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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.

Condensing 40 years of teaching experience, this unique textbook will provide students with an unrivalled understanding of the fundamentals of fluid mechanics, and enable them to place that understanding firmly within a biological context. Each chapter introduces, explains, and expands a core concept in biofluid mechanics, establishing a firm theoretical framework for students to build upon in further study. Practical biofluid applications, clinical correlations, and worked examples throughout the book provide real-world scenarios to help students quickly master key theoretical topics. Examples are drawn from biology, medicine, and biotechnology with applications to normal function, disease, and devices, accompanied by over 500 figures to reinforce student understanding. Featuring over 120 multicomponent end-of-chapter problems, flexible teaching pathways to enable tailor-made course structures, and extensive Matlab and Maple code examples, this is the definitive textbook for advanced undergraduate and graduate students studying a biologically-grounded course in fluid mechanics.

Employing the moving particles' semi-implicit (MPS) method, this study presents a numerical framework for solving the Navier–Stokes equations for the propagation and the split of a liquid plug through a three-dimensional air-filled bifurcating tube, where the inner surface is coated by a thin fluid film, and surface tension acts on the air–liquid interface. The detailed derivation of a modified MPS method to handle the air–liquid interface of liquid plugs is presented. When the front air–liquid interface of the plug splits at the bifurcation, the interface deforms quickly and causes large wall shear stress. We observe that the presence of a transverse gravitational force causes asymmetries in plug splitting, which becomes more pronounced as the capillary number decreases or the Bond number increases. We also observe that there exists a critical capillary number below which the plug does not split into two daughter tubes but propagates into the lower daughter tube only. In order to deliver the plug into the upper daughter tube, the driving pressure to push the plug is required to overcome the hydrostatic pressure due to gravity. These tendencies agree with our previous experimental and theoretical studies.

The closure of a human lung airway is modelled 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 preclosure phase is dominated by the Newtonian behaviour 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 sublethal 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 postcoalescence 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 sublethal response of the epithelial cells is induced., Scientific and Technological Research Council of Turkey (TÜBİTAK); National Institutes of Health (NIH)

The flow inside the perivascular space (PVS) is modeled using a first-principles approach in order to investigate how the cerebrospinal fluid (CSF) enters the brain through a permeable layer of glial cells. Lubrication theory is employed to deal with the flow in the thin annular gap of the perivascular space between an impermeable artery and the brain tissue. The artery has an imposed peristaltic deformation and the deformable brain tissue is modeled by means of an elastic Hooke’s law. The perivascular flow model is solved numerically, discovering that the peristaltic wave induces a steady streaming to/from the brain which strongly depends on the rigidity and the permeability of the brain tissue. A detailed quantification of the through flow across the glial boundary is obtained for a large parameter space of physiologically relevant conditions. The parameters include the elasticity and permeability of the brain, the curvature of the artery, its length and the amplitude of the peristaltic wave. A steady streaming component of the through flow due to the peristaltic wave is characterized by an in-depth physical analysis and the velocity across the glial layer is found to flow from and to the PVS, depending on the elasticity and permeability of the brain. The through CSF flow velocity is quantified to be of the order of micrometers per seconds.

We study the effects of surface tension and yield stress on mucus plug rupture. A three-dimensional simplified configuration is employed to simulate mucus plug rupture in a collapsed lung airway of the tenth generation. The Herschel–Bulkley model is used to take into account the non-Newtonian viscoplastic fluid properties of mucus. Results show that the maximum wall shear stress greatly changes right prior to the rupture of the mucus plug. The surface tension influences mainly the late stage of the rupture process when the plug deforms greatly and the curvature of the mucus–air interface becomes significant. High surface tension increases the wall shear stress and the time needed to rupture since it produces a resistance to the rupture, as well as strong stress and velocity gradients across the mucus–air interface. The yield stress effects are pronounced mainly at the beginning. High yield stress makes the plug take a long time to yield and slows down the whole rupture process. When the effects induced by the surface tension and yield forces are comparable, dynamical quantities strongly depend on the ratio of the two forces. The pressure difference (the only driving in the study) contributes to wall shear stress much more than yield stress and surface tension per unit length. Wall shear stress is less sensitive to the variation in yield stress than that in surface tension. In general, wall shear stress can be effectively reduced by the smaller pressure difference and surface tension.

We study the disturbance on two-dimensional flow generated by a circular obstacle of radius r placed downwind in front of a duct of width w at a distance λ between the center of the obstacle and the inlet position of the channel. Our results show that, at low Reynolds conditions, the flux ϕ at the duct exhibits distinct regimes for different λ intervals.

Elderly populations have a higher risk of rib fractures and other associated thoracic injuries than younger adults, and the changes in body morphology that occur with age are a potential cause of this increased risk. Rib centroidal path geometry for 20 627 ribs was extracted from computed tomography (CT) scans of 1042 live adult subjects, then fitted to a six‐parameter mathematical model that accurately characterizes rib size and shape, and a three‐parameter model of rib orientation within the body. Multivariable regression characterized the independent effect of age, height, weight, and sex on the rib shape and orientation across the adult population, and statistically significant effects were seen from all demographic factors (P

Complex in vitro models of the tissue microenvironment, termed microphysiological systems, have enormous potential to transform the process of discovering drugs and disease mechanisms. Such a paradigm shift is urgently needed in acute respiratory distress syndrome (ARDS), an acute lung condition with no successful therapies and a 40% mortality rate. Here, we consider how microphysiological systems could improve understanding of biological mechanisms driving ARDS and ultimately improve the success of therapies in clinical trials. We first discuss how microphysiological systems could explain the biological mechanisms underlying the segregation of ARDS patients into two clinically distinct phenotypes. Then, we contend that ARDS-mimetic microphysiological systems should recapitulate three critical aspects of the distal airway microenvironment, namely, mechanical force, inflammation, and fibrosis, and we review models that incorporate each of these aspects. Finally, we recognize the substantial challenges associated with combining inflammation, fibrosis, and/or mechanical force in microphysiological systems. Nevertheless, complex in vitro models are a novel paradigm for studying ARDS, and they could ultimately improve patient care.

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 bifrontal 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, in either ordinary or pathological situations. Our simulations can represent the physical process from pre- to postcoalescence phases. Previous studies have been limited to precoalescence 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 sublethal or lethal responses. We find that postcoalescence wall stresses can be in the range of 300% to 600% greater than precoalescence values and so introduce an important source of mechanical perturbation to the cells., National Institutes of Health (NIH)

Objective: Both females and the elderly have been identified as vulnerable populations with increased injury and mortality risk in multiple crash scenarios. Particularly in frontal impacts, older females show higher risk to the chest and thorax than their younger or male counterparts. Thoracic geometry plays a role in this increase, and this study aims to quantify key parts of that geometry in a way that can directly inform human body models that incorporate the concept of person age. Methods: Computed tomography scans from 2 female subject groups aged 20–35 and 65–99 were selected from the International Center for Automotive Medicine scan database representing young and old female populations. A model of thoracic skeletal anatomy was built for each subject from independent parametric models of the spine, ribs, and sternum, along with further parametric models of those components’ spatial relationships. Parameter values between the 2 groups are directly compared, and average parameter values within each group are used to generate statistically average skeletal geometry for young and old females. In addition to the anatomic measures explicitly used in the parameterization scheme, key measures of rib cage depth and spine curvature are taken from both the underlying subject pool and from the resultant representative geometries. Results: Statistically significant differences were seen between the young and old groups’ spine and rib anatomic components, with no significant differences in local sternal geometry found. Vertebral segments in older females had higher angles relative to their inferior neighbors, providing a quantification of the kyphotic curvature known to be associated with age. Ribs in older females had greater end-to-end span, greater aspect ratio, and reduced out-of-plane deviation, producing an elongated and overall flatter curvature that leads to distal rib ends extending further anteriorly in older individuals. Combined differences in spine curvature and rib geometry led to an 18-mm difference in anterior placement of the sternum between young and old subjects. Conclusions: This study provides new geometric data regarding the variability in anthropometry of adult females with age and has utility in advancing the veracity of current human body models. A simplified scaffold representation of underlying 3-dimensional bones within the thorax is presented, and the reported young and old female parameter sets can be used to characterize the anatomic differences expected with age and to both validate and drive morphing algorithms for aged human body models. The modular approach taken allows model parameters to hold inherent and intuitive meaning, offering advantages over more generalized methods such as principal component analysis. Geometry can be assessed on a component level or a whole thorax level, and the parametric representation of thorax shape allows direct comparisons between the current study and other individuals or human body models.

Surfactant Replacement Therapy (SRT), which involves instillation of a liquid-surfactant mixture directly into the lung airway tree, is a major therapeutic treatment in neonatal patients with respiratory distress syndrome (RDS). This procedure has proved to be remarkably effective in premature newborns, inducing a five-fold decrease of mortality in the past 35 years. Disappointingly, its use in adults for treating acute respiratory distress syndrome (ARDS) experienced initial success followed by failures. Our recently developed numerical model has demonstrated that transition from success to failure of SRT in adults could, in fact, have a fluid mechanical origin that is potentially reversible. Here, we present the first numerical simulations of surfactant delivery into a realistic asymmetric conducting airway tree of the rat lung and compare them with experimental results. The roles of dose volume (VD), flow rate, and multiple aliquot delivery are investigated. We find that our simulations of surfactant delivery in rat lungs are in good agreement with our experimental data. In particular, we show that the monopodial architecture of the rat airway tree plays a major role in surfactant delivery, contributing to the poor homogeneity of the end distribution of surfactant. In addition, we observe that increasing VD increases the amount of surfactant delivered to the acini after losing a portion to coating the involved airways, the coating cost volume, VCC. Finally, we quantitatively assess the improvement resulting from a multiple aliquot delivery, a method sometimes employed clinically, and find that a much larger fraction of surfactant reaches the alveolar regions in this case. This is the first direct qualitative and quantitative comparison of our numerical model with experimental studies, which enhances our previous predictions in adults and neonates while providing a tool for predicting, engineering, and optimizing patient-specific surfactant delivery in complex situations., Author summary Surfactant Replacement Therapy (SRT), which involves instillation of a liquid-surfactant mixture directly into the lung airway tree, is a major therapeutic treatment in neonatal patients with respiratory distress syndrome (RDS). This procedure has contributed to a major decrease of the infant mortality in the past 35 years. Disappointingly, its use in adults for treating acute respiratory distress syndrome (ARDS) experienced initial success followed by failures. In this article, we present the first numerical simulations of surfactant delivery into realistic models of the conducting airway tree of the rat lung and compare them with experimental results. In particular, we show that the monopodial architecture of the rat airway tree plays a major role in surfactant delivery, contributing to the poor homogeneity of the end distribution of surfactant. This is the first direct qualitative and quantitative comparison of our numerical model with experimental studies, which enhances our previous predictions in adults and neonates while providing a tool for predicting, engineering, and optimizing patient-specific surfactant delivery in complex situations.

In this study we present a novel six-parameter shape model of the human rib centroidal path using logarithmic spirals. It provides a reduction in parameter space from previous models of overall rib shape, while simultaneously reducing fitting error by 34% and increasing curvature continuity. Furthermore, the model directly utilizes geometric properties such as rib end-to-end span, aspect ratio, rib "skewness", and inner angle with the spine in its parameterization, making the effects of each parameter on overall shape intuitive and easy to visualize. The model was tested against 2197 rib geometries extracted from CT scans from a population of 100 adult females and males of uniformly distributed ages between 20 and 70. Significant size and shape differences between genders were identified, and shape model utility is demonstrated by the production of statistically average male and female rib shapes for all rib levels. Simulated mechanical loading of the resulting model rib shapes showed that the stiffness of statistically average male and female ribs matched well with the average rib stiffness from each separate population. This in-plane rib shape model can be used to characterize variation in human rib geometry seen throughout the population, including investigation of the overall changes in shape and resultant mechanical properties that ribs undergo during aging or disease progression.

Certain medical treatments involve the introduction of exogenous liquids in the lungs. These liquids can form plugs within the airways. The plugs propagate throughout the branching network in the lungs being forced by airflow. They leave a deposited film on the airway walls and split at bifurcations. Understanding the resulting distribution of liquid throughout the lungs is important for the effective administration of the prescribed treatments. In this paper, we investigate numerically the splitting of a liquid plug by a two-dimensional pulmonary bifurcation under the influence of a transverse gravitational field. The splitting is characterized by the splitting ratio, which is the ratio of volume of the liquid plug in the daughter channels and depends on the capillary number and the orientation of the bifurcation plane with respect to a three-dimensional gravitational field. It is observed that gravity induces asymmetry in the splitting, causing the splitting ratio to be reduced. This effect is mitigated as the capillary number is increased. It is also observed that there exists a critical capillary number where the plug will not split and will instead propagate entirely into the gravitationally favoured daughter channel. We also compute the wall stresses on the bifurcation walls and observe the locations where stresses and their gradients are the highest in magnitude.

Bingham fluids behave like solids below a von Mises stress threshold, the yield stress, while above it they behave like Newtonian fluids. They are characterized by a dimensionless parameter, Bingham number (Bn), which is the ratio of the yield stress to a characteristic viscous stress. In this study, the non-inertial steady motion of a finite size gas bubble in both a plane 2D channel and an axi-symmetric tube filled by a Bingham fluid has been studied numerically. The Bingham number, Bn, is in the range 0 ≤ Bn ≤ 3, where Bn=0 is the Newtonian case, while the Capillary number which is the ratio of a characteristic viscous force to the surface tension has values Ca=0.05, 0.10, and 0.25. The volume of all axi-symmetric and 2D bubbles has been chosen to be identical for all parameter choices and large enough for the bubbles to be long compared to the channel/tube width/diameter. The Bingham fluid constitutive equation is approximated by a regularized equation. During the motion, the bubble interface is separated from the wall by a static liquid film. The film thickness scaled by the tube radius (axi-symmetric)/half of the channel height (2D) is the dimensionless film thickness, h. The results show that increasing Bn initially leads to an increase in h, however, the profile h versus Bn can be monotonic or non-monotonic depending on Ca values and 2D/axi-symmetric configurations. The yield stress also alters the shape of the front and rear of the bubble and suppresses the capillary waves at the rear of the bubble. The yield stress increases the magnitude of the wall shear stress and its gradient and therefore increases the potential for epithelial cell injuries in applications to lung airway mucus plugs. The topology of the yield surfaces as well the flow pattern in the bubble frame of reference varies significantly by Ca and Bn.

Mucociliary clearance is one of the major lines of defense of the human respiratory system. The mucus layer coating the airways is constantly moved along and out of the lung by the activity of motile cilia, expelling at the same time particles trapped in it. The efficiency of the cilia motion can experimentally be assessed by measuring the velocity of micro-beads traveling through the fluid surrounding the cilia. Here we present a mathematical model of the fluid flow and of the micro-beads motion. The coordinated movement of the ciliated edge is represented as a continuous envelope imposing a periodic moving velocity boundary condition on the surrounding fluid. Vanishing velocity and vanishing shear stress boundary conditions are applied to the fluid at a finite distance above the ciliated edge. The flow field is expanded in powers of the amplitude of the individual cilium movement. It is found that the continuous component of the horizontal velocity at the ciliated edge generates a 2D fluid velocity field with a parabolic profile in the vertical direction, in agreement with the experimental measurements. Conversely, we show than this model can be used to extract microscopic properties of the cilia motion by extrapolating the micro-bead velocity measurement at the ciliated edge. Finally, we derive from these measurements a scalar index providing a direct assessment of the cilia beating efficiency. This index can easily be measured in patients without any modification of the current clinical procedures., Author summary Mucociliary clearance is the first line of defense mechanisms of the human airways. The mucus transporting debris, particles, microorganisms and pollutants is carried away by the coordinated motion of cilia beating at the surface of the airway epithelium. We present here a mathematical and numerical model aiming at defining a global index for assessing the efficiency of this beating. Numerical simulations show that the bead velocity parallel to the wall varies according a parabolic profile with the distance to the wall. The velocity extrapolated at the wall is demonstrated to be a measurement of the momentum transfer between cilia and the surrounding fluid. This model allows us to interpret experimental measurements performed in a companion article and to propose a universal index characterizing the beating efficiency, which can be extracted in the current clinical setting.

Mucociliary clearance is one of the major lines of defense of the respiratory system. The mucus layer coating the pulmonary airways is moved along and out of the lung by the activity of motile cilia, thus expelling the particles trapped in it. Here we compare ex vivo measurements of a Newtonian flow induced by cilia beating (using micro-beads as tracers) and a mathematical model of this fluid flow, presented in greater detail in a second companion article. Samples of nasal epithelial cells placed in water are recorded by high-speed video-microscopy and ciliary beat pattern is inferred. Automatic tracking of micro-beads, used as markers of the flow generated by cilia motion, enables us also to assess the velocity profile as a function of the distance above the cilia. This profile is shown to be essentially parabolic. The obtained experimental data are used to feed a 2D mathematical and numerical model of the coupling between cilia, fluid, and micro-bead motion. From the model and the experimental measurements, the shear stress exerted by the cilia is deduced. Finally, this shear stress, which can easily be measured in the clinical setting, is proposed as a new index for characterizing the efficiency of ciliary beating., Author summary Mucociliary clearance is the first line of defense of the human pulmonary airways. Mucus transporting debris, particles, microorganisms and pollutants is carried away by the coordinated motion of cilia beating at the surface of the airway epithelium. We present here an experimental, mathematical and numerical study aiming at defining a global index for assessing the efficiency of this beating. We measure experimentally the ciliary beat frequency, ciliary beat amplitude, and metachronal wavelength on ciliated edges obtained from nasal brushing. Properties of fluid motion are simultaneously extracted from micro-bead tracking next to the ciliated edge. A mathematical and numerical model is developed to describe the fluid motion induced by the cilia tips considered as a moving wall. Experimental and numerical results show that the bead velocity is a parabolic function of the distance to the wall. It allows us to infer the shear stress exerted by the cilia on fluid from micro-bead tracking. This quantity is proposed as a universal index characterizing the beating efficiency, which can be extracted in the current clinical setting.

In the creation of engineered tissue constructs, the successful transport of nutrients and oxygen to the contained cells is a significant challenge. In highly porous scaffolds subject to cyclic strain, the mechanical deformations can induce substantial fluid pressure gradients, which affect the transport of solutes. In this article, we describe a poroelastic model to predict the solid and fluid mechanics of a highly porous hydrogel subject to cyclic strain. The model was validated by matching the predicted penetration of a bead into the hydrogel from the model with experimental observations and provides insight into nutrient transport. Additionally, the model provides estimates of the wall-shear stresses experienced by the cells embedded within the scaffold. These results provide insight into the mechanics of and convective nutrient transport within a cyclically strained hydrogel, which could lead to the improved design of engineered tissues.

This study investigates the isolated effect of rib shape on the mechanical characteristics of ribs subjected to multiple forms of loading. It aims to measure the variation in stiffness due to shape that is seen throughout the population and, in particular, provide a tool for researchers to better understand the influence of shape on resulting stiffness. A previously published six-parameter shape model of the central axis of human ribs was used. It has been shown to accurately model the overall rib path using intrinsic geometric properties such as size, aspect ratio, and skewness, through shapes based on logarithmic spirals with high curvature continuity. In this study the model was fitted to 19,500 ribs from 989 adult female and male CT scans having demographic distributions matching the US adult population. Mechanical loading was simulated through a simplified finite element model aimed at isolating rib shape from other factors influencing mechanical response. Four loading scenarios were used representing idealized free and constrained loading conditions in axial (body-anterior) and lateral directions. Characteristic rib stiffness and maximum stress location were tracked as simulation output measures. Regression models of rib stiffness found that all shape model parameters added information when predicting stiffness under each loading condition, with their linear combination able to account for 95% of the population stiffness variation due to shape in midlevel ribs for free axial loading, and 92%-98% in other conditions. Full regression models including interactive terms explained up to 99% of population variability. Results allow researchers to better evaluate the differences in stiffness results that are obtained from physical testing by providing a framework with which to explain variation due to rib shape.

We use lubrication theory and matched asymptotic expansions to model the quasi-steady propagation of a liquid plug or bolus through an elastic tube. In the limit of small capillary number, asymptotic expressions are found for the pressure drop across the bolus and the thickness of the liquid film left behind, as functions of the capillary number, the thickness of the liquid lining ahead of the bolus and the elastic characteristics of the tube wall. These results generalize the well-known theory for the low capillary number motion of a bubble through a rigid tube (Bretherton 1961). As in that theory, both the pressure drop across the bolus and the thickness of the film it leaves behind vary like the two-thirds power of the capillary number. In our generalized theory, the coefficients in the power laws depend on the elastic properties of the tube.For a given thickness of the liquid lining ahead of the bolus, we identify a critical imposed pressure drop above which the bolus will eventually rupture, and hence the tube will reopen. We find that generically a tube with smaller hoop tension or smaller longitudinal tension is easier to reopen. This flow regime is fundamental to reopening of pulmonary airways, which may become plugged through disease or by instilled/aspirated fluids.

We study numerically the steady creeping motion of Bingham liquid plugs in two-dimensional channels as a model of mucus behaviour during airway reopening in pulmonary airways. In addition to flow analysis related to propagation of the plug, the stress distribution on the wall is studied for better understanding of potential airway epithelial cell injury mechanisms. The yield stress behaviour of the fluid was implemented through a regularized constitutive equation. The capillary number, $\mathit{Ca}$, and the Bingham number, $\mathit{Bn}$, which is the ratio of the yield stress to a characteristic viscous stress, varied over the ranges 0.025–0.1 and 0–1.5, respectively. For the range of parameters studied, it was found that, while the yield stress reduces the magnitude of the shearing along the wall, it can magnify the amplitude of the wall shear stress gradient significantly, and also it can elevate the magnitude of the wall shear stress and wall pressure gradient up to 30 % and 15 %, respectively. Therefore, the motion of mucus plugs can be more damaging to the airway epithelial cells due to the yield stress properties of mucus. The yield stress also modifies the profile of the plug where the amplitude of the capillary waves at the leading meniscus decreases with increase in $\mathit{Bn}$. Other findings are that: the thickness of the static film increases with increasing $\mathit{Bn}$; the driving pressure difference increases linearly with $\mathit{Bn}$; and increasing $\mathit{Bn}$ extends any wall stagnation point beneath the leading meniscus to an unyielded line segment beneath the leading meniscus. With an increase in $\mathit{Bn}$, the unyielded areas appear and grow in the adjacent wall film as well as the core region of the plug between the two menisci. The plug length, ${L}_{P} $, mostly modifies the topology of the yield surfaces. It was found that the unyielded area in the core region between the two menisci grows as the plug length decreases. The very short Bingham plug behaves like a solid lamella. In all computed liquid plugs moving steadily, the von Mises stress attains its maximum value near the interface of the leading meniscus in the transition region. For Bingham plugs moving very slowly, $\mathit{Ca}\ensuremath{\rightarrow} 0$, the driving pressure is non-zero.

Understanding the impact distribution of particles entering the human respiratory system is of primary importance as it concerns not only atmospheric pollutants or dusts of various kinds but also the efficiency of aerosol therapy and drug delivery. To model this process, current approaches consist of increasingly complex computations of the aerodynamics and particle capture phenomena, performed in geometries trying to mimic lungs in a more and more realistic manner for as many airway generations as possible. Their capture results from the complex interplay between the details of the aerodynamic streamlines and the particle drag mechanics in the resulting flow. In contrast, the present work proposes a major simplification valid for most airway generations at quiet breathing. Within this context, focusing on particle escape rather than capture reveals a simpler structure in the entire process. When gravity can be neglected, we show by computing the escape rates in various model geometries that, although still complicated, the escape process can be depicted as a multiplicative escape cascade in which each elementary step is associated with a single bifurcation. As a net result, understanding of the particle capture may not require computing particle deposition in the entire lung structure but can be abbreviated in some regions using our simpler approach of successive computations in single realistic bifurcations. Introducing gravity back into our model, we show that this multiplicative model can still be successfully applied on up to nine generations, depending on particle type and breathing conditions.

Airways of the peripheral lung are prone to closure at low lung volumes. Deficiency or dysfunction of pulmonary surfactant during various lung diseases compounds this event by destabilizing the liquid lining of small airways and giving rise to occluding liquid plugs in airways. Propagation of liquid plugs in airways during inflation of the lung exerts large mechanical forces on airway cells. We describe a microfluidic model of small airways of the lung that mimics airway architecture, recreates physiologic levels of pulmonary pressures, and allows studying cellular response to repeated liquid plug propagation events. Substantial cellular injury happens due to the propagation of liquid plugs devoid of surfactant. We show that addition of a physiologic concentration of a clinical surfactant, Survanta, to propagating liquid plugs protects the epithelium and significantly reduces cell death. Although the protective role of surfactants has been demonstrated in models of a propagating air finger in liquid-filled airways, this is the first time to study the protective role of surfactants in liquid plugs where fluid mechanical stresses are expected to be higher than in air fingers. Our parallel computational simulations revealed a significant decrease in mechanical forces in the presence of surfactant, confirming the experimental observations. The results support the practice of providing exogenous surfactant to patients in certain clinical settings as a protective mechanism against pathologic flows. More importantly, this platform provides a useful model to investigate various surface tension-mediated lung diseases at the cellular level.

The liquid lining in small human airways can become unstable and form liquid plugs that close off the airways. Direct numerical simulations are carried out on an airway model to study this airway instability and the flow-induced stresses on the airway walls. The equations governing the fluid motion and the interfacial boundary conditions are solved using the finite-volume method coupled with the sharp interface method for the free surface. The dynamics of the closure process is simulated for a viscous Newtonian film with constant surface tension and a passive core gas phase. In addition, a special case is examined that considers the core dynamics so that comparisons can be made with the experiments of Bian et al. (J. Fluid Mech., vol. 647, 2010, p. 391). The computed flow fields and stress distributions are consistent with the experimental findings. Within the short time span of the closure process, there are large fluctuations in the wall shear stress. Furthermore, dramatic velocity changes in the film during closure indicate a steep normal stress gradient on the airway wall. The computational results show that the wall shear stress, normal stress and their gradients during closure can be high enough to injure airway epithelial cells.

We describe a bio-inspired microfluidic system that resembles pulmonary airways and enables on-chip generation of airway occluding liquid plugs from a stratified air-liquid two-phase flow. User-defined changes in the air stream pressure facilitated by mechanical components and tuning the wettability of the microchannels enable generation of well-defined liquid plugs. Significant differences are observed in liquid plug generation and propagation when surfactant is added to the buffer. The plug flow patterns suggest a protective role of surfactant for airway epithelial cells against pathological flow-induced mechanical stresses. We discuss the implications of the findings for clinical settings. This approach and the described platform will enable systematic investigation of the effect of different degrees of fluid mechanical stresses on lung injury at the cellular level and administration of exogenous therapeutic surfactants.

The lungs are the major organs of the respiratory system and contain a branching network of airway tubes that become shorter, narrower, and more numerous as they penetrate deeper into the lung. The tracheobronchial tree comprises 3 major types of airways: cartilaginous bronchi, membranous bronchioles, and gas exchange alveolar ducts. Upper airways and terminal bronchioles act merely as conduits for the passage of gas, whereas respiratory bronchioles and alveolar ducts carry out both conducting and gas exchange functions. Airways less than 1 to 2 mm in diameter that include membranous, terminal, and respiratory bronchioles as well as alveolar ducts are known as distal airways.1 These airways have a very large total cross-sectional area and relatively low resistance to the flow of gas (~10% to 20% of the total lung resistance).2 Due to their small size and high compliance, distal airways are prone to instabilities and closure at low lung volumes (eg, at the end of expiration). To prevent these fine structures from collapse (atelectasis), secretory cells of alveolar and neighboring airway epithelium produce pulmonary surfactant that distributes at the surface of the liquid lining layer of distal lung epithelium.3,4 Functional surfactant reduces surface tension at the luminal air-liquid interface and, thus, maintains the patency of airways and alveoli at low lung volumes. The presence of hysteresis in the pressure-volume curve of the lung indeed reflects this point ( Figure 1 ): the pressure required to support a certain volume (V) of the lung units during deflation (P2) is smaller than that when lungs are inflated (P1)5. During deflation, the surfactant film is compressed and presumably a more compact layer of surfactant lipid molecules is present at the air-liquid interface, which results in a lower surface tension. Active surfactant at the luminal air-liquid …

Purpose Effective treatment of respiratory failure in premature infants remains an unsolved problem. The development of an artificial placenta, in the form of a pumpless arteriovenous extracorporeal life support (AV-ECLS) circuit that maintains fetal circulation, is an appealing alternative. Methods A near-term (140 d/term = 145 days) neonatal lamb model was used (n = 7). Fetuses were exposed by hysterotomy, and flow probes were placed on the ductus arteriosus, aorta, and carotid artery. Catheters were placed into the umbilical vessels, and pumpless AV-ECLS was initiated. Fetuses were submerged in a warm saline bath, and support was maintained for up to 4 hours. Results Mean initial device flow was 383 mL/min but steadily declined to 177 mL/min at 4 hours. Mean initial pO2 was 24 mm Hg and 18 mm Hg at 4 hours. Initial mean pCO2 was 60 mm Hg and declined to 42 mm Hg at 4 hours. Mean arterial pressure was initially 43 mm Hg and decreased to 34 mm Hg at 4 hours. Flow in the ductus arteriosus was maintained for 4 hours. Of 7 fetuses, 5 survived 4 hours of support. Conclusions Pumpless AV-ECLS can support gas exchange and maintain fetal circulation in a neonatal lamb model for a 4-hour period. Prolonged support (>4 hours) is hampered by high cannula resistance and declining device flow.

We describe the mechanisms by which liquids and surfactants can be delivered into the pulmonary airways. These are instilled and transported throughout the lung in clinical therapies such as surfactant replacement therapy, partial liquid ventilation and drug delivery. The success of these treatments is contingent on the liquid distribution and the delivery to targeted regions of the lung. The targeting of a liquid plug can be influenced by a variety of factors such as the physical properties of the liquid, the interfacial activity, the gravitational orientation, instillation method and propagation speed. We provide a review of experimental and theoretical studies that examine these effects in single tubes or channels, in tubes with single bifurcations and in the whole lung.

We describe a microfabricated airway system integrated with computerized air–liquid two-phase microfluidics that enables on-chip engineering of human airway epithelia and precise reproduction of physiologic or pathologic liquid plug flows found in the respiratory system. Using this device, we demonstrate cellular-level lung injury under flow conditions that cause symptoms characteristic of a wide range of pulmonary diseases. Specifically, propagation and rupture of liquid plugs that simulate surfactant-deficient reopening of closed airways lead to significant injury of small airway epithelial cells by generating deleterious fluid mechanical stresses. We also show that the explosive pressure waves produced by plug rupture enable detection of the mechanical cellular injury as crackling sounds.

This paper describes a simple microfluidic sorting system that can perform size-profiling and continuous mass-dependent separation of particles through combined use of gravity (1g) and hydrodynamic flows capable of rapidly amplifying sedimentation-based separation between particles. Operation of the device relies on two microfluidic transport processes: i) initial hydrodynamic focusing of particles in a microchannel oriented parallel to gravity, ii) subsequent sample separation where positional difference between particles with different mass generated by sedimentation is further amplified by hydrodynamic flows whose streamlines gradually widen out due to the geometry of a widening microchannel oriented perpendicular to gravity. The microfluidic sorting device was fabricated in poly(dimethylsiloxane) (PDMS), and hydrodynamic flows in microchannels were driven by gravity without using external pumps. We conducted theoretical and experimental studies on fluid dynamic characteristics of laminar flows in widening microchannels and hydrodynamic amplification of particle separation. Direct trajectory monitoring, collection, and post-analysis of separated particles were performed using polystyrene microbeads with different sizes to demonstrate rapid (< 1 min) and high-purity (> 99.9 %) separation. Finally, we demonstrated biomedical applications of our system by isolating small-sized (diameter < 6 μm) perfluorocarbon liquid droplets from polydisperse droplet emulsions, which is crucial in preparing contrast agents for safe, reliable ultrasound medical imaging, tracers for magnetic resonance imaging, or transpulmonary droplets used in ultrasound-based occlusion therapy for cancer treatment. Our method enables straightforward, rapid real-time size-monitoring and continuous separation of particles in simple stand-alone microfabricated devices without the need for bulky and complex external power sources. We believe that this system will provide a useful tool o separate colloids and particles for various analytical and preparative applications, and may hold 3 potential for separation of cells or development of diagnostic tools requiring point-of-care sample preparation or testing.

The mucociliary clearance in the bronchial tree is the main mechanism by which the lungs clear themselves of deposited particulate matter. In this work, a macroscopic model of the clearance mechanism is proposed. Lubrication theory is applied for thin films with both surface tension effects and a moving wall boundary. The flow field is computed by the use of a finite-volume scheme on an unstructured grid that replicates a bronchial bifurcation. The carina in bronchial bifurcations is of special interest because it is a location of increased deposition of inhaled particles. In this study, the mucus flow is computed for different values of the surface tension. It is found that a minimal surface tension is necessary for efficiently removing the mucus while maintaining the mucus film thickness at physiological levels.

Surfactant replacement therapy (SRT) involves instillation of a liquid-surfactant mixture directly into the lung airway tree. It is widely successful for treating surfactant deficiency in premature neonates who develop neonatal respiratory distress syndrome (NRDS). However, when applied to adults with acute respiratory distress syndrome (ARDS), early successes were followed by failures. This unexpected and puzzling situation is a vexing issue in the pulmonary community. A pressing question is whether the instilled surfactant mixture actually reaches the adult alveoli/acinus in therapeutic amounts. In this study, to our knowledge, we present the first mathematical model of SRT in a 3D lung structure to provide insight into answering this and other questions. The delivery is computed from fluid mechanical principals for 3D models of the lung airway tree for neonates and adults. A liquid plug propagates through the tree from forced inspiration. In two separate modeling steps, the plug deposits a coating film on the airway wall and then splits unevenly at the bifurcation due to gravity. The model generates 3D images of the resulting acinar distribution and calculates two global indexes, efficiency and homogeneity. Simulating published procedural methods, we show the neonatal lung is a well-mixed compartment, whereas the adult lung is not. The earlier, successful adult SRT studies show comparatively good index values implying adequate delivery. The later, failed studies used different protocols resulting in very low values of both indexes, consistent with inadequate acinar delivery. Reasons for these differences and the evolution of failure from success are outlined and potential remedies discussed.

Liquid plugs may form in pulmonary airways during the process of liquid instillation or removal in many clinical treatments. During inspiration the plug may split at airway bifurcations and lead to a nonuniform final liquid distribution, which can adversely affect treatment outcomes. In this paper, a combination of bench top experimental and theoretical studies is presented to study the effects of inertia and gravity on plug splitting in an airway bifurcation model to simulate the liquid distributions in large airways. The splitting ratio, Rs, is defined as the ratio of the plug volume entering the upper (gravitationally opposed) daughter tube to the lower (gravitationally favored) one. Rs is measured as a function of parent tube Reynolds number, Rep; gravitational orientations for roll angle, phi, and pitch angle, gamma; parent plug length LP; and the presence of pre-existing plug blockages in downstream daughter tubes. Results show that increasing Rep causes more homogeneous splitting. A critical Reynolds number Rec is found to exist so that when Rep < or = Rec, Rs = 0, i.e., no liquid enters the upper daughter tube. Rec increases while Rs decreases with increasing the gravitational effect, i.e., increasing phi and gamma. When a blockage exists in the lower daughter, Rec is only found at phi = 60 deg in the range of Rep studied, and the resulting total mass ratio can be as high as 6, which also asymptotes to a finite value for different phi as Rep increases. Inertia is further demonstrated to cause more homogeneous plug splitting from a comparison study of Rs versus Cap (another characteristic speed) for three liquids: water, glycerin, and LB-400X. A theoretical model based on entrance flow for the plug in the daughters is developed and predicts Rs versus Rep. The frictional pressure drop, as a part of the total pressure drop, is estimated by two fitting parameters and shows a linear relationship with Rep. The theory provides a good prediction on liquid plug splitting and well simulates the liquid distributions in the large airways of human lungs.

Flow limitation in liquid-filled lungs is examined in intact rabbit experiments and a theoretical model. Flow limitation (“choked” flow) occurs when the expiratory flow reaches a maximum value and further increases in driving pressure do not increase the flow. In total liquid ventilation this is characterized by the sudden development of excessively negative airway pressures and airway collapse at the choke point. The occurrence of flow limitation limits the efficacy of total liquid ventilation by reducing the minute ventilation. In this paper we investigate the effects of liquid properties on flow limitation in liquid-filled lungs. It is found that the behavior of liquids with similar densities and viscosities can be quite different. The results of the theoretical model, which incorporates alveolar compliance and airway resistance, agrees qualitatively well with the experimental results. Lung compliance and airway resistance are shown to vary with the perfluorocarbon liquid used to fill the lungs. Surfactant is found to modify the interfacial tension between saline and perfluorocarbon, and surfactant activity at the interface of perfluorocarbon and the native aqueous lining of the lungs appears to induce hysteresis in pressure–volume curves for liquid-filled lungs. Ventilation with a liquid that results in low viscous resistance and high elastic recoil can reduce the amount of liquid remaining in the lungs when choke occurs, and, therefore, may be desirable for liquid ventilation.

This review describes recent developments in microfabricated flow cytometers and related microfluidic devices that can detect, analyze, and sort cells or particles. The high-speed analytical capabilities of flow cytometry depend on the cooperative use of microfluidics, optics and electronics. Along with the improvement of other components, replacement of conventional glass capillary-based fluidics with microfluidic sample handling systems operating in microfabricated structures enables volume- and power-efficient, inexpensive and flexible analysis of particulate samples. In this review, we present various efforts that take advantage of novel microscale flow phenomena and microfabrication techniques to build microfluidic cell analysis systems.

In this study, we investigate the steady propagation of a liquid plug within a two-dimensional channel lined by a uniform, thin liquid film. The Navier-Stokes equations with free-surface boundary conditions are solved using the finite volume numerical scheme. We examine the effect of varying plug propagation speed and plug length in both the Stokes flow limit and for finite Reynolds number (Re). For a fixed plug length, the trailing film thickness increases with plug propagation speed. If the plug length is greater than the channel width, the trailing film thickness agrees with previous theories for semi-infinite bubble propagation. As the plug length decreases below the channel width, the trailing film thickness decreases, and for finite Re there is significant interaction between the leading and trailing menisci and their local flow effects. A recirculation flow forms inside the plug core and is skewed towards the rear meniscus as Re increases. The recirculation velocity between both tips decreases with the plug length. The macroscopic pressure gradient, which is the pressure drop between the leading and trailing gas phases divided by the plug length, is a function of U and U2, where U is the plug propagation speed, when the fluid property and the channel geometry are fixed. The U2 term becomes dominant at small values of the plug length. A capillary wave develops at the front meniscus, with an amplitude that increases with Re, and this causes large local changes in wall shear stresses and pressures.

Soluble surfactant and airway surface liquid transport are examined using a mathematical model of Marangoni flows which accounts for airway branching and for cyclic airway stretching. Both radial and longitudinal wall strains are considered. The model allows for variation of the amplitude and frequency of the motion, as may occur under a variety of ventilatory situations occurring during surfactant replacement therapy. The soluble surfactant dynamics of the thin fluid film are modeled by linear sorption. The delivery of surfactants into the lung is handled by setting the proximal boundary condition to a higher concentration compared to the distal boundary condition. Starting with a steady-state, nonuniform, surfactant distribution, we find that transport of surfactant into the lung is enhanced for increasing strain amplitudes. However, for fixed amplitude, increasing frequency has a smaller effect. At small strain amplitudes, increasing frequency enhances transport, but at large strain amplitudes, increasing cycling frequency has the opposite effect.

Liquid can be instilled into the pulmonary airways during medical procedures such as surfactant replacement therapy, partial liquid ventilation, and pulmonary drug delivery. For all cases, understanding the dynamics of liquid distribution in the lung will increase the efficacy of treatment. A recently developed imaging technique for the study of real-time liquid transport dynamics in the pulmonary airways was used to investigate the effect of respiratory rate on the distribution of an instilled liquid, surfactant, in a rat lung. Twelve excised rat lungs were suspended vertically, and a single bolus (0.05 ml) of exogenous surfactant (Survanta, Ross Laboratories, Columbus, OH) mixed with radiopaque tracer was instilled as a plug into the trachea. The lungs were ventilated with a 4-ml tidal volume for 20 breaths at one of two respiratory rates: 20 or 60 breaths/min. The motion of radiodense surfactant was imaged at 30 frames/s with a microfocal X-ray source and an image intensifier. Dynamics of surfactant distribution were quantified for each image by use of distribution statistics and a homogeneity index. We found that the liquid distribution depended on the time to liquid plug rupture, which depends on ventilation rate. At 20 breaths/min, liquid was localized in the gravity-dependent region of the lung. At 60 breaths/min, the liquid coated the airways, providing a more vertically uniform liquid distribution.