo-Hookean materials. In order to compare the experimental and theoretical results, the effective shear modulus (Geff, defined by H/Geff=H1/G1+H2/G2) of the two-layer gel is found to be useful, where H=H1+H2. Here, Hi and Gi (i=1,2), respectively, denote the thickness and shear modulus of each layer. Results for the nondimensional parameter Γeff=ηV/(dGeff) (V is the velocity of the top plate; η is fluid viscosity, d is the fluid thickness) as a function of solid to fluid thickness H/d obtained from the stability analysis agree well with experimental observations, without any fitting parameters. In general, we find that the flow is more unstable if the softer gel is adjacent to the fluid flow compared to the case when it is not. This suggests that the instability is more interfacial in nature and is crucially dependent on the relative placement of the two layers, and not just on the effective modulus of the two-layer gel. We further show that the theoretical and experimental data for two-layer gels can be suitably collapsed onto the results obtained for a single-gel layer.

Final state of a perturbed liquid film inside a container under the effect of solid-liquid molecular forces and gravity

We investigate theoretically the possible final stationary configurations that can be reached by a laterally confined uniform liquid film inside a container. The liquid is under the action of gravity, surface tension, and the molecular interaction with the solid substrate. We study the case when the container is in an upright position as well as when it is turned upside down. The governing parameters of the problem are the initial thickness of the film, the size of the recipient that contains the liquid, and a dimensionless number that quantifies the relative strength of gravity with respect to the molecular interaction. The uniform film is always a possible final state and depending on the value of the parameters, up to three different additional final states may exist, each one consisting in a droplet surrounded by a thin film. We derive analytical expressions for the energy of these possible final configurations and from these we analyze which state is indeed reached. A uniform thin film may show three different behaviors after a perturbation: The system recovers its initial shape after any perturbation, the fluid evolves towards a drop (if more than one is possible, it tends toward that with the thinnest precursor film) for any perturbation, or the system ends as a uniform film or a drop depending on the details of the perturbation.

Microfluidic shear stress-regulated surfactant secretion in alveolar epithelial type II cells in vitro

We investigated the role of flow-induced shear stress on the mechanisms regulating surfactant secretion in type II alveolar epithelial cells (ATII) using microfluidic models. Following flow stimulation spanning a range of wall shear stress (WSS) magnitudes, monolayers of ATII (MLE-12 and A549) cells were examined for surfactant secretion by evaluating essential steps of the process, including relative changes in the number of fusion events of lamellar bodies (LBs) with the plasma membrane (PM) and intracellular redistribution of LBs. F-actin cytoskeleton and calcium levels were analyzed in A549 cells subjected to WSS spanning 4-20 dyn/cm(2). Results reveal an enhancement in LB fusion events with the PM in MLE-12 cells upon flow stimulation, whereas A549 cells exhibit no foreseeable changes in the monitored number of fusion events for WSS levels ranging up to a threshold of ∼8 dyn/cm(2); above this threshold, we witness instead a decrease in LB fusion events in A549 cells. However, patterns of LB redistribution suggest that WSS can potentially serve as a stimulus for A549 cells to trigger the intracellular transport of LBs toward the cell periphery. This observation is accompanied by a fragmentation of F-actin, indicating that disorganization of the F-actin cytoskeleton might act as a limiting factor for LB fusion events. Moreover, we note a rise in cytosolic calcium ([Ca(2+)]c) levels following stimulation of A549 cells with WSS magnitudes ranging near or above the experimental threshold. Overall, WSS stimulation can influence key components of molecular machinery for regulated surfactant secretion in ATII cells in vitro.

Gradient dynamics description for films of mixtures and suspensions: dewetting triggered by coupled film height and concentration fluctuations

A thermodynamically consistent gradient dynamics model for the evolution of thin layers of liquid mixtures, solutions, and suspensions on solid substrates is presented which is based on a film-height- and mean-concentration-dependent free energy functional. It is able to describe a large variety of structuring processes, including coupled dewetting and decomposition processes. As an example, the model is employed to investigate the dewetting of thin films of liquid mixtures and suspensions under the influence of effective long-range van der Waals forces that depend on solute concentration. The occurring fluxes are discussed, and it is shown that spinodal dewetting may be triggered through the coupling of film height and concentration fluctuations. Fully nonlinear calculations provide the time evolution and resulting steady film height and concentration profiles.

Behavior of liquid plugs at bifurcations in a microfluidic tree network

Flows in complex geometries, such as porous media or biological networks, often contain plugs of liquid flowing within air bubbles. These flows can be modeled in microfluidic devices in which the geometric complexity is well defined and controlled. We study the flow of wetting liquid plugs in a bifurcating network of micro-channels. In particular, we focus on the process by which the plugs divide as they pass each bifurcation. The key events are identified, corresponding to large modifications of the interface curvature, the formation of new interfaces, or the division of a single interface into two new ones. The timing of the different events and the amplitude of the curvature variations are analyzed in view of the design of an event-driven model of flow in branching micro-networks. They are found to collapse onto a master curve dictated by the network geometry.

Respiratory physiology on a chip

Our current understanding of respiratory physiology and pathophysiological mechanisms of lung diseases is often limited by challenges in developing in vitro models faithful to the respiratory environment, both in cellular structure and physiological function. The recent establishment and adaptation of microfluidic-based in vitro devices (μFIVDs) of lung airways have enabled a wide range of developments in modern respiratory physiology. In this paper, we address recent efforts over the past decade aimed at advancing in vitro models of lung structure and airways using microfluidic technology and discuss their applications. We specifically focus on μFIVDs covering four major areas of respiratory physiology, namely, artificial lungs (AL), the air-liquid interface (ALI), liquid plugs and cellular injury, and the alveolar-capillary barrier (ACB).