Patient-Specific Airway Wall Remodeling in Chronic Lung Disease

Morphometric analysis of airways in pre-COPD and mild COPD lungs using continuous surface representations of the bronchial lumen

Introduction: Chronic Obstructive Pulmonary Disease (COPD) is a prevalent respiratory disease that presents a high rate of underdiagnosis during onset and early stages. Studies have shown that in mild COPD patients, remodeling of the small airways occurs concurrently with morphological changes in the proximal airways. Despite this evidence, the geometrical study of the airway tree from computed tomography (CT) lung images remains underexplored due to poor representations and limited tools to characterize the airway structure. Methods: We perform a comprehensive morphometric study of the proximal airways based on geometrical measures associated with the different airway generations. To this end, we leverage the geometric flexibility of the Snakes IsoGeometric Analysis method to accurately represent and characterize the airway luminal surface and volume informed by CT images of the respiratory tree. Based on this framework, we study the airway geometry of smoking pre-COPD and mild COPD individuals. Results: Our results show a significant difference between groups in airway volume, length, luminal eccentricity, minimum radius, and surface-area-to-volume ratio in the most distal airways. Discussion: Our findings suggest a higher degree of airway narrowing and collapse in COPD patients when compared to pre-COPD patients. We envision that our work has the potential to deliver a comprehensive tool for assessing morphological changes in airway geometry that take place in the early stages of COPD.

Effects of tissue degradation by collagenase and elastase on the biaxial mechanics of porcine airways

BACKGROUND

Common respiratory illnesses, such as emphysema and chronic obstructive pulmonary disease, are characterized by connective tissue damage and remodeling. Two major fibers govern the mechanics of airway tissue: elastin enables stretch and permits airway recoil, while collagen prevents overextension with stiffer properties. Collagenase and elastase degradation treatments are common avenues for contrasting the role of collagen and elastin in healthy and diseased states; while previous lung studies of collagen and elastin have analyzed parenchymal strips in animal and human specimens, none have focused on the airways to date.

METHODS

Specimens were extracted from the proximal and distal airways, namely the trachea, large bronchi, and small bronchi to facilitate evaluations of material heterogeneity, and subjected to biaxial planar loading in the circumferential and axial directions to assess airway anisotropy. Next, samples were subjected to collagenase and elastase enzymatic treatment and tensile tests were repeated. Airway tissue mechanical properties pre- and post-treatment were comprehensively characterized via measures of initial and ultimate moduli, strain transitions, maximum stress, hysteresis, energy loss, and viscoelasticity to gain insights regarding the specialized role of individual connective tissue fibers and network interactions.

RESULTS

Enzymatic treatment demonstrated an increase in airway tissue compliance throughout loading and resulted in at least a 50% decrease in maximum stress overall. Strain transition values led to significant anisotropic manifestation post-treatment, where circumferential tissues transitioned at higher strains compared to axial counterparts. Hysteresis values and energy loss decreased after enzymatic treatment, where hysteresis reduced by almost half of the untreated value. Anisotropic ratios exhibited axially led stiffness at low strains which transitioned to circumferentially led stiffness when subjected to higher strains. Viscoelastic stress relaxation was found to be greater in the circumferential direction for bronchial airway regions compared to axial counterparts.

CONCLUSION

Targeted fiber treatment resulted in mechanical alterations across the loading range and interactions between elastin and collagen connective tissue networks was observed. Providing novel mechanical characterization of elastase and collagenase treated airways aids our understanding of individual and interconnected fiber roles, ultimately helping to establish a foundation for constructing constitutive models to represent various states and progressions of pulmonary disease.

Programmable Tissue Folding Patterns in Structured Hydrogels

Folding of mucosal tissues, such as the tissue within the epithelium of the upper respiratory airways, is critical for organ function. Studying the influence of folded tissue patterns on cellular function is challenging mainly due to the lack of suitable cell culture platforms that can recreate dynamic tissue folding in vitro. Here, a bilayer hydrogel folding system, composed of alginate/polyacrylamide double-network (DN) and hyaluronic acid (HA) hydrogels, to generate static folding patterns based on mechanical instabilities, is described. By encapsulating human fibroblasts into patterned HA hydrogels, human bronchial epithelial cells form a folded pseudostratified monolayer. Using magnetic microparticles, DN hydrogels reversibly fold into pre-defined patterns and enable programmable on-demand folding of cell-laden hydrogel systems upon applying a magnetic field. This hydrogel construction provides a dynamic culture system for mimicking tissue folding in vitro, which is extendable to other cell types and organ systems.

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.

Associating local strains to global pressure-volume mouse lung mechanics using digital image correlation

Pulmonary diseases alter lung mechanical properties, can cause loss of function, and necessitate use of mechanical ventilation, which can be detrimental. Investigations of lung tissue (local) scale mechanical properties are sparse compared to that of the whole organ (global) level, despite connections between regional strain injury and ventilation. We examine ex vivo mouse lung mechanics by investigating strain values, local compliance, tissue surface heterogeneity, and strain evolutionary behavior for various inflation rates and volumes. A custom electromechanical, pressure-volume ventilator is coupled with digital image correlation to measure regional lung strains and associate local to global mechanics by analyzing novel pressure-strain evolutionary measures. Mean strains at 5 breaths per minute (BPM) for applied volumes of 0.3, 0.5, and 0.7 ml are 5.0, 7.8, and 11.3%, respectively, and 4.7, 8.8, and 12.2% for 20 BPM. Similarly, maximum strains among all rate and volume combinations range 10.7%-22.4%. Strain values (mean, range, mode, and maximum) at peak inflation often exhibit significant volume dependencies. Additionally, select evolutionary behavior (e.g., local lung compliance quantification) and tissue heterogeneity show significant volume dependence. Rate dependencies are generally found to be insignificant; however, strain values and surface lobe heterogeneity tend to increase with increasing rates. By quantifying strain evolutionary behavior in relation to pressure-volume measures, we associate time-continuous local to global mouse lung mechanics for the first time and further examine the role of volume and rate dependency. The interplay of multiscale deformations evaluated in this work can offer insights for clinical applications, such as ventilator-induced lung injury.

PDE-constrained shape registration to characterize biological growth and morphogenesis from imaging data

We propose a PDE-constrained shape registration algorithm that captures the deformation and growth of biological tissue from imaging data. Shape registration is the process of evaluating optimum alignment between pairs of geometries through a spatial transformation function. We start from our previously reported work, which uses 3D tensor product B-spline basis functions to interpolate 3D space. Here, the movement of the B-spline control points, composed with an implicit function describing the shape of the tissue, yields the total deformation gradient field. The deformation gradient is then split into growth and elastic contributions. The growth tensor captures addition of mass, i.e. growth, and evolves according to a constitutive equation which is usually a function of the elastic deformation. Stress is generated in the material due to the elastic component of the deformation alone. The result of the registration is obtained by minimizing a total energy functional which includes: a distance measure reflecting similarity between the shapes, and the total elastic energy accounting for the growth of the tissue. We apply the proposed shape registration framework to study zebrafish embryo epiboly process and tissue expansion during skin reconstruction surgery. We anticipate that our PDE-constrained shape registration method will improve our understanding of biological and medical problems in which tissues undergo extreme deformations over time.

Patient-specific finite element analysis of heart failure and the impact of surgical intervention in pulmonary hypertension secondary to mitral valve disease

Pulmonary hypertension (PH), a chronic and complex medical condition affecting 1% of the global population, requires clinical evaluation of right ventricular maladaptation patterns under various conditions. A particular challenge for clinicians is a proper quantitative assessment of the right ventricle (RV) owing to its intimate coupling to the left ventricle (LV). We, thus, proposed a patient-specific computational approach to simulate PH caused by left heart disease and its main adverse functional and structural effects on the whole heart. Information obtained from both prospective and retrospective studies of two patients with severe PH, a 72-year-old female and a 61-year-old male, is used to present patient-specific versions of the Living Heart Human Model (LHHM) for the pre-operative and post-operative cardiac surgery. Our findings suggest that before mitral and tricuspid valve repair, the patients were at risk of right ventricular dilatation which may progress to right ventricular failure secondary to their mitral valve disease and left ventricular dysfunction. Our analysis provides detailed evidence that mitral valve replacement and subsequent chamber pressure unloading are associated with a significant decrease in failure risk post-operatively in the context of pulmonary hypertension. In particular, right-sided strain markers, such as tricuspid annular plane systolic excursion (TAPSE) and circumferential and longitudinal strains, indicate a transition from a range representative of disease to within typical values after surgery. Furthermore, the wall stresses across the RV and the interventricular septum showed a notable decrease during the systolic phase after surgery, lessening the drive for further RV maladaptation and significantly reducing the risk of RV failure.

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.

Three-Dimensional Whole-Organ Characterization of the Regional Alveolar Morphology in Normal Murine Lungs

Alveolar architecture plays a fundamental role in the processes of ventilation and perfusion in the lung. Alterations in the alveolar surface area and alveolar cavity volume constitute the pathophysiological basis of chronic respiratory diseases such as pulmonary emphysema. Previous studies based on micro-computed tomography (micro-CT) of lung samples have allowed the geometrical study of acinar units. However, our current knowledge is based on the study of a few tissue samples in random locations of the lung that do not give an account of the spatial distributions of the alveolar architecture in the whole lung. In this work, we combine micro-CT imaging and computational geometry algorithms to study the regional distribution of key morphological parameters throughout the whole lung. To this end, 3D whole-lung images of Sprague–Dawley rats are acquired using high-resolution micro-CT imaging and analyzed to estimate porosity, alveolar surface density, and surface-to-volume ratio. We assess the effect of current gold-standard dehydration methods in the preparation of lung samples and propose a fixation protocol that includes the application of a methanol-PBS solution before dehydration. Our results show that regional porosity, alveolar surface density, and surface-to-volume ratio have a uniform distribution in normal lungs, which do not seem to be affected by gravitational effects. We further show that sample fixation based on ethanol baths for dehydration introduces shrinking and affects the acinar architecture in the subpleural regions. In contrast, preparations based on the proposed dehydration protocol effectively preserve the alveolar morphology.

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.

Local and global growth and remodeling in calcific aortic valve disease and aging

Aging and calcific aortic valve disease (CAVD) are the main factors leading to aortic stenosis. Both processes are accompanied by growth and remodeling pathways that play a crucial role in aortic valve pathophysiology. Herein, a computational growth and remodeling (G&R) framework was developed to investigate the effects of aging and calcification on aortic valve dynamics. Particularly, an algorithm was developed to couple the global growth and stiffening of the aortic valve due to aging and the local growth and stiffening due to calcification with the aortic valve transient dynamics. The aortic valve dynamics during baseline were validated with available data in the literature. Subsequently, the changes in aortic valve dynamic patterns during aging and CAVD progression were studied. The results revealed the patterns in geometric orifice area reduction and an increase in the valve stress during local and global growth and remodeling of the aortic valve. The proposed algorithm provides a framework to couple mechanobiology models of disease growth with tissue-scale transient structural mechanics models to study the biomechanical changes during cardiovascular disease growth and aging.

Reduced biomechanical models for precision-cut lung-slice stretching experiments

Precision-cut lung-slices (PCLS), in which viable airways embedded within lung parenchyma are stretched or induced to contract, are a widely used ex vivo assay to investigate bronchoconstriction and, more recently, mechanical activation of pro-remodelling cytokines in asthmatic airways. We develop a nonlinear fibre-reinforced biomechanical model accounting for smooth muscle contraction and extracellular matrix strain-stiffening. Through numerical simulation, we describe the stresses and contractile responses of an airway within a PCLS of finite thickness, exposing the importance of smooth muscle contraction on the local stress state within the airway. We then consider two simplifying limits of the model (a membrane representation and an asymptotic reduction in the thin-PCLS-limit), that permit analytical progress. Comparison against numerical solution of the full problem shows that the asymptotic reduction successfully captures the key elements of the full model behaviour. The more tractable reduced model that we develop is suitable to be employed in investigations to elucidate the time-dependent feedback mechanisms linking airway mechanics and cytokine activation in asthma.

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.

Biomechanical Force Prediction for Lengthening of Small Intestine during Distraction Enterogenesis

Distraction enterogenesis has been extensively studied as a potential treatment for short bowel syndrome, which is the most common form of intestinal failure. Different strategies including parenteral nutrition and surgical lengthening to manage patients with short bowel syndrome are associated with high complication rates. More recently, self-expanding springs have been used to lengthen the small intestine using an intraluminal axial mechanical force, where this biomechanical force stimulates the growth and elongation of the small intestine. Differences in physical characteristics of patients with short bowel syndrome would require a different mechanical force—this is crucial in order to achieve an efficient and safe lengthening outcome. In this study, we aimed to predict the required mechanical force for each potential intestinal size. Based on our previous experimental observations and computational findings, we integrated our experimental measurements of patient biometrics along with mechanical characterization of the soft tissue into our numerical simulations to develop a series of computational models. These computational models can predict the required mechanical force for any potential patient where this can be advantageous in predicting an individual’s tissue response to spring-mediated distraction enterogenesis and can be used toward a safe delivery of the mechanical force.

Introducing a Custom-Designed Volume-Pressure Machine for Novel Measurements of Whole Lung Organ Viscoelasticity and Direct Comparisons Between Positive- and Negative-Pressure Ventilation

Asthma, emphysema, COVID-19 and other lung-impacting diseases cause the remodeling of tissue structural properties and can lead to changes in conducting pulmonary volume, viscoelasticity, and air flow distribution. Whole organ experimental inflation tests are commonly used to understand the impact of these modifications on lung mechanics. Here we introduce a novel, automated, custom-designed device for measuring the volume and pressure response of lungs, surpassing the capabilities of traditional machines and built to range size-scales to accommodate both murine and porcine tests. The software-controlled system is capable of constructing standardized continuous volume-pressure curves, while accounting for air compressibility, yielding consistent and reproducible measures while eliminating the need for pulmonary degassing. This device uses volume-control to enable viscoelastic whole lung macromechanical insights from rate dependencies and pressure-time curves. Moreover, the conceptual design of this device facilitates studies relating the phenomenon of diaphragm breathing and artificial ventilation induced by pushing air inside the lungs. System capabilities are demonstrated and validated via a comparative study between ex vivo murine lungs and elastic balloons, using various testing protocols. Volume-pressure curve comparisons with previous pressure-controlled systems yield good agreement, confirming accuracy. This work expands the capabilities of current lung experiments, improving scientific investigations of healthy and diseased pulmonary biomechanics. Ultimately, the methodologies demonstrated in the manufacturing of this system enable future studies centered on investigating viscoelasticity as a potential biomarker and improvements to patient ventilators based on direct assessment and comparisons of positive- and negative-pressure mechanics.

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.

Propagation of uncertainty in the mechanical and biological response of growing tissues using multi-fidelity Gaussian process regression

A key feature of living tissues is their capacity to remodel and grow in response to environmental cues. Within continuum mechanics, this process can be captured with the multiplicative split of the deformation gradient into growth and elastic contributions. The mechanical and biological response during tissue adaptation is characterized by inherent variability. Accounting for this uncertainty is critical to better understand tissue mechanobiology, and, moreover, it is of practical importance if we aim to develop predictive models for clinical use. However, the current gold standard in computational models of growth and remodeling remains the use of deterministic finite element (FE) simulations. Here we focus on tissue expansion, a popular technique in which skin is stretched by a balloon-like device inducing its growth. We construct FE models of tissue expansion with various levels of detail, and show that a sufficiently broad set of FE simulations from these models can be used to train an accurate and efficient multi-fidelity Gaussian process (GP) surrogate. The approach is not limited to simulation data, rather, it can fuse different kinds of data, including from experiments. The main appeal of the framework relies on the common experience that highly detailed models (or experiments) are more accurate but also more costly, while simpler models (or experiments) can be easily evaluated but are bound to have some error. In these situations, doing uncertainty analysis tasks with the high fidelity models alone is not feasible and, conversely, relying solely on low fidelity approximations is also undesirable. We show that a multi-fidelity GP outperforms the high fidelity GP and low fidelity GP when tested against the most detailed FE model. In turn, having trained the multi-fidelity GP model, we showcase the propagation of uncertainty from the mechanical and biological response parameters to the spatio-temporal growth outcomes. We expect that the methods and applications in this paper will enable future research in parameter calibration under uncertainty and uncertainty propagation in real clinical scenarios involving tissue growth and remodeling.

Mechanics of pulmonary airways: Linking structure to function through constitutive modeling, biochemistry, and histology

Breathing involves fluid-solid interactions in the lung; however, the lack of experimental data inhibits combining the mechanics of air flow to airway deformation, challenging the understanding of how biomaterial constituents contribute to tissue response. As such, lung mechanics research is increasingly focused on exploring the relationship between structure and function. To address these needs, we characterize mechanical properties of porcine airways using uniaxial tensile experiments, accounting for bronchial orientation- and location- dependency. Structurally-reinforced constitutive models are developed to incorporate the role of collagen and elastin fibers embedded within the extrafibrillar matrix. The strain-energy function combines a matrix description (evaluating six models: compressible NeoHookean, unconstrained Ogden, uncoupled Mooney-Rivlin, incompressible Ogden, incompressible Demiray and incompressible NeoHookean), superimposed with non-linear fibers (evaluating two models: exponential and polynomial). The best constitutive formulation representative of all bronchial regions is determined based on curve-fit results to experimental data, accounting for uniqueness and sensitivity. Glycosaminoglycan and collagen composition, alongside tissue architecture, indicate fiber form to be primarily responsible for observed airway anisotropy and heterogeneous mechanical behavior. To the authors' best knowledge, this study is the first to formulate a structurally-motivated constitutive model, augmented with biochemical analysis and microstructural observations, to investigate the mechanical function of proximal and distal bronchi. Our systematic pulmonary tissue characterization provides a necessary foundation for understanding pulmonary mechanics; furthermore, these results enable clinical translation through simulations of airway obstruction in disease, fluid-structure interaction insights during breathing, and potentially, predictive capabilities for medical interventions. STATEMENT OF SIGNIFICANCE: The advancement of pulmonary research relies on investigating the biomechanical response of the bronchial tree. Experiments demonstrating the non-linear, heterogeneous, and anisotropic material behavior of porcine airways are used to develop a structural constitutive model representative of proximal and distal bronchial behavior. Calibrated material parameters exhibit regional variation in biomaterial properties, initially hypothesized to originate from tissue constituents. Further exploration through biochemical and histological analysis indicates mechanical function is primarily governed by microstructural form. The results of this study can be directly used in finite element and fluid-structure interaction models to enable physiologically relevant and more accurate computational simulations aimed to help diagnose and monitor pulmonary disease.

AFM-based nanomechanical characterization of bronchoscopic samples in asthma patients

Asthma is not a single disease, but recently, it is considered as a syndrome characterized through various clinical presentations and different etiopathologies. Large degree of the disease heterogeneity manifests in distinct characteristics that translate into variability of properties at single cell and molecular levels. Here, we conducted measurements of mechanical properties of bronchial tissue samples collected from patients suffering from asthma. The results obtained from different applied protocols for sample preparation may indicate that deep freezing and storage in liquid nitrogen, followed by consecutive unfreezing of tissue samples, preserve tissue mechanical properties as indicated by a parameter referred here as a tissue relative stiffness index. Tissue relative stiffness index quantifies both the degree of heterogeneity and deformability of tissue samples regarding healthy one. These studies demonstrate that the freezing protocol, optimized towards asthma tissue, can facilitate atomic force microscopy use what, together with recent findings on standardization of elasticity measurements, enables the measurements of large group of samples with minimized influence of errors stemming from the applied methodology of tissue stiffness determination.

Mechanical properties of the airway tree: heterogeneous and anisotropic pseudoelastic and viscoelastic tissue responses

Airway obstruction and pulmonary mechanics remain understudied despite lung disease being the third cause of death in the United States. Lack of relevant data has led computational pulmonary models to infer mechanical properties from available material data for the trachea. Additionally, the time-dependent, viscoelastic behaviors of airways have been largely overlooked, despite their potential physiological relevance and utility as metrics of tissue remodeling and disease progression. Here, we address the clear need for airway-specific material characterization to inform biophysical studies of the bronchial tree. Specimens from three airway levels (trachea, large bronchi, and small bronchi) and two orientations (axial and circumferential) were prepared from five fresh pig lungs. Uniaxial tensile tests revealed substantial heterogeneity and anisotropy. Overall, the linear pseudoelastic modulus was significantly higher axially than circumferentially (30.5 ± 3.1 vs. 8.4 ± 1.1 kPa) and significantly higher among circumferential samples for small bronchi than for the trachea and large bronchi (12.5 ± 1.9 vs. 6.0 ± 0.6 and 6.6 ± 0.9 kPa). Circumferential samples exhibited greater percent stress relaxation over 300 s than their axial counterparts (38.0 ± 1.4 vs. 23.1 ± 1.5%). Axial and circumferential trachea samples displayed greater percent stress relaxation (26.4 ± 1.6 and 42.5 ± 1.7%) than corresponding large and small bronchi. This ex vivo pseudoelastic and viscoelastic characterization reveals novel anisotropic and heterogeneous behaviors and equips us to construct airway-specific constitutive relations. Our results establish necessary fundamentals for airway mechanics, laying the groundwork for future studies to extend to clinical questions surrounding lung injury, and further directly enables computational tools for lung disease obstruction predictions. NEW & NOTEWORTHY Understanding the mechanics of the lung is necessary for investigating disease progression. Trachea mechanics comprises the vast majority of ex vivo airway tissue characterization despite distal airways being the site of disease manifestation and occlusion. Furthermore, viscoelastic studies are scarce, whereas time-dependent behaviors could be potential physiological metrics of tissue remodeling. In this study, the critical need for airway-specific material properties is addressed, reporting bronchial tree anisotropic and heterogeneous material properties.

Evaluation of Ventilation-Induced Lung Inflammation Through Multi-Scale Simulations

Ventilation-induced lung injury is a common problem faced by patients with respiratory problems who require mechanical ventilation (MV). This injury may lead to a greater chance of developing or exacerbating the acute respiratory distress syndrome which further complicates the therapeutic use of MV. The chain of events begins with the MV initiating an immune response that leads to inflammation induced tissue material alteration (stiffening) and eventually the loss of lung resistance. It is clear from this sequence of events that the phenomenon of ventilation induced injury is multi-scale by nature and, hence, requires holistic analysis involving simulations and informatics. An effective approach to this problem is to break it down into several major physical models. Each physical model is developed separately and can be seen as a component in a larger system that comprises the scale of the problem being investigated. In this paper, a multi-scale system consisting of breathing mechanics, tissue deformation, and cellular mechanics models is developed to assess the immune response. To demonstrate the potential of the model, a fluid–solid model is employed for breathing mechanics, a plane-strain elasticity model is applied to assess tissue deformation, and a cellular automata (CA) model is developed to account for immune response. A case study of three lower airways is presented. The CA model shows that this increased the immune response by five times, which correlates with alteration in the tissue microstructure. This alteration in turn is reflected in the material constant value obtained in the tissue mechanics model. However, the changes in strain rates in the airways after inflammation (and hence, lung compliance) were not as significant as the rates of change in immune response. Finally, results from the fluid–solid model demonstrate its potential for airflow characterization caused by tissue deformation that could lead to disease identification.

The effect of disease and respiration on airway shape in patients with moderate persistent asthma

Computational models of gas transport and aerosol deposition frequently utilize idealized models of bronchial tree structure, where airways are considered a network of bifurcating cylinders. However, changes in the shape of the lung during respiration affect the geometry of the airways, especially in disease conditions. In this study, the internal airway geometry was examined, concentrating on comparisons between mean lung volume (MLV) and total lung capacity (TLC). A set of High Resolution CT images were acquired during breath hold on a group of moderate persistent asthmatics at MLV and TLC after challenge with a broncho-constrictor (methacholine) and the airway trees were segmented and measured. The airway hydraulic diameter (Dh) was calculated through the use of average lumen area (Ai) and average internal perimeter (Pi) at both lung volumes and was found to be systematically higher at TLC by 13.5±9% on average, with the lower lobes displaying higher percent change in comparison to the lower lobes. The average internal diameter (Din) was evaluated to be 12.4±6.8% (MLV) and 10.8±6.3% (TLC) lower than the Dh, for all the examined bronchi, a result displaying statistical significance. Finally, the airway distensibility per bronchial segment and per generation was calculated to have an average value of 0.45±0.28, exhibiting high variability both between and within lung regions and generations. Mixed constriction/dilation patterns were recorded between the lung volumes, where a number of airways either failed to dilate or even constricted when observed at TLC. We conclude that the Dh is higher than Din, a fact that may have considerable effects on bronchial resistance or airway loss at proximal regions. Differences in caliber changes between lung regions are indicative of asthma-expression variability in the lung. However, airway distensibility at generation 3 seems to predict distensibility more distally.

Mechanics Reveals the Biological Trigger in Wrinkly Fingers

Fingertips wrinkle due to long exposure to water. The biological reason for this morphological change is unclear and still not fully understood. There are two main hypotheses for the underlying mechanism of fingertip wrinkling: the 'shrink' model (in which the wrinkling is driven by the contraction of the lower layers of skin, associated with the shrinking of the underlying vasculature), and the 'swell' model (in which the wrinkling is driven by the swelling of the upper layers of the skin, associated with osmosis). In reality, contraction of the lower layers of the skin and swelling of the upper layers will happen simultaneously. However, the relative importance of these two mechanisms to drive fingertip wrinkling also remains unclear. Simulating the swelling in the upper layers of skin alone, which is associated with neurological disorders, we found that wrinkles appeared above an increase of volume of [Formula: see text] Therefore, the upper layers can not exceed this swelling level in order to not contradict in vivo observations in patients with such neurological disorders. Simulating the contraction of the lower layers of the skin alone, we found that the volume have to decrease a [Formula: see text] to observe wrinkles. Furthermore, we found that the combined effect of both mechanisms leads to pronounced wrinkles even at low levels of swelling and contraction when individually they do not. This latter results indicates that the collaborative effect of both hypothesis are needed to induce wrinkles in the fingertips. Our results demonstrate how models from continuum mechanics can be successfully applied to testing hypotheses for the mechanisms that underly fingertip wrinkling, and how these effects can be quantified.

Mechanism of Consistent Gyrus Formation: an Experimental and Computational Study

As a significant type of cerebral cortical convolution pattern, the gyrus is widely preserved across species. Although many hypotheses have been proposed to study the underlying mechanisms of gyrus formation, it is currently still far from clear which factors contribute to the regulation of consistent gyrus formation. In this paper, we employ a joint analysis scheme of experimental data and computational modeling to investigate the fundamental mechanism of gyrus formation. Experimental data on mature human brains and fetal brains show that thicker cortices are consistently found in gyral regions and gyral cortices have higher growth rates. We hypothesize that gyral convolution patterns might stem from heterogeneous regional growth in the cortex. Our computational simulations show that gyral convex patterns may occur in locations where the cortical plate grows faster than the cortex of the brain. Global differential growth can only produce a random gyrification pattern, but it cannot guarantee gyrus formation at certain locations. Based on extensive computational modeling and simulations, it is suggested that a special area in the cerebral cortex with a relatively faster growth speed could consistently engender gyri.

Surface and interfacial creases in a bilayer tubular soft tissue

Surface and interfacial creases induced by biological growth are common types of instability in soft biological tissues. This study focuses on the criteria for the onset of surface and interfacial creases as well as their morphological evolution in a growing bilayer soft tube within a confined environment. Critical growth ratios for triggering surface and interfacial creases are investigated both analytically and numerically. Analytical interpretations provide preliminary insights into critical stretches and growth ratios for the onset of instability and formation of both surface and interfacial creases. However, the analytical approach cannot predict the evolution pattern of the model after instability; therefore nonlinear finite element simulations are carried out to replicate the poststability morphological patterns of the structure. Analytical and computational simulation results demonstrate that the initial geometry, growth ratio, and shear modulus ratio of the layers are the most influential factors to control surface and interfacial crease formation in this soft tubular bilayer. The competition between the stretch ratios in the free and interfacial surfaces is one of the key driving factors to determine the location of the first crease initiation. These findings may provide some fundamental understanding in the growth modeling of tubular biological tissues such as esophagi and airways as well as offering useful clues into normal and pathological functions of these tissues.

Elastosis during airway wall remodeling explains multiple co-existing instability patterns

Living structures can undergo morphological changes in response to growth and alterations in microstructural properties in response to remodeling. From a biological perspective, airway wall inflammation and airway elastosis are classical hallmarks of growth and remodeling during chronic lung disease. From a mechanical point of view, growth and remodeling trigger mechanical instabilities that result in inward folding and airway obstruction. While previous analytical and computational studies have focused on identifying the critical parameters at the onset of folding, few have considered the post-buckling behavior. All prior studies assume constant microstructural properties during the folding process; yet, clinical studies now reveal progressive airway elastosis, the degeneration of elastic fibers associated with a gradual stiffening of the inner layer. Here, we explore the influence of temporally evolving material properties on the post-bifurcation behavior of the airway wall. We show that a growing and stiffening inner layer triggers an additional subsequent bifurcation after the first instability occurs. Evolving material stiffnesses provoke failure modes with multiple co-existing wavelengths, associated with the superposition of larger folds evolving on top of the initial smaller folds. This phenomenon is exclusive to material stiffening and conceptually different from the phenomenon of period doubling observed in constant-stiffness growth. Our study suggests that the clinically observed multiple wavelengths in diseased airways are a result of gradual airway wall stiffening. While our evolving material properties are inspired by the clinical phenomenon of airway elastosis, the underlying concept is broadly applicable to other types of remodeling including aneurysm formation or brain folding.

Systems biology and mechanics of growth

In contrast to inert systems, living biological systems have the advantage to adapt to their environment through growth and evolution. This transfiguration is evident during embryonic development, when the predisposed need to grow allows form to follow function. Alterations in the equilibrium state of biological systems breed disease and mutation in response to environmental triggers. The need to characterize the growth of biological systems to better understand these phenomena has motivated the continuum theory of growth and stimulated the development of computational tools in systems biology. Biological growth in development and disease is increasingly studied using the framework of morphoelasticity. Here, we demonstrate the potential for morphoelastic simulations through examples of volume, area, and length growth, inspired by tumor expansion, chronic bronchitis, brain development, intestine formation, plant shape, and myopia. We review the systems biology of living systems in light of biochemical and optical stimuli and classify different types of growth to facilitate the design of growth models for various biological systems within this generic framework. Exploring the systems biology of growth introduces a new venue to control and manipulate embryonic development, disease progression, and clinical intervention.

Upper Airway Elasticity Estimation in Pediatric Down Syndrome Sleep Apnea Patients Using Collapsible Tube Theory

Elasticity of the soft tissues surrounding the upper airway lumen is one of the important factors contributing to upper airway disorders such as snoring and obstructive sleep apnea. The objective of this study is to calculate patient specific elasticity of the pharynx from magnetic resonance (MR) images using a 'tube law', i.e., the relationship between airway cross-sectional area and transmural pressure difference. MR imaging was performed under anesthesia in children with Down syndrome (DS) and obstructive sleep apnea (OSA). An airway segmentation algorithm was employed to evaluate changes in airway cross-sectional area dilated by continuous positive airway pressure (CPAP). A pressure-area relation was used to make localized estimates of airway wall stiffness for each patient. Optimized values of patient specific Young's modulus for tissue in the velopharynx and oropharynx, were estimated from finite element simulations of airway collapse. Patient specific deformation of the airway wall under CPAP was found to exhibit either a non-linear 'hardening' or 'softening' behavior. The localized airway and tissue elasticity were found to increase with increasing severity of OSA. Elasticity based patient phenotyping can potentially assist clinicians in decision making on CPAP and airway or tissue elasticity can supplement well-known clinical measures of OSA severity.