A viscoelastic nonlinear compressible material model of lung parenchyma - Experiments and numerical identification

Biomechanical Properties and Cellular Responses in Pulmonary Fibrosis

Pulmonary fibrosis is a fatal lung disease affecting approximately 5 million people worldwide, with a 5-year survival rate of less than 50%. Currently, the only available treatments are palliative care and lung transplantation, as there is no curative drug for this condition. The disease involves the excessive synthesis of the extracellular matrix (ECM) due to alveolar epithelial cell damage, leading to scarring and stiffening of the lung tissue and ultimately causing respiratory failure. Although multiple factors contribute to the disease, the exact causes remain unclear. The mechanical properties of lung tissue, including elasticity, viscoelasticity, and surface tension, are not only affected by fibrosis but also contribute to its progression. This paper reviews the alteration in these mechanical properties as pulmonary fibrosis progresses and how cells in the lung, including alveolar epithelial cells, fibroblasts, and macrophages, respond to these changes, contributing to disease exacerbation. Furthermore, it highlights the importance of developing advanced in vitro models, based on hydrogels and 3D bioprinting, which can accurately replicate the mechanical and structural properties of fibrotic lungs and are conducive to studying the effects of mechanical stimuli on cellular responses. This review aims to summarize the current understanding of the interaction between the progression of pulmonary fibrosis and the alterations in mechanical properties, which could aid in the development of novel therapeutic strategies for the disease.

Stress-strain curve and elastic behavior of the fibrotic lung with usual interstitial pneumonia pattern during protective mechanical ventilation

Patients with acute exacerbation of lung fibrosis with usual interstitial pneumonia (EUIP) pattern are at increased risk for ventilator-induced lung injury (VILI) and mortality when exposed to mechanical ventilation (MV). Yet, lack of a mechanical model describing UIP-lung deformation during MV represents a research gap. Aim of this study was to develop a constitutive mathematical model for UIP-lung deformation during lung protective MV based on the stress-strain behavior and the specific elastance of patients with EUIP as compared to that of acute respiratory distress syndrome (ARDS) and healthy lung. Partitioned lung and chest wall mechanics were assessed for patients with EUIP and primary ARDS (1:1 matched based on body mass index and PaO2/FiO2 ratio) during a PEEP trial performed within 24 h from intubation. Patient's stress-strain curve and the lung specific elastance were computed and compared with those of healthy lungs, derived from literature. Respiratory mechanics were used to fit a novel mathematical model of the lung describing mechanical-inflation-induced lung parenchyma deformation, differentiating the contributions of elastin and collagen, the main components of lung extracellular matrix. Five patients with EUIP and 5 matched with primary ARDS were included and analyzed. Global strain was not different at low PEEP between the groups. Overall specific elastance was significantly higher in EUIP as compared to ARDS (28.9 [22.8-33.2] cmH2O versus 11.4 [10.3-14.6] cmH2O, respectively). Compared to ARDS and healthy lung, the stress/strain curve of EUIP showed a steeper increase, crossing the VILI threshold stress risk for strain values greater than 0.55. The contribution of elastin was prevalent at lower strains, while the contribution of collagen was prevalent at large strains. The stress/strain curve for collagen showed an upward shift passing from ARDS and healthy lungs to EUIP lungs. During MV, patients with EUIP showed different respiratory mechanics, stress-strain curve and specific elastance as compared to ARDS patients and healthy subjects and may experience VILI even when protective MV is applied. According to our mathematical model of lung deformation during mechanical inflation, the elastic response of UIP-lung is peculiar and different from ARDS. Our data suggest that patients with EUIP experience VILI with ventilatory setting that are lung-protective for patients with ARDS.

Mechanical and morphological characterization of the emphysematous lung tissue

Irreversible alveolar airspace enlargement is the main characteristic of pulmonary emphysema, which has been extensively studied using animal models. While the alterations in lung mechanics associated with these morphological changes have been documented in the literature, the study of the mechanical behavior of parenchymal tissue from emphysematous lungs has been poorly investigated. In this work, we characterize the mechanical and morphological properties of lung tissue in elastase-induced emphysema rat models under varying severity conditions. We analyze the non-linear tissue behavior using suitable hyperelastic constitutive models that enable to compare different non-linear responses in terms of hyperelastic material parameters. We further analyze the effect of the elastase dose on alveolar morphology and tissue material parameters and study their connection with respiratory-system mechanical parameters. Our results show that while the lung mechanical function is not significantly influenced by the elastase treatment, the tissue mechanical behavior and alveolar morphology are markedly affected by it. We further show a strong association between alveolar enlargement and tissue softening, not evidenced by respiratory-system compliance. Our findings highlight the importance of understanding tissue mechanics in emphysematous lungs, as changes in tissue properties could detect the early stages of emphysema remodeling. STATEMENT OF SIGNIFICANCE: Gas exchange is vital for life and strongly relies on the mechanical function of the lungs. Pulmonary emphysema is a prevalent respiratory disease where alveolar walls are damaged, causing alveolar enlargement that induces harmful changes in the mechanical response of the lungs. In this work, we study how the mechanical properties of lung tissue change during emphysema. Our results from animal models show that tissue properties are more sensitive to alveolar enlargement due to emphysema than other mechanical properties that describe the function of the whole respiratory system.

The dynamic response of human lungs due to underwater shock wave exposure

Since the 19th century, underwater explosions have posed a significant threat to service members. While there have been attempts to establish injury criteria for the most vulnerable organs, namely the lungs, existing criteria are highly variable due to insufficient human data and the corresponding inability to understand the underlying injury mechanisms. This study presents an experimental characterization of isolated human lung dynamics during simulated exposure to underwater shock waves. We found that the large acoustic impedance at the surface of the lung severely attenuated transmission of the shock wave into the lungs. However, the shock wave initiated large bulk pressure-volume cycles that are distinct from the response of the solid organs under similar loading. These pressure-volume cycles are due to compression of the contained gas, which we modeled with the Rayleigh-Plesset equation. The extent of these lung dynamics was dependent on physical confinement, which in real underwater blast conditions is influenced by factors such as rib cage properties and donned equipment. Findings demonstrate a potential causal mechanism for implosion injuries, which has significant implications for the understanding of primary blast lung injury due to underwater blast exposures.

Electropneumatic system for the simulation of the pulmonary viscoelastic effect in a mechanical ventilation scenario

The viscoelastic properties of the lung have important implications during respiratory mechanics in terms of lung movement or work of breathing, for example. However, this property has not been well characterized due to several reasons, such as the complex nature of the lung, difficulty accessing its tissues, and the lack of physical simulators that represent viscoelastic effects. This research proposes an electropneumatic system and a method to simulate the viscoelastic effect from temporary forces generated by the opposition of magnetic poles. The study was tested in a mechanical ventilation scenario with inspiratory pause, using a Hamilton-S1 mechanical ventilator (Hamilton Medical) and a simulator of the human respiratory system (SAMI-SII). The implemented system was able to simulate the stress relaxation response of a Standard Linear Solid model in the Maxwell form and showed the capacity to control elastic and viscous parameters independently. To the best of our knowledge, this is the first system incorporated into a physical lung simulator that represents the viscoelastic effect in a mechanical ventilation scenario.

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.

Role of lung lobar sliding on parenchymal distortion during breathing

Sliding between lung lobes along lobar fissures is a poorly understood aspect of lung mechanics. The objective of this study was to test the hypothesis that lobar sliding helps reduce distortion in the lung parenchyma during breathing. Finite element models of left lungs with geometries and boundary conditions derived from medical images of human subjects were developed. Effect of lobar sliding was studied by comparing nonlinear finite elastic contact mechanics simulations that allowed and disallowed lobar sliding. Lung parenchymal distortion during simulated breath-holds and tidal breathing was quantified with the model's spatial mean anisotropic deformation index (ADI), a measure of directional preference in volume change that varies spatially in the lung. Models that allowed lobar sliding had significantly lower mean ADI (i.e., lesser parenchymal distortion) than models that disallowed lobar sliding under simulations of both tidal breathing (5.3% median difference, P = 0.008, n = 8) and lung deformation between breath-holds at total lung capacity and functional residual capacity (3.2% median difference, P = 0.03, n = 6). This effect was most pronounced in the lower lobe where lobar sliding reduced parenchymal distortion with statistical significance, but not in the upper lobe. In addition, more lobar sliding was correlated with greater reduction in distortion between sliding and nonsliding models in our study cohorts (Pearson's correlation coefficient of 0.95 for tidal breathing, 0.87 for breath-holds, and 0.91 for the combined dataset). These findings are consistent with the hypothesis that lung lobar sliding reduces parenchymal distortion during breathing.NEW & NOTEWORTHY The role of lobar sliding in lung mechanics is poorly understood. Delineating this role could help explain how breathing is affected by anatomical differences between subjects such as incomplete and missing lobar fissures. We used computational contact mechanics models of lungs from human subjects to delineate the effect of lobar sliding by comparing simulations that allowed and disallowed sliding. We found evidence consistent with the hypothesis that lung lobar sliding reduces parenchymal distortion during breathing.

Pressure-volume mechanics of inflating and deflating intact whole organ porcine lungs

Pressure-volume curves of the lung are classical measurements of lung function and are impacted by changes in lung structure due to disease or shifts in air-delivery volume or cycling rate. Diseased and preterm infant lungs have been found to show heterogeneous behavior which is highly frequency dependent. This breathing rate dependency has motivated the exploration of multi-frequency oscillatory ventilators to deliver volume oscillation with optimal frequencies for various portions of the lung to provide more uniform air distribution. The design of these advanced ventilators requires the examination of lung function and mechanics, and an improved understanding of the pressure-volume response of the lung. Therefore, to comprehensively analyze whole lung organ mechanics, we investigate six combinations of varying applied volumes and frequencies using ex-vivo porcine specimens and our custom-designed electromechanical breathing apparatus. Lung responses were evaluated through measurements of inflation and deflation slopes, static compliance, peak pressure and volume, as well as hysteresis, energy loss, and pressure relaxation. Generally, we observed that the lungs were stiffer when subjected to faster breathing rates and lower inflation volumes. The lungs exhibited greater inflation volume dependencies compared to frequency dependencies. This study's reported response of the lung to variations of inflation volume and breathing rate can help the optimization of conventional mechanical ventilators and inform the design of advanced ventilators. Although frequency dependency is found to be minimal in normal porcine lungs, this preliminary study lays a foundation for comparison with pathological lungs, which are known to demonstrate marked rate dependency.

A Unified Determinant-Preserving Formulation for Compressible/Incompressible Finite Viscoelasticity

This paper presents a formulation alongside a numerical solution algorithm to describe the mechanical response of bodies made of a large class of viscoelastic materials undergoing arbitrary quasistatic finite deformations. With the objective of having a unified formulation that applies to a wide range of highly compressible, nearly incompressible, and fully incompressible soft organic materials in a numerically tractable manner, the viscoelasticity is described within a Lagrangian setting by a two-potential mixed formulation. In this formulation, the deformation field, a pressure field that ensues from a Legendre transform, and an internal variable of state F v that describes the viscous part of the deformation are the independent fields. Consistent with the experimental evidence that viscous deformation is a volume-preserving process, the internal variable F v is required to satisfy the constraint det F v = 1 . To solve the resulting initial-boundary-value problem, a numerical solution algorithm is proposed that is based on a finite-element (FE) discretization of space and a finite-difference discretization of time. Specifically, a Variational Multiscale FE method is employed that allows for an arbitrary combination of shape functions for the deformation and pressure fields. To deal with the challenging non-convex constraint det F v = 1 , a new time integration scheme is introduced that allows to convert any explicit or implicit scheme of choice into a stable scheme that preserves the constraint det F v = 1 identically. A series of test cases is presented that showcase the capabilities of the proposed formulation.

Quasi-dynamic breathing model of the lung incorporating viscoelasticity of the lung tissue

We advanced a novel model to calculate viscoelastic lung compliance and airflow resistance in presence of mucus, accounting for the quasi-linear viscoelastic stress-strain response of the parenchyma (alveoli) tissue. We adapted a continuum-based numerical modeling approach for the lung, integrating the fluid mechanics of the airflow within individual generations of the bronchi and alveoli. The model accounts for elasticity of the deformable bronchioles, resistance to airflow due to the presence of mucus within the bronchioles, and subsequent mucus flow. Simulated quasi-dynamic inhalation and expiration cycles were used to characterize the net compliance and resistance of the lung, considering the rheology of the mucus and viscoelastic properties of the parenchyma tissue. The structure and material properties of the lung were identified to have an important contribution to the lung compliance and airflow resistance. The secondary objective of this work was to assess whether a higher frequency and smaller volume of harmonic air flow rate compared to a normal ventilator breathing cycle enhanced mucus outflow. Results predict, lower mucus viscosity and higher excitation frequency of breathing are favorable for the flow of mucus up the bronchi tree, towards the trachea.

Diseased and healthy murine local lung strains evaluated using digital image correlation

Tissue remodeling in pulmonary disease irreversibly alters lung functionality and impacts quality of life. Mechanical ventilation is amongst the few pulmonary interventions to aid respiration, but can be harmful or fatal, inducing excessive regional (i.e., local) lung strains. Previous studies have advanced understanding of diseased global-level lung response under ventilation, but do not adequately capture the critical local-level response. Here, we pair a custom-designed pressure-volume ventilator with new applications of digital image correlation, to directly assess regional strains in the fibrosis-induced ex-vivo mouse lung, analyzed via regions of interest. We discuss differences between diseased and healthy lung mechanics, such as distensibility, heterogeneity, anisotropy, alveolar recruitment, and rate dependencies. Notably, we compare local and global compliance between diseased and healthy states by assessing the evolution of pressure-strain and pressure-volume curves resulting from various ventilation volumes and rates. We find fibrotic lungs are less-distensible, with altered recruitment behaviors and regional strains, and exhibit disparate behaviors between local and global compliance. Moreover, these diseased characteristics show volume-dependence and rate trends. Ultimately, we demonstrate how fibrotic lungs may be particularly susceptible to damage when contrasted to the strain patterns of healthy counterparts, helping to advance understanding of how ventilator induced lung injury develops.

Lung Mechanics: A Review of Solid Mechanical Elasticity in Lung Parenchyma

The lung is the main organ of the respiratory system. Its purpose is to facilitate gas exchange (breathing). Mechanically, breathing may be described as the cyclic application of stresses acting upon the lung surface. These forces are offset by prominent stress-bearing components of lung tissue. These components result from the mechanical elastic properties of lung parenchyma. Various studies have been dedicated to understanding the macroscopic behaviour of parenchyma. This has been achieved through pressure-volume analysis, numerical methods, the development of constitutive equations or strain-energy functions, finite element methods, image processing and elastography. Constitutive equations can describe the elastic behaviour exhibited by lung parenchyma through the relationship between the macroscopic stress and strain. The research conducted within lung mechanics around the elastic and resistive properties of the lung has allowed scientists to develop new methods and equipment for evaluating and treating pulmonary pathogens. This paper establishes a review of mathematical studies conducted within lung mechanics, centering on the development and implementation of solid mechanics to the understanding of the mechanical properties of the lung. Under the classical theory of elasticity, the lung is said to behave as an isotropic elastic continuum undergoing small deformations. However, the lung has also been known to display heterogeneous anisotropic behaviour associated with large deformations. Therefore, focus is placed on the assumptions and development of the various models, their mechanical influence on lung physiology, and the development of constitutive equations through the classical and non-classical theory of elasticity. Lastly, we also look at lung blast mechanics. No explicit emphasis is placed on lung pathology.

Biaxial mechanical properties of the bronchial tree: Characterization of elasticity, extensibility, and energetics, including the effect of strain rate and preconditioning

Distal airways commonly obstruct in lung disease and despite their importance, their mechanical properties are vastly underexplored. The lack of bronchial experiments restricts current airway models to either assume rigid structures, or extrapolate the material properties of the trachea to represent the small airways. Furthermore, past works are exclusively limited to uniaxial testing; investigating the multidirectional tensile loads of both the proximal and distal pulmonary airways is long overdue. Here we present comprehensive mechanical and viscoelastic properties of the porcine airway tree, including the trachea, trachealis muscle, large bronchi, and small bronchi, via measures of elasticity, extensibility, and energetics to explore regional and directional dependencies, cross-examining strain rate and preconditioning effects using planar equibiaxial tensile tests for the first time. We find bronchial regions are notably heterogeneous, where the trachea exhibits greater stiffness, energy loss, and preconditioning sensitivity than the smaller airways. Interestingly, the trachealis muscle is similar to the distal bronchi, despite being anatomically located adjacent to the proximal ring. Tissues are anisotropic and axially stiffer under initial loading, losing more energy with greater stress relaxation circumferentially. Strain rate dependency is also noted, where tissues are more energetically efficient at the faster strain rate, likely attributable to the microstructure. Findings highlight assumptions of homogeneity and isotropy are inadequate, and enable the improvement of aerosol flow and dynamic airway deformation computational predictive models. These results provide much needed fundamental material properties for future explorations contrasting healthy versus diseased pulmonary airway mechanics to better understand the relationship between structure and lung function. STATEMENT OF SIGNIFICANCE: We present comprehensive multiaxial mechanical tensile experiments of the proximal and distal airways via measures of maximum stress, initial and ultimate moduli, strain and stress transitions, hysteresis, energy loss, and stress relaxation, and further assess preconditioning and strain rate dependencies to examine the relationship between lung function and structure. The mechanical response of the bronchial tree demonstrates significant anisotropy and heterogeneity, even within the tracheal ring, and emphasizes that contrary to past studies, the behavior of the proximal airways cannot be extended to distal bronchial tree analyses. Establishing these material properties is critical to advancing our understanding of airway function and in developing accurate computational simulations to help diagnose and monitor pulmonary diseases.

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.

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.

Mouse lung mechanical properties under varying inflation volumes and cycling frequencies

Respiratory pathologies alter the structure of the lung and impact its mechanics. Mice are widely used in the study of lung pathologies, but there is a lack of fundamental mechanical measurements assessing the interdependent effect of varying inflation volumes and cycling frequency. In this study, the mechanical properties of five male C57BL/6J mice (29-33 weeks of age) lungs were evaluated ex vivo using our custom-designed electromechanical, continuous measure ventilation apparatus. We comprehensively quantify and analyze the effect of loading volumes (0.3, 0.5, 0.7, 0.9 ml) and breathing rates (5, 10, 20 breaths per minute) on pulmonary inflation and deflation mechanical properties. We report means of static compliance between 5.4-16.1 µl/cmH2O, deflation compliance of 5.3-22.2 µl/cmH2O, percent relaxation of 21.7-39.1%, hysteresis of 1.11-7.6 ml•cmH2O, and energy loss of 39-58% for the range of four volumes and three rates tested, along with additional measures. We conclude that inflation volume was found to significantly affect hysteresis, static compliance, starting compliance, top compliance, deflation compliance, and percent relaxation, and cycling rate was found to affect only hysteresis, energy loss, percent relaxation, static compliance and deflation compliance.

Examining lung mechanical strains as influenced by breathing volumes and rates using experimental digital image correlation

BACKGROUND

Mechanical ventilation is often employed to facilitate breathing in patients suffering from respiratory illnesses and disabilities. Despite the benefits, there are risks associated with ventilator-induced lung injuries and death, driving investigations for alternative ventilation techniques to improve mechanical ventilation, such as multi-oscillatory and high-frequency ventilation; however, few studies have evaluated fundamental lung mechanical local deformations under variable loading.

METHODS

Porcine whole lung samples were analyzed using a novel application of digital image correlation interfaced with an electromechanical ventilation system to associate the local behavior to the global volume and pressure loading in response to various inflation volumes and breathing rates. Strains, anisotropy, tissue compliance, and the evolutionary response of the inflating lung were analyzed.

RESULTS

Experiments demonstrated a direct and near one-to-one linear relationship between applied lung volumes and resulting local mean strain, and a nonlinear relationship between lung pressures and strains. As the applied air delivery volume was doubled, the tissue surface mean strains approximately increased from 20 to 40%, and average maximum strains measured 70-110%. The tissue strain anisotropic ratio ranged from 0.81 to 0.86 and decreased with greater inflation volumes. Local tissue compliance during the inflation cycle, associating evolutionary strains in response to inflation pressures, was also quantified.

CONCLUSION

Ventilation frequencies were not found to influence the local stretch response. Strain measures significantly increased and the anisotropic ratio decreased between the smallest and greatest tidal volumes. Tissue compliance did not exhibit a unifying trend. The insights provided by the real-time continuous measures, and the kinetics to kinematics pulmonary linkage established by this study offers valuable characterizations for computational models and establishes a framework for future studies to compare healthy and diseased lung mechanics to further consider alternatives for effective ventilation strategies.

Estimation of Regional Pulmonary Compliance in Idiopathic Pulmonary Fibrosis Based On Personalized Lung Poromechanical Modeling

Pulmonary function is tightly linked to the lung mechanical behavior, especially large deformation during breathing. Interstitial lung diseases, such as Idiopathic Pulmonary Fibrosis (IPF), have an impact on the pulmonary mechanics and consequently alter lung function. However, IPF remains poorly understood, poorly diagnosed and poorly treated. Currently, the mechanical impact of such diseases is assessed by pressure-volume curves, giving only global information. We developed a poromechanical model of the lung that can be personalized to a patient based on routine clinical data. The personalization pipeline uses clinical data, mainly CT-images at two time steps and involves the formulation of an inverse problem to estimate regional compliances. The estimation problem can be formulated both in terms of "effective", i.e., without considering the mixture porosity, or "rescaled", i.e., where the first-order effect of the porosity has been taken into account, compliances. Regional compliances are estimated for one control subject and three IPF patients, allowing to quantify the IPF-induced tissue stiffening. This personalized model could be used in the clinic as an objective and quantitative tool for IPF diagnosis.

Baseline Stiffness Modulates the Non-Linear Response to Stretch of the Extracellular Matrix in Pulmonary Fibrosis

Pulmonary fibrosis (PF) is a progressive disease that disrupts the mechanical homeostasis of the lung extracellular matrix (ECM). These effects are particularly relevant in the lung context, given the dynamic nature of cyclic stretch that the ECM is continuously subjected to during breathing. This work uses an in vivo model of pulmonary fibrosis to characterize the macro- and micromechanical properties of lung ECM subjected to stretch. To that aim, we have compared the micromechanical properties of fibrotic ECM in baseline and under stretch conditions, using a novel combination of Atomic Force Microscopy (AFM) and a stretchable membrane-based chip. At the macroscale, fibrotic ECM displayed strain-hardening, with a stiffness one order of magnitude higher than its healthy counterpart. Conversely, at the microscale, we found a switch in the stretch-induced mechanical behaviour of the lung ECM from strain-hardening at physiological ECM stiffnesses to strain-softening at fibrotic ECM stiffnesses. Similarly, we observed solidification of healthy ECM versus fluidization of fibrotic ECM in response to stretch. Our results suggest that the mechanical behaviour of fibrotic ECM under stretch involves a potential built-in mechanotransduction mechanism that may slow down the progression of PF by steering resident fibroblasts away from a pro-fibrotic profile.

Developing a Lung Model in the Age of COVID-19: A Digital Image Correlation and Inverse Finite Element Analysis Framework

Pulmonary diseases, driven by pollution, industrial farming, vaping, and the infamous COVID-19 pandemic, lead morbidity and mortality rates worldwide. Computational biomechanical models can enhance predictive capabilities to understand fundamental lung physiology; however, such investigations are hindered by the lung’s complex and hierarchical structure, and the lack of mechanical experiments linking the load-bearing organ-level response to local behaviors. In this study we address these impedances by introducing a novel reduced-order surface model of the lung, combining the response of the intricate bronchial network, parenchymal tissue, and visceral pleura. The inverse finite element analysis (IFEA) framework is developed using 3-D digital image correlation (DIC) from experimentally measured non-contact strains and displacements from an ex-vivo porcine lung specimen for the first time. A custom-designed inflation device is employed to uniquely correlate the multiscale classical pressure-volume bulk breathing measures to local-level deformation topologies and principal expansion directions. Optimal material parameters are found by minimizing the error between experimental and simulation-based lung surface displacement values, using both classes of gradient-based and gradient-free optimization algorithms and by developing an adjoint formulation for efficiency. The heterogeneous and anisotropic characteristics of pulmonary breathing are represented using various hyperelastic continuum formulations to divulge compound material parameters and evaluate the best performing model. While accounting for tissue anisotropy with fibers assumed along medial-lateral direction did not benefit model calibration, allowing for regional material heterogeneity enabled accurate reconstruction of lung deformations when compared to the homogeneous model. The proof-of-concept framework established here can be readily applied to investigate the impact of assorted organ-level ventilation strategies on local pulmonary force and strain distributions, and to further explore how diseased states may alter the load-bearing material behavior of the lung. In the age of a respiratory pandemic, advancing our understanding of lung biomechanics is more pressing than ever before.

Combined forced oscillation and fractional-order modeling in patients with work-related asthma: a case-control study analyzing respiratory biomechanics and diagnostic accuracy

BACKGROUND

Fractional-order (FrOr) models have a high potential to improve pulmonary science. These models could be useful for biomechanical studies and diagnostic purposes, offering accurate models with an improved ability to describe nature. This paper evaluates the performance of the Forced Oscillation (FO) associated with integer (InOr) and FrOr models in the analysis of respiratory alterations in work-related asthma (WRA).

METHODS

Sixty-two individuals were evaluated: 31 healthy and 31 with WRA with mild obstruction. Patients were analyzed pre- and post-bronchodilation. The diagnostic accuracy was evaluated using the area under the receiver operating characteristic curve (AUC). To evaluate how well do the studied models correspond to observed data, we analyzed the mean square root of the sum (MSEt) and the relative distance (Rd) of the estimated model values to the measured resistance and reactance measured values.

RESULTS AND DISCUSSION

Initially, the use of InOr and FrOr models increased our understanding of the WRA physiopathology, showing increased peripheral resistance, damping, and hysteresivity. The FrOr model (AUC = 0.970) outperformed standard FO (AUC = 0.929), as well as InOr modeling (AUC = 0.838) in the diagnosis of respiratory changes, achieving high accuracy. FrOr improved the curve fitting (MSEt = 0.156 ± 0.340; Rd = 3.026 ± 1.072) in comparison with the InOr model (MSEt = 0.367 ± 0.991; Rd = 3.363 ± 1.098). Finally, we demonstrated that bronchodilator use increased dynamic compliance, as well as reduced damping and peripheral resistance.

CONCLUSIONS

Taken together, these results show clear evidence of the utility of FO associated with fractional-order modeling in patients with WRA, improving our knowledge of the biomechanical abnormalities and the diagnostic accuracy in this disease.

Characterizing the viscoelasticity of extra- and intra-parenchymal lung bronchi

Pulmonary disease is known to cause remodeling of tissue structure, resulting in altered viscoelastic properties; yet the foundation for understanding this phenomenon is still nascent and will enable scientific insights regarding lung functionality. In order to characterize the viscoelastic response of pulmonary airways, uniaxial tensile experiments are conducted on porcine extra- and intra-parenchymal bronchial regions, measuring both axially and circumferentially oriented tissue. Anisotropic and heterogeneous effects on preconditioning and hysteresis are substantial, linking to energy dissipation expectancies. Stress relaxation is rheologically modeled using several classical configurations of discrete spring and dashpot elements; among them, Standard Linear Solid (SLS) and Maxwell-Weichart exhibit better fit performance. Enhanced fractional order derivative SLS (FSLS) model is also evaluated through use of a hybrid spring-pot of order α. FSLS outperforms the conventional models, demonstrating superior representation of the stress-relaxation curve's initial value and non-linear asymptotic decent. FSLS parameters exhibit notable orientation- and region-specific values, trending with observed tissue structural constituents, such as glycosaminoglycan and collagen. To the best of our knowledge, this work is the first to characterize proximal and distal bronchial energy efficiency and contextualize tissue biochemical composition in view of experimental measures and viscoelastic trends. Results provide a foundation for future investigations, particularly for understanding the role of viscoelasticity in diseased states.

An efficient and accurate method for modeling nonlinear fractional viscoelastic biomaterials

Computational biomechanics plays an important role in biomedical engineering: using modeling to understand pathophysiology, treatment and device design. While experimental evidence indicates that the mechanical response of most tissues is viscoelastic, current biomechanical models in the computational community often assume hyperelastic material models. Fractional viscoelastic constitutive models have been successfully used in literature to capture viscoelastic material response; however, the translation of these models into computational platforms remains limited. Many experimentally derived viscoelastic constitutive models are not suitable for three-dimensional simulations. Furthermore, the use of fractional derivatives can be computationally prohibitive, with a number of current numerical approximations having a computational cost that is 𝒪 ( N T 2 ) and a storage cost that is 𝒪(N_T ) (N_T denotes the number of time steps). In this paper, we present a novel numerical approximation to the Caputo derivative which exploits a recurrence relation similar to those used to discretize classic temporal derivatives, giving a computational cost that is 𝒪(N_T ) and a storage cost that is fixed over time. The approximation is optimized for numerical applications, and an error estimate is presented to demonstrate the efficacy of the method. The method, integrated into a finite element solid mechanics framework, is shown to be unconditionally stable in the linear viscoelastic case. It was then integrated into a computational biomechanical framework, with several numerical examples verifying the accuracy and computational efficiency of the method, including in an analytic test, in an analytic fractional differential equation, as well as in a computational biomechanical model problem.

Viscoelastic properties of doxorubicin-treated HT-29 cancer cells by atomic force microscopy: the fractional Zener model as an optimal viscoelastic model for cells

The malignancy of cancer cells and their response to drug treatments have been traditionally studied using solely their elastic properties. However, the study of the combined viscous and elastic properties provides a richer description of the mechanics of the cell, and achieves a more precise assessment of the effect exerted by anti-cancer treatments. We used an atomic force microscope to obtain the morphological, elastic and viscous properties of HT-29 colorectal cancer cells. Changes in these parameters were observed during exposure of the cells to doxorubicin at different times. The elastic properties were analyzed using the Hertz and Sneddon models. Furthermore, we analyzed the data to study the viscoelasticity of the cells comparing the models known as the standard linear solid, fractional Zener, generalized Maxwell, and power law. A discussion about the optimal model based in the accuracy and physical assumptions for this particular system is included. From the morphological data and viscoelasticity of HT-29 cells exposed to doxorubicin, we found that some parameters were affected differently at shorter or longer exposure times. For instance, the relaxation time suggests a measure of the cell to self-heal and it was observed to increase at shorter exposure times and then to reduce for longer exposure times to the drug. The fractional Zener model better described the mechanical properties of the cell due to the reduced number of parameters and the quality of the fit to experimental data.

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.