A model of ventilation of the healthy human lung

Pulmonary response prediction through personalized basis functions in a virtual patient model

BACKGROUND AND OBJECTIVE

Recruitment maneuvers with subsequent positive-end-expiratory-pressure (PEEP) have proven effective in recruiting lung volume and preventing alveoli collapse. However, determining a safe, effective, and patient-specific PEEP is not standardized, and this more optimal PEEP level evolves with patient condition, requiring personalised monitoring and care approaches to maintain optimal ventilation settings.

METHODS

This research examines 3 physiologically relevant basis function sets (exponential, parabolic, cumulative) to enable better prediction of elastance evolution for a virtual patient or digital twin model of MV lung mechanics, including novel elements to model and predict distension elastance. Prediction accuracy and robustness are validated against recruitment maneuver data from 18 volume-controlled ventilation (VCV) patients at 7 different baseline PEEP levels (0 to 12 cmH2O) and 14 pressure-controlled ventilation (PCV) patients at 4 different baseline PEEP levels (6 to 12 cmH2O), yielding 623 and 294 prediction cases, respectively. Predictions were made up to 12 cmH2O of added PEEP ahead, covering 6 × 2 cmH2O PEEP steps.

RESULTS

The 3 basis function sets yield median absolute peak inspiratory pressure (PIP) prediction error of 1.63 cmH2O for VCV patients, and median peak inspiratory volume (PIV) prediction error of 0.028 L for PCV patients. The exponential basis function set yields a better trade-off of overall performance across VCV and PCV prediction than parabolic and cumulative basis function sets from other studies. Comparing predicted and clinically measured distension prediction in VCV demonstrated consistent, robust high accuracy with R2 = 0.90-0.95.

CONCLUSIONS

The results demonstrate recruitment mechanics are best captured by an exponential basis function across different mechanical ventilation modes, matching physiological expectations, and accurately capture, for the first time, distension mechanics to within 5-10 % accuracy. Enabling the risk of lung injury to be predicted before changing ventilator settings. The overall outcomes significantly extend and more fully validate this digital twin or virtual mechanical ventilation patient model.

Exposure to Aldehyde Cherry e-Liquid Flavoring and Its Vaping Byproduct Disrupt Pulmonary Surfactant Biophysical Function

Over the past decade, there has been a significant rise in the use of vaping devices, particularly among adolescents, raising concerns for effects on respiratory health. Pressingly, many recent vaping-related lung injuries are unexplained by current knowledge, and the overall implications of vaping for respiratory health are poorly understood. This study investigates the effect of hydrophobic vaping liquid chemicals on the pulmonary surfactant biophysical function. We focus on the commonly used flavoring benzaldehyde and its vaping byproduct, benzaldehyde propylene glycol acetal. The study involves rigorous testing of the surfactant biophysical function in Langmuir trough and constrained sessile drop surfactometer experiments with both protein-free synthetic surfactant and hydrophobic protein-containing clinical surfactant models. The study reveals that exposure to these vaping chemicals significantly interferes with the synthetic and clinical surfactant biophysical function. Further atomistic simulations reveal preferential interactions with SP-B and SP-C surfactant proteins. Additionally, data show surfactant lipid-vaping chemical interactions and suggest significant transfer of vaping chemicals to the experimental subphase, indicating a toxicological mechanism for the alveolar epithelium. Our study, therefore, reveals novel mechanisms for the inhalational toxicity of vaping. This highlights the need to reassess the safety of vaping liquids for respiratory health, particularly the use of aldehyde chemicals as vaping flavorings.

Surfactant Proteins SP-B and SP-C in Pulmonary Surfactant Monolayers: Physical Properties Controlled by Specific Protein-Lipid Interactions

The lining of the alveoli is covered by pulmonary surfactant, a complex mixture of surface-active lipids and proteins that enables efficient gas exchange between inhaled air and the circulation. Despite decades of advancements in the study of the pulmonary surfactant, the molecular scale behavior of the surfactant and the inherent role of the number of different lipids and proteins in surfactant behavior are not fully understood. The most important proteins in this complex system are the surfactant proteins SP-B and SP-C. Given this, in this work we performed nonequilibrium all-atom molecular dynamics simulations to study the interplay of SP-B and SP-C with multicomponent lipid monolayers mimicking the pulmonary surfactant in composition. The simulations were complemented by z-scan fluorescence correlation spectroscopy and atomic force microscopy measurements. Our state-of-the-art simulation model reproduces experimental pressure-area isotherms and lateral diffusion coefficients. In agreement with previous research, the inclusion of either SP-B and SP-C increases surface pressure, and our simulations provide a molecular scale explanation for this effect: The proteins display preferential lipid interactions with phosphatidylglycerol, they reside predominantly in the lipid acyl chain region, and they partition into the liquid expanded phase or even induce it in an otherwise packed monolayer. The latter effect is also visible in our atomic force microscopy images. The research done contributes to a better understanding of the roles of specific lipids and proteins in surfactant function, thus helping to develop better synthetic products for surfactant replacement therapy used in the treatment of many fatal lung-related injuries and diseases.

Nonlinear N - Compartments model of respiratory mechanics considering viscoelasticity, inertia and surface tension properties

Respiratory biomechanics constitutes an important topic in clinical practice. Different strategies like mathematical models have been implemented to understand and replicate scenarios allowing deeper analysis. In this paper, a nonlinear N - compartments model is presented, allowing to represent the lung in a heterogeneous way. It considers the resistance of each generation of the airway and each alveolar compartment characterized independently. Includes properties of nonlinear elastance, viscoelasticity, inertia, and surface tension. In this work, to show the functionality of the model, a simulation of four alveolar units coupled to the airway model is presented using pressure as input signal simulating mechanical ventilation. However, the model can be used to simulate any desired number of alveolar units. Values at airway output were compared to the linear model, obtaining a correlation close to 1. Also, was compared to a physical test lung using Hamilton - S1 mechanical ventilator obtaining a positive correlation. The model makes it possible to evaluate the effects of different properties during spontaneous respiration or mechanical ventilation, both at the airway opening and alveolar. These properties include viscoelasticity, surface tension, inertia, among others.

Whole-lung finite-element models for mechanical ventilation and respiratory research applications

Mechanical ventilation has been a vital treatment for Covid-19 patients with respiratory failure. Lungs assisted with mechanical ventilators present a wide variability in their response that strongly depends on air-tissue interactions, which motivates the creation of simulation tools to enhance the design of ventilatory protocols. In this work, we aim to create anatomical computational models of the lungs that predict clinically-relevant respiratory variables. To this end, we formulate a continuum poromechanical framework that seamlessly accounts for the air-tissue interaction in the lung parenchyma. Based on this formulation, we construct anatomical finite-element models of the human lungs from computed-tomography images. We simulate the 3D response of lungs connected to mechanical ventilation, from which we recover physiological parameters of high clinical relevance. In particular, we provide a framework to estimate respiratory-system compliance and resistance from continuum lung dynamic simulations. We further study our computational framework in the simulation of the supersyringe method to construct pressure-volume curves. In addition, we run these simulations using several state-of-the-art lung tissue models to understand how the choice of constitutive models impacts the whole-organ mechanical response. We show that the proposed lung model predicts physiological variables, such as airway pressure, flow and volume, that capture many distinctive features observed in mechanical ventilation and the supersyringe method. We further conclude that some constitutive lung tissue models may not adequately capture the physiological behavior of lungs, as measured in terms of lung respiratory-system compliance. Our findings constitute a proof of concept that finite-element poromechanical models of the lungs can be predictive of clinically-relevant variables in respiratory medicine.

Over-distension prediction via hysteresis loop analysis and patient-specific basis functions in a virtual patient model

BACKGROUND AND OBJECTIVE

Recruitment maneuvers (RMs) with subsequent positive-end-expiratory-pressure (PEEP) have proven effective in recruiting lung volume and preventing alveolar collapse. However, a suboptimal PEEP could induce undesired injury in lungs by insufficient or excessive breath support. Thus, a predictive model for patient response under PEEP changes could improve clinical care and lower risks.

METHODS

This research adds novel elements to a virtual patient model to identify and predict patient-specific lung distension to optimise and personalise care. Model validity and accuracy are validated using data from 18 volume-controlled ventilation (VCV) patients at 7 different baseline PEEP levels (0-12cmH₂O), yielding 623 prediction cases. Predictions were made up to ΔPEEP = 12cmH₂O ahead covering 6x2cmH₂O PEEP steps.

RESULTS

Using the proposed lung distension model, 90% of absolute peak inspiratory pressure (PIP) prediction errors compared to clinical measurement are within 3.95cmH₂O, compared with 4.76cmH₂O without this distension term. Comparing model-predicted and clinically measured distension had high correlation increasing to R² = 0.93-0.95 if maximum ΔPEEP ≤ 6cmH₂O. Predicted dynamic functional residual capacity (V_frc) changes as PEEP rises yield 0.013L median prediction error for both prediction groups and overall R² of 0.84.

CONCLUSIONS

Overall results demonstrate nonlinear distension mechanics are accurately captured in virtual lung mechanics patients for mechanical ventilation, for the first time. This result can minimise the risk of lung injury by predicting its potential occurrence of distension before changing ventilator settings. The overall outcomes significantly extend and more fully validate this virtual mechanical ventilation patient model.

Virtual patients for mechanical ventilation in the intensive care unit

BACKGROUND

Mechanical ventilation (MV) is a core intensive care unit (ICU) therapy. Significant inter- and intra- patient variability in lung mechanics and condition makes managing MV difficult. Accurate prediction of patient-specific response to changes in MV settings would enable optimised, personalised, and more productive care, improving outcomes and reducing cost. This study develops a generalised digital clone model, or in-silico virtual patient, to accurately predict lung mechanics in response to changes in MV.

METHODS

An identifiable, nonlinear hysteresis loop model (HLM) captures patient-specific lung dynamics identified from measured ventilator data. Identification and creation of the virtual patient model is fully automated using the hysteresis loop analysis (HLA) method to identify lung elastances from clinical data. Performance is evaluated using clinical data from 18 volume-control (VC) and 14 pressure-control (PC) ventilated patients who underwent step-wise recruitment maneuvers.

RESULTS

Patient-specific virtual patient models accurately predict lung response for changes in PEEP up to 12 cmH₂O for both volume and pressure control cohorts. R² values for predicting peak inspiration pressure (PIP) and additional retained lung volume, V_frc in VC, are R²=0.86 and R²=0.90 for 106 predictions over 18 patients. For 14 PC patients and 84 predictions, predicting peak inspiratory volume (PIV) and V_frc yield R²=0.86 and R²=0.83. Absolute PIP, PIV and V_frc errors are relatively small.

CONCLUSIONS

Overall results validate the accuracy and versatility of the virtual patient model for capturing and predicting nonlinear changes in patient-specific lung mechanics. Accurate response prediction enables mechanically and physiologically relevant virtual patients to guide personalised and optimised MV therapy.

Understanding the Functional Properties of Lipid Heterogeneity in Pulmonary Surfactant Monolayers at the Atomistic Level

Pulmonary surfactant is a complex mixture of lipids and proteins lining the interior of the alveoli, and constitutes the first barrier to both oxygen and pathogens as they progress toward blood circulation. Despite decades of study, the behavior of the pulmonary surfactant at the molecular scale is poorly understood, which hinders the development of effective surfactant replacement therapies, useful in the treatment of several lung-related diseases. In this work, we combined all-atom molecular dynamics simulations, Langmuir trough measurements, and AFM imaging to study synthetic four-component lipid monolayers designed to model protein-free pulmonary surfactant. We characterized the structural and dynamic properties of the monolayers with a special focus on lateral heterogeneity. Remarkably, simulations reproduce almost quantitatively the experimental data on pressure-area isotherms and the presence of lateral heterogeneities highlighted by AFM. Quite surprisingly, the pressure-area isotherms do not show a plateau region, despite the presence of liquid-condensed nanometer-sized domains at surface pressures larger than 20 mN/m. In the simulations, the liquid-condensed domains were small and transient, but they did not coalesce to yield a separate phase. They were only slightly enriched in DPPC and cholesterol, and their chemical composition remained very similar to the overall composition of the monolayer membrane. Instead, they differed from liquid-expanded regions in terms of membrane thickness (in agreement with AFM data), diffusion rates, as well as acyl chain packing and orientation. We hypothesize that such lateral heterogeneities are crucial for lung surfactant function, as they allow both efficient packing, to achieve low surface tension, and sufficient fluidity, critical for rapid adsorption to the air–liquid interface during the breathing cycle.

Effects of Breath-Hold Deep Diving on the Pulmonary System

This short review focuses on pulmonary injury in breath-hold (BH) divers. When practicing their extreme leisure sport, they are exposed to increased pressure on pulmonary gas volumes, hypoxia, and increased partial gas pressures. Increasing ambient pressures do present a serious problem to BH deep divers, because the semi-rigid thorax prevents the deformation required by the Boyle-Mariotte law. As a result, a negative-pressure barotrauma (lung squeeze) with acute hemoptysis is not uncommon. Respiratory maneuvers such as glossopharyngeal insufflation (GI) and glossopharyngeal exsufflation (GE) are practiced to prevent lung squeeze and to permit equalizing the paranasal sinuses and the middle ear. GI not only impairs venous return, thereby provoking hypotension and even fainting, but also produces intrathoracic pressures likely to induce pulmonary barotrauma that is speculated to induce long-term injury. GE, in turn, further increases the already negative intrapulmonary pressure, thereby favoring alveolar collapse (atelectasis). Finally, hypoxia seemingly not only induces brain injury but initiates the opening of intrapulmonary shunts. These pathways are large enough to permit transpulmonary passage of venous N2 bubbles, making stroke-like phenomena in deep BH divers possible.

Biomedical engineer's guide to the clinical aspects of intensive care mechanical ventilation

Background

Mechanical ventilation is an essential therapy to support critically ill respiratory failure patients. Current standards of care consist of generalised approaches, such as the use of positive end expiratory pressure to inspired oxygen fraction (PEEP–FiO₂) tables, which fail to account for the inter- and intra-patient variability between and within patients. The benefits of higher or lower tidal volume, PEEP, and other settings are highly debated and no consensus has been reached. Moreover, clinicians implicitly account for patient-specific factors such as disease condition and progression as they manually titrate ventilator settings. Hence, care is highly variable and potentially often non-optimal. These conditions create a situation that could benefit greatly from an engineered approach. The overall goal is a review of ventilation that is accessible to both clinicians and engineers, to bridge the divide between the two fields and enable collaboration to improve patient care and outcomes. This review does not take the form of a typical systematic review. Instead, it defines the standard terminology and introduces key clinical and biomedical measurements before introducing the key clinical studies and their influence in clinical practice which in turn flows into the needs and requirements around how biomedical engineering research can play a role in improving care. Given the significant clinical research to date and its impact on this complex area of care, this review thus provides a tutorial introduction around the review of the state of the art relevant to a biomedical engineering perspective.

Discussion

This review presents the significant clinical aspects and variables of ventilation management, the potential risks associated with suboptimal ventilation management, and a review of the major recent attempts to improve ventilation in the context of these variables. The unique aspect of this review is a focus on these key elements relevant to engineering new approaches. In particular, the need for ventilation strategies which consider, and directly account for, the significant differences in patient condition, disease etiology, and progression within patients is demonstrated with the subsequent requirement for optimal ventilation strategies to titrate for patient- and time-specific conditions.

Conclusion

Engineered, protective lung strategies that can directly account for and manage inter- and intra-patient variability thus offer great potential to improve both individual care, as well as cohort clinical outcomes.

Analysis of the method for ventilation heterogeneity assessment using the Otis model and forced oscillations

Increased heterogeneity of the lung disturbs pulmonary gas exchange. During bronchoconstriction, inflammation of lung parenchyma or acute respiratory distress syndrome, inhomogeneous lung ventilation can become bimodal and increase the risk of ventilator-induced lung injury during mechanical ventilation. A simple index sensitive to ventilation heterogeneity would be very useful in clinical practice. In the case of bimodal ventilation, the index (H) can be defined as the ratio between the longer and shorter time constant characterising regions of contrary mechanical properties. These time constants can be derived from the Otis model fitted to input impedance (Zin) measured using forced oscillations. In this paper we systematically investigated properties of the aforementioned approach. The research included both numerical simulations and real experiments with a dual-lung simulator. Firstly, a computational model mimicking the physical simulator was derived and then used as a forward model to generate synthetic flow and pressure signals. These data were used to calculate the input impedance and then the Otis inverse model was fitted to Zin by means of the Levenberg-Marquardt (LM) algorithm. Finally, the obtained estimates of model parameters were used to compute H. The analysis of the above procedure was performed in the frame of Monte Carlo simulations. For each selected value of H, forward simulations with randomly chosen lung parameters were repeated 1000 times. Resulting signals were superimposed by additive Gaussian noise. The estimated values of H properly indicated the increasing level of simulated inhomogeneity, however with underestimation and variation increasing with H. The main factor responsible for the growing estimation bias was the fixed starting vector required by the LM algorithm. Introduction of a correction formula perfectly reduced this systematic error. The experimental results with the dual-lung simulator confirmed potential of the proposed procedure to properly deduce the lung heterogeneity level. We conclude that the heterogeneity index H can be used to assess bimodal ventilation imbalances in cases when this phenomenon dominates lung properties, however future analyses, including the impact of lung tissue viscoelasticity and distributed airway or tissue inhomogeneity on H estimates, as well as studies in the time domain, are advisable.

Time-varying respiratory system elastance: a physiological model for patients who are spontaneously breathing

BACKGROUND

Respiratory mechanics models can aid in optimising patient-specific mechanical ventilation (MV), but the applications are limited to fully sedated MV patients who have little or no spontaneously breathing efforts. This research presents a time-varying elastance (E(drs)) model that can be used in spontaneously breathing patients to determine their respiratory mechanics.

METHODS

A time-varying respiratory elastance model is developed with a negative elastic component (E(demand)), to describe the driving pressure generated during a patient initiated breathing cycle. Data from 22 patients who are partially mechanically ventilated using Pressure Support (PS) and Neurally Adjusted Ventilatory Assist (NAVA) are used to investigate the physiology relevance of the time-varying elastance model and its clinical potential. E(drs) of every breathing cycle for each patient at different ventilation modes are presented for comparison.

RESULTS

At the start of every breathing cycle initiated by patient, E(drs) is < 0. This negativity is attributed from the E(demand) due to a positive lung volume intake at through negative pressure in the lung compartment. The mapping of E(drs) trajectories was able to give unique information to patients' breathing variability under different ventilation modes. The area under the curve of E(drs) (AUCE(drs)) for most patients is > 25 cmH2Os/l and thus can be used as an acute respiratory distress syndrome (ARDS) severity indicator.

CONCLUSION

The E(drs) model captures unique dynamic respiratory mechanics for spontaneously breathing patients with respiratory failure. The model is fully general and is applicable to both fully controlled and partially assisted MV modes.

Can computer simulators accurately represent the pathophysiology of individual COPD patients?

BACKGROUND

Computer simulation models could play a key role in developing novel therapeutic strategies for patients with chronic obstructive pulmonary disease (COPD) if they can be shown to accurately represent the pathophysiological characteristics of individual patients.

METHODS

We evaluated the capability of a computational simulator to reproduce the heterogeneous effects of COPD on alveolar mechanics as captured in a number of different patient datasets.

RESULTS

Our results show that accurately representing the pathophysiology of individual COPD patients necessitates the use of simulation models with large numbers (up to 200) of compartments for gas exchange. The tuning of such complex simulation models 'by hand' to match patient data is not feasible, and thus we present an automated approach based on the use of global optimization algorithms and high-performance computing. Using this approach, we are able to achieve extremely close matches between the simulator and a range of patient data including PaO2, PaCO2, pulmonary deadspace fraction, pulmonary shunt fraction, and ventilation/perfusion (/Q) curves. Using the simulator, we computed combinations of ventilator settings that optimally manage the trade-off between ensuring adequate gas exchange and minimizing the risk of ventilator-associated lung injury for an individual COPD patient.

CONCLUSIONS

Our results significantly strengthen the credibility of computer simulation models as research tools for the development of novel management protocols in COPD and other pulmonary disease states.

A functional mathematical model to simulate the single-breath nitrogen washout

A nonlinear dynamic model is proposed to reproduce and interpret the influence of pulmonary inhomogeneities on the single-breath nitrogen washout (SBNW) curve. The model is characterized by two parallel zones. In each zone, the upper airways are described by a Rohrer resistor. Intermediate airways are represented as a collapsible segment, the volume of which depends on transmural pressure. Smaller airways are described by a resistance which increases when transpulmonary pressure decreases. The respiratory region is modeled as a Voigt element. Three different conditions were simulated: a reference case, characterized by airway-parameter values for normal conditions, and two pathological states corresponding to different levels of disease. In the reference case, a straight line was a good approximation of SBNW phase III and the last point of departure of the nitrogen trace from this line unambiguously identified the onset of phase IV. The slope of phase III rose with disease severity (from a 1.1% increase in nitrogen concentration per 1000 ml of expired volume in the reference case to 3.6% and 7.7% in the pathological cases) and the distinction between phases III and IV became less evident. The results obtained indicate that the slope of phase III depends primarily on nitrogen-concentration differences between lung zones, as determined by different mechanical properties of the respiratory airways. In spite of the simplified representation of the lungs, the similarity of the simulation results to actual data suggests that the proposed model describes important physiological mechanisms underlying changes observed during SBNW in normal and pathological patients.

Paradoxical and bidirectional drug effects

A paradoxical drug reaction constitutes an outcome that is opposite from the outcome that would be expected from the drug's known actions. There are three types: 1. A paradoxical response in a condition for which the drug is being explicitly prescribed. 2. Paradoxical precipitation of a condition for which the drug is indicated, when the drug is being used for an alternative indication. 3. Effects that are paradoxical in relation to an aspect of the pharmacology of the drug but unrelated to the usual indication. In bidirectional drug reactions, a drug may produce opposite effects, either in the same or different individuals, the effects usually being different from the expected beneficial effect. Paradoxical and bidirectional drug effects can sometimes be harnessed for benefit; some may be adverse. Such reactions arise in a wide variety of drug classes. Some are common; others are reported in single case reports. Paradoxical effects are often adverse, since they are opposite the direction of the expected effect. They may complicate the assessment of adverse drug reactions, pharmacovigilance, and clinical management. Bidirectional effects may be clinically useful or adverse. From a clinical toxicological perspective, altered pharmacokinetics or pharmacodynamics in overdose may exacerbate paradoxical and bidirectional effects. Certain antidotes have paradoxical attributes, complicating management. Apparent clinical paradoxical or bidirectional effects and reactions ensue when conflicts arise at different levels in self-regulating biological systems, as complexity increases from subcellular components, such as receptors, to cells, tissues, organs, and the whole individual. These may be incompletely understood. Mechanisms of such effects include different actions at the same receptor, owing to changes with time and downstream effects; stereochemical effects; multiple receptor targets with or without associated temporal effects; antibody-mediated reactions; three-dimensional architectural constraints; pharmacokinetic competing compartment effects; disruption and non-linear effects in oscillating systems, systemic overcompensation, and other higher-level feedback mechanisms and feedback response loops at multiple levels. Here we review and provide a compendium of multiple class effects and individual reactions, relevant mechanisms, and specific clinical toxicological considerations of antibiotics, immune modulators, antineoplastic drugs, and cardiovascular, CNS, dermal, endocrine, musculoskeletal, gastrointestinal, haematological, respiratory, and psychotropic agents.

A model of perfusion of the healthy human lung

This study presents a model that simulates the pulmonary capillary perfusion. The model describes the lungs as divided into horizontal layers and includes: capillary geometry; capillary wall elasticity; pressure at the pulmonary artery; blood viscosity; the effect of the chest wall; the change in lung height and hydrostatic effects of the lung tissue and of the blood during breathing. The model simulates pulsatile blood perfusion with an increasing blood distribution down the lungs, in agreement with previous experimental studies. Moreover the model is in agreement with experimentally measured total capillary perfusion, total capillary volume, total capillary surface area and transition time of red blood cells passing through the pulmonary capillary network. The presented model is the first to be validated against the mentioned experimental data and to model the link between airway pressure, lung volume and perfusion.

The effect of tissue elastic properties and surfactant on alveolar stability

This paper presents a novel mathematical model of alveoli, which simulates the effects of tissue elasticity and surfactant on the stability of human alveoli. The model incorporates a spherical approximation to the alveolar geometry, the hysteretic behavior of pulmonary surfactant and tissue elasticity. The model shows that the alveolus without surfactant and the elastic properties of the lung tissue are always at an unstable equilibrium, with the capability both to collapse irreversibly and to open with infinite volume when the alveolus has small opening radii. During normal tidal breathing, the alveolus can becomes stable, if surfactant is added. Including the passive effect of tissue elasticity stabilizes the alveolus, further allowing the alveoli to be stable, even for lung volumes below residual volume. The model is the first to describe the combined effects of tissue elasticity and surfactant on alveolar stability. The model may be used as an integrated part of a more comprehensive model of the respiratory system, since it can predict opening pressures of alveoli.