A theoretical study of chemical delivery within the lung using exogenous surfactant

Interaction of impinging marangoni fields

HYPOTHESIS

Surface tension gradient driven Marangoni flows originating from multiple sources are important to many industrial and medical applications, but the theoretical literature focuses on single surfactant sources. Understanding how two spreading surfactant sources interact allows insights from single source experiments to be applied to multi-source applications. Two key features of multi-source spreading - source translation and source deformation - can be explained by transport modeling of a two-source system.

MODELING

Numerical simulations of two oleic acid disks placed at varying initial separation distances on a glycerol subphase were performed using COMSOL Multiphysics and compared to spreading of a single surfactant source.

FINDINGS

Interaction of two spreading sources can be split into three regimes: the independent regime - where each source is unaffected by the other, the interaction regime - where the presence of a second source alters one or more features of the spreading dynamics, and the quasi-one disk regime - where the two sources merge together. The translation of the sources, manifested as increasing separation distance between disk centers of mass, is driven by the flow fields within the subphase and the resultant surface deformation, while deformation of the sources occurs only once the surfactant fronts of the two sources meet.

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.

Flow regime transitions and effects on solute transport in surfactant-driven Marangoni flows

HYPOTHESIS

Surfactant-driven Marangoni flow on liquid films is predicted to depend on subphase depth and initial surface tension difference between the subphase and deposited surfactant solution drop. Changes in flow behavior will impact transport of soluble species entrained in the Marangoni flow along the surface. In extreme cases, the subphase film may rupture, limiting transport. Understanding this behavior is important for applications in drug delivery, coatings, and oil spill remediation.

EXPERIMENTS

A trans-illumination optical technique measured the subphase height profiles and drop content transport after drop deposition when varying initial subphase depth, surfactant concentration, and subphase viscosity.

FINDINGS

Three distinct flow regimes were identified depending on the subphase depth and surfactant concentration and mapped onto an operating diagram. These are characterized as a "central depression" bounded by an outwardly traveling ridge, an "annular depression" bounded by a central dome and the traveling ridge, and an "annular dewetting" when the subphase ruptures. Well above the critical micelle concentration, transitions between regimes occur at characteristic ratios of gravitational and initial surface tension gradient stresses; transitions shift when surfactant dilution during spreading weakens the stress before the completion of the spreading event. Drop contents travel with the ridge, but dewetting hinders transport.

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.

Biophysical interaction between corticosteroids and natural surfactant preparation: implications for pulmonary drug delivery using surfactant a a carrier

Intratracheal administration of corticosteroids using a natural pulmonary surfactant as a delivery vehicle has recently received significant attention in hopes of treating premature newborns with or at high risk for chronic lung disease. As a new practice, both the surfactant preparation used as the carrier and the corticosteroid delivered as the anti-inflammatory agent, and their mixing ratios, have not been standardized and optimized. Given the concern that corticosteroids delivered via a pulmonary surfactant may compromise its surface activity and thus worsen lung mechanics, the present study was carried out to characterize the biophysical interaction between a natural surfactant preparation, Infasurf, and two commonly used inhaled corticosteroids, budesonide and beclomethasone dipropionate (BDP). Based on surface activity measurements by the Langmuir balance and lateral film structure studied by atomic force microscopy, our findings suggest that when Infasurf is used as a carrier, a budesonide concentration less than 1 wt% of surfactant or a BDP concentration up to 10 wt % should not significantly affect the biophysical properties of Infasurf, thus being feasible for pulmonary delivery. Increasing corticosteroid concentration beyond this range leads to early collapse of the surfactant film due to increased film fluidization. Our study further suggests that different affinities to the surfactant films are responsible for the different behavior of budesonide and BDP. In addition to the translational value in treating chronic lung disease, this study may also have implications in inhaled steroid therapy to treat asthma.

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.

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.

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.

Localized morphometric deformations of small airways and alveoli in intact mouse lungs under quasi-static inflation

Localized morphometric deformations of small airways and alveoli during respiration have several biomechanical and physiological implications. We developed fast synchrotron radiation CT system to visualize the small airways and alveoli of an intact mouse lung without fixation and dehydration, and analyzed their localized morphometric deformations between functional residual capacity (FRC) and total lung capacity (TLC). The maximum resolution of 32.6lp/mm at the 5% modulation transfer function level can be achieved with 11.8-microm voxels and 7-min scanning. Compared with the values at FRC, the diameter and length for smaller airways (diameter at FRC <200 microm) increased by 68.8% and 29.5% (averaged value), and those for larger airways (diameter at FRC >400 microm) increased by 45.2 and 22.9% (averaged value), at TLC. Moreover we defined the volume behavior as the percentage of airway volume at FRC for TLC. The volume behavior for the small airways was not similar to that of the lung volume. These results indicated that all airways did not behave homogenously.

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.

Simultaneous thermal and surfactant-induced Marangoni effects in thin liquid films

The deformation of a thin liquid film in the presence of a surfactant monolayer, varying temperature distributions, and limited mass flux is considered. Use of lubrication theory yields a coupled pair of partial differential equations for the film height and surfactant surface monolayer concentration. The long-wave stability of the isothermal film is examined over a wide range of parameter values. It is shown that droplet patterns are obtained under certain thermal conditions for both an isothermal and nonisothermal underlying substrate. For the case of a localized thermal gradient initially imposed at the air-liquid interface, severe film thinning beneath the heat source was observed, which was not accompanied by droplet formation; pseudo steady states are observed in this case. In all situations the surfactant is found to rigidify the air-liquid interface, retarding thermally driven flow, while evaporation (condensation) acts to destabilize (stabilize) the film.

Localized compliance of small airways in excised rat lungs using microfocal X-ray computed tomography

Airway compliance is a key factor in understanding lung mechanics and is used as a clinical diagnostic index. Understanding such mechanics in small airways physiologically and clinically is critical. We have determined the "morphometric change" and "localized compliance" of small airways under "near"-physiological conditions; namely, the airways were embedded in parenchyma without dehydration and fixation. Previously, we developed a two-step method to visualize small airways in detail by staining the lung tissue with a radiopaque solution and then visualizing the tissue with a cone-beam microfocal X-ray computed tomography system (Sera et al. J Biomech 36: 1587-1594, 2003). In this study, we used this technique to analyze changes in diameter and length of the same small airways ( approximately 150 microm ID) and then evaluated the localized compliance as a function of airway generation (Z). For smaller (<300-microm-diameter) airways, diameter was 36% larger at end-tidal inspiration and 89% larger at total lung capacity; length was 18% larger at end-tidal inspiration and 43% larger at total lung capacity than at functional residual capacity. Diameter, especially at smaller airways, did not behave linearly with V(1/3) (where V is volume). With increasing lung pressure, diameter changed dramatically at a particular pressure and length changed approximately linearly during inflation and deflation. Percentage of airway volume for smaller airways did not behave linearly with that of lung volume. Smaller airways were generally more compliant than larger airways with increasing Z and exhibited hysteresis in their diameter behavior. Airways at higher Z deformed at a lower pressure than those at lower Z. These results indicated that smaller airways did not behave homogeneously.

Three-dimensional visualization and morphometry of small airways from microfocal X-ray computed tomography

Physiological morphometry is a critical factor in the flow dynamics in small airways. In this study, we visualized and analyzed the three-dimensional structure of the small airways without dehydration and fixation. We developed a two-step method to visualize small airways in detail by staining the lung tissue with a radiopaque solution and then visualizing the tissue with a cone-beam microfocal X-ray computed tomographic (CT) system. To verify the applicability of this staining and CT imaging (SCT) method, we used the method to visualize small airways in excised rat lungs. By using the SCT method to obtain continuous CT images, three-dimensional branching and merging bronchi ranging from 500 to 150 microm (the airway generation=8-16) were successfully reconstructed. The morphometry of the small airways (diameter, length, branching angle and gravity angle between the gravity direction and airway vector) was analyzed using the three-dimensional thinning algorithm. The diameter and length exponentially decreased with the airway generation. The asymmetry of the bifurcation decreased with generation and one branching angle decided the other pair branching angle. The SCT method is the first reported method that yields faithful high-resolution images of soft tissue geometry without fixation and the three-dimensional morphometry of small airways is useful for studying the biomechanical dynamics in small airways.

Surfactant driven flows overlying a hydrophobic epithelium: film rupture in the presence of slip

Both for tear films and along the airways within the lung, one has an extremely thin fluid layer overlying a biological substrate; in both cases surfactants either of natural origin, or artificially introduced, are important in driving fluid flows. There is evidence that slip can occur when hydrophilic liquids, similar to mucus or aqueous tear films, overlie hydrophobic epithelium. Utilizing results from recent experimental findings we examine the possible influence of slip upon tear film rupture, important in so-called dry eye, and upon surfactant-induced flows within the lung, used in surfactant replacement therapy.