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.

Computational pulmonary edema: A microvascular model of alveolar capillary and interstitial flow

We present a microvascular model of fluid transport in the alveolar septa related to pulmonary edema. It consists of a two-dimensional capillary sheet coursing by several alveoli. The alveolar epithelial membrane runs parallel to the capillary endothelial membrane with an interstitial layer in between, making one long septal tract. A coupled system of equations uses lubrication theory for the capillary blood, Darcy flow for the porous media of the interstitium, a passive alveolus, and the Starling equation at both membranes. Case examples include normal physiology, cardiogenic pulmonary edema, acute respiratory distress syndrome (ARDS), hypoalbuminemia, and effects of PEEP. COVID-19 has dramatically increased ARDS in the world population, raising the urgency for such a model to create an analytical framework. Under normal conditions fluid exits the alveolus, crosses the interstitium, and enters the capillary. For edema, this crossflow is reversed with fluid leaving the capillary and entering the alveolus. Because both the interstitial and capillary pressures decrease downstream, the reversal can occur within a single septal tract, with edema upstream and clearance downstream. Clinically useful solution forms are provided allowing calculation of interstitial fluid pressure, crossflows, and critical capillary pressures. Overall, the interstitial pressures are found to be significantly more positive than values used in the traditional physiological literature. That creates steep gradients near the upstream and downstream end outlets, driving significant flows toward the distant lymphatics. This new physiological flow provides an explanation to the puzzle, noted since 1896, of how pulmonary lymphatics can function so far from the alveoli: the interstitium is self-clearing.

Retraction: "Computational pulmonary edema: A microvascular model of alveolar capillary and interstitial flow" [APL Bioeng. , 046104 (2022)]

[This retracts the article DOI: 10.1063/5.0109107.].

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.

Computational pulmonary edema: A microvascular model of alveolar capillary and interstitial flow

We present a microvascular model of fluid transport in the alveolar septa related to pulmonary edema. It consists of a two-dimensional capillary sheet coursing by several alveoli. The alveolar epithelial membrane runs parallel to the capillary endothelial membrane with an interstitial layer in between, making one long septal tract. A coupled system of equations is derived using lubrication theory for the capillary blood, Darcy flow for the porous media of the interstitium, a passive alveolus, and the Starling equation at both membranes. Case examples include normal physiology, cardiogenic pulmonary edema, noncardiogenic edema Acute Respiratory Distress Syndrome (ARDS) and hypoalbuminemia, and the effects of positive end expiratory pressure. COVID-19 has dramatically increased ARDS in the world population, raising the urgency for such a model to create an analytical framework. Under normal conditions, the fluid exits the alveolus, crosses the interstitium, and enters the capillary. For edema, this crossflow is reversed with the fluid leaving the capillary and entering the alveolus. Because both the interstitial and capillary pressures decrease downstream, the reversal can occur within a single septal tract, with edema upstream and clearance downstream. Overall, the interstitial pressures are found to be significantly more positive than values used in the traditional physiological literature that creates steep gradients near the upstream and downstream end outlets, driving significant flows toward the distant lymphatics. This new physiological flow may provide a possible explanation to the puzzle, noted since 1896, of how pulmonary lymphatics can function so far from the alveoli: the interstitium can be self-clearing.

Splitting of a three-dimensional liquid plug at an airway bifurcation

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.

Pulmonary Interstitial Matrix and Lung Fluid Balance From Normal to the Acutely Injured Lung

This review analyses the mechanisms by which lung fluid balance is strictly controlled in the air-blood barrier (ABB). Relatively large trans-endothelial and trans-epithelial Starling pressure gradients result in a minimal flow across the ABB thanks to low microvascular permeability aided by the macromolecular structure of the interstitial matrix. These edema safety factors are lost when the integrity of the interstitial matrix is damaged. The result is that small Starling pressure gradients, acting on a progressively expanding alveolar barrier with high permeability, generate a high transvascular flow that causes alveolar flooding in minutes. We modeled the trans-endothelial and trans-epithelial Starling pressure gradients under control conditions, as well as under increasing alveolar pressure (Palv) conditions of up to 25 cmH2O. We referred to the wet-to-dry weight (W/D) ratio, a specific index of lung water balance, to be correlated with the functional state of the interstitial structure. W/D averages ∼5 in control and might increase by up to ∼9 in severe edema, corresponding to ∼70% loss in the integrity of the native matrix. Factors buffering edemagenic conditions include: (i) an interstitial capacity for fluid accumulation located in the thick portion of ABB, (ii) the increase in interstitial pressure due to water binding by hyaluronan (the "safety factor" opposing the filtration gradient), and (iii) increased lymphatic flow. Inflammatory factors causing lung tissue damage include those of bacterial/viral and those of sterile nature. Production of reactive oxygen species (ROS) during hypoxia or hyperoxia, or excessive parenchymal stress/strain [lung overdistension caused by patient self-induced lung injury (P-SILI)] can all cause excessive inflammation. We discuss the heterogeneity of intrapulmonary distribution of W/D ratios. A W/D ∼6.5 has been identified as being critical for the transition to severe edema formation. Increasing Palv for W/D > 6.5, both trans-endothelial and trans-epithelial gradients favor filtration leading to alveolar flooding. Neither CT scan nor ultrasound can identify this initial level of lung fluid balance perturbation. A suggestion is put forward to identify a non-invasive tool to detect the earliest stages of perturbation of lung fluid balance before the condition becomes life-threatening.

Peristaltic flow in the glymphatic system

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.

Effects of Surface Tension and Yield Stress on Mucus Plug Rupture: A Numerical Study

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.

Microphysiological systems modeling acute respiratory distress syndrome that capture mechanical force-induced injury-inflammation-repair

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.

Surfactant delivery in rat lungs: Comparing 3D geometrical simulation model with experimental instillation

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.

Steady Displacement of Long Gas Bubbles in Channels and Tubes Filled by a Bingham Fluid

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.

A new index for characterizing micro-bead motion in a flow induced by ciliary beating: Part II, modeling

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.

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.

A new index for characterizing micro-bead motion in a flow induced by ciliary beating: Part I, experimental analysis

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.

The effect of age and demographics on rib shape

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 < 0.0001). This study reports a novel aging effect whereby both the rib end-to-end separation and rib aspect ratio are seen to increase with age, producing elongated and flatter overall rib shapes in elderly populations, with age alone explaining up to 20% of population variability in the aspect ratio of mid-level ribs. Age was not strongly associated with overall rib arc length, indicating that age effects were related to shape change rather than overall bone length. The rib shape effect was found to be more strongly and directly associated with age than previously documented age-related changes in rib angulation. Other demographic results showed height and sex being most strongly associated with rib size, and weight most strongly associated with rib pump-handle angle. Results from the study provide a statistical model for building rib shapes typical of any given demographic by age, height, weight, and sex, and can be used to help build population-specific computational models of the thoracic rib cage. Furthermore, results also quantify normal population ranges for rib shape parameters which can be used to improve the assessment and treatment of rib skeletal deformity and disease.

Age-related changes in thoracic skeletal geometry of elderly females

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.

A Macroscopic Model for Simulating the Mucociliary Clearance in a Bronchial Bifurcation: The Role of Surface Tension

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.

The Effect of Rib Shape on Stiffness

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.

Modeling female and male rib geometry with logarithmic spirals

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.

A microfluidic model to study fluid dynamics of mucus plug rupture in small lung airways

Fluid dynamics of mucus plug rupture is important to understand mucus clearance in lung airways and potential effects of mucus plug rupture on epithelial cells at lung airway walls. We established a microfluidic model to study mucus plug rupture in a collapsed airway of the 12th generation. Mucus plugs were simulated using Carbopol 940 (C940) gels at concentrations of 0.15%, 0.2%, 0.25%, and 0.3%, which have non-Newtonian properties close to healthy and diseased lung mucus. The airway was modeled with a polydimethylsiloxane microfluidic channel. Plug motion was driven by pressurized air. Global strain rates and shear stress were defined to quantitatively describe plug deformation and rupture. Results show that a plug needs to overcome yield stress before deformation and rupture. The plug takes relatively long time to yield at the high Bingham number. Plug length shortening is the more significant deformation than shearing at gel concentration higher than 0.15%. Although strain rates increase dramatically at rupture, the transient shear stress drops due to the shear-thinning effect of the C940 gels. Dimensionless time-averaged shear stress, T xy , linearly increases from 3.7 to 5.6 times the Bingham number as the Bingham number varies from 0.018 to 0.1. The dimensionless time-averaged shear rate simply equals to T xy /2. In dimension, shear stress magnitude is about one order lower than the pressure drop, and one order higher than yield stress. Mucus with high yield stress leads to high shear stress, and therefore would be more likely to cause epithelial cell damage. Crackling sounds produced with plug rupture might be more detectable for gels with higher concentration.

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.

Trapping of embolic particles in a vessel phantom by cavitation-enhanced acoustic streaming

Cavitation clouds generated by short, high-amplitude, focused ultrasound pulses were previously observed to attract, trap, and erode thrombus fragments in a vessel phantom. This phenomenon may offer a noninvasive method to capture and eliminate embolic fragments flowing through the bloodstream during a cardiovascular intervention. In this article, the mechanism of embolus trapping was explored by particle image velocimetry (PIV). PIV was used to examine the fluid streaming patterns generated by ultrasound in a vessel phantom with and without crossflow of blood-mimicking fluid. Cavitation enhanced streaming, which generated fluid vortices adjacent to the focus. The focal streaming velocity, uf, was as high as 120 cm/s, while mean crossflow velocities, uc, were imposed up to 14 cm/s. When a solid particle 3-4 mm diameter was introduced into crossflow, it was trapped near the focus. Increasing uf promoted particle trapping while increasing uc promoted particle escape. The maximum crossflow Reynolds number at which particles could be trapped, Rec, was approximately linear with focal streaming number, Ref, i.e. Rec = 0.25Ref + 67.44 (R(2) = 0.76) corresponding to dimensional velocities uc = 0.084uf + 3.122 for 20 < uf < 120 cm/s. The fluidic pressure map was estimated from PIV and indicated a negative pressure gradient towards the focus, trapping the embolus near this location.

A poroelastic model describing nutrient transport and cell stresses within a cyclically strained collagen hydrogel

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.

An asymptotic model of particle deposition at an airway bifurcation

Particle transport and deposition associated with flow over a wedge is investigated as a model for particle transport and flow at the carina of an airway bifurcation during inspiration. Using matched asymptotics, a uniformly valid solution is obtained to represent the high Reynolds number flow over a wedge that considers the viscous boundary layer near the wedge and the outer inviscid region and is then used to solve the particle transport equations. Sometimes particle impaction on the wedge is prevented due to the boundary layer. We call this boundary layer shielding (BLS). This effect can be broken down into different types: rejection, trapping and deflection that are described by what happens to the particle's initial negative velocity normal to the wall either changing sign, reaching zero, or remaining negative in the boundary layer region. The deposition efficiency depends on the critical Stokes number but exhibits a weak dependence on Reynolds number. Deposition efficiency for S(c) in the range 0 < S(c) < 0.4 yields the following relationship De ≈ (1.867S(c)¹·⁷⁸-0.016) sin(βπ/2) at large Reynolds numbers, where βπ is the wedge angle. For a specific deposition efficiency, S(c) decreases as βπ increases. The distribution of impacted particles was also computed and revealed that particles primarily impact within one airway diameter of the carina, consistent with computational fluid dynamics approaches. This work provides a new insight that the BLS inherent to the wedge component of the structure is the dominant reason for the particle distribution. This finding is important in linking aerosol deposition to the location of airway disease as well as target sites for therapeutic deposition.

Epithelium damage and protection during reopening of occluded airways in a physiologic microfluidic pulmonary airway model

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.

Microprinted feeder cells guide embryonic stem cell fate

We introduce a non-contact approach to microprint multiple types of feeder cells in a microarray format using immiscible aqueous solutions of two biopolymers. Droplets of cell suspension in the denser aqueous phase are printed on a substrate residing within a bath of the immersion aqueous phase. Due to their affinity to the denser phase, cells remain localized within the drops and adhere to regions of the substrate underneath the drops. We show the utility of this technology for creating duplex heterocellular stem cell niches by printing two different support cell types on a gel surface and overlaying them with mouse embryonic stem cells (mESCs). As desired, the type of printed support cell spatially direct the fate of overlaid mESCs. Interestingly, we found that interspaced mESCs colonies on differentiation-inducing feeder cells show enhanced neuronal differentiation and give rise to dense networks of neurons. This cell printing technology provides unprecedented capabilities to efficiently identify the role of various feeder cells in guiding the fate of stem cells.

Particle capture into the lung made simple?

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.

Combination of fluid and solid mechanical stresses contribute to cell death and detachment in a microfluidic alveolar model

Studies using this micro-system demonstrated significant morphological differences between alveolar epithelial cells (transformed human alveolar epithelial cell line, A549 and primary murine alveolar epithelial cells, AECs) exposed to combination of solid mechanical and surface-tension stresses (cyclic propagation of air-liquid interface and wall stretch) compared to cell populations exposed solely to cyclic stretch. We have also measured significant differences in both cell death and cell detachment rates in cell monolayers experiencing combination of stresses. This research describes new tools for studying the combined effects of fluid mechanical and solid mechanical stress on alveolar cells. It also highlights the role that surface tension forces may play in the development of clinical pathology, especially under conditions of surfactant dysfunction. The results support the need for further research and improved understanding on techniques to reduce and eliminate fluid stresses in clinical settings.

Respiratory fluid mechanics

This article covers several aspects of respiratory fluid mechanics that have been actively investigated by our group over the years. For the most part, the topics involve two-phase flows in the respiratory system with applications to normal and diseased lungs, as well as therapeutic interventions. Specifically, the topics include liquid plug flow in airways and at airway bifurcations as it relates to surfactant, drug, gene, or stem cell delivery into the lung; liquid plug rupture and its damaging effects on underlying airway epithelial cells as well as a source of crackling sounds in the lung; airway closure from "capillary-elastic instabilities," as well as nonlinear stabilization from oscillatory core flow which we call the "oscillating butter knife;" liquid film, and surfactant dynamics in an oscillating alveolus and the steady streaming, and surfactant spreading on thin viscous films including our discovery of the Grotberg-Borgas-Gaver shock.

Dynamics of liquid plugs of buffer and surfactant solutions in a micro-engineered pulmonary airway model

We describe a bioinspired 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 effect of viscoelasticity on the stability of a pulmonary airway liquid layer

The lungs consist of a network of bifurcating airways that are lined with a thin liquid film. This film is a bilayer consisting of a mucus layer on top of a periciliary fluid layer. Mucus is a non-Newtonian fluid possessing viscoelastic characteristics. Surface tension induces flows within the layer, which may cause the lung's airways to close due to liquid plug formation if the liquid film is sufficiently thick. The stability of the liquid layer is also influenced by the viscoelastic nature of the liquid, which is modeled using the Oldroyd-B constitutive equation or as a Jeffreys fluid. To examine the role of mucus alone, a single layer of a viscoelastic fluid is considered. A system of nonlinear evolution equations is derived using lubrication theory for the film thickness and the film flow rate. A uniform film is initially perturbed and a normal mode analysis is carried out that shows that the growth rate g for a viscoelastic layer is larger than for a Newtonian fluid with the same viscosity. Closure occurs if the minimum core radius, R(min)(t), reaches zero within one breath. Solutions of the nonlinear evolution equations reveal that R(min) normally decreases to zero faster with increasing relaxation time parameter, the Weissenberg number We. For small values of the dimensionless film thickness parameter epsilon, the closure time, t(c), increases slightly with We, while for moderate values of epsilon, ranging from 14% to 18% of the tube radius, t(c) decreases rapidly with We provided the solvent viscosity is sufficiently small. Viscoelasticity was found to have little effect for epsilon>0.18, indicating the strong influence of surface tension. The film thickness parameter epsilon and the Weissenberg number We also have a significant effect on the maximum shear stress on tube wall, max(tau(w)), and thus, potentially, an impact on cell damage. Max(tau(w)) increases with epsilon for fixed We, and it decreases with increasing We for small We provided the solvent viscosity parameter is sufficiently small. For large epsilon approximately 0.2, there is no significant difference between the Newtonian flow case and the large We cases.

Liquid plug propagation in flexible microchannels: A small airway model

In the present study, we investigate the effect of wall flexibility on the plug propagation and the resulting wall stresses in small airway models with experimental measurements and numerical simulations. Experimentally, a flexible microchannel was fabricated to mimic the flexible small airways using soft lithography. Liquid plugs were generated and propagated through the microchannels. The local wall deformation is observed instantaneously during plug propagation with the maximum increasing with plug speed. The pressure drop across the plug is measured and observed to increase with plug speed, and is slightly smaller in a flexible channel compared to that in a rigid channel. A computational model is then presented to model the steady plug propagation through a flexible channel corresponding to the middle plane in the experimental device. The results show qualitative agreements with experiments on wall shapes and pressure drops and the discrepancies bring up interesting questions on current field of modeling. The flexible wall deforms inward near the plug core region, the deformation and pressure drop across the plug increase with the plug speed. The wall deformation and resulting stresses vary with different longitudinal tensions, i.e., for large wall longitudinal tension, the wall deforms slightly, which causes decreased fluid stress and stress gradients on the flexible wall comparing to that on rigid walls; however, the wall stress gradients are found to be much larger on highly deformable walls with small longitudinal tensions. Therefore, in diseases such as emphysema, with more deformable airways, there is a high possibility of induced injuries on lining cells along the airways because of larger wall stresses and stress gradients.

Gas-liquid two-phase flow patterns in rectangular polymeric microchannels: effect of surface wetting properties

Here we map gas-liquid two-phase flow regimes observed in polymeric microchannels with different wetting properties. We utilized video and confocal microscopy to examine two-phase flow patterns produced by parallel injection of air and water through a Y-shaped junction into a rectangular microchannel made of poly(dimethylsiloxane) (PDMS). We observed seven flow regimes in microchannels with hydrophobic walls, whereas only two flow patterns were identified in hydrophilic microchannels. Our study demonstrates that surface wettability has a profound influence on the spatial distribution of air and water moving in microchannels.

Unsteady propagation of a liquid plug in a liquid-lined straight tube

This paper considers the propagation of a liquid plug driven by a constant pressure within a rigid axisymmetric tube whose inner surface is coated by a thin liquid film. The Navier-Stokes equations are solved using the finite-volume method and the SIMPLEST algorithm. The effects of precursor film thickness, initial plug length, pressure drop across the plug, and constant surface tension on the plug behavior and tube wall mechanical stresses are investigated. As a plug propagates through a liquid-lined tube, the plug gains liquid from the leading front film, and it deposits liquid into the trailing film. If the trailing film is thicker (thinner) than the precursor film, the plug volume decreases (increases) as it propagates. For a decreasing volume, eventually the plug ruptures. Under a specific set of conditions, the trailing film thickness equals the precursor film thickness, which leads to steady state results. The plug speed decreases as the precursor film thins because the resistance to the moving front meniscus increases. As the pressure drop across the plug decreases, the plug speed decreases resulting in thinning of the trailing film. As the plug length becomes longer, the viscous resistance in the plug core region increases, which slows the plug and causes the trailing film to become even thinner. The magnitude of the pressure and shear stress at the tube inner wall is maximum in the front meniscus region, and it increases with a thinner precursor film. As the surface tension increases, the plug propagation speed decreases, the strength of the wall pressure in the front meniscus region increases, and the pressure gradient around the peak pressure becomes steeper.

Liquid and surfactant delivery into pulmonary airways

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.

Pulsatile Flow and Oxygen Transport Past Cylindrical Fiber Arrays for an Artificial Lung: Computational and Experimental Studies

The influence of time-dependent flows on oxygen transport from hollow fibers was computationally and experimentally investigated. The fluid average pressure drop, a measure of resistance, and the work required by the heart to drive fluid past the hollow fibers were also computationally explored. This study has particular relevance to the development of an artificial lung, which is perfused by blood leaving the right ventricle and in some cases passing through a compliance chamber before entering the device. Computational studies modeled the fiber bundle using cylindrical fiber arrays arranged in in-line and staggered rectangular configurations. The flow leaving the compliance chamber was modeled as dampened pulsatile and consisted of a sinusoidal perturbation superimposed on a steady flow. The right ventricular flow was modeled to depict the period of rapid flow acceleration and then deceleration during systole followed by zero flow during diastole. Experimental studies examined oxygen transfer across a fiber bundle with either steady, dampened pulsatile, or right ventricular flow. It was observed that the dampened pulsatile flow yielded similar oxygen transport efficiency to the steady flow, while the right ventricular flow resulted in smaller oxygen transport efficiency, with the decrease increasing with Re. Both computations and experiments yielded qualitatively similar results. In the computational modeling, the average pressure drop was similar for steady and dampened pulsatile flows and larger for right ventricular flow while the pump work required of the heart was greatest for right ventricular flow followed by dampened pulsatile flow and then steady flow. In conclusion, dampening the artificial lung inlet flow would be expected to maximize oxygen transport, minimize work, and thus improve performance.

Pulsatile Blood Flow and Oxygen Transport Past a Circular Cylinder

The fundamental study of blood flow past a circular cylinder filled with an oxygen source is investigated as a building block for an artificial lung. The Casson constitutive equation is used to describe the shear-thinning and yield stress properties of blood. The presence of hemoglobin is also considered. Far from the cylinder, a pulsatile blood flow in the x direction is prescribed, represented by a time periodic (sinusoidal) component superimposed on a steady velocity. The dimensionless parameters of interest for the characterization of the flow and transport are the steady Reynolds number (Re), Womersley parameter (α), pulsation amplitude (A), and the Schmidt number (Sc). The Hill equation is used to describe the saturation curve of hemoglobin with oxygen. Two different feed-gas mixtures were considered: pure O2 and air. The flow and concentration fields were computed for Re=5, 10, and 40, 0≤A≤0.75, α=0.25, 0.4, and Schmidt number, Sc=1000. The Casson fluid properties result in reduced recirculations (when present) downstream of the cylinder as compared to a Newtonian fluid. These vortices oscillate in size and strength as A and α are varied. Hemoglobin enhances mass transport and is especially important for an air feed which is dominated by oxyhemoglobin dispersion near the cylinder. For a pure O2 feed, oxygen transport in the plasma dominates near the cylinder. Maximum oxygen transport is achieved by operating near steady flow (small A) for both feed-gas mixtures. The time averaged Sherwood number, Sh̿, is found to be largely influenced by the steady Reynolds number, increasing as Re increases and decreasing with A. Little change is observed with varying α for the ranges investigated. The effect of pulsatility on Sh̿ is greater at larger Re. Increasing Re aids transport, but yields a higher cylinder drag force and shear stresses on the cylinder surface which are potentially undesirable.

Pulsatile Blood Flow and Gas Exchange Across a Cylindrical Fiber Array

The pulsatile blood flow and gas transport of oxygen and carbon dioxide through a cylindrical array of microfibers are numerically simulated. Blood is modeled as a homogeneous Casson fluid, and hemoglobin molecules in blood are assumed to be in local equilibrium with oxygen and carbon dioxide. It is shown that flow pulsatility enhances gas transport and the amount of gas exchange is sensitive to the blood flow field across the fibers. The steady Sherwood number dependence on Reynolds number was shown to have a linear relation consistent with experimental findings. For most cases, an enhancement in gas transport is accompanied with an increase in flow resistance. Maximum local shear stress is provided as a possible indicator of thrombosis, and the computed shear stress is shown to be below the threshold value for thrombosis formation for all cases evaluated.

Gravity-driven microfluidic particle sorting device with hydrodynamic separation amplification

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 (1 g) 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 and (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), 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 microm) 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 to separate colloids and particles for various analytical and preparative applications and may hold potential for separation of cells or development of diagnostic tools requiring point-of-care sample preparation or testing.

Linear stability of a surfactant-laden annular film in a time-periodic pressure-driven flow through a capillary

This paper analyzes the effect of surfactant on the linear stability of an annular film in a capillary undergoing a time-periodic pressure gradient force. The annular film is thin compared to the radius of the tube. An asymptotic analysis yields a coupled set of equations with time-periodic coefficients for the perturbed fluid-fluid interface and the interfacial surfactant concentration. Wei and Rumschitzki (submitted for publication) previously showed that the interaction between a surfactant and a steady base flow could induce a more severe instability than a stationary base state. The present work demonstrates that time-periodic base flows can modify the features of the steady-flow-based instability, depending on surface tension, surfactant activity, and oscillatory frequency. For an oscillatory base flow (with zero mean), the growth rate decreases monotonically as the frequency increases. In the low-frequency limit, the growth rate approaches a maximum corresponding to the growth rate of a steady base flow having the same amplitude. In the high-frequency limit, the growth rate reaches a minimum corresponding to the growth rate in the limit of a stationary base state. The underlying mechanisms are explained in detail, and extension to other time-periodic forms is further exploited.

Vascular dynamics and BOLD fMRI: CBF level effects and analysis considerations

Changes in the cerebral blood flow (CBF) baseline produce significant changes to the hemodynamic response. This work shows that increases in the baseline blood flow level produce blood oxygenation-level dependent (BOLD) and blood flow responses that are slower and lower in amplitude, while decreases in the baseline blood flow level produce faster and higher amplitude hemodynamic responses. This effect was characterized using a vascular model of the hemodynamic response that separated arterial blood flow response from the venous blood volume response and linked the input stimulus to the vascular response. The model predicted the baseline blood flow level effects to be dominated by changes in the arterial vasculature. Specifically, it predicted changes in the arterial blood flow time constant and venous blood volume time constant parameters of +294% and -24%, respectively, for a 27% increase in the baseline blood flow. The vascular model performance was compared to an empirical model of the hemodynamic response. The vascular and empirical hemodynamic models captured most of the baseline blood flow level effects observed and can be used to correct for these effects in fMRI data. While the empirical hemodynamic model is easy to implement, it did not incorporate any explicit physiological information.

Effects of Inertia and Gravity on Liquid Plug Splitting at a Bifurcation

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, ϕ, and pitch angle, γ; 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⩽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 ϕ and γ. When a blockage exists in the lower daughter, Rec is only found at ϕ=60deg 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 ϕ 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.

Expiratory flow limitation during gravitational drainage of perfluorocarbons from liquid-filled lungs

Flow limitation during pressure-driven expiration in liquid-filled lungs was examined in intact, euthanized New Zealand white rabbits. The aim of this study was to further characterize expiratory flow limitation during gravitational drainage of perfluorocarbon liquids from the lungs, and to study the effect of perfluorocarbon type and negative mouth pressure on this phenomenon. Four different perfluorocarbons (PP4, perfluorodecalin, perfluoro-octyl-bromide, and FC-77) were used to examine the effects of density and kinematic viscosity on volume recovered and maximum expiratory flow. It was demonstrated that flow limitation occurs during gravitational drainage when the airway pressure is < or = -15 cm H(2)O, and that this critical value of pressure did not depend on mouth pressure or perfluorocarbon type. The perfluorocarbon properties affect the volume recovered, maximum expiratory flow, and the time to drain, with the most viscous perfluorocarbon (perfluorodecalin) taking the longest time to drain and resulting in lowest maximum expiratory flow. Perfluoro-octyl-bromide resulted in the highest recovered volume. The findings of this study are relevant to the selection of perfluorocarbons to reduce the occurrence of flow limitation and provide adequate minute ventilation during total liquid ventilation.

Effect of gravity on liquid plug transport through an airway bifurcation model

Many medical therapies require liquid plugs to be instilled into and delivered throughout the pulmonary airways. Improving these treatments requires a better understanding of how liquid distributes throughout these airways. In this study, gravitational and surface mechanisms determining the distribution of instilled liquids are examined experimentally using a bench-top model of a symmetrically bifurcating airway. A liquid plug was instilled into the parent tube and driven through the bifurcation by a syringe pump. The effect of gravity was adjusted by changing the roll angle (phi) and pitch angle (gamma) of the bifurcation (phi = gamma =0 deg was isogravitational). Phi determines the relative gravitational orientation of the two daughter tubes: when phi not equal to 0 deg, one daughter tube was lower (gravitationally favored) compared to the other. Gamma determines the component of gravity acting along the axial direction of the parent tube: when gamma not equal to 0 deg, a nonzero component of gravity acts along the axial direction of the parent tube. A splitting ratio Rs, is defined as the ratio of the liquid volume in the upper daughter to the lower just after plug splitting. We measured the splitting ratio, Rs, as a function of: the parent-tube capillary number (Cap); the Bond number (Bo); phi; gamma; and the presence of pre-existing plugs initially blocking either daughter tube. A critical capillary number (Cac) was found to exist below which no liquid entered the upper daughter (Rs = 0), and above which Rs increased and leveled off with Cap. Cac increased while Rs decreased with increasing phi, gamma, and Bo for blocked and unblocked cases at a given Cap > Ca,. Compared to the nonblockage cases, Rs decreased (increased) at a given Cap while Cac increased (decreased) with an upper (lower) liquid blockage. More liquid entered the unblocked daughter with a blockage in one daughter tube, and this effect was larger with larger gravity effect. A simple theoretical model that predicts Rs and Cac is in qualitative agreement with the experiments over a wide range of parameters.

Pulsatile Flow and Mass Transport Over an Array of Cylinders: Gas Transfer in a Cardiac-Driven Artificial Lung

The pulsatile flow and gas transport of a Newtonian passive fluid across an array of cylindrical microfibers are numerically investigated. It is related to an implantable, artificial lung where the blood flow is driven by the right heart. The fibers are modeled as either squared or staggered arrays. The pulsatile flow inputs considered in this study are a steady flow with a sinusoidal perturbation and a cardiac flow. The aims of this study are twofold: identifying favorable array geometry/spacing and system conditions that enhance gas transport; and providing pressure drop data that indicate the degree of flow resistance or the demand on the right heart in driving the flow through the fiber bundle. The results show that pulsatile flow improves the gas transfer to the fluid compared to steady flow. The degree of enhancement is found to be significant when the oscillation frequency is large, when the void fraction of the fiber bundle is decreased, and when the Reynolds number is increased; the use of a cardiac flow input can also improve gas transfer. In terms of array geometry, the staggered array gives both a better gas transfer per fiber (for relatively large void fraction) and a smaller pressure drop (for all cases). For most cases shown, an increase in gas transfer is accompanied by a higher pressure drop required to power the flow through the device.

Steady propagation of a liquid plug in a two-dimensional channel

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.

A Mathematical Model of Alveolar Gas Exchange in Partial Liquid Ventilation

In partial liquid ventilation (PLV), perfluorocarbon (PFC) acts as a diffusion barrier to gas transport in the alveolar space since the diffusivities of oxygen and carbon dioxide in this medium are four orders of magnitude lower than in air. Therefore convection in the PFC layer resulting from the oscillatory motions of the alveolar sac during ventilation can significantly affect gas transport. For example, a typical value of the Pe´clet number in air ventilation is Pe∼0.01, whereas in PLV it is Pe∼20. To study the importance of convection, a single terminal alveolar sac is modeled as an oscillating spherical shell with gas, PFC, tissue and capillary blood compartments. Differential equations describing mass conservation within each compartment are derived and solved to obtain time periodic partial pressures. Significant partial pressure gradients in the PFC layer and partial pressure differences between the capillary and gas compartments PC-Pg are found to exist. Because Pe≫1, temporal phase differences are found to exist between PC-Pg and the ventilatory cycle that cannot be adequately described by existing non-convective models of gas exchange in PLV. The mass transfer rate is nearly constant throughout the breath when Pe≫1, but when Pe≪1 nearly 100% of the transport occurs during inspiration. A range of respiratory rates (RR), including those relevant to high frequency oscillation (HFO)+PLV, tidal volumes VT and perfusion rates are studied to determine the effect of heterogeneous distributions of ventilation and perfusion on gas exchange. The largest changes in PCO2 and PCCO2 occur at normal and low perfusion rates respectively as RR and VT are varied. At a given ventilation rate, a low RR-high VT combination results in higher PCO2, lower PCCO2 and lower PC-Pg than a high RR-low VT one.

Total liquid ventilation: dynamic airway pressure and the development of expiratory flow limitation

Expiratory flow limitation occurs during total liquid ventilation (TLV), and is characterized by the sudden development of excessively negative intratracheal pressures without increases in flow. The purpose of this study was to identify a dynamic signal for the servoregulation of expiratory flow (Ve), by determining the range of dynamic intratracheal pressures [P(T)], which mark the onset of flow limitation during liquid expiration, where choke occurs at the critical pressure (Pc). The lungs of rabbits were filled with perflurocarbon to an end-inspiratory lung volume (EILV) of 20, 30, or 40cc/kg and connected to a piston driven liquid ventilator, which removed perfluorocarbon at a rate (Vs) of 2.5, 5.0, or 7.5 ml/s. Nine animals per EILV group were used (27 animals total), and within each EILV group each (Vs) was used three times. P(T) and (Ve) (T) were measured at the tracheostomy tube, and dP/dT was calculated from P(T). Pc was determined within each EILV/(Vs) group by examining the average dP/dT curve for the first significant change from baseline. Pc ranged from -6.02 +/- 1.83 to -9.02 +/- 3.2 mm Hg. In general, the higher the EILV, the more negative the Pc. We conclude that Pc during TLV varies within a limited range in rabbits. These data may be used to maximize expired volume during TLV by sequentially tapering flow rates as this critical range of pressures is approached.