Force heterogeneity in a two-dimensional network model of lung tissue elasticity

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.

Predicting alveolar ventilation heterogeneity in pulmonary fibrosis using a non-uniform polyhedral spring network model

Pulmonary Fibrosis (PF) is a deadly disease that has limited treatment options and is caused by excessive deposition and cross-linking of collagen leading to stiffening of the lung parenchyma. The link between lung structure and function in PF remains poorly understood, although its spatially heterogeneous nature has important implications for alveolar ventilation. Computational models of lung parenchyma utilize uniform arrays of space-filling shapes to represent individual alveoli, but have inherent anisotropy, whereas actual lung tissue is isotropic on average. We developed a novel Voronoi-based 3D spring network model of the lung parenchyma, the Amorphous Network, that exhibits more 2D and 3D similarity to lung geometry than regular polyhedral networks. In contrast to regular networks that show anisotropic force transmission, the structural randomness in the Amorphous Network dissipates this anisotropy with important implications for mechanotransduction. We then added agents to the network that were allowed to carry out a random walk to mimic the migratory behavior of fibroblasts. To model progressive fibrosis, agents were moved around the network and increased the stiffness of springs along their path. Agents migrated at various path lengths until a certain percentage of the network was stiffened. Alveolar ventilation heterogeneity increased with both percent of the network stiffened, and walk length of the agents, until the percolation threshold was reached. The bulk modulus of the network also increased with both percent of network stiffened and path length. This model thus represents a step forward in the creation of physiologically accurate computational models of lung tissue disease.

Perioperative Lung Protection: Clinical Implications

In the past, it was common practice to use a high tidal volume (VT) during intraoperative ventilation, because this reduced the need for high oxygen fractions to compensate for the ventilation-perfusion mismatches due to atelectasis in a time when it was uncommon to use positive end-expiratory pressure (PEEP) in the operating room. Convincing and increasing evidence for harm induced by ventilation with a high VT has emerged over recent decades, also in the operating room, and by now intraoperative ventilation with a low VT is a well-adopted approach. There is less certainty about the level of PEEP during intraoperative ventilation. Evidence for benefit and harm of higher PEEP during intraoperative ventilation is at least contradicting. While some PEEP may prevent lung injury through reduction of atelectasis, higher PEEP is undeniably associated with an increased risk of intraoperative hypotension that frequently requires administration of vasoactive drugs. The optimal level of inspired oxygen fraction (FIO2) during surgery is even more uncertain. The suggestion that hyperoxemia prevents against surgical site infections has not been confirmed in recent research. In addition, gas absorption-induced atelectasis and its association with adverse outcomes like postoperative pulmonary complications actually makes use of a high FIO2 less attractive. Based on the available evidence, we recommend the use of a low VT of 6-8 mL/kg predicted body weight in all surgery patients, and to restrict use of a high PEEP and high FIO2 during intraoperative ventilation to cases in which hypoxemia develops. Here, we prefer to first increase FIO2 before using high PEEP.

A viscoelastic two-dimensional network model of the lung extracellular matrix

The extracellular matrix (ECM) comprises a large proportion of the lung parenchymal tissue and is an important contributor to the mechanical properties of the lung. The lung tissue is a biologically active scaffold with a complex ECM matrix structure and composition that provides physical support to the surrounding cells. Nearly all respiratory pathologies result in changes in the structure and composition of the ECM; however, the impact of these alterations on the mechanical properties of the tissue is not well understood. In this study, a novel network model was developed to incorporate the combinatorial effect of lung tissue ECM constituents such as collagen, elastin and proteoglycans (PGs) and used to mimic the experimentally derived length-tension response of the tissue to uniaxial loading. By modelling the effect of collagen elasticity as an exponential function with strain, and in concert with the linear elastic response of elastin, the network model's mechanical response matched experimental stress-strain curves from the literature. In addition, by incorporating spring-dashpot viscoelastic elements, to represent the PGs, the hysteresis response was also simulated. Finally, by selectively reducing volume fractions of the different ECM constituents, we were able to gain insight into their relative mechanical contribution to the larger scale tissue mechanical response.

An Analytical Model for Estimating Alveolar Wall Elastic Moduli From Lung Tissue Uniaxial Stress-Strain Curves

The non-linear stress-strain behavior of uniaxially-stretched lung parenchyma is thought to be an emergent phenomenon arising from the ensemble behavior of its microscopic constituents. Such behavior includes the alignment and elongation of randomly oriented alveolar walls with initially flaccid fibers in the direction of strain. To account for the link between microscopic wall behavior and the macroscopic stress-strain curve, we developed an analytical model that represents both alignment and elongation of alveolar walls during uniaxial stretching. The model includes the kinetics and mechanical behavior of randomly oriented elastic alveolar walls that have a bending stiffness at their intersections. The alignment and stretch of the walls following incremental stretch of the tissue were determined based on energy minimization, and the total stress was obtained by differentiating the total energy density with respect to strain. The stress-strain curves predicted by the model were comparable to curves generated by a previously published numerical alveolar network model. The model was also fit to experimentally measured stress-strain curves in parenchymal strips obtained from mice with decreased lung collagen content, and from young and aged mice. This yielded estimates for the elastic modulus of an alveolar wall, which increased with age from 4.4 to 5.9 kPa (p = 0.043), and for the elastic modulus of fibers within the wall, which increased with age from 311 to 620 kPa (p = 0.001). This demonstrates the possibility of estimating alveolar wall mechanical properties in biological soft tissue from its macroscopic behavior given appropriate assumptions about tissue structure.

One-hit Models of Ventilator-induced Lung Injury: Benign Inflammation versus Inflammation as a By-product

BACKGROUND

One important explanation for the detrimental effects of conventional mechanical ventilation is the biotrauma hypothesis that ventilation may trigger proinflammatory responses that subsequently cause lung injury. This hypothesis has frequently been studied in so-called one-hit models (overventilation of healthy lungs) that so far have failed to establish an unequivocal link between inflammation and hypoxemic lung failure. This study was designed to develop a one-hit biotrauma model.

METHODS

Mice (six per group) were ventilated for up to 7 h (positive end-expiratory pressure 2 cm H2O) and received 300 μl/h fluid support. Series_1: initial plateau pressures of 10, 24, 27, or 30 cm H2O. Series_2: ventilation with pressure release at 34 cm H2O and initial plateau pressure of 10, 24, 27, or 30 cm H2O. To study the significance of inflammation, the latter groups were also pretreated with the steroid dexamethasone.

RESULTS

Within 7 h, 20 of 24 mice ventilated with plateau pressure of 27 cm H2O or more died of a catastrophic lung failure characterized by strongly increased proinflammatory markers and a precipitous decrease in pulmonary compliance, blood pressure, and oxygenation. Pretreatment with dexamethasone reduced inflammation, but prolonged median survival time by 30 min.

CONCLUSIONS

Our findings demonstrate a sharp distinction between ventilation with 24 cm H2O that was well tolerated and ventilation with 27 cm H2O that was lethal for most animals due to catastrophic lung failure. In the former case, inflammation was benign and in the latter, a by-product that only accelerated lung failure. The authors suggest that biotrauma-when defined as a ventilation-induced and inflammation-dependent hypoxemia-is difficult to study in murine one-hit models of ventilation, at least not within 7 h. (Anesthesiology 2017; 126:909-22).

Modeling and incorporating cardiac-induced lung tissue motion in a breathing motion model

PURPOSE

The purpose of this work is to develop a cardiac-induced lung motion model to be integrated into an existing breathing motion model.

METHODS

The authors' proposed cardiac-induced lung motion model represents the lung tissue's specific response to the subject's cardiac cycle. The model is mathematically defined as a product of a converging polynomial function h of the cardiac phase (c) and the maximum displacement y(X0) of each voxel (X0) among all the cardiac phases. The function h(c) was estimated from cardiac-gated MR imaging of ten healthy volunteers using an Akaike Information Criteria optimization algorithm. For each volunteer, a total of 24 short-axis and 18 radial planar views were acquired on a 1.5 T MR scanner during a series of 12-15 s breath-hold maneuvers. Each view contained 30 temporal frames of equal time-duration beginning with the end-diastolic cardiac phase. The frames in each of the planar views were resampled to create a set of three-dimensional (3D) anatomical volumes representing thoracic anatomy at different cardiac phases. A 3D multiresolution optical flow deformable image registration algorithm was used to quantify the difference in tissue position between the end-diastolic cardiac phase and the remaining cardiac phases. To account for image noise, voxel displacements whose maximum values were less than 0.3 mm, were excluded. In addition, the blood vessels were segmented and excluded in order to eliminate registration artifacts caused by blood-flow.

RESULTS

The average cardiac-induced lung motions for displacements greater than 0.3 mm were found to be 0.86 ± 0.74 and 0.97 ± 0.93 mm in the left and right lungs, respectively. The average model residual error for the ten healthy volunteers was found to be 0.29 ± 0.08 mm in the left lung and 0.38 ± 0.14 mm in the right lung for tissue displacements greater than 0.3 mm. The relative error decreased with increasing cardiac-induced lung tissue motion. While the relative error was > 60% for submillimeter cardiac-induced lung tissue motion, the relative error decreased to < 5% for cardiac-induced lung tissue motion that exceeded 10 mm in displacement.

CONCLUSIONS

The authors' studies implied that modeling and including cardiac-induced lung motion would improve breathing motion model accuracy for tissues with cardiac-induced motion greater than 0.3 mm.

In situ determination of alveolar septal strain, stress and effective Young's modulus: an experimental/computational approach

Alveolar septa, which have often been modeled as linear elements, may distend due to inflation-induced reduction in slack or increase in tissue stretch. The distended septum supports tissue elastic and interfacial forces. An effective Young's modulus, describing the inflation-induced relative displacement of septal end points, has not been determined in situ for lack of a means of determining the forces supported by septa in situ. Here we determine such forces indirectly according to Mead, Takishima, and Leith's classic lung mechanics analysis (J Appl Physiol 28: 596-608, 1970), which demonstrates that septal connections transmit the transpulmonary pressure, PTP, from the pleural surface to interior regions. We combine experimental septal strain determination and computational stress determination, according to Mead et al., to calculate effective Young's modulus. In the isolated, perfused rat lung, we label the perfusate with fluorescence to visualize the alveolar septa. At eight PTP values around a ventilation loop between 4 and 25 cmH2O, and upon total deflation, we image the same region by confocal microscopy. Within an analysis region, we measure septal lengths. Normalizing by unstressed lengths at total deflation, we calculate septal strains for all PTP > 0 cmH2O. For the static imaging conditions, we computationally model application of PTP to the boundary of the analysis region and solve for septal stresses by least squares fit of an overdetermined system. From group septal strain and stress values, we find effective septal Young's modulus to range from 1.2 × 10(5) dyn/cm(2) at low P(TP) to 1.4 × 10(6) dyn/cm(2) at high P(TP).

Lung parenchymal mechanics

The lung parenchyma comprises a large number of thin-walled alveoli, forming an enormous surface area, which serves to maintain proper gas exchange. The alveoli are held open by the transpulmonary pressure, or prestress, which is balanced by tissues forces and alveolar surface film forces. Gas exchange efficiency is thus inextricably linked to three fundamental features of the lung: parenchymal architecture, prestress, and the mechanical properties of the parenchyma. The prestress is a key determinant of lung deformability that influences many phenomena including local ventilation, regional blood flow, tissue stiffness, smooth muscle contractility, and alveolar stability. The main pathway for stress transmission is through the extracellular matrix. Thus, the mechanical properties of the matrix play a key role both in lung function and biology. These mechanical properties in turn are determined by the constituents of the tissue, including elastin, collagen, and proteoglycans. In addition, the macroscopic mechanical properties are also influenced by the surface tension and, to some extent, the contractile state of the adherent cells. This chapter focuses on the biomechanical properties of the main constituents of the parenchyma in the presence of prestress and how these properties define normal function or change in disease. An integrated view of lung mechanics is presented and the utility of parenchymal mechanics at the bedside as well as its possible future role in lung physiology and medicine are discussed.

Complexity and emergent phenomena

Complex biological systems operate under non-equilibrium conditions and exhibit emergent properties associated with correlated spatial and temporal structures. These properties may be individually unpredictable, but tend to be governed by power-law probability distributions and/or correlation. This article reviews the concepts that are invoked in the treatment of complex systems through a wide range of respiratory-related examples. Following a brief historical overview, some of the tools to characterize structural variabilities and temporal fluctuations associated with complex systems are introduced. By invoking the concept of percolation, the notion of multiscale behavior and related modeling issues are discussed. Spatial complexity is then examined in the airway and parenchymal structures with implications for gas exchange followed by a short glimpse of complexity at the cellular and subcellular network levels. Variability and complexity in the time domain are then reviewed in relation to temporal fluctuations in airway function. Next, an attempt is given to link spatial and temporal complexities through examples of airway opening and lung tissue viscoelasticity. Specific examples of possible and more direct clinical implications are also offered through examples of optimal future treatment of fibrosis, exacerbation risk prediction in asthma, and a novel method in mechanical ventilation. Finally, the potential role of the science of complexity in the future of physiology, biology, and medicine is discussed.

Distribution of lung tissue hysteresis during free breathing

PURPOSE

To characterize and quantify free breathing lung tissue motion distributions.

METHODS

Forty seven patient data sets were acquired using a 4DCT protocol consisting of 25 ciné scans at abutting couch positions on a 16-slice scanner. The tidal volume of each scan was measured by simultaneously acquiring spirometry and an abdominal pneumatic bellows. The concept of a characteristic breath was developed to manage otherwise natural breathing pattern variations. The characteristic breath was found by first dividing the breathing traces into individual breaths, from maximum exhalation to maximum exhalation. A linear breathing drift model was assumed and the drift removed for each breath. Breaths that exceeded one standard deviation in period or amplitude were removed from further analysis. A characteristic breath was defined by normalizing each breath to a common amplitude, aligning the peak inhalation times for all of the breaths, and determining the average time at each tidal volume, keeping inhalation and exhalation separate. Breathing motion trajectories were computed using a previously published five-dimensional lung tissue trajectory model which expresses the position of internal lung tissue, X, as: X(v,f:X0)=X0+α(X0)v+β(X0)f, where X0 is the internal lung tissue position at zero tidal volume and zero airflow, the scalar values v and f are the measured tidal volume and airflow, respectively, and the vectors α and β are fitted free parameters. In order to characterize the motion patterns, the trajectory elongations were examined throughout the subject's lungs. Elongation was defined here by generating a rectangular bounding box with one side parallel to the α vector and the box oriented in the plane defined by the α and β motion vectors. Hysteresis motion was defined as the ratio of the box dimensions aligned orthogonal to and parallel to the α vector. The 15th and 85th percentile of the elongation were used to characterize tissue trajectory hysteresis.

RESULTS

The 15th and 85th percentile bounding box elongations were 0.090 ± 0.005 and 0.083 ± 0.013 in the upper left lung and 0.187 ± 0.037 and 0.203 ± 0.053, in the lower left lung. The 15th and 85th percentiles for the upper right lung were 0.092 ± 0.006 and 0.085 ± 0.013, and 0.184 ± 0.038, and 0.196 ± 0.043 in the lower right lung. Both percentiles were calculated for tidal volume displacements between 5 and 15 mm. In the left lung, the average elongations in the upper and lower lung were ζ=0.120 ± 0.064 and ζ=0.090 ± 0.055, respectively. The average elongations in the upper and lower right lung were ζ=0.107 ± 0.060 and ζ=0.082 ± 0.048, respectively. The elongation varied smoothly throughout the lungs.

CONCLUSIONS

The hysteresis motion was relatively small compared to the volume-filling motion, contributing between 8% and 20% of the overall motion. Statistically significant differences were observed in the range of hysteresis contribution for upper and lower lung regions. The characteristic breath process provided an excellent method for defining an average breath. The characteristic breath had continuous tidal volume and airflow characteristics when the breath was continuously repeated,useful for generating patterns representative of realistic motion for breathing motion studies.

Multiscale model predicts tissue-level failure from collagen fiber-level damage

Excessive tissue-level forces communicated to the microstructure and extracellular matrix of soft tissues can lead to damage and failure through poorly understood physical processes that are multiscale in nature. In this work, we propose a multiscale mechanical model for the failure of collagenous soft tissues that incorporates spatial heterogeneity in the microstructure and links the failure of discrete collagen fibers to the material response of the tissue. The model, which is based on experimental failure data derived from different collagen gel geometries, was able to predict the mechanical response and failure of type I collagen gels, and it demonstrated that a fiber-based rule (at the micrometer scale) for discrete failure can strongly shape the macroscale failure response of the gel (at the millimeter scale). The model may be a useful tool in predicting the macroscale failure conditions for soft tissues and engineered tissue analogs. In addition, the multiscale model provides a framework for the study of failure in complex fiber-based mechanical systems in general.

A multi-scale approach to airway hyperresponsiveness: from molecule to organ

Airway hyperresponsiveness (AHR), a characteristic of asthma that involves an excessive reduction in airway caliber, is a complex mechanism reflecting multiple processes that manifest over a large range of length and time scales. At one extreme, molecular interactions determine the force generated by airway smooth muscle (ASM). At the other, the spatially distributed constriction of the branching airways leads to breathing difficulties. Similarly, asthma therapies act at the molecular scale while clinical outcomes are determined by lung function. These extremes are linked by events operating over intermediate scales of length and time. Thus, AHR is an emergent phenomenon that limits our understanding of asthma and confounds the interpretation of studies that address physiological mechanisms over a limited range of scales. A solution is a modular computational model that integrates experimental and mathematical data from multiple scales. This includes, at the molecular scale, kinetics, and force production of actin-myosin contractile proteins during cross-bridge and latch-state cycling; at the cellular scale, Ca²⁺ signaling mechanisms that regulate ASM force production; at the tissue scale, forces acting between contracting ASM and opposing viscoelastic tissue that determine airway narrowing; at the organ scale, the topographic distribution of ASM contraction dynamics that determine mechanical impedance of the lung. At each scale, models are constructed with iterations between theory and experimentation to identify the parameters that link adjacent scales. This modular model establishes algorithms for modeling over a wide range of scales and provides a framework for the inclusion of other responses such as inflammation or therapeutic regimes. The goal is to develop this lung model so that it can make predictions about bronchoconstriction and identify the pathophysiologic mechanisms having the greatest impact on AHR and its therapy.

Continuum vs. spring network models of airway-parenchymal interdependence

The outward tethering forces exerted by the lung parenchyma on the airways embedded within it are potent modulators of the ability of the airway smooth muscle to shorten. Much of our understanding of these tethering forces is based on treating the parenchyma as an elastic continuum; yet, on a small enough scale, the lung parenchyma in two dimensions would seem to be more appropriately described as a discrete spring network. We therefore compared how the forces and displacements in the parenchyma surrounding a contracting airway are predicted to differ depending on whether the parenchyma is modeled as an elastic continuum or as a spring network. When the springs were arranged hexagonally to represent alveolar walls, the predicted parenchymal stresses and displacements propagated substantially farther away from the airway than when the springs were arranged in a triangular pattern or when the parenchyma was modeled as a continuum. Thus, to the extent that the parenchyma in vivo behaves as a hexagonal spring network, our results suggest that the range of interdependence forces due to airway contraction may have a greater influence than was previously thought.

Dynamic nonlinearity of lung tissue: frequency dependence and harmonic distortion

Harmonic distortion (HD) is a simple approach to analyze lung tissue nonlinear phenomena. This study aimed to characterize frequency-dependent behavior of HD at several amplitudes in lung tissue strips from healthy rats and its influence on the parameters of linear analysis. Lung strips (n = 17) were subjected to sinusoidal deformation at three different strain amplitudes (Δε) and fixed operational stress (12 hPa) among various frequencies, between 0.03 and 3 Hz. Input HD was <2% in all cases. The main findings in our study can be summarized as follows: 1) harmonic distortion of stress (HD) showed a positive frequency and amplitude dependence following a power law with frequency; 2) HD correlated significantly with the frequency response of dynamic elastance, seeming to converge to a limited range at an extrapolated point where HD=0; 3) the relationship between tissue damping (G) and HD(ω=1) (the harmonic distortion at ω=1 rad/s) was linear and accounted for a large part of the interindividual variability of G; 4) hysteresivity depended linearly on κ (the power law exponent of HD with ω); and 5) the error of the constant phase model could be corrected by taking into account the frequency dependence of harmonic distortion. We concluded that tissue elasticity and tissue damping are coupled at the level of the stress-bearing element and to the mechanisms underlying dynamic nonlinearity of lung tissue.

Dynamic nonlinearity of lung tissue: effects of strain amplitude and stress level

Lung tissue presents substantial nonlinear phenomena not accounted for by linear models; however, nonlinear approaches are less available. Our aim was to characterize the behavior of total harmonic distortion, an index of nonlinearity, in lung tissue strips under sinusoidal deformation at a single frequency as a function of strain amplitude and operational stress. To that end, lung parenchymal strips from healthy rats ( n = 6) were subjected to sinusoidal deformation (1 Hz) at different strain amplitudes (Δε = 4, 8, 12, 16, and 20%) and operating stresses (σop = 6, 8, 10, 12, 14, and 16 hPa). Additional rats ( n = 9) were intratracheally instilled with saline or bleomycin (2.5 U/kg, 3 times 1 wk apart), killed 28 days after the last instillation, and their lung tissue strips were studied at 5 and 10 hPa σop and 5% Δε. In both cases, harmonic distortion (HD%) of input (strain) and output (stress) signals were determined. In healthy strips, HD% increased linearly with Δε, stress amplitude, and minimum stress by cycle variations, but showed no significant change with σop levels. A prediction model could be determined as a function of operational stress and stress amplitude. Harmonic distortion was significantly increased in bleomycin-treated strips compared with controls and showed positive correlation with E behavior in both normal and diseased strips. We concluded that HD% can be useful as a single and simple parameter of lung tissue nonlinearity.

Ventilator-induced lung injury: the anatomical and physiological framework

Since its introduction into the management of the acute respiratory distress syndrome, mechanical ventilation has been so strongly interwoven with its side effects that it came to be considered as invariably dangerous. Over the decades, attention has shifted from gross barotrauma to volutrauma and, more recently, to atelectrauma and biotrauma. In this article, we describe the anatomical and physiologic framework in which ventilator-induced lung injury may occur. We address the concept of lung stress/strain as applied to the whole lung or specific pulmonary regions. We challenge some common beliefs, such as separately studying the dangerous effects of different tidal volumes (end inspiration) and end-expiratory positive pressures. Based on available data, we suggest that stress at rupture is only rarely reached and that high tidal volume induces ventilator-induced lung injury by augmenting the pressure heterogeneity at the interface between open and constantly closed units. We believe that ventilator-induced lung injury occurs only when a given threshold is exceeded; below this limit, mechanical ventilation is likely to be safe.

Lung tissue mechanics as an emergent phenomenon

The mechanical properties of lung parenchymal tissue are both elastic and dissipative, as well as being highly nonlinear. These properties cannot be fully understood, however, in terms of the individual constituents of the tissue. Rather, the mechanical behavior of lung tissue emerges as a macroscopic phenomenon from the interactions of its microscopic components in a way that is neither intuitive nor easily understood. In this review, we first consider the quasi-static mechanical behavior of lung tissue and discuss computational models that show how smooth nonlinear stress-strain behavior can arise through a percolation-like process in which the sequential recruitment of collagen fibers with increasing strain causes them to progressively take over the load-bearing role from elastin. We also show how the concept of percolation can be used to link the pathologic progression of parenchymal disease at the micro scale to physiological symptoms at the macro scale. We then examine the dynamic mechanical behavior of lung tissue, which invokes the notion of tissue resistance. Although usually modeled phenomenologically in terms of collections of springs and dashpots, lung tissue viscoelasticity again can be seen to reflect various types of complex dynamic interactions at the molecular level. Finally, we discuss the inevitability of why lung tissue mechanics need to be complex.

Lung parenchymal mechanics in health and disease

The mechanical properties of lung tissue are important determinants of lung physiological functions. The connective tissue is composed mainly of cells and extracellular matrix, where collagen and elastic fibers are the main determinants of lung tissue mechanical properties. These fibers have essentially different elastic properties, form a continuous network along the lungs, and are responsible for passive expiration. In the last decade, many studies analyzed the relationship between tissue composition, microstructure, and macrophysiology, showing that the lung physiological behavior reflects both the mechanical properties of tissue individual components and its complex structural organization. Different lung pathologies such as acute respiratory distress syndrome, fibrosis, inflammation, and emphysema can affect the extracellular matrix. This review focuses on the mechanical properties of lung tissue and how the stress-bearing elements of lung parenchyma can influence its behavior.

Lung stress and strain during mechanical ventilation for acute respiratory distress syndrome

RATIONALE

Lung injury caused by a ventilator results from nonphysiologic lung stress (transpulmonary pressure) and strain (inflated volume to functional residual capacity ratio).

OBJECTIVES

To determine whether plateau pressure and tidal volume are adequate surrogates for stress and strain, and to quantify the stress to strain relationship in patients and control subjects.

METHODS

Nineteen postsurgical healthy patients (group 1), 11 patients with medical diseases (group 2), 26 patients with acute lung injury (group 3), and 24 patients with acute respiratory distress syndrome (group 4) underwent a positive end-expiratory pressure (PEEP) trial (5 and 15 cm H2O) with 6, 8, 10, and 12 ml/kg tidal volume.

MEASUREMENTS AND MAIN RESULTS

Plateau airway pressure, lung and chest wall elastances, and lung stress and strain significantly increased from groups 1 to 4 and with increasing PEEP and tidal volume. Within each group, a given applied airway pressure produced largely variable stress due to the variability of the lung elastance to respiratory system elastance ratio (range, 0.33-0.95). Analogously, for the same applied tidal volume, the strain variability within subgroups was remarkable, due to the functional residual capacity variability. Therefore, low or high tidal volume, such as 6 and 12 ml/kg, respectively, could produce similar stress and strain in a remarkable fraction of patients in each subgroup. In contrast, the stress to strain ratio-that is, specific lung elastance-was similar throughout the subgroups (13.4 +/- 3.4, 12.6 +/- 3.0, 14.4 +/- 3.6, and 13.5 +/- 4.1 cm H2O for groups 1 through 4, respectively; P = 0.58) and did not change with PEEP and tidal volume.

CONCLUSIONS

Plateau pressure and tidal volume are inadequate surrogates for lung stress and strain. Clinical trial registered with www.clinicaltrials.gov (NCT 00143468).

Extracellular matrix mechanics in lung parenchymal diseases

In this review, we examine how the extracellular matrix (ECM) of the lung contributes to the overall mechanical properties of the parenchyma, and how these properties change in disease. The connective tissues of the lung are composed of cells and ECM, which includes a variety of biological macromolecules and water. The macromolecules that are most important in determining the mechanical properties of the ECM are collagen, elastin, and proteoglycans. We first discuss the various components of the ECM and how their architectural organization gives rise to the mechanical properties of the parenchyma. Next, we examine how mechanical forces can affect the physiological functioning of the lung parenchyma. Collagen plays an especially important role in determining the homeostasis and cellular responses to injury because it is the most important load-bearing component of the parenchyma. We then demonstrate how the concept of percolation can be used to link microscopic pathologic alterations in the parenchyma to clinically measurable lung function during the progression of emphysema and fibrosis. Finally, we speculate about the possibility of using targeted tissue engineering to optimize treatment of these two major lung diseases.

Mechanical and failure properties of extracellular matrix sheets as a function of structural protein composition

The goal of this study was to determine how alterations in protein composition of the extracellular matrix (ECM) affect its functional properties. To achieve this, we investigated the changes in the mechanical and failure properties of ECM sheets generated by neonatal rat aortic smooth muscle cells engineered to contain varying amounts of collagen and elastin. Samples underwent static and dynamic mechanical measurements before, during, and after 30 min of elastase digestion followed by a failure test. Microscopic imaging was used to measure thickness at two strain levels to estimate the true stress and moduli in the ECM sheets. We found that adding collagen to the ECM increased the stiffness. However, further increasing collagen content altered matrix organization with a subsequent decrease in the failure strain. We also introduced collagen-related percolation in a nonlinear elastic network model to interpret these results. Additionally, linear elastic moduli correlated with failure stress which may allow the in vivo estimation of the stress tolerance of ECM. We conclude that, in engineered replacement tissues, there is a tradeoff between improved mechanical properties and decreased extensibility, which can impact their effectiveness and how well they match the mechanical properties of native tissue.

In silico modeling of interstitial lung mechanics: implications for disease development and repair

In this perspective, we first review some of the published literature on structural modeling of the mechanical properties of the lung parenchyma. Based on a recent study, we demonstrate why mechanical dysfunction accompanying parenchymal diseases such as pulmonary fibrosis and emphysema can follow a very different course from the progression of the underlying microscopic pathophysiology itself, particularly in the early stages. The key idea is related to the concept of percolation on elastic networks where the bulk modulus of the network suddenly changes when the fibrotic stiff regions or the emphysematous holes become suddenly connected across the network. We also introduce the concept of depercolation as a basis for the rational optimization of tissue repair. Specifically, we use these network models to predict the functional improvements that a hypothetical biological or tissue engineering repair could achieve. We find that rational targeted repair can have significant benefits over generic random repair. This concept may find application in the treatment of lung fibrosis, surgical, bronchoscopic, or biological lung volume reduction, or any future alveolar regeneration or tissue engineering solution to the repair of connective tissue damage of the lung.

Alveolar expansion imaged by optical sectioning microscopy

During lung expansion, the pattern of alveolar perimeter distension is likely to be an important determinant of lung functions as, for example, surfactant secretion. However, the segmental characteristics of alveolar perimeter distension remain unknown. Here, we applied real-time confocal microscopy in the isolated, perfused rat lung to determine the micromechanics of alveolar perimeter distension. To image the alveolar perimeter, we loaded alveolar epithelial cells with a fluorescent dye that we microinjected into the alveolus. Then we viewed single alveoli in a 2-microm-thick optical section at a focal plane 20 mum deep to the pleural surface at baseline. In each alveolus, we identified five to eight segments of the perimeter. For each segment, we determined length (L(seg)) by means of image analysis. At baseline alveolar pressure (P(alv)) of 5 cmH(2)O, L(seg) averaged 46 microm. We hyperinflated the lung to P(alv) of 20 cmH(2)O and identified the same optical section as referenced against morphological landmarks. Hyperinflation increased mean L(seg) by 14%. However, segment distension was heterogeneous, even within the single alveolus. Furthermore, distension was greater in alveolar type 1 than type 2 epithelial cells. These findings indicate that alveoli expand nonuniformly, suggesting that segments that distend the most might be preferred alveolar locations for injury in conditions associated with lung overdistension.

Linking parenchymal disease progression to changes in lung mechanical function by percolation

RATIONALE

The mechanical dysfunction accompanying parenchymal diseases such as pulmonary fibrosis and emphysema may follow a different course from the progression of the underlying microscopic pathophysiology itself, particularly in the early stages. It is tempting to speculate that this may reflect the geographical nature of lung pathology. However, merely ascribing mechanical dysfunction of the parenchyma to the vagaries of lesional organization is unhelpful without some understanding of how the two are linked.

OBJECTIVES

We attempt to forge such a link through a concept known as percolation, which has been invoked to account for numerous natural processes involving transmission of events across complex networks.

METHODS

We numerically determined the bulk stiffness (corresponding to the inverse of lung compliance) of a network of springs representing the lung parenchyma. We simulated the development of fibrosis by randomly stiffening individual springs in the network, and the development of emphysema by preferentially cutting springs under the greatest tension.

MEASUREMENTS AND MAIN RESULTS

When the number of stiff springs was increased to the point that they suddenly became connected across the network, the model developed a sharp increase in its bulk modulus. Conversely, when the cut springs became sufficiently numerous, the elasticity of the network fell to zero. These two conditions represent percolation thresholds that we show are mirrored structurally in both tissue pathology and macroscopic computed tomography images of human idiopathic fibrosis and emphysema.

CONCLUSIONS

The concept of percolation may explain why the development of symptoms related to lung function and the development of parenchymal pathology often do not progress together.

Differential effects of static and cyclic stretching during elastase digestion on the mechanical properties of extracellular matrices

Enzyme activity plays an essential role in many physiological processes and diseases such as pulmonary emphysema. While the lung is constantly exposed to cyclic stretching, the effects of stretch on the mechanical properties of the extracellular matrix (ECM) during digestion have not been determined. We measured the mechanical and failure properties of elastin-rich ECM sheets loaded with static or cyclic uniaxial stretch (40% peak strain) during elastase digestion. Quasistatic stress-strain measurements were taken during 30 min of digestion. The incremental stiffness of the sheets decreased exponentially with time during digestion. However, digestion in the presence of static stretch resulted in an accelerated stiffness decrease, with a time constant that was nearly 3 x smaller (7.1 min) than during digestion alone (18.4 min). These results were supported by simulations that used a nonlinear spring network model. The reduction in stiffness was larger during static than cyclic stretch, and the latter also depended on the frequency. Stretching at 20 cycles/min decreased stiffness less than stretching at 5 cycles/min, suggesting a rate-dependent coupling between mechanical forces and enzyme activity. Furthermore, pure digestion reduced the failure stress of the sheets from 88 +/- 21 kPa in control to 29 +/- 15 kPa (P < 0.05), while static and cyclic stretch resulted in a failure stress of 7 +/- 5 kPa (P < 0.05). We conclude that not only the presence but the dynamic nature of mechanical forces have a significant impact on enzyme activity, hence the deterioration of the functional properties of the ECM during exposure to enzymes.

Modeling cell and matrix anisotropy in fibroblast populated collagen vessels

Microstructurally based models for bio-artificial tissues are needed to predict in vivo mechanical behavior and to validate assumptions for models of biologic tissues. We develop a microstructural model, based on on Zahalak et al. (2000) [Biophys 79(5):2369-2381], to describe matrix and tissue anisotropy observed in recent biaxial tests of fibroblast populated collagen vessels (FPCVs) with different cell orientations (Wagenseil et al. in Ann Biomed Eng 32(5):720-731 2004). The model includes pseudo-elastic cell behavior and pseudo-elastic, non-linear matrix behavior with recruitment of initially buckled collagen fibers. We obtained estimates of collagen matrix parameters from measurements of FPCVs treated with 2x 10(-6) M Cytochalasin D and used these estimates to determine cell parameters in FPCVs activated with 5% fetal calf serum. The estimated stiffness of individual fibroblasts was 41-1,165 kPa. Parameter estimates for both cell and matrix were influenced by the non-linearity of the biaxial test data, making it difficult to obtain unique parameter values for some experiments. Additional microstructural measurements of the collagen matrix may help to more precisely determine the relative contributions of cells and matrix.

Biomechanics of the lung parenchyma: critical roles of collagen and mechanical forces

The biomechanical properties of connective tissues play fundamental roles in how mechanical interactions of the body with its environment produce physical forces at the cellular level. It is now recognized that mechanical interactions between cells and the extracellular matrix (ECM) have major regulatory effects on cellular physiology and cell-cycle kinetics that can lead to the reorganization and remodeling of the ECM. The connective tissues are composed of cells and the ECM, which includes water and a variety of biological macromolecules. The macromolecules that are most important in determining the mechanical properties of these tissues are collagen, elastin, and proteoglycans. Among these macromolecules, the most abundant and perhaps most critical for structural integrity is collagen. In this review, we examine how mechanical forces affect the physiological functioning of the lung parenchyma, with special emphasis on the role of collagen. First, we overview the composition of the connective tissue of the lung and their complex structural organization. We then describe how mechanical properties of the parenchyma arise from its composition as well as from the architectural organization of the connective tissue. We argue that, because collagen is the most important load-bearing component of the parenchymal connective tissue, it is also critical in determining the homeostasis and cellular responses to injury. Finally, we overview the interactions between the parenchymal collagen network and cellular remodeling and speculate how mechanotransduction might contribute to disease propagation and the development of small- and large-scale heterogeneities with implications to impaired lung function in emphysema.

Mechanical interactions between collagen and proteoglycans: implications for the stability of lung tissue

Collagen and elastin are thought to dominate the elasticity of the connective tissue including lung parenchyma. The glycosaminoglycans on the proteoglycans may also play a role because osmolarity of interstitial fluid can alter the repulsive forces on the negatively charged glycosaminoglycans, allowing them to collapse or inflate, which can affect the stretching and folding pattern of the fibers. Hence, we hypothesized that the elasticity of lung tissue arises primarily from 1) the topology of the collagen-elastin network and 2) the mechanical interaction between proteoglycans and fibers. We measured the quasi-static, uniaxial stress-strain curves of lung tissue sheets in hypotonic, normal, and hypertonic solutions. We found that the stress-strain curve was sensitive to osmolarity, but this sensitivity decreased after proteoglycan digestion. Images of immunofluorescently labeled collagen networks showed that the fibers follow the alveolar walls that form a hexagonal-like structure. Despite the large heterogeneity, the aspect ratio of the hexagons at 30% uniaxial strain increased linearly with osmolarity. We developed a two-dimensional hexagonal network model of the alveolar structure incorporating the mechanical properties of the collagen-elastin fibers and their interaction with proteoglycans. The model accounted for the stress-strain curves observed under all experimental conditions. The model also predicted how aspect ratio changed with osmolarity and strain, which allowed us to estimate the Young's modulus of a single alveolar wall and a collagen fiber. We therefore identify a novel and important role for the proteoglycans: they stabilize the collagen-elastin network of connective tissues and contribute to lung elasticity and alveolar stability at low to medium lung volumes.

Elasticity of passive blood vessels: a new concept

The mechanical properties of passive blood vessels are generally thought to depend on the parallel arrangement of elastin and collagen with linear elasticity and collagen recruitment depending on vessel strain [hook-on (HO) model]. We evaluated an alternative model [serial element (SE) model] consisting of the series arrangement of an infinite number of elements, each containing elastin with a constant elastic modulus and collagen that switches stepwise from slack (zero stress) to fully rigid (infinite stiffness) on ongoing element strain. Both models were implemented with Weibull distributions for collagen recruitment strain (HO model) and collagen tightening strain (SE model). The models were tested in experiments on rat mesenteric small arteries. Strain-tension relations were obtained before and after two rounds of digestion by collagenase. Both models fitted the data prior to digestion. However, for the HO model, this required unrealistically low estimates for collagen recruitment or elastic modulus and unrealistically high estimates for distension of collagen fibers. Furthermore, the data after digestion were far better predicted by the SE model compared with the HO model. Finally, the SE model required one parameter less (collagen elastic modulus). Therefore, the SE model provides a valuable starting point for the understanding of vascular mechanics and remodeling of vessels.

An in vitro airway wall model of remodeling

Recent studies have shown that mechanical forces on airway epithelial cells can induce upregulation of genes involved in airway remodeling in diseases such as asthma. However, the relevance of these responses to airway wall remodeling is still unclear since 1). mechanotransduction is highly dependent on environment (e.g., matrix and other cell types) and 2). inflammatory mediators, which strongly affect remodeling, are also present in asthma. To assess the effects of mechanical forces on the airway wall in a relevant three-dimensional inflammatory context, we have established a tissue culture model of the human airway wall that can be induced to undergo matrix remodeling. Our model contains differentiated human bronchial epithelial cells characterized by tight junctions, cilia formation, and mucus secretion atop a collagen gel embedded with human lung fibroblasts. We found that addition of activated eosinophils and the application of 50% strain to the same system increased the epithelial thickness compared with either condition alone, suggesting that mechanical strain affects airway wall remodeling synergistically with inflammation. This integrated model more closely mimics airway wall remodeling than single-cell, conditioned media, or even two-dimensional coculture systems and is relevant for examining the importance of mechanical strain on airway wall remodeling in an inflammatory environment, which may be crucial for understanding and treating pathologies such as asthma.

Effects of collagenase and elastase on the mechanical properties of lung tissue strips

The dynamic stiffness (H), damping coefficient (G), and harmonic distortion (k(d)) characterizing tissue nonlinearity of lung parenchymal strips from guinea pigs were assessed before and after treatment with elastase or collagenase between 0.1 and 3.74 Hz. After digestion, data were obtained both at the same mean length and at the same mean force of the strip as before digestion. At the same mean length, G and H decreased by approximately 33% after elastase and by approximately 47% after collagenase treatment. At the same mean force, G and H increased by approximately 7% after elastase and by approximately 25% after collagenase treatment. The k(d) increased more after collagenase (40%) than after elastase (20%) treatment. These findings suggest that, after digestion, the fraction of intact fibers decreases, which, at the same mean length, leads to a decrease in moduli. At the same mean force, collagen fibers operate at a higher portion of their stress-strain curve, which results in an increase in moduli. Also, G and H were coupled so that hysteresivity (G/H) did not change after treatments. However, k(d) was decoupled from elasticity and was sensitive to stretching of collagen, which may be of value in detecting structural alterations in the connective tissue of the lung.