A poroelastic model coupled to a fluid network with applications in lung modelling

Machine learning modeling of lung mechanics: Assessing the variability and propagation of uncertainty in respiratory-system compliance and airway resistance

BACKGROUND AND OBJECTIVE

Traditional assessment of patient response in mechanical ventilation relies on respiratory-system compliance and airway resistance. Clinical evidence has shown high variability in these parameters, highlighting the difficulty of predicting them before the start of ventilation therapy. This motivates the creation of computational models that can connect structural and tissue features with lung mechanics. In this work, we leverage machine learning (ML) techniques to construct predictive lung function models informed by non-linear finite element simulations, and use them to investigate the propagation of uncertainty in the lung mechanical response.

METHODS

We revisit a continuum poromechanical formulation of the lungs suitable for determining patient response. Based on this framework, we create high-fidelity finite element models of human lungs from medical images. We also develop a low-fidelity model based on an idealized sphere geometry. We then use these models to train and validate three ML architectures: single-fidelity and multi-fidelity Gaussian process regression, and artificial neural networks. We use the best predictive ML model to further study the sensitivity of lung response to variations in tissue structural parameters and boundary conditions via sensitivity analysis and forward uncertainty quantification. Codes are available for download at https://github.com/comp-medicine-uc/ML-lung-mechanics-UQ RESULTS: The low-fidelity model delivers a lung response very close to that predicted by high-fidelity simulations and at a fraction of the computational time. Regarding the trained ML models, the multi-fidelity GP model consistently delivers better accuracy than the single-fidelity GP and neural network models in estimating respiratory-system compliance and resistance (R2∼0.99). In terms of computational efficiency, our ML model delivers a massive speed-up of ∼970,000× with respect to high-fidelity simulations. Regarding lung function, we observed an almost matched and non-linear behavior between specific structural parameters and chest wall stiffness with compliance. Also, we observed a strong modulation of airways resistance with tissue permeability.

CONCLUSIONS

Our findings unveil the relevance of specific lung tissue parameters and boundary conditions in the respiratory-system response. Furthermore, we highlight the advantages of adopting a multi-fidelity ML approach that combines data from different levels to yield accurate and efficient estimates of clinical mechanical markers. We envision that the methods presented here can open the way to the development of predictive ML models of the lung response that can inform clinical decisions.

A novel computer modeling and simulation technique for bronchi motion tracking in human lungs under respiration

In this work, we proposed a novel computer modeling and simulation technique for motion tracking of lung bronchi (or tumors) under respiration using 9 cases of computed tomography (CT)-based patient-specific finite element (FE) models and Ogden's hyperelastic model. In the fabrication of patient-specific FE models for the respiratory system, various organs such as the mediastinum, diaphragm, and thorax that could affect the lung motions during breathing were considered. To describe the nonlinear material behavior of lung parenchyma, the comparative simulation for biaxial tension-compression of lung parenchyma was carried out using several hyperelastic models in ABAQUS, and then, Ogden's model was adopted as an optimal model. Based on the aforementioned FE models and Ogden's material model, the 9 cases of respiration simulation were carried out from exhalation to inhalation, and the motion of lung bronchi (or tumors) was tracked. In addition, the changes in lung volume, lung cross-sectional area on the axial plane during breathing were calculated. Finally, the simulation results were quantitatively compared to the inhalation/exhalation CT images of 9 subjects to validate the proposed technique. Through the simulation, it was confirmed that the average relative errors of simulation to clinical data regarding to the displacement of 258 landmarks in the lung bronchi branches of total subjects were 1.10%~2.67%. In addition, the average relative errors of those with respect to the lung cross-sectional area changes and the volume changes in the superior-inferior direction were 0.20%~5.00% and 1.29 ~ 9.23%, respectively. Hence, it was considered that the simulation results were coincided well with the clinical data. The novelty of the present study is as follows: (1) The framework from fabrication of the human respiratory system to validation of the bronchi motion tracking is provided step by step. (2) The comparative simulation study for nonlinear material behavior of lung parenchyma was carried out to describe the realistic lung motion. (3) Various organs surrounding the lung parenchyma and restricting its motion were considered in respiration simulation. (4) The simulation results such as landmark displacement, lung cross-sectional area/volume changes were quantitatively compared to the clinical data of 9 subjects.

Comparison of optimization parametrizations for regional lung compliance estimation using personalized pulmonary poromechanical modeling

Interstitial lung diseases, such as idiopathic pulmonary fibrosis (IPF) or post-COVID-19 pulmonary fibrosis, are progressive and severe diseases characterized by an irreversible scarring of interstitial tissues that affects lung function. Despite many efforts, these diseases remain poorly understood and poorly treated. In this paper, we propose an automated method for the estimation of personalized regional lung compliances based on a poromechanical model of the lung. The model is personalized by integrating routine clinical imaging data - namely computed tomography images taken at two breathing levels in order to reproduce the breathing kinematic-notably through an inverse problem with fully personalized boundary conditions that is solved to estimate patient-specific regional lung compliances. A new parametrization of the inverse problem is introduced in this paper, based on the combined estimation of a personalized breathing pressure in addition to material parameters, improving the robustness and consistency of estimation results. The method is applied to three IPF patients and one post-COVID-19 patient. This personalized model could help better understand the role of mechanics in pulmonary remodeling due to fibrosis; moreover, patient-specific regional lung compliances could be used as an objective and quantitative biomarker for improved diagnosis and treatment follow up for various interstitial lung diseases.

A coupled model for the dynamics of gas exchanges in the human lung with Haldane and Bohr's effects

We propose an integrated dynamical model for oxygen and carbon dioxide transfer from the lung into the blood, coupled with a lumped mechanical model for the ventilation process, for healthy patients as well as in pathological cases. In particular, we take into account the nonlinear interaction between oxygen and carbon dioxide in the blood volume, referred to as the Bohr and Haldane effects. We also propose a definition of the physiological dead space volume (the lung volume that does not contribute to gas exchange) which depends on the pathological state and the breathing scenario. This coupled ventilation-gas diffusion model is driven by the sole action of the respiratory muscles. We analyse its sensitivity with respect to characteristic parameters: the resistance of the bronchial tree, the elastance of the lung tissue and the oxygen and carbon dioxide diffusion coefficients of the alveolo-capillary membrane. Idealized pathological situations are also numerically investigated. We obtain realistic qualitative tendencies, which represent a first step towards classification of the pathological behaviours with respect to the considered input parameters.

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.

Mechanical properties of the premature lung: From tissue deformation under load to mechanosensitivity of alveolar cells

Many preterm infants require mechanical ventilation as life-saving therapy. However, ventilation-induced overpressure can result in lung diseases. Considering the lung as a viscoelastic material, positive pressure inside the lung results in increased hydrostatic pressure and tissue compression. To elucidate the effect of positive pressure on lung tissue mechanics and cell behavior, we mimic the effect of overpressure by employing an uniaxial load onto fetal and adult rat lungs with different deformation rates. Additionally, tissue expansion during tidal breathing due to a negative intrathoracic pressure was addressed by uniaxial tension. We found a hyperelastic deformation behavior of fetal tissues under compression and tension with a remarkable strain stiffening. In contrast, adult lungs exhibited a similar response only during compression. Young’s moduli were always larger during tension compared to compression, while only during compression a strong deformation-rate dependency was found. In fact, fetal lung tissue under compression showed clear viscoelastic features even for small strains. Thus, we propose that the fetal lung is much more vulnerable during inflation by mechanical ventilation compared to normal inspiration. Electrophysiological experiments with different hydrostatic pressure gradients acting on primary fetal distal lung epithelial cells revealed that the activity of the epithelial sodium channel (ENaC) and the sodium-potassium pump (Na,K-ATPase) dropped during pressures of 30 cmH₂O. Thus, pressures used during mechanical ventilation might impair alveolar fluid clearance important for normal lung function.

A Poroelastic Approach for Modelling Myocardial Oedema in Acute Myocarditis

Myocarditis is a general set of mechanisms that manifest themselves into the inflammation of the heart muscle. In 2017, more than 3 million people were affected by this disease worldwide, causing about 47,000 deaths. Many aspects of the origin of this disease are well known, but several important questions regarding the disease remain open. One of them is why some patients develop a significantly localised inflammation while others develop a much more diffuse inflammation, reaching across large portions of the heart. Furthermore, the specific role of the pathogenic agent that causes inflammation as well as the interaction with the immune system in the progression of the disease are still under discussion. Providing answers to these crucial questions can have an important impact on patient treatment. In this scenario, computational methods can aid specialists to understand better the relationships between pathogens and the immune system and elucidate why some patients develop diffuse myocarditis. This paper alters a recently developed model to study the myocardial oedema formation in acute infectious myocarditis. The model describes the finite deformation regime using partial differential equations to represent tissue displacement, fluid pressure, fluid phase, and the concentrations of pathogens and leukocytes. A sensitivity analysis was performed to understand better the influence of the most relevant model parameters on the disease dynamics. The results showed that the poroelastic model could reproduce local and diffuse myocarditis dynamics in simplified and complex geometrical domains.

Computational lung modelling in respiratory medicine

Computational modelling of the lungs is an active field of study that integrates computational advances with lung biophysics, biomechanics, physiology and medical imaging to promote individualized diagnosis, prognosis and therapy evaluation in lung diseases. The complex and hierarchical architecture of the lung offers a rich, but also challenging, research area demanding a cross-scale understanding of lung mechanics and advanced computational tools to effectively model lung biomechanics in both health and disease. Various approaches have been proposed to study different aspects of respiration, ranging from compartmental to discrete micromechanical and continuum representations of the lungs. This article reviews several developments in computational lung modelling and how they are integrated with preclinical and clinical data. We begin with a description of lung anatomy and how different tissue components across multiple length scales affect lung mechanics at the organ level. We then review common physiological and imaging data acquisition methods used to inform modelling efforts. Building on these reviews, we next present a selection of model-based paradigms that integrate data acquisitions with modelling to understand, simulate and predict lung dynamics in health and disease. Finally, we highlight possible future directions where computational modelling can improve our understanding of the structure–function relationship in the lung.

Towards a multi-scale computer modeling workflow for simulation of pulmonary ventilation in advanced COVID-19

Physics-based multi-scale in silico models offer an excellent opportunity to study the effects of heterogeneous tissue damage on airflow and pressure distributions in COVID-19-afflicted lungs. The main objective of this study is to develop a computational modeling workflow, coupling airflow and tissue mechanics as the first step towards a virtual hypothesis-testing platform for studying injury mechanics of COVID-19-afflicted lungs. We developed a CT-based modeling approach to simulate the regional changes in lung dynamics associated with heterogeneous subject-specific COVID-19-induced damage patterns in the parenchyma. Furthermore, we investigated the effect of various levels of inflammation in a meso-scale acinar mechanics model on global lung dynamics. Our simulation results showed that as the severity of damage in the patient's right lower, left lower, and to some extent in the right upper lobe increased, ventilation was redistributed to the least injured right middle and left upper lobes. Furthermore, our multi-scale model reasonably simulated a decrease in overall tidal volume as the level of tissue injury and surfactant loss in the meso-scale acinar mechanics model was increased. This study presents a major step towards multi-scale computational modeling workflows capable of simulating the effect of subject-specific heterogenous COVID-19-induced lung damage on ventilation dynamics.

A Hybrid Biphasic Mixture Formulation for Modeling Dynamics in Porous Deformable Biological Tissues

The primary aim of this study is to establish the theoretical foundations for a solid-fluid biphasic mixture domain that can accommodate inertial effects and a viscous interstitial fluid, which can interface with a dynamic viscous fluid domain. Most mixture formulations consist of constituents that are either all intrinsically incompressible or compressible, thereby introducing inherent limitations. In particular, mixtures with intrinsically incompressible constituents can only model wave propagation in the porous solid matrix, whereas those with compressible constituents require internal variables, and related evolution equations, to distinguish the compressibility of the solid and fluid under hydrostatic pressure. In this study, we propose a hybrid framework for a biphasic mixture where the skeleton of the porous solid is intrinsically incompressible but the interstitial fluid is compressible. We define a state variable as a measure of the fluid volumetric strain. Within an isothermal framework, the Clausius-Duhem inequality shows that a function of state arises for the fluid pressure as a function of this strain measure. We derive jump conditions across hybrid biphasic interfaces, which are suitable for modeling hydrated biological tissues. We then illustrate this framework using confined compression and dilatational wave propagation analyses. The governing equations for this hybrid biphasic framework reduce to those of the classical biphasic theory whenever the bulk modulus of the fluid is set to infinity and inertia terms and viscous fluid effects are neglected. The availability of this novel framework facilitates the implementation of finite element solvers for fluid-structure interactions at interfaces between viscous fluids and porous-deformable biphasic domains, which can include fluid exchanges across those interfaces.

Finite Element Implementation of Biphasic-Fluid Structure Interactions in febio

In biomechanics, solid-fluid mixtures have commonly been used to model the response of hydrated biological tissues. In cartilage mechanics, this type of mixture, where the fluid and solid constituents are both assumed to be intrinsically incompressible, is often called a biphasic material. Various physiological processes involve the interaction of a viscous fluid with a porous-hydrated tissue, as encountered in synovial joint lubrication, cardiovascular mechanics, and respiratory mechanics. The objective of this study was to implement a finite element solver in the open-source software febio that models dynamic interactions between a viscous fluid and a biphasic domain, accommodating finite deformations of both domains as well as fluid exchanges between them. For compatibility with our recent implementation of solvers for computational fluid dynamics (CFD) and fluid-structure interactions (FSI), where the fluid is slightly compressible, this study employs a novel hybrid biphasic formulation where the porous skeleton is intrinsically incompressible but the fluid is also slightly compressible. The resulting biphasic-FSI (BFSI) implementation is verified against published analytical and numerical benchmark problems, as well as novel analytical solutions derived for the purposes of this study. An illustration of this BFSI solver is presented for two-dimensional (2D) airflow through a simulated face mask under five cycles of breathing, showing that masks significantly reduce air dispersion compared to the no-mask control analysis. In addition, we model three-dimensional (3D) blood flow in a bifurcated carotid artery assuming porous arterial walls and verify that mass is conserved across all fluid-permeable boundaries. The successful formulation and implementation of this BFSI solver offers enhanced multiphysics modeling capabilities that are accessible via an open-source software platform.

Integrative Computational Models of Lung Structure-Function Interactions

Anatomically based integrative models of the lung and their interaction with other key components of the respiratory system provide unique capabilities for investigating both normal and abnormal lung function. There is substantial regional variability in both structure and function within the normal lung, yet it remains capable of relatively efficient gas exchange by providing close matching of air delivery (ventilation) and blood delivery (perfusion) to regions of gas exchange tissue from the scale of the whole organ to the smallest continuous gas exchange units. This is despite remarkably different mechanisms of air and blood delivery, different fluid properties, and unique scale-dependent anatomical structures through which the blood and air are transported. This inherent heterogeneity can be exacerbated in the presence of disease or when the body is under stress. Current computational power and data availability allow for the construction of sophisticated data-driven integrative models that can mimic respiratory system structure, function, and response to intervention. Computational models do not have the same technical and ethical issues that can limit experimental studies and biomedical imaging, and if they are solidly grounded in physiology and physics they facilitate investigation of the underlying interaction between mechanisms that determine respiratory function and dysfunction, and to estimate otherwise difficult-to-access measures. © 2021 American Physiological Society. Compr Physiol 11:1501-1530, 2021.

A hybrid, image-based and biomechanics-based registration approach to markerless intraoperative nodule localization during video-assisted thoracoscopic surgery

The resection of small, low-dense or deep lung nodules during video-assisted thoracoscopic surgery (VATS) is surgically challenging. Nodule localization methods in clinical practice typically rely on the preoperative placement of markers, which may lead to clinical complications. We propose a markerless lung nodule localization framework for VATS based on a hybrid method combining intraoperative cone-beam CT (CBCT) imaging, free-form deformation image registration, and a poroelastic lung model with allowance for air evacuation. The difficult problem of estimating intraoperative lung deformations is decomposed into two more tractable sub-problems: (i) estimating the deformation due the change of patient pose from preoperative CT (supine) to intraoperative CBCT (lateral decubitus); and (ii) estimating the pneumothorax deformation, i.e. a collapse of the lung within the thoracic cage. We were able to demonstrate the feasibility of our localization framework with a retrospective validation study on 5 VATS clinical cases. Average initial errors in the range of 22 to 38 mm were reduced to the range of 4 to 14 mm, corresponding to an error correction in the range of 63 to 85%. To our knowledge, this is the first markerless lung deformation compensation method dedicated to VATS and validated on actual clinical data.

A personalized computational model of edema formation in myocarditis based on long-axis biventricular MRI images

Background

Myocarditis is defined as the inflammation of the myocardium, i.e. the cardiac muscle. Among the reasons that lead to this disease, we may include infections caused by a virus, bacteria, protozoa, fungus, and others. One of the signs of the inflammation is the formation of edema, which may be a consequence of the interaction between interstitial fluid dynamics and immune response. This complex physiological process was mathematically modeled using a nonlinear system of partial differential equations (PDE) based on porous media approach. By combing a model based on Biot’s poroelasticity theory with a model for the immune response we developed a new hydro-mechanical model for inflammatory edema. To verify this new computational model, T2 parametric mapping obtained by Magnetic Resonance (MR) imaging was used to identify the region of edema in a patient diagnosed with unspecific myocarditis.

Results

A patient-specific geometrical model was created using MRI images from the patient with myocarditis. With this model, edema formation was simulated using the proposed hydro-mechanical mathematical model in a two-dimensional domain. The computer simulations allowed us to correlate spatiotemporal dynamics of representative cells of the immune systems, such as leucocytes and the pathogen, with fluid accumulation and cardiac tissue deformation.

Conclusions

This study demonstrates that the proposed mathematical model is a very promising tool to better understand edema formation in myocarditis. Simulations obtained from a patient-specific model reproduced important aspects related to the formation of cardiac edema, its area, position, and shape, and how these features are related to immune response.

CT-based Airway Flow Model to Assess Ventilation in Chronic Obstructive Pulmonary Disease: A Pilot Study

Background The lack of functional information in thoracic CT remains a limitation of its use in the clinical management of chronic obstructive pulmonary disease (COPD). Purpose To compare the distribution of pulmonary ventilation assessed by a CT-based full-scale airway network (FAN) flow model with hyperpolarized xenon 129 (¹²⁹Xe) MRI (hereafter, ¹²⁹Xe MRI) and technetium 99m-diethylenetriaminepentaacetic acid aerosol SPECT ventilation imaging (hereafter, V-SPECT) in participants with COPD. Materials and Methods In this prospective study performed between May and August 2017, pulmonary ventilation in participants with COPD was computed by using the FAN flow model. The modeled pulmonary ventilation was compared with functional imaging data from breath-hold time-series ¹²⁹Xe MRI and V-SPECT. FAN-derived ventilation images on the coronal plane and volumes of interest were compared with functional lung images. Percentage lobar ventilation estimated by the FAN model was compared with that measured at ¹²⁹Xe MRI and V-SPECT. The statistical significance of ventilation distribution between FAN and functional images was demonstrated with the Spearman correlation coefficient and χ² distance. Results For this study, nine participants (seven men [mean age, 65 years ± 5 {standard deviation}] and two women [mean age, 63 years ± 7]) with COPD that was Global Initiative for Chronic Obstructive Lung Disease stage II-IV were enrolled. FAN-modeled ventilation profile showed strong positive correlation with images from ¹²⁹Xe MRI (ρ = 0.67; P < .001) and V-SPECT (ρ = 0.65; P < .001). The χ² distances of the ventilation histograms in the volumes of interest between the FAN and ¹²⁹Xe MRI and FAN and V-SPECT were 0.16 ± 0.08 and 0.28 ± 0.14, respectively. The ratios of lobar ventilations in the models were linearly correlated to images from ¹²⁹Xe MRI (ρ = 0.67; P < .001) and V-SPECT (ρ = 0.59; P < .001). Conclusion A CT-based full-scale airway network flow model provided regional pulmonary ventilation information for chronic obstructive pulmonary disease and correlates with hyperpolarized xenon 129 MRI and technetium 99m-diethylenetriaminepentaacetic acid aerosol SPECT ventilation imaging. © RSNA, 2019 Online supplemental material is available for this article. See also the editorial by Schiebler and Parraga in this issue.

Integrated lung tissue mechanics one piece at a time: Computational modeling across the scales of biology

The lung is a delicately balanced and highly integrated mechanical system. Lung tissue is continuously exposed to the environment via the air we breathe, making it susceptible to damage. As a consequence, respiratory diseases present a huge burden on society and their prevalence continues to rise. Emergent function is produced not only by the sum of the function of its individual components but also by the complex feedback and interactions occurring across the biological scales - from genes to proteins, cells, tissue and whole organ - and back again. Computational modeling provides the necessary framework for pulling apart and putting back together the pieces of the body and organ systems so that we can fully understand how they function in both health and disease. In this review, we discuss models of lung tissue mechanics spanning from the protein level (the extracellular matrix) through to the level of cells, tissue and whole organ, many of which have been developed in isolation. This is a vital step in the process but to understand the emergent behavior of the lung, we must work towards integrating these component parts and accounting for feedback across the scales, such as mechanotransduction. These interactions will be key to unlocking the mechanisms occurring in disease and in seeking new pharmacological targets and improving personalized healthcare.

Constituent-specific material behavior of soft biological tissue: experimental quantification and numerical identification for lung parenchyma

In this study, we present a method to experimentally quantify and numerically identify the constituent-specific material behavior of soft biological tissues. This allows the clear identification of the individual contributions of major load-bearing constituents and their interactions in the constitutive law. While the overall approach is applicable for many tissues, here it will be presented for the identification of a sophisticated constituent-specific material model of viable lung parenchyma. This material model will help to better model the effects of various lung diseases that feature altered fiber content in the lungs, such as emphysema or fibrosis. To experimentally quantify the mechanical properties of collagen, elastin, collagen-elastin-fiber interactions, and ground substance, we examined 18 collagenase and elastase treated rat lung parenchymal slices. The mechanical contributions of the collagen and elastin fibers in the living tissue were inferred from uniaxial tension tests comparing the behavior before and after the selective digestion of the respective fibers. In order to also obtain the mechanical influence of the ground substance, we consecutively treated the samples with both proteases. Collagen and elastin fibers are morphologically interconnected. Thus, a mechanical interaction between these fibers appears likely, but has not yet been experimentally verified. In this paper, we propose an experimental method to quantitatively assess the mechanical behavior of these collagen-elastin-fiber interactions. Based on our experiments, we have identified individual material models within a nonlinear continuum mechanics framework for each load-bearing component via an inverse analysis. The proposed constituent-specific material law can be incorporated into computational models of the respiratory system to simulate and even predict the behavior and alteration of the individual constituents and their effect on the whole respiratory system during normal and artificial breathing, in particular in the case of diseases that alter the fibers in the tissue.

Interplay Between Optimal Ventilation and Gas Transport in a Model of the Human Lung

Ventilation is at the origin of a spending of energy coming from air circulation in the bronchial tree and from the mechanical resistance of the tissue to motion. Both amplitude and frequency of ventilation are submitted to a trade-off related to this energy, but they are also submitted to a constraint linked to the function of the lung: to transport enough oxygen and carbon dioxide in order to respect metabolism needs. We propose a model for oxygen and carbon dioxide transport in the lung that accounts for the core physical phenomena: lung's tree-like geometry, transport of gas by convection and diffusion, exchanges with blood and a sinusoidal ventilation. Then we optimize the power dissipated by the ventilation of our model relatively to ventilation amplitude and period under gas flow constraints. Our model is able to predict physiological ventilation properties and brings interesting insights on the robustness of different regimes. Hence, at rest, the power dissipated depends very little on the period near the optimal value. Whereas, at strong exercise any shift from the optimal has dramatic effect on the power. These results are fully coherent with the physiological observation and raises the question: how the control of ventilation could select for the optimal configuration? Also, interesting insights about pathologies affecting ventilation could be derived, and our model might give insights on therapeutical responses, with specific breathing strategies or for better driving mechanical ventilation.

A review of inflammatory mechanism in airway diseases

BACKGROUND

Inflammation in the lung is the body's natural response to injury. It acts to remove harmful stimuli such as pathogens, irritants, and damaged cells and initiate the healing process. Acute and chronic pulmonary inflammation are seen in different respiratory diseases such as; acute respiratory distress syndrome, chronic obstructive pulmonary disease (COPD), asthma, and cystic fibrosis (CF).

FINDINGS

In this review, we found that inflammatory response in COPD is determined by the activation of epithelial cells and macrophages in the respiratory tract. Epithelial cells and macrophages discharge transforming growth factor-β (TGF-β), which trigger fibroblast proliferation and tissue remodeling. Asthma leads to airway hyper-responsiveness, obstruction, mucus hyper-production, and airway-wall remodeling. Cytokines, allergens, chemokines, and infectious agents are the main stimuli that activate signaling pathways in epithelial cells in asthma. Mutation of the CF transmembrane conductance regulator (CFTR) gene results in CF. Mutations in CFTR influence the lung epithelial innate immune function that leads to exaggerated and ineffective airway inflammation that fails to abolish pulmonary pathogens. We present mechanistic computational models (based on ordinary differential equations, partial differential equations and agent-based models) that have been applied in studying the complex physiological and pathological mechanisms of chronic inflammation in different airway diseases.

CONCLUSION

The scope of the present review is to explore the inflammatory mechanism in airway diseases and highlight the influence of aging on airways' inflammation mechanism. The main goal of this review is to encourage research collaborations between experimentalist and modelers to promote our understanding of the physiological and pathological mechanisms that control inflammation in different airway diseases.

Coupled Immunological and Biomechanical Model of Emphysema Progression

Chronic Obstructive Pulmonary Disease (COPD) is a disabling respiratory pathology, with a high prevalence and a significant economic and social cost. It is characterized by different clinical phenotypes with different risk profiles. Detecting the correct phenotype, especially for the emphysema subtype, and predicting the risk of major exacerbations are key elements in order to deliver more effective treatments. However, emphysema onset and progression are influenced by a complex interaction between the immune system and the mechanical properties of biological tissue. The former causes chronic inflammation and tissue remodeling. The latter influences the effective resistance or appropriate mechanical response of the lung tissue to repeated breathing cycles. In this work we present a multi-scale model of both aspects, coupling Finite Element (FE) and Agent Based (AB) techniques that we would like to use to predict the onset and progression of emphysema in patients. The AB part is based on existing biological models of inflammation and immunological response as a set of coupled non-linear differential equations. The FE part simulates the biomechanical effects of repeated strain on the biological tissue. We devise a strategy to couple the discrete biological model at the molecular /cellular level and the biomechanical finite element simulations at the tissue level. We tested our implementation on a public emphysema image database and found that it can indeed simulate the evolution of clinical image biomarkers during disease progression.

A stabilized finite element method for finite-strain three-field poroelasticity

We construct a stabilized finite-element method to compute flow and finite-strain deformations in an incompressible poroelastic medium. We employ a three-field mixed formulation to calculate displacement, fluid flux and pressure directly and introduce a Lagrange multiplier to enforce flux boundary conditions. We use a low order approximation, namely, continuous piecewise-linear approximation for the displacements and fluid flux, and piecewise-constant approximation for the pressure. This results in a simple matrix structure with low bandwidth. The method is stable in both the limiting cases of small and large permeability. Moreover, the discontinuous pressure space enables efficient approximation of steep gradients such as those occurring due to rapidly changing material coefficients or boundary conditions, both of which are commonly seen in physical and biological applications.

Systems-level airway models of bronchoconstriction

Understanding lung and airway behavior presents a number of challenges, both experimental and theoretical, but the potential rewards are great in terms of both potential treatments for disease and interesting biophysical phenomena. This presents an opportunity for modeling to contribute to greater understanding, and here, we focus on modeling efforts that work toward understanding the behavior of airways in vivo, with an emphasis on asthma. We look particularly at those models that address not just isolated airways but many of the important ways in which airways are coupled both with each other and with other structures. This includes both interesting phenomena involving the airways and the layer of airway smooth muscle that surrounds them, and also the emergence of spatial ventilation patterns via dynamic airway interaction. WIREs Syst Biol Med 2016, 8:459-467. doi: 10.1002/wsbm.1349 For further resources related to this article, please visit the WIREs website.