Respiratory fluid mechanics and transport processes

Virtual disease landscape using mechanics-informed machine learning: Application to esophageal disorders

Esophageal disorders are related to the mechanical properties and function of the esophageal wall. Therefore, to understand the underlying fundamental mechanisms behind various esophageal disorders, it is crucial to map mechanical behavior of the esophageal wall in terms of mechanics-based parameters corresponding to altered bolus transit and increased intrabolus pressure. We present a hybrid framework that combines fluid mechanics and machine learning to identify the underlying physics of various esophageal disorders (motility disorders, eosinophilic esophagitis, reflux disease, scleroderma esophagus) and maps them onto a parameter space which we call the virtual disease landscape (VDL). A one-dimensional inverse model processes the output from an esophageal diagnostic device called the functional lumen imaging probe (FLIP) to estimate the mechanical "health" of the esophagus by predicting a set of mechanics-based parameters such as esophageal wall stiffness, muscle contraction pattern and active relaxation of esophageal wall. The mechanics-based parameters were then used to train a neural network that consists of a variational autoencoder that generated a latent space and a side network that predicted mechanical work metrics for estimating esophagogastric junction motility. The latent vectors along with a set of discrete mechanics-based parameters define the VDL and formed clusters corresponding to specific esophageal disorders. The VDL not only distinguishes among disorders but also displayed disease progression over time. Finally, we demonstrated the clinical applicability of this framework for estimating the effectiveness of a treatment and tracking patients' condition after a treatment.

Continuum soft tissue models from upscaling of arrays of hyperelastic cells

Constitutive models for soft tissue mechanics are typically constructed by fitting phenomenological models to experimental measurements. However, a significant challenge is to rationally construct soft tissue models that encode the properties of the constituent cells and their extracellular matrix. This work presents a framework to derive multiscale soft tissue models that incorporate properties of individual cells without assuming homogeneity or periodicity at the cell level. We consider a viscoelastic model for each cell (which can deform, grow and divide), that we couple to form a network description of a one-dimensional line of cells. We use a discrete-to-continuum approach to form (nonlinear) continuum partial differential equation models for the tissue. These models elucidate the contrasting role of the two forms of dissipation: substrate dissipation localizes the deformation to the neighbourhood of the free boundary and inhibits morphoelastic growth, whereas internal cell dissipation promotes spatial uniformity and does not influence the elongation length. Furthermore, cell division is shown to increase the rate of elongation of the array compared with growth alone, provided the substrate dissipation is proportional to the cell surface area.

Coupled discrete phase model and Eulerian wall film model for numerical simulation of respiratory droplet generation during coughing

Computational fluid dynamics is widely used to simulate droplet-spreading behavior due to respiratory events. However, droplet generation inside the body, such as the number, mass, and particle size distribution, has not been quantitatively analyzed. The aim of this study was to identify quantitative characteristics of droplet generation during coughing. Airflow simulations were performed by coupling the discrete phase model and Eulerian wall film model to reproduce shear-induced stripping of airway mucosa. An ideal airway model with symmetric bifurcations was constructed, and the wall domain was covered by a mucous liquid film. The results of the transient airflow simulation indicated that the droplets had a wide particle size distribution of 0.1–400 µm, and smaller droplets were generated in larger numbers. In addition, the total mass and number of droplets generated increased with an increasing airflow. The total mass of the droplets also increased with an increasing mucous viscosity, and the largest number and size of droplets were obtained at a viscosity of 8 mPa s. The simulation methods used in this study can be used to quantify the particle size distribution and maximum particle diameter under various conditions.

Administration of Drugs/Gene Products to the Respiratory System: A Historical Perspective of the Use of Inert Liquids

The present review is a historical perspective of methodology and applications using inert liquids for respiratory support and as a vehicle to deliver biological agents to the respiratory system. As such, the background of using oxygenated inert liquids (considered a drug when used in the lungs) opposed to an oxygen-nitrogen gas mixture for respiratory support is presented. The properties of these inert liquids and the mechanisms of gas exchange and lung function alterations using this technology are described. In addition, published preclinical and clinical trial results are discussed with respect to treatment modalities for respiratory diseases. Finally, this forward-looking review provides a comprehensive overview of potential methods for administration of drugs/gene products to the respiratory system and potential biomedical applications.

Passive concentration dynamics incorporated into the library IB2d, a two-dimensional implementation of the immersed boundary method

In this paper, we present an open-source software library that can be used to numerically simulate the advection and diffusion of a chemical concentration or heat density in a viscous fluid where a moving, elastic boundary drives the fluid and acts as a source or sink. The fully-coupled fluid-structure interaction problem of an elastic boundary in a viscous fluid is solved using Peskin's immersed boundary method. The addition or removal of the concentration or heat density from the boundary is solved using an immersed boundary-like approach in which the concentration is spread from the immersed boundary to the fluid using a regularized delta function. The concentration or density over time is then described by the advection-diffusion equation and numerically solved. This functionality has been added to our software library,IB2d, which provides an easy-to-use immersed boundary method in two dimensions with full implementations in MATLAB and Python. We provide four examples that illustrate the usefulness of the method. A simple rubber band that resists stretching and absorbs and releases a chemical concentration is simulated as a first example. Complete convergence results are presented for this benchmark case. Three more biological examples are presented: (1) an oscillating row of cylinders, representative of an idealized appendage used for filter-feeding or sniffing, (2) an oscillating plate in a background flow is considered to study the case of heat dissipation in a vibrating leaf, and (3) a simplified model of a pulsing soft coral where carbon dioxide is taken up and oxygen is released as a byproduct from the moving tentacles. This method is applicable to a broad range of problems in the life sciences, including chemical sensing by antennae, heat dissipation in plants and other structures, the advection-diffusion of morphogens during development, filter-feeding by marine organisms, and the release of waste products from organisms in flows.

Surfactant spreading on a deep subphase: Coupling of Marangoni flow and capillary waves

HYPOTHESIS

Surfactant-driven Marangoni spreading generates a fluid flow characterized by an outwardly moving "Marangoni ridge". Spreading on thin and/or high viscosity subphases, as most of the prior literature emphasizes, does not allow the formation of capillary waves. On deep, low viscosity subphases, Marangoni stresses may launch capillary waves coupled with the Marangoni ridge, and new dependencies emerge for key spreading characteristics on surfactant thermodynamic and kinetic properties.

EXPERIMENTS AND MODELING

Computational and physical experiments were performed using a broad range of surfactants to report the post-deposition motion of the surfactant front and the deformation of the subphase surface. Modeling coupled the Navier-Stokes and advective diffusion equations with an adsorption model. Separate experiments employed tracer particles or an optical density method to track surfactant front motion or surface deformation, respectively.

FINDINGS

Marangoni stresses on thick subphases induce capillary waves, the slowest of which is co-mingled with the Marangoni ridge. Changing Marangoni stresses by varying the surfactant system alters the surfactant front velocity and the amplitude - but not the velocity - of the slowest capillary wave. As spreading progresses, the surfactant front and its associated surface deformation separate from the slowest moving capillary wave.

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

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

Computational Study of the Dynamics of the Taylor Bubble

We perform high-resolution numerical simulations of three-dimensional dynamics of an elongated bubble in a microchannel at moderate Reynolds numbers up to 1800. For this purpose, we use the coupled Brinkman penalization and volume of fluid methods implemented in the open-source framework Basilisk. The new results are validated with available experimental data and compared with previous numerical and theoretical predictions. We extend existing results to regimes with significant inertia, which are characterized by intense deformations of the bubble, including cases with azimuthal symmetry breaking. Various dynamical features are analyzed in terms of their spatiotemporal characteristics, such as frequencies and wavelengths of the bubble surface undulations and vortical structures in the flow.

Physiological and Disease Models of Respiratory System Based on Organ-on-a-Chip Technology

The pathogenesis of respiratory diseases is complex, and its occurrence and development also involve a series of pathological processes. The present research methods are have difficulty simulating the natural developing state of the disease in the body, and the results cannot reflect the real growth state and function in vivo. The development of microfluidic chip technology provides a technical platform for better research on respiratory diseases. The size of its microchannel can be similar to the space for cell growth in vivo. In addition, organ-on-a-chip can achieve long-term co-cultivation of multiple cells and produce precisely controllable fluid shear force, periodically changing mechanical force, and perfusate with varying solute concentration gradient. To sum up, the chip can be used to analyze the specific pathophysiological changes of organs meticulously, and it is widely used in scientific research on respiratory diseases. The focus of this review is to describe and discuss current studies of artificial respiratory systems based on organ-on-a-chip technology and to summarize their applications in the real world.

Fluid Dynamics of Respiratory Infectious Diseases

The host-to-host transmission of respiratory infectious diseases is fundamentally enabled by the interaction of pathogens with a variety of fluids (gas or liquid) that shape pathogen encapsulation and emission, transport and persistence in the environment, and new host invasion and infection. Deciphering the mechanisms and fluid properties that govern and promote these steps of pathogen transmission will enable better risk assessment and infection control strategies, and may reveal previously underappreciated ways in which the pathogens might actually adapt to or manipulate the physical and chemical characteristics of these carrier fluids to benefit their own transmission. In this article, I review our current understanding of the mechanisms shaping the fluid dynamics of respiratory infectious diseases.

Mathematical study of a system of multi-dimensional non-local evolution equations describing surfactant-laden two-fluid shear flows

This article studies a coupled system of model multi-dimensional partial differential equations (PDEs) that arise in the nonlinear dynamics of two-fluid Couette flow when insoluble surfactants are present on the interface. The equations have been derived previously, but a rigorous study of local and global existence of their solutions, or indeed solutions of analogous systems, has not been considered previously. The evolution PDEs are two-dimensional in space and contain novel pseudo-differential terms that emerge from asymptotic analysis and matching in the multi-scale problem at hand. The one-dimensional surfactant-free case was studied previously, where travelling wave solutions were constructed numerically and their stability investigated; in addition, the travelling wave solutions were justified mathematically. The present study is concerned with some rigorous results of the multi-dimensional surfactant system, including local well posedness and smoothing results when there is full coupling between surfactant dynamics and interfacial motion, and global existence results when such coupling is absent. As far as we know such results are new for non-local thin film equations in either one or two dimensions.

The effect of viscoelasticity in an airway closure model

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

Surfactant Driven Marangoni Spreading in the Presence of Predeposited Insoluble Surfactant Monolayers

When an insoluble surfactant is deposited on the surface of a thin fluid film, stresses induced by surface tension gradients drive Marangoni spreading across the subphase surface. The presence of a predeposited layer of an insoluble surfactant alters that spreading. In this study, the fluid film was aqueous, the predeposited insoluble surfactant was dipalmitoylphosphatidylcholine (DPPC), and the deposited insoluble surfactant was oleic acid. An optical density-based method was used to measure subphase surface distortion, called the Marangoni ridge, associated with propagation of the spreading front. The movement of the Marangoni ridge was correlated with movement of surface tracer particles that indicated both the boundary between the two surfactant layers and the surface fluid velocities. As the deposited oleic acid monolayer spread, it compressed the predeposited DPPC monolayer. During spreading, the surface tension gradient extended into the predeposited monolayer, which was compressed nonuniformly, from the deposited monolayer. The spreading was so rapid that the compressed predeposited surfactant could not have been in quasi-equilibrium states during the spreading. As the initial concentrations of the predeposited surfactant were increased, the shape of the Marangoni ridge deformed. When the initial concentration of the predeposited surfactant reached about 70 A²/molecule, there was no longer a Marangoni ridge but rather a broadly distributed excess of fluid above the initial fluid height. The nonuniform compression of the annulus of the predeposited monolayer also caused tangential motion ahead of both the Marangoni ridge and the boundary between the two monolayers. Spreading ceased when the two monolayers reached the same final surface tension. The final area per molecule of the DPPC monolayer matched that expected from the equilibrium DPPC isotherm at the same final surface tension. Thus, at the end of spreading, there was a simple surface tension balance between the two distinct monolayers.

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

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

Liquid plug formation in an airway closure model

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

Subnanometer imaging and controlled dynamical patterning of thermocapillary driven deformation of thin liquid films

Exploring and controlling the physical factors that determine the topography of thin liquid dielectric films are of interest in manifold fields of research in physics, applied mathematics, and engineering and have been a key aspect of many technological advancements. Visualization of thin liquid dielectric film topography and local thickness measurements are essential tools for characterizing and interpreting the underlying processes. However, achieving high sensitivity with respect to subnanometric changes in thickness via standard optical methods is challenging. We propose a combined imaging and optical patterning projection platform that is capable of optically inducing dynamical flows in thin liquid dielectric films and plasmonically resolving the resulting changes in topography and thickness. In particular, we employ the thermocapillary effect in fluids as a novel heat-based method to tune plasmonic resonances and visualize dynamical processes in thin liquid dielectric films. The presented results indicate that light-induced thermocapillary flows can form and translate droplets and create indentation patterns on demand in thin liquid dielectric films of subwavelength thickness and that plasmonic microscopy can image these fluid dynamical processes with a subnanometer sensitivity along the vertical direction.

Airway morphology and inspiratory flow features in the early stages of Chronic Obstructive Pulmonary Disease

BACKGROUND

Chronic Obstructive Pulmonary Disease (COPD) is among the leading causes of death worldwide. Inhaled pollutants are the prime risk factor, but the pathogenesis and progression of the diseased is poorly understood. Most studies on the disease onset and trajectory have focused on genetic and molecular biomarkers. Here we investigate the role of the airway anatomy and the consequent respiratory fluid mechanics on the development of COPD.

METHODS

We segmented CT scans from a five-year longitudinal study in three groups of smokers (18 subjects each) having: (i) minimal/mild obstruction at baseline with declining lung function at year five; (ii) minimal/mild obstruction at baseline with stable function, and (iii) normal and stable lung function over the five year period. We reconstructed the bronchial trees up to the 7th generation, and for one subject in each group we performed MRI velocimetry in 3D printed models.

FINDINGS

The subjects with airflow obstruction at baseline have smaller airway diameters, smaller child-to-parent diameter ratios, larger length-to-diameter ratios, and smaller fractal dimensions. The differences are more significant for subjects that develop severe decline in pulmonary function. The secondary flows that characterize lateral dispersion along the airways are found to be less intense in the subjects with airflow obstruction.

INTERPRETATION

These results indicate that morphology of the conducting airways and inspiratory flow features are correlated with the status and progression of COPD already at an early stage of the disease. This suggests that imaging-based biomarkers may allow a pre-symptomatic diagnosis of disease progression.

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

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

Analysis of the volume of fluid (VOF) method for the simulation of the mucus clearance process with CFD

The clearance of mucus through coughing is a complex, multiphase process, which is affected principally by mucus viscosity and airflow velocity; however, it is also critically affected by the thickness of the two layers of mucus-the serous and gel layers-and oscillation level. The present study examines the effects of the latter parameters more closely. To do so, the mucus clearance process is simulated with a transient 3D volume of fluid (VOF) multiphase model in ANSYS Fluent. The model includes mucus' bilayer properties and a wide range of boundary conditions were tested. The model was analysed in both a straight tube and a realistic trachea. Ultimately, the model was able to both capture air-mucus interface wave evolution and predict the overall behaviour of the clearance process. The results were consistent with experimental clearance data and numerical airflow simulations, which indicates our methodology is appropriate for future studies. Ultimately, the mere presence of the serous layer was found to increase mucus clearance by more than 15 percent. An oscillating flow enhanced clearance by up to 5 percent. Interestingly, interface wave steepness was found to be inversely correlated with mucus thickness, but directly with mucus velocity, which suggests it will be an interesting parameter for further study.

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

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

A bioinspired microfluidic model of liquid plug-induced mechanical airway injury

Occlusion of distal airways due to mucus plugs is a key pathological feature common to a wide variety of obstructive pulmonary diseases. Breathing-induced movement of airway mucus plugs along the respiratory tract has been shown to generate abnormally large mechanical stresses, acting as an insult that can incite acute injury to the airway epithelium. Here, we describe a unique microengineering strategy to model this pathophysiological process using a bioinspired microfluidic device. Our system combines an air-liquid interface culture of primary human small airway epithelial cells with a microengineered biomimetic platform to replicate the process of mucus exudation induced by airway constriction that leads to the formation of mucus plugs across the airway lumen. Specifically, we constructed a compartmentalized three-dimensional (3D) microfluidic device in which extracellular matrix hydrogel scaffolds reminiscent of airway stroma were compressed to discharge fluid into the airway compartment and form liquid plugs. We demonstrated that this plug formation process and subsequent movement of liquid plugs through the airway channel can be regulated in a precisely controlled manner. Furthermore, we examined the detrimental effect of plug propagation on the airway epithelium to simulate acute epithelial injury during airway closure. Our system allows for a novel biomimetic approach to modeling a complex and dynamic biophysical microenvironment of diseased human airways and may serve as an enabling platform for mechanistic investigation of key disease processes that drive the progression and exacerbation of obstructive pulmonary diseases.

Surfactant-induced Marangoni transport of lipids and therapeutics within the lung

Understanding the fundamentals of surface transport on thin viscous films has important application in pulmonary drug delivery. The human lung contains a large-area interface between its complex fluid lining and inhaled air. Marangoni flows driven by surface tension gradients along this interface would promote enhanced distribution of inhaled therapeutics by carrying them from where they are deposited in the upper airways, along the fluid interface to deeper regions of the lung. Motivated by the potential to improve therapies for acute and chronic lung diseases, we review recent progress in modeling and experimental studies of Marangoni transport induced by the deposition of surfactant-containing microliter drops and liquid aerosols (picoliter drops) onto a fluid interface. The roles of key system variables are identified, including surfactant solubility, drop miscibility with the subphase, and the thickness, composition and surface properties of the subphase liquid. Of particular interest is the unanticipated but crucial role of aerosol processing to achieve Marangoni transport via phospholipid vesicle dispersions, which are likely candidates for a biocompatible delivery system. Progress in this field has the potential to not only improve outcomes in patients with chronic and acute lung diseases, but also to further our understanding of surface transport in complex systems.

Morphological and functional properties of the conducting human airways investigated by in vivo computed tomography and in vitro MRI

The accurate representation of the human airway anatomy is crucial for understanding and modeling the structure-function relationship in both healthy and diseased lungs. The present knowledge in this area is based on morphometric studies of excised lung casts, partially complemented by in vivo studies in which computed tomography (CT) was used on a small number of subjects. In the present study, we analyzed CT scans of a cohort of healthy subjects and obtained comprehensive morphometric information down to the seventh generation of bronchial branching, including airway diameter, length, branching angle, and rotation angle. Although some of the geometric parameters (such as the child-to-parent branch diameter ratio) are found to be in line with accepted values, for others (such as the branch length-to-diameter ratio) our findings challenge the common assumptions. We also evaluated several metrics of self-similarity, including the fractal dimension of the airway tree. Additionally, we used phase-contrast magnetic resonance imaging (MRI) to obtain the volumetric flow field in the three-dimensional-printed airway model of one of the subjects during steady inhalation. This is used to relate structural and functional parameters and, in particular, to close the power-law relationship between branch flow rate and diameter. The diameter exponent is found to be significantly lower than in the usually assumed Poiseuille regime, which we attribute to the strong secondary (i.e., transverse) velocity component. The strength of the secondary velocity with respect to the axial component exceeds the levels found in idealized airway models and persists within the first seven generations. NEW & NOTEWORTHY We performed a comprehensive computed tomography-based study of the conductive airway morphology in normal human subjects, including branch diameter, length, and mutual angles. We found significant departure from classic homothetic relationships. We also carried out MRI measurements of the three-dimensional inspiratory flow in an anatomy-based model and directly assessed structure-function relationships that have so far been assumed. We found that strong secondary flows (i.e., transverse velocity components) persist through the first seven generations of bronchial branching.

Adsorption and Co-Adsorption of Polyaldehyde Dextran Nanoparticles and Nonionic Surfactant at an Air–Water Interface: Potential Implications for Pulmonary Drug Delivery

Measurements of dynamic surface tension were carried out in aqueous systems (water or 0.1 mM Triton X-100) comprising nanoparticles formed from chemically modified polyaldehyde dextran (PAD). The nanostructures, considered as potential drug carriers in aerosol therapy, were obtained from biocompatible polysaccharides by successive oxidation and reactive coiling in an aqueous solution. The dynamic surface tension of the samples was determined by the maximum bubble pressure (MBP) method and by the axisymmetric drop shape analysis (ADSA). Experiments with harmonic area perturbations were also carried out in order to determine surface dilatational viscoelasticity. PAD showed a remarkable surface activity. Ward-Tordai equation was used to determine the equilibrium surface tension and diffusion coefficient of PAD nanoparticles (D = 2.3×10-6 m2/s). In a mixture with Triton X-100, PAD particles showed co-adsorption and synergic effect in surface tension reduction at short times (below 10 s). Tested nanoparticles had impact on surface rheology in a mixed system with nonionic surfactant, suggesting their possible interactions with the lung surfactant system after inhalation. This preliminary investigation sets the methodological approach for further research related to the influence of inhaled PAD nanoparticles on the lung surfactant and mass transfer processes in the respiratory system.

Enabling Marangoni flow at air-liquid interfaces through deposition of aerosolized lipid dispersions

It has long been known that deposited drops of surfactant solution induce Marangoni flows at air-liquid interfaces. These surfactant drops create a surface tension gradient, which causes an outward flow at the fluid interface. We show that aqueous phospholipid dispersions may be used for this same purpose. In aqueous dispersions, phospholipids aggregate into vesicles that are not surface-active; therefore, drops of these dispersions do not initiate Marangoni flow. However, aerosolization of these dispersions disrupts the vesicles, allowing access to the surface-active monomers within. These lipid monomers do have the ability to induce Marangoni flow. We hypothesize that monomers released from broken vesicles adsorb on the surfaces of individual aerosol droplets and then create localized surface tension reduction upon droplet deposition. Deposition of lipid monomers via aerosolization produces surface tensions as low as 1mN/m on water. In addition, aerosolized lipid deposition also drives Marangoni flow on entangled polymer solution subphases with low initial surface tensions (∼34mN/m). The fact that aerosolization of phospholipids naturally found within pulmonary surfactant can drive Marangoni flows on low surface tension liquids suggests that aerosolized lipids may be used to promote uniform pulmonary drug delivery without the need for exogenous spreading agents.

Patterns of recruitment and injury in a heterogeneous airway network model

In respiratory distress, lung airways become flooded with liquid and may collapse due to surface-tension forces acting on air-liquid interfaces, inhibiting gas exchange. This paper proposes a mathematical multiscale model for the mechanical ventilation of a network of occluded airways, where air is forced into the network at a fixed tidal volume, allowing investigation of optimal recruitment strategies. The temporal response is derived from mechanistic models of individual airway reopening, incorporating feedback on the airway pressure due to recruitment. The model accounts for stochastic variability in airway diameter and stiffness across and between generations. For weak heterogeneity, the network is completely ventilated via one or more avalanches of recruitment (with airways recruited in quick succession), each characterized by a transient decrease in the airway pressure; avalanches become more erratic for airways that are initially more flooded. However, the time taken for complete ventilation of the network increases significantly as the network becomes more heterogeneous, leading to increased stresses on airway walls. The model predicts that the most peripheral airways are most at risk of ventilation-induced damage. A positive-end-expiratory pressure reduces the total recruitment time but at the cost of larger stresses exerted on airway walls.

Organ-on-a-Chip Systems: Microengineering to Biomimic Living Systems

"Organ-on-a-chip" systems integrate microengineering, microfluidic technologies, and biomimetic principles to create key aspects of living organs faithfully, including critical microarchitecture, spatiotemporal cell-cell interactions, and extracellular microenvironments. This creative platform and its multiorgan integration recapitulating organ-level structures and functions can bring unprecedented benefits to a diversity of applications, such as developing human in vitro models for healthy or diseased organs, enabling the investigation of fundamental mechanisms in disease etiology and organogenesis, benefiting drug development in toxicity screening and target discovery, and potentially serving as replacements for animal testing. Recent advances in novel designs and examples for developing organ-on-a-chip platforms are reviewed. The potential for using this emerging technology in understanding human physiology including mechanical, chemical, and electrical signals with precise spatiotemporal controls are discussed. The current challenges and future directions that need to be pursued for these proof-of-concept studies are also be highlighted.

Surfactant Driven Post-Deposition Spreading of Aerosols on Complex Aqueous Subphases. 2: Low Deposition Flux Representative of Aerosol Delivery to Small Airways

BACKGROUND

Cystic fibrosis (CF) is associated with the accumulation of dehydrated mucus in the pulmonary airways. This alters ventilation and aerosol deposition patterns in ways that limit drug delivery to peripheral lung regions. We investigated the use of surfactant-based, self-dispersing aerosol carriers that produce surface tension gradients to drive two-dimensional transport of aerosolized medications via Marangoni flows after deposition on the airway surface liquid (ASL). We considered the post-deposition spreading of individual aerosol droplets and two-dimensional expansion of a field of aerosol droplets, when deposited at low fluxes that are representative of aerosol deposition in the small airways.

METHODS

We used physically entangled aqueous solutions of poly(acrylamide) or porcine gastric mucin as simple ASL mimics that adequately capture the full miscibility but slow penetration of entangled macromolecular chains of the ASL into the deposited drop. Surfactant formulations were prepared with aqueous solutions of nonionic tyloxapol or FS-3100 fluorosurfactant. Fluorescein dye served as a model "drug" tracer and to visualize the extent of post-deposition spreading.

RESULTS

The surfactants not only enhanced post-deposition spreading of individual aerosol droplets due to localized Marangoni stresses, as previously observed with macroscopic drops, but they also produced large-scale Marangoni stresses that caused the deposited aerosol fields to expand into initially unexposed regions of the subphase. We show that the latter is the main mechanism for spreading drug over large distances when aerosol is deposited at low fluxes representative of the small airways. The large scale convective expansion of the aerosol field drives the tracer (drug mimic) over areas that would cover an entire airway generation or more, in peripheral airways, where sub-monolayer droplet deposition is expected during aerosol inhalation.

CONCLUSIONS

The results suggest that aerosolized surfactant formulations may provide the means to maximize deposited drug uniformity in and access to small airways.

Airway hydration and COPD

Chronic obstructive pulmonary disease (COPD) is one of the prevalent causes of worldwide mortality and encompasses two major clinical phenotypes, i.e., chronic bronchitis (CB) and emphysema. The most common cause of COPD is chronic tobacco inhalation. Research focused on the chronic bronchitic phenotype of COPD has identified several pathological processes that drive disease initiation and progression. For example, the lung's mucociliary clearance (MCC) system performs the critical task of clearing inhaled pathogens and toxic materials from the lung. MCC efficiency is dependent on: (1) the ability of apical plasma membrane ion channels such as the cystic fibrosis transmembrane conductance regulator (CFTR) and the epithelial Na(+) channel (ENaC) to maintain airway hydration; (2) ciliary beating; and (3) appropriate rates of mucin secretion. Each of these components is impaired in CB and likely contributes to the mucus stasis/accumulation seen in CB patients. This review highlights the cellular components responsible for maintaining MCC and how this process is disrupted following tobacco exposure and with CB. We shall also discuss existing therapeutic strategies for the treatment of chronic bronchitis and how components of the MCC can be used as biomarkers for the evaluation of tobacco or tobacco-like-product exposure.

Toward the modeling of mucus draining from human lung: role of airways deformation on air-mucus interaction

Chest physiotherapy is an empirical technique used to help secretions to get out of the lung whenever stagnation occurs. Although commonly used, little is known about the inner mechanisms of chest physiotherapy and controversies about its use are coming out regularly. Thus, a scientific validation of chest physiotherapy is needed to evaluate its effects on secretions. We setup a quasi-static numerical model of chest physiotherapy based on thorax and lung physiology and on their respective biophysics. We modeled the lung with an idealized deformable symmetric bifurcating tree. Bronchi and their inner fluids mechanics are assumed axisymmetric. Static data from the literature is used to build a model for the lung's mechanics. Secretions motion is the consequence of the shear constraints apply by the air flow. The input of the model is the pressure on the chest wall at each time, and the output is the bronchi geometry and air and secretions properties. In the limit of our model, we mimicked manual and mechanical chest physiotherapy techniques. We show that for secretions to move, air flow has to be high enough to overcome secretion resistance to motion. Moreover, the higher the pressure or the quicker it is applied, the higher is the air flow and thus the mobilization of secretions. However, pressures too high are efficient up to a point where airways compressions prevents air flow to increase any further. Generally, the first effects of manipulations is a decrease of the airway tree hydrodynamic resistance, thus improving ventilation even if secretions do not get out of the lungs. Also, some secretions might be pushed deeper into the lungs; this effect is stronger for high pressures and for mechanical chest physiotherapy. Finally, we propose and tested two a dimensional numbers that depend on lung properties and that allow to measure the efficiency and comfort of a manipulation.

An estimation of mechanical stress on alveolar walls during repetitive alveolar reopening and closure

Alveolar overdistension and mechanical stresses generated by repetitive opening and closing of small airways and alveoli have been widely recognized as two primary mechanistic factors that may contribute to the development of ventilator-induced lung injury. A long-duration exposure of alveolar epithelial cells to even small, shear stresses could lead to the changes in cytoskeleton and the production of inflammatory mediators. In this paper, we have made an attempt to estimate in situ the magnitudes of mechanical stresses exerted on the alveolar walls during repetitive alveolar reopening by using a tape-peeling model of McEwan and Taylor (35). To this end, we first speculate the possible ranges of capillary number ( Ca) ≡ μU/ γ (a dimensionless combination of surface tension γ, fluid viscosity μ, and alveolar opening velocity U) during in vivo alveolar opening. Subsequent calculations show that increasing respiratory rate or inflation rate serves to increase the values of mechanical stresses. For a normal lung, the predicted maximum shear stresses are <15 dyn/cm2 at all respiratory rates, whereas for a lung with elevated surface tension or viscosity, the maximum shear stress will notably increase, even at a slow respiratory rate. Similarly, the increased pressure gradients in the case of elevated surface or viscosity may lead to a pressure drop >300 dyn/cm2 across a cell, possibly inducing epithelial hydraulic cracks. In addition, we have conceived of a geometrical model of alveolar opening to make a prediction of the positive end-expiratory pressure (PEEP) required to splint open a collapsed alveolus, which as shown by our results, covers a wide range of pressures, from several centimeters to dozens of centimeters of water, strongly depending on the underlying pulmonary conditions. The establishment of adequate regional ventilation-to-perfusion ratios may prevent recruited alveoli from reabsorption atelectasis and accordingly, reduce the required levels of PEEP. The present study and several recent animal experiments likewise suggest that a lung-protective ventilation strategy should not only include small tidal volume and plateau pressure limitations but also consider such cofactors as ventilation frequency and inflation rate.

Surfactant Driven Post-Deposition Spreading of Aerosols on Complex Aqueous Subphases. 1: High Deposition Flux Representative of Aerosol Delivery to Large Airways

BACKGROUND

Aerosol drug delivery is a viable option for treating diseased airways, but airway obstructions associated with diseases such as cystic fibrosis cause non-uniform drug distribution and limit efficacy. Marangoni stresses produced by surfactant addition to aerosol formulations may enhance delivery uniformity by post-deposition spreading of medications over the airway surface, improving access to poorly ventilated regions. We examine the roles of different variables affecting the maximum post-deposition spreading of a dye (drug mimic).

METHODS

Entangled aqueous solutions of either poly(acrylamide) (PA) or porcine gastric mucin (PGM) serve as airway surface liquid (ASL) mimicking subphases for in vitro models of aerosol deposition. Measured aerosol deposition fluxes indicate that the experimental delivery conditions are representative of aerosol delivery to the conducting airways. Post-deposition spreading beyond the locale of direct aerosol deposition is tracked by fluorescence microscopy. Aqueous aerosols formulated with either nonionic surfactant (tyloxapol) or fluorosurfactant (FS-3100) are compared with surfactant-free control aerosols.

RESULTS

Significant enhancement of post-deposition spreading is observed with surfactant solutions relative to surfactant-free control solutions, provided the surfactant solution surface tension is less than that of the subphase. Amongst the variables considered--surfactant concentration, aerosol flow-rate, total deposited volume, time of delivery, and total deposited surfactant mass--surfactant mass is the primary predictor of maximum spread distance. This dependence is also observed for solutions deposited as a single, microliter-scale drop with a volume comparable to the total volume of deposited aerosol.

CONCLUSIONS

Marangoni stress-assisted spreading after surfactant-laden aerosol deposition at high fluxes on a complex fluid subphase is capable of driving aerosol contents over significantly greater distances compared to surfactant-free controls. Total delivered surfactant mass is the primary determinant of the extent of spreading, suggesting a great potential to extend the reach of aerosolized medication in partially obstructed airways via a purely physical mechanism.

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.

Optimisations and evolution of the mammalian respiratory system : A suggestion of possible gene sharing in evolution

The respiratory system of mammalians is made of two successive branched structures with different physiological functions. The upper structure, or bronchial tree, is a fluid transportation system made of approximately 15 generations of bifurcations leading to the order of about 2(15) = 30, 000 terminal bronchioles with a diameter of approximately 0.5mm in the human lung. The branching pattern continues up to generation 23 but the structure and function of each of the subsequent structures, called acini, is different. Each acinus consists in a branched system of ducts surrounded by alveoli and plays the role of a diffusion cell where oxygen and carbon dioxide are exchanged with blood across the alveolar membrane. We show here that the bronchial tree simultaneously presents several different optimal properties. It is first energy efficient, second, it is space filling and third it is also "rapid". This physically based multi-optimality suggests that, in the course of evolution, an organ selected against one criterion could have been used later for a totally different purpose. For example, once selected for its energetic efficiency for the transport of a viscous fluid like blood, the same genetic material could have been used for its optimized rapidity. This would have allowed the emergence of atmospheric respiration made of inspiration-expiration cycles. For this phenomenon to exist, rapidity is essential as fresh air has to reach the gas exchange organs, the pulmonary acini, before the beginning of expiration. We finally show that the pulmonary acinus is optimized in the sense that the acinus morphology is directly related to the notion of a "best possible" extraction of entropic energy by a diffusion exchanger that has to feed oxygen efficiently from air to blood across a membrane of finite permeability.

Quasi-immiscible spreading of aqueous surfactant solutions on entangled aqueous polymer solution subphases

Motivated by the possibility of enhancing aerosol drug delivery to mucus-obstructed lungs, the spreading of a drop of aqueous surfactant solution on a physically entangled aqueous poly(acrylamide) solution subphase that mimics lung airway surface liquid was investigated. Sodium dodecyl sulfate was used as the surfactant. To visualize spreading of the drop and mimic the inclusion of a drug substance, fluorescein, a hydrophilic and non-surface-active dye, was added to the surfactant solution. The spreading progresses through a series of events. Marangoni stresses initiate the convective spreading of the drop. Simultaneously, surfactant escapes across the drop's contact line within a second of deposition and causes a change in subphase surface tension outside the drop on the order of 1 mN/m. Convective spreading of the drop ends within 2-3 s of drop deposition, when a new interfacial tension balance is achieved. Surfactant escape depletes the drop of surfactant, and the residual drop takes the form of a static lens of nonzero contact angle. On longer time scales, the surfactant dissolves into the subphase. The lens formed by the water in the deposited drop persists for as long as 3 min after the convective spreading process ends due to the long diffusional time scales associated with the underlying entangled polymer solution. The persistence of the lens suggests that the drop phase behaves as if it were immiscible with the subphase during this time period. Whereas surfactant escapes the spreading drop and advances on the subphase/vapor interface, hydrophilic dye molecules in the drop do not escape but remain with the drop throughout the convective spreading. The quasi-immiscible nature of the spreading event suggests that the chemical properties of the surfactant and subphase are much less important than their physical properties, consistent with prior qualitative studies of spreading of different types of surfactants on entangled polymer subphases: the selection of surfactant for pulmonary delivery applications may be limited only by physical and toxicological considerations. Further, the escape of surfactant from individual drops may provide an additional spreading mechanism in the lung, as hydrodynamic and/or surface pressure repulsions may drive individual droplets apart after deposition.

Physiology of transition from intrauterine to extrauterine life

The transition from fetus to newborn is the most complex adaptation that occurs in human experience. Lung adaptation requires coordinated clearance of fetal lung fluid, surfactant secretion, and onset of consistent breathing. The cardiovascular response requires striking changes in blood flow, pressures, and pulmonary vasodilation. Energy metabolism and thermoregulation must be quickly controlled. The primary mediators that prepare the fetus for birth and support the multiorgan transition are cortisol and catecholamine. Abnormalities in adaptation are frequently found following preterm birth or cesarean delivery at term, and many of these infants need delivery room resuscitation to assist in this transition.

Surface tension-induced gel fracture. Part 1. Fracture of agar gels

This work involves an experimental investigation of the spreading of liquids on gel layers in the presence of surfactants. Of primary interest is the instability that accompanies the cracking of gels through the deposition and subsequent spreading of a drop of surfactant solution on their surfaces. This instability manifests itself via the shaping of crack-like spreading "arms", in formations that resemble starbursts. The main aim of this study is to elucidate the complex interactions between spreading surfactants and underlying gels and to achieve a fundamental understanding of the mechanism behind the observed phenomenon of the cracking pattern formation. By spreading SDS and Silwet L-77 surfactant solutions on the surfaces of agar gels, the different ways that system parameters such as the surfactant chemistry and concentration and the gel strength can affect the morphology and dynamics of the starburst patterns are explored. The crack propagation dynamics is fitted to a power law by measuring the temporal evolution of the length of the spreading arms that form each one of the observed patterns. The values of the exponent of the power law are within the predicted limits for Marangoni-driven spreading on thick layers. Therefore, Marangoni stresses, induced by surface tension gradients between the spreading surfactant and the underlying gel layer, are identified to be the main driving force behind these phenomena, whereas gravitational forces were also found to play an important role. A mechanism that involves the "unzipping" of the gel in a manner perpendicular to the direction of the largest surface tension gradient is proposed. This mechanism highlights the important role of the width of the arms in the process; it is demonstrated that a cracking pattern is formed only within the experimental conditions that allow S/Δw to be greater than G', where S is the spreading coefficient, Δw is the change in the width of the crack, and G' is the storage modulus of the substrate.

Dynamics of a climbing surfactant-laden film--I: base-state flow

The dynamics of a surfactant-laden film climbing up an inclined plane is investigated through a two-dimensional (2-D), nonlinear evolution equation for the interface coupled to convective-diffusion equations for the surfactant, derived using lubrication theory. One-dimensional (1-D) solutions, representing the base-state flow, are investigated for constant flux and constant volume configurations; these flows are parameterised by capillarity, gravity, convection-diffusion ratios (represented by Péclét numbers at the surface and bulk), a solubility parameter, sorption kinetics constants, the number of surfactant monomers in a micelle, and the nonlinearity of the surfactant equation of state. In both configurations studied, a front develops spreading up the substrate against the direction of gravity whereby the leading edge of the front follows a power-law as a function of time. The effect of system parameters on the base-state flow is explored through an extensive parametric study, while the stability of the above-mentioned system to spanwise perturbations is the focus of Part II.

Filtering microfluidic bubble trains at a symmetric junction

We report how a nominally symmetric microfluidic junction can be used to sort all bubbles of an incoming train exclusively into one of its arms. The existence of this "filter" regime is unexpected, given that the junction is symmetric. We analyze this behavior by quantifying how bubbles modulate the hydrodynamic resistance in microchannels and show how speeding up a bubble train whilst preserving its spatial periodicity can lead to filtering at a nominally symmetric junction. We further show how such an asymmetric traffic of bubble trains can be triggered in symmetric geometries by identifying conditions wherein the resistance to flow decreases with an increase in the number of bubbles in the microchannel and derive an exact criterion to predict the same.

Lagrangian transport properties of pulmonary interfacial flows

Disease states characterized by airway fluid occlusion and pulmonary surfactant insufficiency, such as respiratory distress syndrome, have a high mortality rate. Understanding the mechanics of airway reopening, particularly involving surfactant transport, may provide an avenue to increase patient survival via optimized mechanical ventilation waveforms. We model the occluded airway as a liquid-filled rigid tube with the fluid phase displaced by a finger of air that propagates with both mean and sinusoidal velocity components. Finite-time Lyapunov exponent (FTLE) fields are employed to analyse the convective transport characteristics, taking note of Lagrangian coherent structures (LCSs) and their effects on transport. The Lagrangian perspective of these techniques reveals flow characteristics that are not readily apparent by observing Eulerian measures. These analysis techniques are applied to surfactant-free velocity fields determined computationally, with the boundary element method, and measured experimentally with micro particle image velocimetry (μ-PIV). We find that the LCS divides the fluid into two regimes, one advected upstream (into the thin residual film) and the other downstream ahead of the advancing bubble. At higher oscillatory frequencies particles originating immediately inside the LCS experience long residence times at the air-liquid interface, which may be conducive to surfactant transport. At high frequencies a well-mixed attractor region is identified; this volume of fluid cyclically travels along the interface and into the bulk fluid. The Lagrangian analysis is applied to velocity data measured with 0.01 mg ml(-1) of the clinical pulmonary surfactant Infasurf in the bulk fluid, demonstrating flow field modifications with respect to the surfactant-free system that were not visible in the Eulerian frame.

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.

Toward the modeling of mucus draining from the human lung: role of the geometry of the airway tree

Mucociliary clearance and cough are the two main natural mucus draining methods in the bronchial tree. If they are affected by a pathology, they can become insufficient or even ineffective, then therapeutic draining of mucus plays a critical role to keep mucus levels in the lungs acceptable. The manipulations of physical therapists are known to be very efficient clinically but they are mostly empirical since the biophysical mechanisms involved in these manipulations have never been studied. We develop in this work a model of mucus clearance in idealized rigid human bronchial trees and focus our study on the interaction between (1) tree geometry, (2) mucus physical properties and (3) amplitude of flow rate in the tree. The mucus is considered as a Bingham fluid (gel-like) which is moved upward in the tree thanks to its viscous interaction with air flow. Our studies point out the important roles played both by the geometry and by the physical properties of mucus (yield stress and viscosity). More particularly, the yield stress has to be overcome to make mucus flow. Air flow rate and yield stress determine the maximal possible mucus thickness in each branch of the tree at equilibrium. This forms a specific distribution of mucus in the tree whose characteristics are strongly related to the multi-scaled structure of the tree. The behavior of any mucus distribution is then dependent on this distribution. Finally, our results indicate that increasing air flow rates ought to be more efficient to drain mucus out of the bronchial tree while minimizing patient discomfort.

Surface tension gradient driven spreading on aqueous mucin solutions: a possible route to enhanced pulmonary drug delivery

Surface tension gradient driven, or "Marangoni", flow can be used to move exogenous fluid, either surfactant dispersions or drug carrying formulations, through the lung. In this paper, we investigate the spreading of aqueous solutions of water-soluble surfactants over entangled, aqueous mucin solutions that mimic the airway surface liquid of the lung. We measure the movement of the formulation by incorporating dyes into the formulation while we measure surface flows of the mucin solution subphase using tracer particles. Surface tension forces and/or Marangoni stresses initiate a convective spreading flow over this rheologically complex subphase. As expected, when the concentration of surfactant is reduced until its surface tension is above that of the mucin solution, the convective spreading does not occur. The convective spreading front moves ahead of the drop containing the formulation. Convective spreading ends with the solution confined to a well-defined static area which must be governed by a surface tension balance. Further motion of the spread solution progresses by much slower diffusive processes. Spreading behaviors are qualitatively similar for formulations based on anionic, cationic, or nonionic surfactants, containing either hydrophilic or hydrophobic dyes, on mucin as well as on other entangled aqueous polymer solution subphases. This independence of qualitative spreading behaviors from the chemistry of the surfactant and subphase indicates that there is little chemical interaction between the formulation and the subphase during the spreading process. The spreading and final solution distributions are controlled by capillary and hydrodynamic phenomena and not by specific chemical interactions among the components of the system. It is suggested that capillary forces and Marangoni flows driven by soluble surfactants may thereby enhance the uniformity of drug delivery to diseased lungs.