Pulmonary fluid flow challenges for experimental and mathematical modeling

Nanoparticle Diffusion in Respiratory Mucus Influenced by Mucociliary Clearance: A Review of Mathematical Modeling

Background: Inhalation and deposition of particles in human airways have attracted considerable attention due to importance of particulate pollutants, transmission of infectious diseases, and therapeutic delivery of drugs at targeted areas. We summarize current state-of-the art research in particle deposition on airway surface liquid (ASL) influenced by mucociliary clearance (MCC) by identifying areas that need further investigation. Methodology: We aim to review focus on governing and constitutive equations describing MCC geometry followed by description of mathematical modeling of ciliary forces, mucus rheology properties, and numerical approaches to solve modified time-dependent Navier-Stokes equations. We also review mathematical modeling of particle deposition in ASL influenced by MCC, particle transport in ASL in terms of Eulerian and Lagrangian approaches, and discuss the corresponding mass transport issues in this layer. Whenever required, numerical predictions are contrasted with the pertinent experimental data. Results: Results indicate that mean mucus and periciliary liquid velocities are strongly influenced by mucus rheological characteristics as well as ciliary abnormalities. However, most of the currently available literature on mucus fiber spacing, ciliary beat frequency, and particle surface chemistry is based on particle deposition on ASL by considering a fixed value of ASL velocity. The effects of real ASL flow regimes on particle deposition in this layer are limited. In addition, no other study is available on modeling nonhomogeneous and viscoelastic characteristics of mucus layer on ASL drug delivery. Conclusion: Simplification of assumptions on governing equations of drug delivery in ASL influenced by MCC leads to imposing some limitations on numerical results.

Physics-informed neural entangled-ladder network for inhalation impedance of the respiratory system

BACKGROUND AND OBJECTIVES

The use of machine learning methods for modelling bio-systems is becoming prominent which can further improve bio-medical technologies. Physics-informed neural networks (PINNs) can embed the knowledge of physical laws that govern a system during the model training process. PINNs utilise differential equations in the model which traditionally used numerical methods that are computationally complex.

METHODS

We integrate PINNs with an entangled ladder network for modelling respiratory systems by considering a lungs conduction zone to evaluate the respiratory impedance for different initial conditions. We evaluate the respiratory impedance for the inhalation phase of breathing for a symmetric model of the human lungs using entanglement and continued fractions.

RESULTS

We obtain the impedance of the conduction zone of the lungs pulmonary airways using PINNs for nine different combinations of velocity and pressure of inhalation. We compare the results from PINNs with the finite element method using the mean absolute error and root mean square error. The results show that the impedance obtained with PINNs contrasts with the conventional forced oscillation test used for deducing the respiratory impedance. The results show similarity with the impedance plots for different respiratory diseases.

CONCLUSION

We find a decrease in impedance when the velocity of breathing is lowered gradually by 20%. Hence, the methodology can be used to design smart ventilators to the improve flow of breathing.

Energy-based advection modelling using bond graphs

Advection, the transport of a substance by the flow of a fluid, is a key process in biological systems. The energy-based bond graph approach to modelling chemical transformation within reaction networks is extended to include transport and thus advection. The approach is illustrated using a simple model of advection via circulating flow and by a simple pharmacokinetic model of anaesthetic gas uptake. This extension provides a physically consistent framework for linking advective flows with the fluxes associated with chemical reactions within the context of physiological systems in general and the human physiome in particular.

Aerosol Transport Modeling: The Key Link Between Lung Infections of Individuals and Populations

The recent COVID-19 pandemic has propelled the field of aerosol science to the forefront, particularly the central role of virus-laden respiratory droplets and aerosols. The pandemic has also highlighted the critical need, and value for, an information bridge between epidemiological models (that inform policymakers to develop public health responses) and within-host models (that inform the public and health care providers how individuals develop respiratory infections). Here, we review existing data and models of generation of respiratory droplets and aerosols, their exhalation and inhalation, and the fate of infectious droplet transport and deposition throughout the respiratory tract. We then articulate how aerosol transport modeling can serve as a bridge between and guide calibration of within-host and epidemiological models, forming a comprehensive tool to formulate and test hypotheses about respiratory tract exposure and infection within and between individuals.

Non-Cellular Layers of the Respiratory Tract: Protection against Pathogens and Target for Drug Delivery

Epithelial barriers separate the human body from the environment to maintain homeostasis. Compared to the skin and gastrointestinal tract, the respiratory barrier is the thinnest and least protective. The properties of the epithelial cells (height, number of layers, intercellular junctions) and non-cellular layers, mucus in the conducting airways and surfactant in the respiratory parts determine the permeability of the barrier. The review focuses on the non-cellular layers and describes the architecture of the mucus and surfactant followed by interaction with gases and pathogens. While the penetration of gases into the respiratory tract is mainly determined by their hydrophobicity, pathogens use different mechanisms to invade the respiratory tract. Often, the combination of mucus adhesion and subsequent permeation of the mucus mesh is used. Similar mechanisms are also employed to improve drug delivery across the respiratory barrier. Depending on the payload and target region, various mucus-targeting delivery systems have been developed. It appears that the mucus-targeting strategy has to be selected according to the planned application.

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.

On the cross-streamline lift of microswimmers in viscoelastic flows

The current work studies the dynamics of a microswimmer in pressure-driven flow of a weakly viscoelastic fluid. Employing a second-order fluid model, we show that a self-propelling swimmer experiences a viscoelastic swimming lift in addition to the well-known passive lift that arises from its resistance to shear flow. Using the reciprocal theorem, we evaluate analytical expressions for the swimming lift experienced by neutral and pusher/puller-type swimmers and show that they depend on the hydrodynamic signature associated with the swimming mechanism. We find that, in comparison to passive particles, the focusing of neutral swimmers towards the centerline can be significantly accelerated, while for force-dipole swimmers no net modification in cross-streamline migration occurs.

Molecular Dynamics Simulations to Explore the Structure and Rheological Properties of Normal and Hyperconcentrated Airway Mucus

We develop the first molecular dynamics model of airway mucus based on the detailed physical properties and chemical structure of the predominant gel-forming mucin MUC5B. Our airway mucus model leverages the LAMMPS open-source code [https://lammps.sandia.gov], based on the statistical physics of polymers, from single molecules to networks. On top of the LAMMPS platform, the chemical structure of MUC5B is used to superimpose proximity-based, non-covalent, transient interactions within and between the specific domains of MUC5B polymers. We explore feasible ranges of hydrophobic and electrostatic interaction strengths between MUC5B domains with 9 nanometer spatial and 1 nanosecond temporal resolution. Our goal here is to propose and test a mechanistic hypothesis for a striking clinical observation with respect to airway mucus: a 10-fold increase in non-swellable, dense structures called flakes during progression of cystic fibrosis disease. Among the myriad possible effects that might promote self-organization of MUC5B networks into flake structures, we hypothesize and confirm that the clinically confirmed increase in mucin concentration, from 1.5 to 5 mg/mL, alone is sufficient to drive the structure changes observed with scanning electron microscopy images from experimental samples. We post-process the LAMMPS simulated datasets at 1.5 and 5 mg/mL, both to image the structure transition and compare with scanning electron micrographs and to show that the 3.33-fold increase in concentration induces closer proximity of interacting electrostatic and hydrophobic domains, thereby amplifying the proximity-based strength of the interactions.

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.

Effect of Non-Newtonian Dynamics on the Clearance of Mucus From Bifurcating Lung Airway Models

Mucus hypersecretion is a common pathophysiological manifestation of several obstructive airway diseases in which the mucociliary clearance is impaired, and the airflow generated by a cough or a forced expiratory maneuver called the huff is primarily responsible for clearing mucus. This airflow driven clearance of mucus is a complex process that is affected by the mucus rheology, airflow rate, airway geometry, and gravity. This study examines the role of mucus rheology in the transport and distribution of mucus in idealized 3D airway geometries. The complex air-mucus interface was tracked by the volume-of-fluid (VOF) model, and the turbulence in the core airflow was modeled using the k-ω shear stress transport (SST) model. Mucus was modeled as a shear-thinning liquid by using a power-law model. The computational model was validated using in vitro experimental data available in the literature. Gravity-dominated eccentric core-annular flow was observed with the core biased toward the outer wall in the inclined daughter branches of the bifurcation models, which transitions into concentric core-annular flow in the trachea. The increase in tangential shear at the interface due to the secondary flow structures developed in the flow divider location resulted in a region of enhanced mucus clearance with reduced mucus layer thickness. Secondary flow developed due to the curvature in the airway geometry resulted in a local redistribution of mucus that reduced the eccentricity. The accumulation of mucus around the carinal ridges and the regions with reduced clearance are sites with the potential for microbial growth.

Determination of rheology and surface tension of airway surface liquid: a review of clinical relevance and measurement techniques

By airway surface liquid, we mean a thin fluid continuum consisting of the airway lining layer and the alveolar lining layer, which not only serves as a protective barrier against foreign particles but also contributes to maintaining normal respiratory mechanics. In recent years, measurements of the rheological properties of airway surface liquid have attracted considerable clinical attention due to new advances in microrheology instruments and methods. This article reviews the clinical relevance of measurements of airway surface liquid viscoelasticity and surface tension from four main aspects: maintaining the stability of the airways and alveoli, preventing ventilator-induced lung injury, optimizing surfactant replacement therapy for respiratory syndrome distress, and characterizing the barrier properties of airway mucus to improve drug and gene delivery. Primary measuring techniques and methods suitable for determining the viscoelasticity and surface tension of airway surface liquid are then introduced with respect to principles, advantages and limitations. Cone and plate viscometers and particle tracking microrheometers are the most commonly used instruments for measuring the bulk viscosity and microviscosity of airway surface liquid, respectively, and pendant drop methods are particularly suitable for the measurement of airway surface liquid surface tension in vitro. Currently, in vivo and in situ measurements of the viscoelasticity and surface tension of the airway surface liquid in humans still presents many challenges.

Challenge in particle delivery to cells in a microfluidic device

Micro and nanotechnology can potentially revolutionize drug delivery systems. Novel microfluidic systems have been employed for the cell culture applications and drug delivery by micro and nanocarriers. Cells in the microchannels are under static and dynamic flow perfusion of culture media that provides nutrition and removes waste from the cells. This exerts hydrostatic and hydrodynamic forces on the cells. These forces can considerably affect the functions of the living cells. In this paper, we simulated the flow of air, culture medium, and the particle transport and deposition in the microchannels under different angles of connection inlet. It was found that the shear stress induced by the medium culture flow is not so high to damage the cells and that it is roughly uniform in the cell culture section (CCS). However, the local shear stresses in the other parts of the microchip differ by changing the angles of the connection inlet. The results showed that the particle deposition was a function of the particle size, the properties of the fluid, and the flow rate. At a lower air flow rate, both small and large particles deposited in the entrance region and none of them reached the CCS. Once the airflow rate increased, the drag of the flow could overcome the diffusion of the small particles and deliver them to the CCS so that more than 88% of the 100 nm and 98% of the 200 nm particles deposited in the CCS. However, larger particles with average diameters in micrometers could not reach the CCS by the airflow even at high flow rate. In contrast, our findings indicated that both small and large particles could be delivered to the CCS by liquid flow. Our experimental data confirm that microparticles (with diameters of 5 and 20 μm) suspended in a liquid can reach the CCS at a well-adjusted flow rate. Consequently, a liquid carrier is suggested to transport large particles through microchannels. As a powerful tool, these numerical simulations provide a nearly complete understanding of the flow field and particle patterns in microchips which can significantly lower the trial and error in the experiment tests and accordingly save researchers considerable cost and time for drug delivery to the cell in the microchip by micro/nanocarriers.

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.

Drop spreading with random viscosity

We examine theoretically the spreading of a viscous liquid drop over a thin film of uniform thickness, assuming the liquid’s viscosity is regulated by the concentration of a solute that is carried passively by the spreading flow. The solute is assumed to be initially heterogeneous, having a spatial distribution with prescribed statistical features. To examine how this variability influences the drop’s motion, we investigate spreading in a planar geometry using lubrication theory, combining numerical simulations with asymptotic analysis. We assume diffusion is sufficient to suppress solute concentration gradients across but not along the film. The solute field beneath the bulk of the drop is stretched by the spreading flow, such that the initial solute concentration immediately behind the drop’s effective contact lines has a long-lived influence on the spreading rate. Over long periods, solute swept up from the precursor film accumulates in a short region behind the contact line, allowing patches of elevated viscosity within the precursor film to hinder spreading. A low-order model provides explicit predictions of the variances in spreading rate and drop location, which are validated against simulations.

Modeling and Simulation of Mucus Flow in Human Bronchial Epithelial Cell Cultures - Part I: Idealized Axisymmetric Swirling Flow

A multi-mode nonlinear constitutive model for mucus is constructed directly from micro- and macro-rheology experimental data on cell culture mucus, and a numerical algorithm is developed for the culture geometry and idealized cilia driving conditions. This study investigates the roles that mucus rheology, wall effects, and HBE culture geometry play in the development of flow profiles and the shape of the air-mucus interface. Simulations show that viscoelasticity captures normal stress generation in shear leading to a peak in the air-mucus interface at the middle of the culture and a depression at the walls. Linear and nonlinear viscoelastic regimes can be observed in cultures by varying the hurricane radius and mean rotational velocity. The advection-diffusion of a drug concentration dropped at the surface of the mucus flow is simulated as a function of Peclet number.

In the lungs, the airway surface liquid protects the airway epithelium from inhaled pathogens and particulates. It is well known that failure to properly clear mucus from the airways leads to chronic, even fatal, lung infections. To date, there is no validated constitutive model capable of recapitulating mucus rheology under diverse, physiological stress and deformation conditions. This gap has hindered studies into the causal relationship between mucus rheology and mucociliary clearance. Our modeling-experimental approach fulfills several purposes: to implement linear and nonlinear constitutive modeling of mucus from micro- and macro-rheology, to test constitutive modeling in an independent experimental system, to build a coarse-grained model of the PCL-mucus boundary condition, to measure and understand modifications in mucociliary transport during and after deposition of a controlled drug concentration, to measure and simulate both the flow and stress fields throughout the mucus layer, and to measure and simulate how the advection profiles in the culture couple with diffusion of particulates landing on the air-mucus interface. These results lay the groundwork for extension of the code to three dimensions and more realistic metachronal wave boundary conditions, both in cell cultures and in airways.

Lung surfactants and different contributions to thin film stability

The surfactant lining the walls of the alveoli in the lungs increases pulmonary compliance and prevents collapse of the lung at the end of expiration. In premature born infants, surfactant deficiency causes problems, and lung surfactant replacements are instilled to facilitate breathing. These pulmonary surfactants, which form complex structured fluid-fluid interfaces, need to spread with great efficiency and once in the alveolus they have to form a thin stable film. In the present work, we investigate the mechanisms affecting the stability of surfactant-laden thin films during spreading, using drainage flows from a hemispherical dome. Three commercial lung surfactant replacements Survanta, Curosurf and Infasurf, along with the phospholipid dipalmitoylphosphatidylcholine (DPPC), are used. The surface of the dome can be covered with human alveolar epithelial cells and experiments are conducted at the physiological temperature. Drainage is slowed down due to the presence of all the different lung surfactant replacements and therefore the thin films show enhanced stability. However, a scaling analysis combined with visualization experiments demonstrates that different mechanisms are involved. For Curosurf and Infasurf, Marangoni stresses are essential to impart stability and interfacial shear rheology does not play a role, in agreement with what is observed for simple surfactants. Survanta, which was historically the first natural surfactant used, is rheologically active. For DPPC the dilatational properties play a role. Understanding these different modes of stabilization for natural surfactants can benefit the design of effective synthetic surfactant replacements for treating infant and adult respiratory disorders.

Coming to terms with tissue engineering and regenerative medicine in the lung

Lung diseases such as emphysema, interstitial fibrosis, and pulmonary vascular diseases cause significant morbidity and mortality, but despite substantial mechanistic understanding, clinical management options for them are limited, with lung transplantation being implemented at end stages. However, limited donor lung availability, graft rejection, and long-term problems after transplantation are major hurdles to lung transplantation being a panacea. Bioengineering the lung is an exciting and emerging solution that has the ultimate aim of generating lung tissues and organs for transplantation. In this article we capture and review the current state of the art in lung bioengineering, from the multimodal approaches, to creating anatomically appropriate lung scaffolds that can be recellularized to eventually yield functioning, transplant-ready lungs. Strategies for decellularizing mammalian lungs to create scaffolds with native extracellular matrix components vs. de novo generation of scaffolds using biocompatible materials are discussed. Strengths vs. limitations of recellularization using different cell types of various pluripotency such as embryonic, mesenchymal, and induced pluripotent stem cells are highlighted. Current hurdles to guide future research toward achieving the clinical goal of transplantation of a bioengineered lung are discussed.

Surface-tension phenomena in organismal biology: an introduction to the symposium

Flows driven by surface tension are both ubiquitous and diverse, involving the drinking of birds and bees, the flow of xylem in plants, the impact of raindrops on animals, respiration in humans, and the transmission of diseases in plants and animals, including humans. The fundamental physical principles underlying such flows provide a unifying framework to interpret the adaptations of the microorganisms, animals, and plants that rely upon them. The symposium on "Surface-Tension Phenomena in Organismal Biology" assembled an interdisciplinary group of researchers to address a large spectrum of topics, all articulated around the role of surface tension in shaping biology, health, and ecology. The contributions to the symposium and the papers in this issue are meant to be a starting point for novices to familiarize themselves with the fundamentals of flows driven by surface tension; to understand how they can play a governing role in many settings in organismal biology; and how such understanding of nature's use of surface tension can, in turn, inspire humans to innovate.