Mathematical model of a heterogeneous pulmonary acinus structure

Fluid-structure interaction analysis of airflow, structural mechanics and aerosol dynamics in a four-generation acinar model

Elucidating the aerosol dynamics in the pulmonary acinar region is imperative for both health risk assessment and inhalation therapy, especially nowadays with the occurrence of the global COVID-19 pandemic. During respiration, the chest's outward elastic recoil and the lungs' inward elastic recoil lead to a change of transmural pressure, which drives the lungs to expand and contract to inhale and expel airflow and aerosol. In contrast to research using predefined wall motion, we developed a four-generation acinar model and applied an oscillatory pressure on the model outface to generate structure deformation and airflow. With such tools at hand, we performed a computational simulation that addressed both the airflow characteristic, structural mechanics, and aerosol dynamics in the human pulmonary acinar region. Our results showed that there is no recirculating flow in the sac. The structural displacement and stress were found to be positively related to the change of model volume and peaked at the end of inspiration. It was noteworthy that the stress distribution on the acinar wall was significantly heterogeneous, and obvious concentrations of stress were found at the junction of the alveoli and the ducts or the junction of the alveoli and alveoli in the sac. Our result demonstrated the effect of breathing cycles and aerosol diameter on deposition fraction and location of aerosols in the size range of 0.1-5 μm. Multiple respiratory cycles were found necessary for adequate deposition or escape of submicron particles while having a negligible influence on the transport of large particles, which were dominated by gravity. Our study can provide new insights into the further investigation of airflow, structural mechanics, and aerosol dynamics in the acinar depth.

Bioengineering and Clinical Translation of Human Lung and its Components

Clinical lung transplantation has rapidly established itself as the gold standard of treatment for end-stage lung diseases in a restricted group of patients since the first successful lung transplant occurred. Although significant progress has been made in lung transplantation, there are still numerous obstacles on the path to clinical success. The development of bioartificial lung grafts using patient-derived cells may serve as an alternative treatment modality; however, challenges include developing appropriate scaffold materials, advanced culture strategies for lung-specific multiple cell populations, and fully matured constructs to ensure increased transplant lifetime following implantation. This review highlights the development of tissue-engineered tracheal and lung equivalents over the past two decades, key problems in lung transplantation in a clinical environment, the advancements made in scaffolds, bioprinting technologies, bioreactors, organoids, and organ-on-a-chip technologies. The review aims to fill the lacuna in existing literature toward a holistic bioartificial lung tissue, including trachea, capillaries, airways, bifurcating bronchioles, lung disease models, and their clinical translation. Herein, the efforts are on bridging the application of lung tissue engineering methods in a clinical environment as it is thought that tissue engineering holds enormous promise for overcoming the challenges associated with the clinical translation of bioengineered human lung and its components.

A computed tomography imaging-based subject-specific whole-lung deposition model

The respiratory tract is an important route for beneficial drug aerosol or harmful particulate matter to enter the body. To assess the therapeutic response or disease risk, whole-lung deposition models have been developed, but were limited by compartment, symmetry or stochastic approaches. In this work, we proposed an imaging-based subject-specific whole-lung deposition model. The geometries of airways and lobes were segmented from computed tomography (CT) lung images at total lung capacity (TLC), and the regional air-volume changes were calculated by registering CT images at TLC and functional residual capacity (FRC). The geometries were used to create the structure of entire subject-specific conducting airways and acinar units. The air-volume changes were used to estimate the function of subject-specific ventilation distributions among acinar units and regulate flow rates in respiratory airway models. With the airway dimensions rescaled to a desired lung volume and the airflow field simulated by a computational fluid dynamics model, particle deposition fractions were calculated using deposition probability formulae adjusted with an enhancement factor to account for the effects of secondary flow and airway geometry in proximal airways. The proposed model was validated in silico against existing whole-lung deposition models, three-dimensional (3D) computational fluid and particle dynamics (CFPD) for an acinar unit, and 3D CFPD deep lung model comprising conducting and respiratory regions. The model was further validated in vivo against the lobar particle distribution and the coefficient of variation of particle distribution obtained from CT and single-photon emission computed tomography (SPECT) images, showing good agreement. Subject-specific airway structure increased the deposition fraction of 10.0-μm particles and 0.01-μm particles by approximately 10%. An enhancement factor increased the overall deposition fractions, especially for particle sizes between 0.1 and 1.0 μm.

Mathematical modeling of pulmonary acinus structure: Verification of acinar shape effects on pathway structure using rat lungs

The pulmonary acinus is the gas exchange unit in the lung and has a very complex microstructure. The structure model is essential to understand the relationship between structural heterogeneity and mechanical phenomena at the acinus level with computational approaches. We propose an acinus structure model represented by a cluster of truncated octahedra in conical, double-conical, inverted conical, or chestnut-like conical confinement to accommodate recent experimental information of rodent acinar shapes. The basis of the model is the combined use of Voronoi and Delaunay tessellations and the optimization of the ductal tree assuming the number of alveoli and the mean path length as quantities related to gas exchange. Before applying the Voronoi tessellation, controlling the seed coordinates enables us to model acinus with arbitrary shapes. Depending on the acinar shape, the distribution of path length varies. The lengths are more widely spread for the cone acinus, with a bias toward higher values, while most of the lengths for the inverted cone acinus primarily take a similar value. Longer pathways have smaller tortuosity and more generations, and duct length per generation is almost constant irrespective of generation, which agrees well with available experimental data. The pathway structure of cone and chestnut-like cone acini is similar to the surface acini's features reported in experiments. According to space-filling requirements in the lung, other conical acini may also be acceptable. The mathematical acinus structure model with various conical shapes can be a platform for computational studies on regional differences in lung functions along the lung surface, underlying respiratory physiology and pathophysiology.

Effects of airway deformation and alveolar pores on particle deposition in the lungs

The distal lung (G14-G23), which are composed of alveoli and bronchi, are responsible for almost all gas exchange and micro- and nanoparticle deposition in the lungs. In the existing research using computational fluid dynamics, the geometric modeling accuracy of the bronchial bifurcation structure is given priority, and then the alveoli are attached to bronchi as discrete spherical crowns. This method ignores the correlation between alveoli. In fact, the alveoli have a tessellated distribution, and adjacent alveoli are connected by several alveolar pores. Due to the huge number of alveoli, this seemingly small difference will be greatly amplified, which may lead to a large deviation in the prediction of the overall flow. Accordingly, the objective of this study is to construct a two-dimensional distal lung model including the bronchi, acini, and alveolar pores by using the methods of regular hexagonal tessellational subdivision, fusion, and coordinate transformation. A moving boundary is introduced to simulate the process of airflow and particle deposition in the distal lung, and the effects of bronchial deformation, respiratory frequency, and alveolar pores are obtained. The results show that there are significant differences in intrapulmonary flow patterns with and without alveolar pores. Alveolar pores can establish bypass ventilation downstream of a blockage, thus providing a pathway for particles to enter the airways downstream of the blockage. Changing the respiratory frequency and the amplitude of bronchial deformation will change the relative velocity between particles and moving wall, which, in turn, will change the particle deposition efficiency in the distal lung. To summarize this study, a geometric modeling method for the distal lung with alveolar pores is established, and the important roles of detailed characteristics of the distal lung are revealed. The findings of this study provide a reasonable hydrodynamic mechanism for the prevention of related respiratory diseases.

Recent advances in the understanding of alveolar flow

Understanding the dynamics of airflow in alveoli and its effect on the behavior of particle transport and deposition is important for understanding lung functions and the cause of many lung diseases. The studies on these areas have drawn substantial attention over the last few decades. This Review discusses the recent progress in the investigation of behavior of airflow in alveoli. The information obtained from studies on the structure of the lung airway tree and alveolar topology is provided first. The current research progress on the modeling of alveoli is then reviewed. The alveolar cell parameters at different generation of branches, issues to model real alveolar flow, and the current numerical and experimental approaches are discussed. The findings on flow behavior, in particular, flow patterns and the mechanism of chaotic flow generation in the alveoli are reviewed next. The different flow patterns under different geometrical and flow conditions are discussed. Finally, developments on microfluidic devices such as lung-on-a-chip devices are reviewed. The issues of current devices are discussed.

Visualizing the Flow Patterns in an Expanding and Contracting Pulmonary Alveolated Duct Based on Microcomputed Tomography Images

We visualized the flow patterns in an alveolated duct model with breathing-like expanding and contracting wall motions using particle image velocimetry, and then, we investigated the effect of acinar deformation on the flow patterns. We reconstructed a compliant, scaled-up model of an alveolated duct from synchrotron microcomputed tomography images of a mammalian lung. The alveolated duct did not include any bifurcation, and its entire surface was covered with alveoli. We embedded the alveolated duct in a sealed container that was filled with fluid. We oscillated the fluid in the duct and container simultaneously and independently to control the flow and duct volume. We examined the flow patterns in alveoli, with the Reynolds number (Re) at 0.03 or 0.22 and the acinar volume change at 0%, 20%, or 80%. At the same Re, the heterogeneous deformation induced different inspiration and expiration flow patterns, and the recirculating regions in alveoli changed during respiratory cycle. During a larger acinar deformation at Re = 0.03, the flow patterns tended to change from recirculating flow to radial flow during inspiration and vice versa during expiration. Additionally, the alveolar geometric characteristics, particularly the angle between the alveolar duct and mouth, affected these differences in flow patterns. At Re = 0.22, recirculating flow patterns tended to form during inspiration and expiration, regardless of the magnitude of the acinar deformation. Our in vitro experiments suggest that the alveolated flows with nonself-similar and heterogeneous wall motions may promote particle mixing and deposition.

Transmission risk of infectious droplets in physical spreading process at different times: A review

Droplets provide a well-known transmission media in the COVID-19 epidemic, and the particle size is closely related to the classification of the transmission route. However, the term "aerosol" covers most particle sizes of suspended particulates because of information asymmetry in different disciplines, which may lead to misunderstandings in the selection of epidemic prevention and control strategies for the public. In this review, the time when these droplets are exhaled by a patient was taken as the initial time. Then, all available viral loads and numerical distribution of the exhaled droplets was analyzed, and the evaporation model of droplets in the air was combined with the deposition model of droplet nuclei in the respiratory tract. Lastly, the perspective that physical spread affects the transmission risk of different size droplets at different times was summarized for the first time. The results showed that although the distribution of exhaled droplets was dominated by small droplets, droplet volume was proportional to the third power of particle diameter, meaning that the viral load of a 100 μm droplet was approximately 10⁶ times that of a 1 μm droplet at the initial time. Furthermore, the exhaled droplets are affected by heat and mass transfer of evaporation, water fraction, salt concentration, and acid-base balance (the water fraction > 98%), which lead them to change rapidly, and the viral survival condition also deteriorates dramatically. The time required for the initial diameter (d_o) of a droplet to shrink to the equilibrium diameter (d_e, about 30% of d_o) is approximately proportional to the second power of the particle diameter, taking only a few milliseconds for a 1 μm droplet but hundreds of milliseconds for a 10 μm droplet; in other words, the viruses carried by the large droplets can be preserved as much as possible. Finally, the infectious droplet nuclei maybe inhaled by the susceptible population through different and random contact routes, and the droplet nuclei with larger d_e decompose more easily into tiny particles on account of the accelerated collision in a complex airway, which can be deposited in the higher risk alveolar region. During disease transmission, the infectious droplet particle size varies widely, and the transmission risk varies significantly at different time nodes; therefore, the fuzzy term "aerosol" is not conducive to analyzing disease exposure risk. Recommendations for epidemic prevention and control strategies are: 1) Large droplets are the main conflict in disease transmission; thus, even if they are blocked by a homemade mask initially, it significantly contains the epidemic. 2) The early phase of contact, such as close-contact and short-range transmission, has the highest infection risk; therefore, social distancing can effectively keep the susceptible population from inhaling active viruses. 3) The risk of the fomite route depends on the time in contact with infectious viruses; thus, it is important to promote good health habits (including frequent hand washing, no-eye rubbing, coughing etiquette, normalization of surface cleaning), although blind and excessive disinfection measures are not advisable. 4) Compared with the large droplets, the small droplets have larger numbers but carry fewer viruses and are more prone to die through evaporation.

A multi-scale model of gas transport in the lung to study heterogeneous lung ventilation during the multiple-breath washout test

The multiple-breath washout (MBW) is a lung function test that measures the degree of ventilation inhomogeneity (VI). The test is used to identify small airway impairment in patients with lung diseases like cystic fibrosis. However, the physical and physiological factors that influence the test outcomes and differentiate health from disease are not well understood. Computational models have been used to better understand the interaction between anatomical structure and physiological properties of the lung, but none of them has dealt in depth with the tracer gas washout test in a whole. Thus, our aim was to create a lung model that simulates the entire MBW and investigate the role of lung morphology and tissue mechanics on the tracer gas washout procedure. To this end, we developed a multi-scale lung model to simulate the inert gas transport in airways of all size. We then applied systematically different modifications to geometrical and mechanical properties of the lung model (compliance, residual airway volume and flow resistance) which have been associated with VI. The modifications were applied to distinct parts of the model, and their effects on the gas distribution within the lung and on the gas concentration profile were assessed. We found that variability in compliance and residual volume of the airways, as well as the spatial distribution of this variability in the lung had a direct influence on gas distribution among airways and on the MBW pattern (washout duration, characteristic concentration profile during each expiration), while the effects of variable flow resistance were negligible. Based on these findings, it is possible to classify different types of inhomogeneities in the lung and relate them to specific features of the MBW pattern, which builds the basis for a more detailed association of lung function and structure.

Obstructive lung diseases, like cystic fibrosis or primary ciliary dyskinesia, lead to inhomogeneous ventilation. The degree of observed inhomogeneity represents a clinical measure for the progression of the disease. The multiple-breath washout (MBW) is a lung function test that measures this inhomogeneity in the lung. However, the factors that influence the results of the test and differentiate between health and disease are not well understood. Computational models help us to understand better the relation between anatomical structure and physiological properties of the lung, but none of them has dealt in depth with the MBW test in whole. Our aim was to create a lung model that simulates the entire MBW test and study the role of lung structure and tissue mechanics on the washout procedure. We developed a multi-scale lung model to simulate the inert gas transport in all airways including the gas exchange area. Our model offers the opportunity to understand the ventilation distribution in the healthy lung. It can also mimic certain patterns of lung disease by applying modifications in mechanical properties out of the physiological limits. Thus, it can be used to study MBW characteristics in health and disease.

Heterogeneous structure and surface tension effects on mechanical response in pulmonary acinus: A finite element analysis

BACKGROUND

The pulmonary acinus is a dead-end microstructure that consists of ducts and alveoli. High-resolution micro-CT imaging has recently provided detailed anatomical information of a complete in vivo acinus, but relating its mechanical response with its detailed acinar structure remains challenging. This study aimed to investigate the mechanical response of acinar tissue in a whole acinus for static inflation using computational approaches.

METHODS

We performed finite element analysis of a whole acinus for static inflation. The acinar structure model was generated based on micro-CT images of an intact acinus. A continuum mechanics model of the lung parenchyma was used for acinar tissue material model, and surface tension effects were explicitly included. An anisotropic mechanical field analysis based on a stretch tensor was combined with a curvature-based local structure analysis.

FINDINGS

The airspace of the acinus exhibited nonspherical deformation as a result of the anisotropic deformation of acinar tissue. A strain hotspot occurred at the ridge-shaped region caused by a rod-like deformation of acinar tissue on the ridge. The local structure becomes bowl-shaped for inflation and, without surface tension effects, the surface of the bowl-shaped region primarily experiences isotropic deformation. Surface tension effects suppressed the increase in airspace volume and inner surface area, while facilitating anisotropic deformation on the alveolar surface.

INTERPRETATION

In the lungs, the heterogeneous acinar structure and surface tension induce anisotropic deformation at the acinar and alveolar scales. Further research is needed on structural variation of acini, inter-acini connectivity, or dynamic behavior to understand multiscale lung mechanics.

Use of computational fluid dynamics deposition modeling in respiratory drug delivery

INTRODUCTION

Respiratory drug delivery is a surprisingly complex process with a number of physical and biological challenges. Computational fluid dynamics (CFD) is a scientific simulation technique that is capable of providing spatially and temporally resolved predictions of many aspects related to respiratory drug delivery from initial aerosol formation through respiratory cellular drug absorption.

AREAS COVERED

This review article focuses on CFD-based deposition modeling applied to pharmaceutical aerosols. Areas covered include the development of new complete-airway CFD deposition models and the application of these models to develop a next-generation of respiratory drug delivery strategies.

EXPERT OPINION

Complete-airway deposition modeling is a valuable research tool that can improve our understanding of pharmaceutical aerosol delivery and is already supporting medical hypotheses, such as the expected under-treatment of the small airways in asthma. These complete-airway models are also being used to advance next-generation aerosol delivery strategies, like controlled condensational growth. We envision future applications of CFD deposition modeling to reduce the need for human subject testing in developing new devices and formulations, to help establish bioequivalence for the accelerated approval of generic inhalers, and to provide valuable new insights related to drug dissolution and clearance leading to microdosimetry maps of drug absorption.

One (sub-)acinus for all: Fate of inhaled aerosols in heterogeneous pulmonary acinar structures

Computational Fluid Dynamics (CFD) have offered an attractive gateway to investigate in silico respiratory flows and aerosol transport in the depths of the lungs. Yet, not only do existing models lack sufficient anatomical realism in capturing the heterogeneity and morphometry of the acinar environment, numerical simulations have been widely restricted to domains capturing a mere few percent of a single acinus. Here, we present to the best of our knowledge the most detailed and comprehensive in silico simulations to date on the fate of aerosols in the acinar depths. Our heterogeneous acinar domains represent complete sub-acinar models (i.e. 1/8th of a full acinus) based on the recent algorithm of Koshiyama & Wada (2015), capturing statistics of human acinar morphometry (Ochs et al. 2004). Our simulations deliver high-resolution, 3D spatial-temporal data on aerosol transport and deposition, emphasizing how variances in acinar heterogeneity only play a minor role in determining general deposition outcomes. With such tools at hand, we revisit whole-lung deposition predictions (i.e. ICRP) based on past 1D lung models. While our findings under quiet breathing substantiate general deposition trends obtained with past predictions in the alveolar regions, we underscore how deposition fractions are anticipated to increase, in particular during deep inhalation. For such inhalation maneuver, our simulations support the notion of significantly augmented deposition for all aerosol sizes (0.005-5.0μm). Overall, our efforts not only help consolidate our mechanistic understanding of inhaled aerosol transport in the acinar depths but also continue to bridge the gap between "bottom-up" in silico models and regional deposition predictions from whole-lung models. Such quantifications provide what is deemed more accurate deposition predictions in morphometrically-faithful models and are particularly useful in assessing inhalation strategies for deep airway deposition (e.g. systemic delivery).

A simplified parametrised model for lung microstructures capable of mimicking realistic geometrical and mechanical properties

The respiratory zone of mammalian lungs contains several millions of so-called alveoli. The geometrical and mechanical properties of this microstructure are crucial for respiration and influence the macroscopic behaviour of the entire organ in health and disease. Hence, if computational models are sought to gain more insight into lung behaviour, predict lung states in certain scenarios or suggest better treatment options in early stages of respiratory dysfunction, an adequate representation of this microstructure is essential. However, investigating the real alveolar architecture requires complex medical-imaging methods and would be computationally extremely expensive. Even worse, there is currently no way of obtaining the real patient-specific microstructure in vivo. Hence, we present a fast and easy to compute parametrised model of lung microstructures based on tetrakaidecahedra which can represent both geometrical and mechanical properties of the parenchyma. We show that gas transport pathways and stress and strain distributions are comparable to real alveolar microstructures and even capable of capturing variations present in biology. The created parametrised lung microstructure models can be utilized in finite element simulations to study, e.g., alveolar flow phenomena, particle deposition, or alveolar stresses and strains during mechanical ventilation. Due to the simpler geometry of the parametrised microgeometries compared to imaging-based microstructures, remarkable savings in CPU time can be achieved. We show that our model requires a minimum of 10% of the computational time for computing the same strain state in structural mechanics simulations compared to imaging-based alveolar microstructures.

Morphometric differences between central vs. surface acini in A/J mice using high-resolution micro-computed tomography

Through interior tomography, high-resolution microcomputed tomography (μCT) systems provide the ability to nondestructively assess the pulmonary acinus at micron and submicron resolutions. With the application of systematic uniform random sampling (SURS) principles applied to in situ fixed, intact, ex vivo lungs, we have sought to characterize morphometric differences in central vs. surface acini to better understand how well surface acini reflect global acinar geometry. Lungs from six mice (A/J strain, 15-20 wk of age) were perfusion fixed in situ and imaged using a multiresolution μCT system (Micro XCT 400, Zeiss). With the use of lower-resolution whole lung images, SURS methods were used for identification of central and surface foci for high-resolution imaging. Acinar morphometric metrics included diameters, lengths, and branching angles for each alveolar duct and total path lengths from entrance of the acinus to the terminal alveolar sacs. In addition, acinar volume, alveolar surface area, and surface area/volume ratios were assessed. A generation-based analysis demonstrated that central acini have significantly smaller branch diameters at each generation with no significant increase in branch lengths. In addition to larger-diameter alveolar ducts, surface acini had significantly increased numbers of branches and terminal alveolar sacs. The total path lengths from the acinar entrance to the terminal nodes were found to be higher in the case of surface acini. Volumes and surface areas of surface acini are greater than central acini, but there were no differences in surface/volume ratios. In conclusion, there are significant structural differences between surface and central acini in the A/J mouse.