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

An image-based biophysical model of the lung to investigate the effect of pulmonary surfactant on lung function

Lung biomechanics aims to understand the structure-function relationship in the lung under normal and pathological conditions. Pulmonary surfactant has a key structural role in lung function with a significant contribution to the mechanical response of the lungs during respiration. Pulmonary surfactant dynamically regulates surface tension at the air-liquid interface to decrease stiffness during respiration and prevent alveolar collapse during lower volumes. Many lung injuries involve alterations to the contribution of surfactants to lung function. We developed a novel biophysical model using a poroelastic formulation that incorporates pulmonary surfactant dynamics and aims to quantify the contribution of the pulmonary surfactant toward lung compliance. The effect of pulmonary surfactant was modeled as a surface energy function, and the surface behavior was converted to bulk behavior by assuming uniform spherical alveoli. The model was used to simulate respiration and investigate the effect of altered surface tension caused by surfactant dysfunction. The model captured the characteristic sigmoidal inspiratory pressure-volume curve and hysteresis observed during clinical measurements. In addition, the model predicted the expected behavior in surfactant dysfunction in lung injuries. We expect this work to serve as an essential step towards de-convoluting and predicting the contributions of the lung parenchyma and pulmonary surfactant to global and regional lung compliance in health and disease.

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.

Empirical study of college students' extracurricular reading preference by functional data analysis of the library book borrowing behavior

Library data contains many students' reading records that reflect their general knowledge acquisition. The purpose of this study is to deeply mine the library book-borrowing data, with concerns on different book catalogues and properties to predict the students' extracurricular interests. An intelligent computing framework is proposed by the fusion of a neural network architecture and a partial differential equations (PDE) function module. In model designs, the architecture is constructed as an adaptive learning backpropagation neural network (BPNN), with automatic tuning of its hyperparameters. The PDE module is embedded into the network structure to enhance the loss functions of each neural perceptron. For model evaluation, a novel comprehensive index is designed using the calculus of information entropy. Empirical experiments are conducted on a diverse and multimodal time-series dataset of library book borrowing records to demonstrate the effectiveness of the proposed methodology. Results validate that the proposed framework is capable of revealing the students' extracurricular reading interests by processing related book borrowing records, and expected to be applied to "big data" analysis for a wide range of various libraries.

Strain-rate-dependent material properties of human lung parenchymal tissue using inverse finite element approach

Automobile crashes and blunt trauma often lead to life-threatening thoracic injuries, especially to the lung tissues. These injuries can be simulated using finite element-based human body models that need dynamic material properties of lung tissue. The strain-rate-dependent material parameters of human parenchymal tissues were determined in this study using uniaxial quasi-static (1 mm/s) and dynamic (1.6, 3, and 5 m/s) compression tests. A bilinear material model was used to capture the nonlinear behavior of the lung tissue, which was implemented using a user-defined material in LS-DYNA. Inverse mapping using genetic algorithm-based optimization of all experimental data with the corresponding FE models yielded a set of strain-rate-dependent material parameters. The bilinear material parameters are obtained for the strain rates of 0.1, 100, 300, and 500 s-1. The estimated elastic modulus increased from 43 to 153 kPa, while the toe strain reduced from 0.39 to 0.29 when the strain rate was increased from 0.1 to 500 s-1. The optimized bilinear material properties of parenchymal tissue exhibit a piecewise linear relationship with the strain rate.

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.

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.

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.

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.

The "Elastic Perspective" of SARS-CoV-2 Infection and the Role of Intrinsic and Extrinsic Factors

Elastin represents the structural component of the extracellular matrix providing elastic recoil to tissues such as skin, blood vessels and lungs. Elastogenic cells secrete soluble tropoelastin monomers into the extracellular space where these monomers associate with other matrix proteins (e.g., microfibrils and glycoproteins) and are crosslinked by lysyl oxidase to form insoluble fibres. Once elastic fibres are formed, they are very stable, highly resistant to degradation and have an almost negligible turnover. However, there are circumstances, mainly related to inflammatory conditions, where increased proteolytic degradation of elastic fibres may lead to consequences of major clinical relevance. In severely affected COVID-19 patients, for instance, the massive recruitment and activation of neutrophils is responsible for the profuse release of elastases and other proteolytic enzymes which cause the irreversible degradation of elastic fibres. Within the lungs, destruction of the elastic network may lead to the permanent impairment of pulmonary function, thus suggesting that elastases can be a promising target to preserve the elastic component in COVID-19 patients. Moreover, intrinsic and extrinsic factors additionally contributing to damaging the elastic component and to increasing the spread and severity of SARS-CoV-2 infection are reviewed.

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.

Novel Mechanical Strain Characterization of Ventilated ex vivo Porcine and Murine Lung using Digital Image Correlation

Respiratory illnesses, such as bronchitis, emphysema, asthma, and COVID-19, substantially remodel lung tissue, deteriorate function, and culminate in a compromised breathing ability. Yet, the structural mechanics of the lung is significantly understudied. Classical pressure-volume air or saline inflation studies of the lung have attempted to characterize the organ’s elasticity and compliance, measuring deviatory responses in diseased states; however, these investigations are exclusively limited to the bulk composite or global response of the entire lung and disregard local expansion and stretch phenomena within the lung lobes, overlooking potentially valuable physiological insights, as particularly related to mechanical ventilation. Here, we present a method to collect the first non-contact, full-field deformation measures of ex vivo porcine and murine lungs and interface with a pressure-volume ventilation system to investigate lung behavior in real time. We share preliminary observations of heterogeneous and anisotropic strain distributions of the parenchymal surface, associative pressure-volume-strain loading dependencies during continuous loading, and consider the influence of inflation rate and maximum volume. This study serves as a crucial basis for future works to comprehensively characterize the regional response of the lung across various species, link local strains to global lung mechanics, examine the effect of breathing frequencies and volumes, investigate deformation gradients and evolutionary behaviors during breathing, and contrast healthy and pathological states. Measurements collected in this framework ultimately aim to inform predictive computational models and enable the effective development of ventilators and early diagnostic strategies.

Modeling lung tissue dynamics and injury under pressure and impact loading

A nonlinear viscoelastic model for the lung is implemented and evaluated for high-rate loading. Principal features of the model include a closed-cell approximation of the bulk compressibility accounting for air inside the lung and a damage-injury component by which local trauma is induced by cumulative normalized internal energy and amplified by gradients of energy density. The latter feature is adapted for use in standard numerical (i.e., explicit finite element) simulations in terms of the local rate of strain energy density and the longitudinal wave speed. Injury predictions for direct loading of a block of extracted lung material, rather than the entire thorax, via pressure pulses are in reasonably close agreement with experimental observations for an extracted rabbit lung: a threshold applied pressure exists above which edema is observed experimentally, correlating with low but non-negligible damage in the numerical results. Responses to impact by cylindrical and spherical projectiles are also interrogated. Penetration depths are comparable to those observed experimentally, as is drastically increasing damage with increasing impact velocity. Damage initiates and propagates from the impact surface, with local severity of injury decreasing with distance from the impact zone, in agreement with some empirical evidence. The model predicts more severe local injury, relative to the aforementioned surface pressure loading, than what is observed experimentally. Possible reasons for the discrepancy are analyzed, and adjustments to the model, with caveats, are suggested accordingly.