Hexagonal network model of lung parenchyma-

Published in Journal of applied physiology Skip to search form Skip to main content. Continuum vs. 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. View PDF.

The compliance C was calculated as the inverse of the estimated network bulk modulus at each Hexagonal network model of lung parenchyma of disease progression. Fratzl, P. In biology, function follows form and form follows function. Therefore, volume changes of the alveolar ducts result primarily in a deformation of the alveolar entrance rings and stretch of the axial fiber system. Statistical Analysis Statistical analyses of the modulus and nonlinearity index across different test groups were done using one- or three-way ANOVA, depending on the comparisons being made.

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Responders demonstrated smaller increases in C and CV area at advanced disease stages indicating more sustainable Avril lavinge fake nude pics and structural improvements compared with marginal-responders. The combined relative benefit index, which represented a clinical measure of quality of life, was defined as the area between the dashed curves and the threshold line solid linesuch that larger values corresponded to greater improvements following lung volume reduction. Figure 1 shows the behavior of the hexagonal Hexxgonal network model following contraction of an airway at the center for 3 different heterogeneity scenarios. It is contingent upon an appropriately thorough Doggy style indian girls, careful physical examination, lung function tests with characterisation of gas exchange at rest, complemented if necessary by stress tests 6-minute walk test, ergospirometryserological tests, an HR-CT examination and, in most cases, bronchoscopy with bronchoalveolar lavage BAL. Without the diagonal struts that form the triangular network, the hexagonal network of springs more easily undergoes shear deformation. Enjoy affordable access to over 18 million articles from more than 15, peer-reviewed journals. A recent study using endobronchial valves [ 14 ] reported that improvements in measured FEV 1 were correlated with effective collapse of the affected lobe, a finding confirmed to be enhanced by fissure completeness Hexwgonal absence of interlobar collateral ventilation [ 6 ]. We have previously shown that slices of agarose-filled lung parenchyma behave mechanically more like a triangular network than a hexagonal one Hexagonal network model of lung parenchyma et al. Bronchoscopic lung volume reduction coil treatment Hexagonal network model of lung parenchyma patients with severe heterogeneous emphysema. References 1.

Histochemistry and Cell Biology.

  • Lung volume reduction surgery LVRS and bronchoscopic lung volume reduction bLVR are palliative treatments aimed at reducing hyperinflation in advanced emphysema.
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  • Pulmonary parenchyma is a term that refers to the parts of the lungs involved in gas transfer.
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Most tissues in the body are under mechanical tension, and while enzymes mediate many cellular and extracellular processes, the effects of mechanical forces on enzyme reactions in the native extracellular matrix ECM are not fully understood.

We hypothesized that physiological levels of mechanical forces are capable of modifying the activity of collagenase, a key remodeling enzyme of the ECM.

Confocal and electron microscopy was used to determine and quantify changes in ECM structure. Generally, mechanical loading increased the effects of enzyme activity characterized by an irreversible decline in stiffness and tissue deterioration seen on both confocal and electron microscopic images. The decline in stiffness during digestion positively correlated with the increase in equivalent alveolar diameters and negatively correlated with the nonlinearity index. These results suggest that the decline in stiffness results from rupture of collagen followed by load transfer and subsequent rupture of alveolar walls.

This study may provide new understanding of the role of collagen degradation in general tissue remodeling and disease progression. Lung tissue is constantly under the influence of a static preexisting tensile stress, called prestress, due to transpulmonary pressure as well as dynamic stresses imposed by tidal breathing Suki et al.

The corresponding mechanical forces within the intact tissue influence a variety of normal cell functions including cellular signaling and tissue remodeling Ingber, The mechanical stresses are transferred through the ECM via the key load bearing components, elastin and collagen, which play essential roles in defining the mechanical properties of the lungs Suki et al. The development, maintenance and remodeling of the ECM require enzymes such as elastase and collagenase. In normal lung tissue ex vivo , the activity of elastase is enhanced by mechanical forces due to unfolding of binding sites and directly increasing the cleaving off rate of elastase Jesudason et al.

In diseases such as emphysema, mechanical forces can enhance the destruction of tissue structure by rupturing the alveolar walls which are enzymatically weakened by the progression of the disease Kononov et al.

However, rupture of an alveolar wall is not possible without collagen remodeling. Since collagen is an integral part of determining the mechanical properties of lung tissue Suki et al. Previous studies have shown that significant collagen remodeling occurs in diseases, such as emphysema Finlay et al. One such study used a transgenic mouse line with lung-specific expression of matrix metalloproteinase MMP -1 to show that emphysema could develop through an elastin-independent mechanism D'Armiento et al.

A series of studies done by the Ruberti group have demonstrated that the presence of static mechanical loading actually protects collagen from digestion by collagenase Ruberti and Hallab, ; Bhole et al. Most of these studies used wide spectrum bacterial collagenase as well as MMP Accordingly, we formulated the null hypothesis that both static and dynamic stretch on the collagen in the native ECM of the lung parenchyma protect against enzymatic digestion.

To this end, we measured the rate of decay of tissue stiffness in the presence of bacterial collagenase during various stretch patterns. The effect of stretch on tissue degradation during digestion was then examined at the micro- and ultra-structural levels using fluorescent and electron microscopy, respectively.

The results were interpreted using a network model of the lung parenchyma. Following anesthesia, a tracheotomy was performed, and a cannula was inserted into the trachea. The heart and lungs of the mice were exposed through opening of the chest, and the mice were exsanguinated. The lungs were then perfused with phosphate buffered saline PBS through the right ventricle to clear the lungs from blood.

Lung tissue strips 3—4 per lung were stored in chilled PBS and used within 4—5 h of excision. In each tissue strip, stress-strain data were obtained using a previously developed uniaxial tissue stretching system Araujo et al.

The system consists of a computer-controlled dual-mode lever arm-force transducer system model B, Aurora Scientific, Ontario, Canada and a separate bidirectional, inductive type force transducer model LC, CSM Instruments, Switzerland.

Both instruments are attached to an acrylic test stand housing a 22 mL tissue bath. The dual-mode system total length range of 10 mm, maximum force of 0. The user-defined displacement signals generated by the computer program were passed through a digital to analog converter, low-pass-filtered at 10 Hz P Filter Bank, Frequency Devices, Haverhill, MA , and sent to the lever arm. The ends of the lung tissue strips were attached to small metal plates using cyanoacrylate glue, and the plates were then attached to the lever arm and transducer arm via stainless steel wires.

The tissue sample was kept submerged throughout the remainder of the experiment. After preconditioning, the tissue was allowed to equilibrate for 5 min prior to the start of the experiment.

The reference length was the longest length at which the sample did not produce force. A laser scanning confocal microscope Olympus FV was used to image the lung tissue structure following the 1-h testing protocol. Since collagen and elastin are autofluorescent in the green spectrum — nm , no specific labeling was necessary. A nm argon laser excited this emission spectrum.

To image throughout the tissue thickness, the confocal pinhole and z -axis step size were matched with the optical objective, optimizing the optical sectioning of the lung tissue.

All tissue strips were imaged in the unstretched state. Formalin-fixed tissue strips were additionally fixed in 2. Strips were washed in PB for 3 changes of 10 min each. Tissue samples were placed in a resin to propylene oxide solution overnight, then in a resin to propylene oxide solution, again overnight.

The polymerized samples were sectioned for thin tissue samples between 90 and nm , using an ultra-microtome Leica Microsystems UltraCut UCT. Sectioned samples were collected, placed on grids, and allowed to dry overnight. A transmission electron microscope Jeol JEM was used to image the lung tissue.

Sections were observed at 80 kV accelerating voltage. Images were captured with Kodak negatives, which were developed and then scanned using a high-resolution scanner Agfa DuoScan First, the force and length recordings were converted to stress and strain by dividing force and extension with the initial cross-sectional area and the initial length of the tissue strip, respectively.

The modulus values were obtained at each time point for each test condition and normalized with the value of Y at time 0. To determine changes in lung tissue structure following digestion and stretch, differences in alveolar morphology were quantified using ImageJ by calculating the equivalent diameter and distortion index of individual alveoli.

The equivalent diameter was measured by manually outlining the alveolar walls of airspaces. An ellipse was fit to the outline and the area of the fitted ellipse was obtained. The equivalent diameter of the alveoli was calculated as the diameter of a circle having the same area. The distortion index characterizing the shape of individual alveoli was calculated as the ratio of the major and minor axes aspect ratio of the fitted ellipse.

Each group included in the analysis contained between 60 and airspaces. To better understand how stretch influences digestion, a simple network model simulation was conducted. The digested, unstretched case was simulated by decreasing k 0 and k 1 , such that first springs were randomly chosen and the k 0 and k 1 of these springs were changed to preset values to mimic the experimental data. This is to simulate how, as the collagen is degraded, the loads carried by previously intact fibers are transferred to neighboring fibers post-rupture, which leads to increased strain on these fibers, and a progressive cycle of destruction.

This may correspond to the increase in unfolding binding sites along the fibers similar to what has been reported for lung elastin Jesudason et al. Statistical analyses of the modulus and nonlinearity index across different test groups were done using one- or three-way ANOVA, depending on the comparisons being made.

Data were also tested for normality and if the normality test failed the log transformation was used before applying the statistical test or the proper non-parametric test was used. Confidence intervals for medians and variances were predicted using bootstrap method. Example stress-strain curves before and after 60 min of digestion are shown in Figure 1. Figure 1. Figure 2. Distribution of the incremental modulus Y of normal lung tissue strips.

Note the highly asymmetric nature of the distribution. The time courses of Y in the remaining groups are compared in Figure 3A. This analysis indicated the presence of strong interactions among time, stretch, and digestion.

Figure 3. B Comparison of the percent decrease in the normalized moduli from time 0 to 60 min. Each bar is statistically significantly different from the other. Figure 4. B Comparison of the percent increase in the normalized nonlinearity index from time 0 to 60 min. For the definition of the groups see the caption in Figure 3. While the effect of time did not depend on what level of frequency or amplitude was present, the effect of frequency 0. Specifically, a larger decrease was observed 1 at 1 Hz than at 0.

Figure 5. A Time course of mean and SD of the normalized modulus during 60 min with or without adding bacterial collagenase. B Comparison of the percent change in the normalized moduli from time 0 to 60 min. C The nonlinearity index for which there was a significant increase with time but there was no difference among the groups. Example images are summarized in Figure 6 and statistical analysis of the structure is shown in Figure 7.

We also examined the heterogeneity of the airspace structure by comparing the variance of equivalent diameters in Figure 7B. Interestingly, the percent drop in Y showed a strong correlation with airspace heterogeneity Figure 7C with an r 2 of 0. Figure 6. In all cases, imaging was done in the unstretched state. Figure 7.

Structure and function in digested tissue strips. A Equivalent diameters in several control and digested groups. C The percent change in Y showed a strong correlation with the variance. It can be seen that the fibers are wavy and closely packed when no enzyme and stretch was present, but they were straighter after stretch even though imaging was obtained in the unstretched condition. The fiber structure became irregular, loosely packed and damaged in the presence of enzymes.

When enzymes were applied in the presence of stretch, the structure became heterogeneous with both intact and highly damaged collagen fibers. Large regions that contained little or no collagen were often seen in the digested and stretched tissues. Figure 8. All images were taken in the unstretched state. Arrows indicate regions of collagen degradation.

A randomized study of endobronchial valves for advanced emphysema. The lung tissue was modeled as a compressible and nonlinearly elastic continuum with homogeneous and isotropic material properties Fung, ; Kowalczyk and Kleiber, ; Tawhai et al. Biophysical Journal. Numerous modeling studies have invoked the homogeneous parenchyma assumption to examine aspects of airway-parenchymal interdependence, with convincing results Bates and Lauzon, ; Gunst et al. The modified network was solved to yield a new configuration and distribution of forces, which corresponded to a later disease stage with different elastic elements at risk for failure. Formal analysis: JRM.

Hexagonal network model of lung parenchyma. Stress concentration around an atelectatic region: A finite element model

Color bar represents strain distribution of individual elements. C Changes in compliance, C for the representative network shown.

To characterize functional changes within the network at each configuration, the network compliance, C was calculated as the inverse of the 2D bulk modulus. To characterize structural changes, network heterogeneity was quantified as the coefficient of variation of individual airspace sizes, CV area. Prior to lung volume reduction, values of C and CV area increased from baseline consistent with the loss of elastic recoil and enlarged airspaces observed in emphysema Fig 1C.

In the representative network shown, both the non-specific LVRS and the region-specific bLVR yielded comparable immediate and long-term improvements in network elasticity as characterized by similar reductions and recoveries in C , respectively.

In contrast, upper network resection with LVRS was less effective in other networks as characterized by differences in reduction and recovery in C S1 Fig. Less heterogeneity in this lower region i. More heterogeneity in this region i. Representative networks for both groups are shown in the supplement S2 Fig. B Skewness of force distributions before and after lung volume reduction. A power law, equivalent to a straight line on a log-log graph, fitted the data well with exponent of Interestingly, bLVR skewed the distribution of forces to the right for all networks and reduction conditions.

This observation demonstrates that macroscopic functional changes immediately after bLVR are linked to the underlying microscopic force redistribution. Taken together, these findings suggest that the introduction of high-force elements plays a critical role in lung volume reduction efficacy and is dependent on pre-treatment structure for LVRS but not bLVR. In addition to the immediate response following lung volume reduction, we also evaluated the long-term response for both LVRS and bLVR.

Disease progression was modeled as consecutive stages of increasing network deterioration characterized by the cumulative number of broken elements at each stage. Fig 3 shows the average changes in C and CV area before and after intervention. Mean values are shown for A increases in compliance, C ; and B the coefficient of variation for airspace size. Disease progression was characterized by the cumulative number of broken elements and shown as a percentage of the total number of elements in the network, error bars represent standard deviation.

Prior to lung volume reduction, average values of C and CV area increased with worsening disease severity consistent with a softening network and expanding emphysematous regions. Comparing networks classified as either responders or marginal-responders, statistically significant differences between groups were detected for C and CV area just before intervention, suggesting that responders were slightly less elastic with more heterogeneous disease progression.

Responders demonstrated smaller increases in C and CV area at advanced disease stages indicating more sustainable functional and structural improvements compared with marginal-responders. This highlights the improved long-term treatment efficacy in networks with smaller vs. Following bLVR, no differences were detected between networks classified as either responders or marginal-responders. Instead, long-term response was related to bLVR reduction size.

Based on the long-term simulations in this computational model, we compared the predicted outcomes for LVRS and bLVR as influenced by lung compliance. We found that all treatments actually accelerated network deterioration, more than doubling the rate of increase in C prior to intervention Fig 4A.

We also calculated a combined index related to the area enclosed by the threshold and the curve defined by values of C schematic shown in Fig 5. A Lung volume reduction accelerated the rate of tissue failure as estimated by the increase in compliance, C after four steps of disease progression.

C Even greater improvements were observed for the relative benefit index, which represented a measure of quality of life. Dashed curves represent changes in compliance, C with and without lung volume reduction. The combined relative benefit index, which represented a clinical measure of quality of life, was defined as the area between the dashed curves and the threshold line solid line , such that larger values corresponded to greater improvements following lung volume reduction.

The area representing simulations without lung volume reduction open region was normalized to unity for comparison with lung volume reduction shaded region. Lung volume reduction represents the primary therapeutic strategy for advanced emphysema. LVRS is a well-established surgical treatment, but is limited by strict indications and significant post-procedural complications.

Several non-surgical bLVR approaches are on the rise providing less invasive alternatives with the potential for considerably lower post-procedural morbidity and mortality. While previous work has evaluated improvements in clinical function and survival advantage provided by these techniques, little is known about the corresponding micromechanical mechanisms responsible for improvement in survival and quality of life.

In this study, we constructed 2D elastic networks to simulate lung volume reduction with LVRS and bLVR in a force-based model of emphysema progression. Our main findings include: 1 analysis of network structure using a simple measure of disease heterogeneity prior to lung volume reduction can predict LVRS efficacy; 2 macroscopic functional improvements following bLVR correspond to microscopic changes in force heterogeneity; and 3 lung volume reduction improves aspects of the predicted survival and quality of life influenced by contributions of lung compliance, albeit while accelerating disease progression.

Mechanical forces have long been suggested to play a role in emphysema progression [ 23 ]. Previous work [ 24 ] provided early evidence demonstrating alveolar wall rupture in elastase-treated tissue slices as a direct result of local mechanical forces.

Subsequently, it was shown that increases in lung compliance paralleled changes in airspace heterogeneity associated with force-induced failure of the extracellular matrix ECM [ 25 ].

Inflammatory processes, concerted action of proteases, and ECM remodeling also likely contribute to emphysema progression [ 26 — 29 ]; however, their role has been proposed more broadly within self-propagating dynamic loops of enzymatically initiated but mechanically driven tissue destruction [ 19 ].

Previous network model simulations have demonstrated that emphysematous tissue breakdown cannot be reproduced by a purely chemical process, such that the inclusion of local forces are critical in developing observed emphysema patterns [ 18 , 19 ].

Alternative models based on uniform softening or random cutting have also been found to poorly characterize these progressive changes [ 25 ]. Thus, we consider the network model described here to provide a suitable description of emphysema progression with the capacity for studying the structure-function relations following lung volume reduction.

It is known that patients with predominately upper-lung emphysema have more favorable outcomes following LVRS [ 3 , 9 ]. In this study, greater improvements in C after LVRS were observed in those with less affected lower network regions Fig 2A as resection of the upper diseased airspaces allowed for the remaining tissue to restore function.

This is consistent with previous experimental data demonstrating that improvements after LVRS are correlated with increased ratios between upper to lower zone emphysema determined by computed tomography, CT , but are not well predicted by pre-surgical measurements of static lung compliance or elastic recoil [ 30 , 31 ].

Moreover, we found that a power law distribution could be used to characterize the distribution of forces before and after intervention S4 Fig. The tail of the distribution varied with the specific intervention and may indicate the emergence of complex network behavior [ 32 ], which would be a unique case when increased lung heterogeneity potentially contributes positively to treatment outcome. Nonetheless, these findings suggest a mechanism that may explain how functional changes evolve based on intrinsic structural differences prior to LVRS.

Motivated by the benefits observed with LVRS, however, non-surgical bronchoscopic alternatives have been the focus of recent investigations, where patient outcomes have improved as bLVR techniques have become more proficient [ 8 , 10 ]. A recent study using endobronchial valves [ 14 ] reported that improvements in measured FEV 1 were correlated with effective collapse of the affected lobe, a finding confirmed to be enhanced by fissure completeness and absence of interlobar collateral ventilation [ 6 ].

This is conceptually similar to our model predictions that bLVR reduction size is inversely related to immediate and long-term improvements in C Fig 2 and Fig 3. Comparing bLVR for multiple reduction sizes revealed that macroscopic functional improvements in C were linked to underlying microscopic changes in force heterogeneity.

Although radiographic evidence indicates near complete reduction is currently not achievable [ 8 , 12 , 15 ], our findings highlight important structure-function interactions between network reorganization after bLVR and its effect on the local mechanical environment in the lung observations which would otherwise be impossible to detect via imaging or functional studies. This unexpected relationship demonstrates that bLVR can be an effective treatment for advanced emphysema, but also suggests a mechanism by which elevated forces in close proximity to reduced areas may promote local tissue destruction.

By simulating LVRS and bLVR in parallel from the same configuration, we were able to directly contrast outcomes and disease progression after treatment. In general, lung volume reduction led to more rapid tissue failure as a result of increased mechanical forces on elastic elements.

This is consistent with clinical reports of accelerated deterioration of lung function relative to pre-surgery observed in patients following LVRS [ 33 , 34 ]. Despite elevated rates of tissue failure, LVRS and bLVR are predicted to lengthen survival and improve quality of life by restoring lung function to levels closer to healthy tissue Fig 4. The modality-specific reduction in bLVR efficacy highlighted by Ingenito et al.

Nonetheless, these computational findings support bLVR application across an even broader treatment population, as suggested by Deslee et al. This is of particular interest given the potential for substantially less invasive bronchoscopic techniques to extend treatment options to those who do not qualify for LVRS.

Changes in relative lung volumes are also correlated with treatment efficacy. Fessler et al. Our results support these findings illustrating that LVRS in heterogeneous networks and bLVR applied to affected regions represent treatments that come closest to the removal of pure RV and allow for expansion of more normal regions.

Interestingly, related studies evaluating the success of bilateral lung transplant somewhat counterintuitively observed significantly better outcomes in cases with donor lungs larger than the recipient thorax as estimated by the donor-recipient predicted TLC ratio [ 36 , 37 ].

It was proposed, however, that a decrease in lung compliance post-transplant was likely a contributing factor for survival and performance, which would agree with the benefits of lung volume reduction modeled here. The importance of these anatomic considerations also suggests the potential for coupling this computational approach with CT imaging in the future.

The non-invasiveness of such an analysis would be uniquely suited to infer patient outcomes prior to treatment and aid clinical decision-making. There are several limitations of the network model that must be considered when associating computational findings with clinical outcomes.

Narrowing and loss of terminal bronchioles are believed to increase small airway resistance in COPD patients [ 38 ], and may even precede emphysema development [ 39 ]. Hiorns et al. Although interactions at this scale are not included here, the stiffer airways would likely be associated with local parenchymal destruction.

The hexagonal network units might alternatively reflect the mechanics of secondary pulmonary lobules, approximating the coalescence of destroyed lobules and enlarged lesions characteristic of emphysema, as described by Hogg et al. Moreover, emphysema progression is modeled by breaking a specified number of elements at each stage of disease.

An alternative approach would be to define a global threshold, as investigated for ventilator-induced lung damage [ 42 ], above which elements are considered to fail. Both approaches yield similar disease patterns, but could influence the apparent rate of tissue failure differently. Nonetheless, observed inter- and intra-subject variability in vivo , along with only few data from follow-up studies, validate the general interpretations of our results presented here.

Future work expanding bLVR in a true multiscale model of emphysema in 3D [ 43 ] that incorporates airway-parenchymal interactions, inflammation, and enzyme kinetics may provide additional insights and enhance the potential for clinical application.

Despite these limitations our network model has been shown to generate disease patterns with strong correlation to those observed using CT imaging [ 18 ] by including contributions of mechanical forces that likely drive emphysema progression [ 19 ].

While these computational simulations represent a simplified view of emphysema progression, this model provides new perspective into the structure-function relations underlying the progressive nature of emphysema before and after lung volume reduction.

Immediate and long-term responses to these interventions appear to be intimately linked to changes in microscopic force heterogeneity within the lung, which could explain known structural limitations for surgical approaches and emphasize pertinent implications in disease progression for bronchoscopic approaches.

Furthermore, our findings suggest that effective bronchoscopic reduction of affected lung tissue can achieve similar if not better functional improvements, survival advantages, and quality of life benefits as currently established surgical techniques. These insights have the potential to inform more rationalized design of lung volume reduction techniques and patient-specific treatment strategies.

Networks were progressively degraded by eliminating elements carrying the highest forces and then finding the network configuration with minimal elastic energy for five sequential iterations. LVRS and bLVR were then applied to the same network configuration and the treated networks were subsequently degraded as before.

Structural and functional parameters were tracked for each network configuration to characterize changes at each stage of disease progression. Finally, predicted survival and quality of life outcomes were compared for both treatments.

The 2D network model used in this study has been described previously [ 18 — 22 ]. Briefly, elastic elements inter-connected via pin joints were allowed to rotate freely while nodes bordering the perimeter of the network were kept fixed to ensure the network was initially pre-stressed and hexagonal units, representing individual acini, were not collapsed.

Each network consisted of 6, elastic elements and 2, hexagonal cells 85x56 nodes. The minimum energy corresponding to the equilibrium configuration of the network was obtained using the equation above with a variant of the simulated annealing technique [ 44 , 45 ].

Here, the position of each node was displaced by a small amount proportional to and in the direction of the local resulting force on the node. Gravity dependence in the network was simulated by applying additional downward forces at each node with magnitude proportional to the number of dependent nodes below. This relatively weak influence represented the net effect of gravity over long time-scales proposed to enhance tissue destruction in the upper lung [ 23 ].

In the absence of this term, emphysema would be expected to progress with equal probability in any region of the network. Tissue failure was then simulated using a force-based destruction approach. Elastic elements were sorted by their corresponding force, and the top 0. Individual elements were not considered to experience fatigue behavior. The modified network was solved to yield a new configuration and distribution of forces, which corresponded to a later disease stage with different elastic elements at risk for failure.

This discretized approach generated a disease progression driven by the spatial distribution of forces while the probabilistic elimination of elements introduced a degree of stochasticity to each network, limiting the deterministic nature of each simulation. These steps were repeated for a total of five iterations simulating progressively more developed disease severity.

To simulate reduction of enlarged airspaces in bLVR, nodes encompassed by a selected perimeter, corresponding to the region to be reduced, were moved toward their geometric center of mass. Regions including a fixed border were asymmetrically reduced in size parallel to the axis of the border. Here, the equilibrium configuration was assumed to correspond to FRC, representing a static measurement of lung function.

The compliance C was calculated as the inverse of the estimated network bulk modulus at each stage of disease progression. Network structure was quantified by considering the sizes of individual airspace units. Each network configuration was converted to a binary image and the number of pixels enclosed by connected spring elements represented the individual airspace area. Overall structural heterogeneity was then assessed as the coefficient of variation of airspace sizes, CV area.

For network configurations directly before intervention, we also considered the coefficient of variation for airspaces below the line of LVRS resection.

The rate of tissue failure was estimated before and after intervention as the increase in C over four stages of disease progression. However, since network deterioration prior to treatment was typically less than this threshold a second order polynomial was fitted to values of C to estimate survival in the absence of any lung volume reduction. The relative benefit of treatment was then calculated as shown in the schematic Fig 5.

The area between the survival threshold and the compliance curve represents a composite index for quality of life, incorporating both the rate and sub-threshold duration of disease progression. Larger values of this area correspond to lower values of C over a longer period of time and hence represent better quality of life.

To compare the benefits provided by lung volume reduction, data are reported as normalized by the estimated values in the absence of any treatment. Network simulations were completed using custom-developed software, which has been utilized previously to generate and analyze networks in conjunction with other experimental studies [ 18 — 22 ].

One-way ANOVA was used to compare estimates of disease progression rate, survival, and relative benefit. Post-hoc Holm-Sidak and Tukey tests were used to determine differences between groups. The average change in C after LVRS for responder and marginal-responders were compared using a t-test. Statistical analyses were performed using SigmaPlot SigmaPlot v A Representative simulation of emphysema progression before intervention, and B comparison of lung volume reduction techniques in a marginal-responder network.

See Fig 1 for additional details on sequence of individual panels. Mead et al. All theoretical studies to date have assumed the parenchyma to be homogeneous, yet it is well known that substantial heterogeneity and anisotropy can develop in the lung parenchyma in disease Chapman et al. Indeed, even normal parenchyma is clearly inhomogeneous Adler et al.

This raises the important question as to whether our understanding of the nature of airway-parenchymal interdependence, which is currently based on the assumption of parenchymal homogeneity, might change significantly if heterogeneity is taken into account.

Accordingly, the goal of the present study was to determine if regional heterogeneities in parenchymal mechanics have any important consequences for the forces of airway-parenchymal interdependence generated by airway narrowing. We performed this investigation using heterogeneous adaptations of computational models that we have investigated previously, namely a 2-dimensional circular airway embedded in homogeneous linear elastic parenchyma Ma and Bates, ; Ma et al. We first modeled the parenchyma as a 2-dimensional network of nonlinear springs Ma and Bates, ; Ma et al.

The springs were connected to each other either in a hexagonal pattern or a triangular pattern. The hexagonal spring pattern is motivated by the idealized space-filling arrangement of alveolar walls in 2 dimensions, while the triangular spring model represents a more structurally stable structure under shear. We have previously shown that slices of agarose-filled lung parenchyma behave mechanically more like a triangular network than a hexagonal one Ma et al.

Given that the lung is not normally filled with agarose, it remains an open question as to how the parenchyma behaves in situ , so we felt it was appropriate to examine both model types in the present study. The springs in the networks were linearly elastic, but their stiffness could be specified individually to create arbitrary degrees of elastic heterogeneity. We could thus represent, for example, the kinds of variations in regional mechanical properties that might occur in pulmonary fibrosis Gonzalez and Ludwig, Accordingly, we investigated the effects of random variations in the stiffness of individual springs.

In addition, we also modeled an extreme case of fiber stiffening, such as might result from structural remodeling, by increasing the elastic moduli of springs along a track emanating radially outward from the airway wall. The spring stiffness along this line was increased from 2 to times in separate simulations. The springs were connected at their points of intersection by pin joints about which they were free to rotate with negligible friction.

At each step in the contraction process, the finite element FE method Yang, was used to determine the equilibrium configuration of the entire network. To explore scarring behavior in nonlinear parenchymal tissue, we constructed a FE model of a slice of lung tissue containing a cross-section of a terminal bronchiole Breen et al.

The lung slice was modeled as a three-dimensional mesh composed of finite elements that were spatially located to produce the desired geometry of the slice. Eight nodes defined each element and adjacent elements shared nodes. Interpolation was accomplished using cubic Hermite basis functions in each of the three coordinate directions Bradley et al. This enforced, at every node, continuity of all variables as well as of the first and second derivatives of the variables.

An airway was represented by a circular hole of diameter 0. The radius of the hole coincided with the boundary between the airway adventitia and the parenchyma, so the model did not include the airway wall itself. The lung tissue was modeled as a compressible and nonlinearly elastic continuum with homogeneous and isotropic material properties Fung, ; Kowalczyk and Kleiber, ; Tawhai et al.

The von Mises stress. The coefficients a 0. Their values are set to correlate with known elastic recoil pressures for uniform volume expansions in zero gravity Burrowes and Tawhai, ; Tawhai et al. A line of scar tissue was modeled via a fold increase in the coefficient c of the strain energy density function Eq.

We performed our simulations from a reference state defined to have zero stress and zero strain because we are interested here in the additional parenchymal forces and displacements that are created as a result of airway contraction note that these forces and displacements can simply be added to any that might already exist as a result of baseline transpulmonary pressure. A series of quasi-static displacements were enforced that decreased the airway diameter to approximately half its initial value.

Nodes on the perimeter of the airway were forced to move stepwise to decrease the airway diameter symmetrically and the derivatives were scaled to maintain circularity.

All other nodes were free to move in response with the exception of the nodes fixing the outer dimensions of the slice. At each step, the Cauchy stress, which represents the force per unit area of the deformed configuration, was calculated for every Gauss point in the FE mesh.

The von Mises stress was calculated from the principal Cauchy stresses. Points nearest the fixed boundary that might introduce edge effects were excluded.

Figure 1 shows the behavior of the hexagonal spring network model following contraction of an airway at the center for 3 different heterogeneity scenarios.

When the springs representing the parenchyma were all identical the contraction led to a radially symmetric strain field Fig. The mean force relative to a pre-contraction value of zero in the parenchyma immediately adjacent to the airway wall showed significant dependence on radial distance from the airway wall, with the radially aligned springs coming under significant tension while the circumferentially aligned springs were less tense Fig.

Close to the borders of the network, at about 6 diameters distance from the airway, spring tension fell off due to edge effects related mostly to our use of softened springs around the network border that helped to ensure numerical convergence of the model. Accordingly, the forces in the springs connected directly to the outer boundary are not plotted in the figures. Very similar results were obtained Fig. The widths of the springs in the left panels indicate stiffness. Forces are expressed in arbitrary units.

By contrast, when the springs were returned to their original equal stiffness with the exception of a single diagonal track of springs that were stiffened by fold, we found that the force along the direction of the stiffened springs was increased compared to the rest of the parenchyma by a factor of 4 to 5 Fig.

The magnitude of this concentrated force along the stiffened springs depended on how stiff these springs were compared to the remainder of the parenchymal springs.

When stiffness was increased 5, 10, 50, and fold, the force along the stiffened springs increased by roughly 1. These effects were also evident in different sized networks i. We also observed, however, that the increased force along a line of stiffened springs was sensitive to whether the springs were oriented co-linearly as opposed to simply being connected contiguously.

That is, if the springs were arranged in a more zigzag pattern then force increase did not occur because the distortion of the parenchyma merely brought the springs more into alignment rather than stretching them. Spring forces versus radial distance from the airway wall in the hexagonal spring network model when the stiffness of the springs along a continuous pathway from the airway wall Fig. A rather different picture emerged when we applied similar conditions to the triangular spring network Fig.

Now the distribution of spring force relative to a baseline force of zero as a function of radial distance from the airway was insensitive to either of the imposed stiffness heterogeneity patterns. Furthermore, while some of the springs came under significant tension next to the airway wall, some were in significant state of compression negative force. All spring forces, however, asymptoted toward zero with distance from the airway as opposed to settling on an elevated plateau as occurred with the hexagonal spring model shown in Fig.

Figure 5A shows the continuum model with a diagonal line of stiffened tissue emanating radially from the airway wall in the lower right quadrant. Figure 5B shows results from the continuum model with nonlinear material properties. The mean von Mises stress per element is shown as a function of radial distance from the center of the airway following airway contraction for both homogeneous tissue and with the diagonal scar shown in Fig.

While the elements along the line of stiffened tissue do exhibit slightly higher stresses than the other elements, both stress distributions asymptote to zero and are sufficiently similar to allow one to conclude that, similar to the triangular spring network model shown in Fig. A Finite element continuum model of lung slice with isolated airway see text for details. The dashed line locates the modeled scar tissue.

Gauss points with altered elasticity are circled in the inset. B Von Mises stress as a function of radial distance from the airway wall for the continuum model when the parenchyma is homogeneous, and when a narrow pathway of tissue having an elastic modulus fold greater than the rest of the tissue propagates away from the airway wall. Increased lung volume has long been known as perhaps the most potent bronchodilator An et al.

The most important contributions in this area, however, are almost certainly those of Lai-Fook Adler et al. Numerous modeling studies have invoked the homogeneous parenchyma assumption to examine aspects of airway-parenchymal interdependence, with convincing results Bates and Lauzon, ; Gunst et al. These studies, however, all assume the parenchyma to be uniform and isotropic, yet the airways in the lung are surrounded by tissue that may be quite heterogeneous, and which may include blood vessels and other airways in the immediate vicinity.

Indeed, the parenchymal distortion field surrounding an airway in an explanted lung slice shows marked departures from radial symmetry Adler et al. The results of the present investigation build on our previous modeling studies of airway-parenchymal interdependence in which we showed that the distribution of displacements and forces within the parenchyma surrounding a contracting airway are rather different depending on whether the parenchyma is modeled as a hexagonal network of springs, a triangular network Ma and Bates, ; Ma et al.

In all cases the parenchymal distortion is greatest next to the airway wall and decreases with radial distance Figs. However, with the hexagonal spring network the increase in parenchymal force due to contraction levels off at a finite value at several airway diameters distance from the airway wall, and continues in this manner virtually all the way to the network boundary Figs.

By contrast, force in the triangular spring network approaches zero with distance from the airway center and is already small by about 3—4 airway diameters Fig. We attribute these differences in predicted behavior to the differences in resistance to shear exhibited by the hexagonal versus the triangular spring networks Ma and Bates, Without the diagonal struts that form the triangular network, the hexagonal network of springs more easily undergoes shear deformation.

We have previously shown that an explanted lung slice embedded in agarose behaves more like the triangular network Ma et al. The present study shows substantial differences between the hexagonal versus triangular spring network models Fig.

This similarity may be due to the fact that the continuum model, by its very nature, averages out the inhomogeneities, while the triangular network is more resistant to shear. In both cases, however, our results indicate that heterogeneities make little difference to the ability of an airway to narrow against the forces of airway-parenchymal interdependence.

In the hexagonal parenchymal network, for example, the heterogeneities were produced by introducing random zero-mean variations in spring modulus. The elastic after-loads on the airway were thus comparable between the homogeneous and heterogeneous cases for a fixed amount of airway narrowing. Even with the stiffened line of springs, which increased the mean network modulus by about 2. For the triangular spring network we applied parenchymal heterogeneities in a similar fashion, but here we imposed the same contraction force for the various conditions, so the similar amount of airway narrowing that occurred in the homogeneous and heterogeneous cases was a direct reflection of the roughly equal opposing forces of interdependence.

It clearly remains an important open question as to how the air-filled lung behaves in vivo. Until that is resolved, however, we have some distinct possibilities to contemplate relative to the question of the importance of parenchymal heterogeneities. When these heterogeneities are randomly distributed on the spatial scale of an alveolar wall, the average parenchymal displacement and force as a function of distance from a contracting airway are essentially identical to the homogeneous case, regardless of which model we use to make the predictions.

This indicates that natural variations in the properties of individual alveolar walls have minimal influence on stress distribution and are not likely to cause the overall nature of airway-parenchymal interdependence to depart significantly from the classic Lai-Fook theory Lai-Fook, b ; Lai-Fook et al. Where we do see a difference, however, between model predictions and Lai-Fook theory is when the parenchymal heterogeneities are highly localized and circumferentially asymmetric Figs.

We modeled an extreme version of this situation by having a contiguous line of stiffened alveolar walls propagating radially away from the airway wall in the hexagonal and triangular spring network models Figs. In this case, the hexagonal spring network model predicts a focusing of force along the stiffened tissue Fig. It must be noted, however, that this effect only occurs to a significant degree in rather contrived circumstances, when the path of fibrotic tissue has a stiffness many fold greater than the rest of the parenchyma, and when the alveolar walls it affects are close to co-linear Figs.

The constraint that springs cannot realign if they are to experience an increase in force may also explain why the forces along lines of scar tend to increase toward the border of the network Figs. That is, near the border the spring positions are more constrained, so in order to absorb the strain due to a contracting airway they are less able to change their orientation and so must stretch and thus bear more stress.

In any case, this increase in force only occurs for rather particular configurations of stiffened springs. Furthermore, neither the triangular spring network Fig. We thus conclude that, barring exceptional circumstances, calculating the effects of airway-parenchymal interdependence on airway narrowing can be done to a useful degree of accuracy by assuming the parenchyma surrounding the airway to be homogeneous.

Furthermore, for a given mean level of parenchymal stiffness, regional variations in stiffness do not significantly alter the impact of airway-parenchymal interdependence on airway narrowing. Nevertheless, to the extent that the air-filled lung in vivo behaves like a hexagonal network of springs, we have identified a potential situation in which significant parenchymal forces caused by a contracting airway can extend much further away from the airway than is usually thought to be the case.

This mechanism could allow one contracting airway to affect the contraction of another airway located some distance away. The effect would be highly directional, of course, so probably only a single airway would be affected in this manner, but it is at least conceivable that such an effect could happen, for example, in pulmonary fibrosis where a number of normal lung units can be replaced by inextensible fibrous tissue Gonzalez and Ludwig, On the other hand, problematic airway narrowing is not usually associated with pulmonary fibrosis, perhaps because it is effectively prevented by the large airway-parenchymal interdependence forces resulting from the increased shear modulus of fibrotic tissue.

Also, as the distal lung parenchyma may often become remodeled in asthma Ludwig, , our results point to the possibility of long-range interactions between small airways during asthma attack. It remains to be seen, of course, whether these predictions play out because we remain uncertain about how real lung parenchyma behaves mechanically.

Interestingly, however, structurally determined long-range force transmission has been demonstrated in cells Blumenfeld, ; Hu et al. Our study has thus revealed some possible ways in which the nature of airway-parenchymal interdependence might differ markedly from the predictions of classic Lai-Fook theory Lai-Fook, a ; Lai-Fook et al.

These predictions, however, are based on model calculations, and therefore are subject to the limitations inherent in these models. For example, the spring network models are 2-dimensional, and by neglecting out-of-plane forces and displacements we may have missed the inclusion of important mechanical constraints that apply in a real lung.

Also, none of our models distinguished between elastic forces due to protein fibers and those due to the air-liquid interface, the latter playing a critically important role in alveolar mechanics and stability Stamenovic, ; Stamenovic and Wilson, In addition, the alveolar walls in our spring network models were joined together by friction-free pin joints, while in reality macromolecules such as glycosaminoglycans offer some limited degree of rotational resistance Cavalcante et al.

Also, our simulations were initialized at a zero stress state, whereas in vivo the baseline stress is positive. Because scar tissue is highly nonlinear in its elastic behavior, we would expect that lung inflation would rapidly stiffen a scar, which would enhance the long-range force propagation mechanism we found in the hexagonal spring model.

Published in Journal of applied physiology Skip to search form Skip to main content. Continuum vs. 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.

View PDF. Save to Library. Create Alert. Share This Paper. Figures, Tables, and Topics from this paper. Figures and Tables. Citations Publications citing this paper. Mechanical interactions between adjacent airways in the lung. Hemantha Lakshmi , Gopinathan Sudheer , Y. Vasudeva Rao. The micromechanics of lung alveoli: structure and function of surfactant and tissue components Lars Knudsen , Matthias Ochs.

A model of surfactant-induced surface tension effects on the parenchymal tethering of pulmonary airways. Hideki Fujioka , David Halpern , D. John Jabaraj , Mohamad Suhaimi Jaafar. References Publications referenced by this paper. A continuum analysis of a two-dimensional mechanical model of the lung parenchyma. TA Wilson. Self-organized patterns of airway narrowing. Tilo Winkler , Jose Gabriel Venegas. A biomechanical model of agonist-initiated contraction in the asthmatic airway Bindi S.

Brook , Samantha E. Computational assessment of airway wall stiffness in vivo in allergically inflamed mouse models of asthma. Ana Cojocaru , Charles G. Airway smooth muscle dynamics: a common pathway of airway obstruction in asthma. Steven S. An , Tony R. Complex airway behavior and paradoxical responses to bronchoprovocation.

Linking parenchymal disease progression to changes in lung mechanical function by percolation. Davis , Arnab Majumdar , Kelly J. Parenchymal tethering, airway wall stiffness, and the dynamics of bronchoconstriction. Isostaticity and controlled force transmission in the cytoskeleton: A model awaiting experimental evidence.

Raphael Blumenfeld. Yan Bai , Michael J. Related Papers. A: hexagonal spring network HSN model. B: continuum mechanics finite-element model.

Published in Journal of applied physiology Continuum vs.