Modeling the influence of gravity and the mechanical properties of elastin and collagen fibers on alveolar and lung pressure-volume curves

The relationship between pressure (P) and volume (V) in the human lung has been extensively studied. However, the combined effects of gravity and the mechanical properties of elastin and collagen on alveolar and lung P–V curves during breathing are not well understood. Here, we extended a previously established thick-walled spherical model of a single alveolus with wavy collagen fibers during positive pressure inflation. First, we updated the model for negative pressure-driven inflation that allowed incorporation of a gravity-induced pleural pressure gradient to predict how the static alveolar P–V relations vary spatially throughout an upright human lung. Second, by introducing dynamic surface tension and collagen viscoelasticity, we computed the hysteresis loop of the lung P–V curve. The model was tested by comparing its predicted regional ventilation to literature data, which offered insight into the effects of microgravity on ventilation. The model has also produced novel testable predictions for future experiments about the variation of mechanical stresses in the septal walls and the contribution of collagen and elastin fibers to the P–V curve and throughout the lung. The model may help us better understand how mechanical stresses arising from breathing and pleural pressure variations affect regional cellular mechanotransduction in the lung.

Inflation instability in the lung: an analytical model of a thick-walled alveolus with wavy fibres under large deformations

Inflation of hollow elastic structures can become unstable and exhibit a runaway phenomenon if the tension in their walls does not rise rapidly enough with increasing volume. Biological systems avoid such inflation instability for reasons that remain poorly understood. This is best exemplified by the lung, which inflates over its functional volume range without instability. The goal of this study was to determine how the constituents of lung parenchyma determine tissue stresses that protect alveoli from instability-related overdistension during inflation. We present an analytical model of a thick-walled alveolus composed of wavy elastic fibres, and investigate its pressure-volume behaviour under large deformations. Using second-harmonic generation imaging, we found that collagen waviness follows a beta distribution. Using this distribution to fit human pressure-volume curves, we estimated collagen and elastin effective stiffnesses to be 1247 kPa and 18.3 kPa, respectively. Furthermore, we demonstrate that linearly elastic but wavy collagen fibres are sufficient to achieve inflation stability within the physiological pressure range if the alveolar thickness-to-radius ratio is greater than 0.05. Our model thus identifies the constraints on alveolar geometry and collagen waviness required for inflation stability and provides a multiscale link between alveolar pressure and stresses on fibres in healthy and diseased lungs.

Stabilizing breathing pattern using local mechanical vibrations: comparison of deterministic and stochastic stimulations in rodent models of apnea of prematurity

Mechanical stimulation has been shown to reduce apnea of prematurity (AOP), a major concern in preterm infants. Previous work suggested that the underlying mechanism is stochastic resonance, amplification of a subthreshold signal by stochastic stimulation. We hypothesized that the mechanism behind the reduction of apnea length may not be a solely stochastic phenomenon, and suggest that a purely deterministic, non-random mechanical stimulation could be equally as effective. Mice and rats were anesthetized, tracheostomized, and mechanically ventilated to halt spontaneous breathing. Two miniature motors controlled by a microcontroller were attached around the abdomen. Ventilation was paused, stimulations were applied, and the time to the rodent's first spontaneous breath (T) was measured. Six spectrally different signals were compared to one another and the no-stimulation control in mice. The most successful deterministic stimulation (D) at reducing apnea was then compared to a pseudo-random noise (PRN) signal of comparable amplitude and frequency. CO₂%, CO₂ stabilization time (T_s), O₂ saturation (SpO₂%), and T were also measured. D significantly reduced T compared to no stimulation for medium and high amplitudes. PRN also reduced T, without  a difference between D and PRN. Furthermore, both stimulations significantly reduced T_s with no significant differences between the respective stimulations. However, there was no effect of D or PRN on SpO₂%. The lack of differences between D and PRN led to an additional series of experiment comparing the same D to a band-limited white noise (WN) signal in young rats. Both D and WN were shown to significantly reduce T, with D showing statistical superiority in reduction of apnea. We further speculate that both deterministic and stochastic mechanical stimulations induce some form of mechanotransduction which is responsible for their efficacy, and our findings suggest that mechanical stimulation may be effective in treating AOP.

Supplementary Information

The online version contains supplementary material available at 10.1007/s13534-021-00203-x.

Percolation of collagen stress in a random network model of the alveolar wall

Fibrotic diseases are characterized by progressive and often irreversible scarring of connective tissue in various organs, leading to substantial changes in tissue mechanics largely as a result of alterations in collagen structure. This is particularly important in the lung because its bulk modulus is so critical to the volume changes that take place during breathing. Nevertheless, it remains unclear how fibrotic abnormalities in the mechanical properties of pulmonary connective tissue can be linked to the stiffening of its individual collagen fibers. To address this question, we developed a network model of randomly oriented collagen and elastin fibers to represent pulmonary alveolar wall tissue. We show that the stress–strain behavior of this model arises via the interactions of collagen and elastin fiber networks and is critically dependent on the relative fiber stiffnesses of the individual collagen and elastin fibers themselves. We also show that the progression from linear to nonlinear stress–strain behavior of the model is associated with the percolation of stress across the collagen fiber network, but that the location of the percolation threshold is influenced by the waviness of collagen fibers.

Breath Hold Facilitates Targeted Deposition of Aerosolized Droplets in a 3D Printed Bifurcating Airway Tree

The lungs have long been considered a desired route for drug delivery but, there is still a lack of strategies to rationally target delivery sites especially in the presence of heterogeneous airway disease. Furthermore, no standardized system has been proposed to rapidly test different ventilation strategies and how they alter the overall and regional deposition pattern in the airways. In this study, a 3D printed symmetric bifurcating tree model mimicking part of the human airway tree was developed that can be used to quantify the regional deposition patterns of different delivery methodologies. The model is constructed in a novel way that allows for repeated measurements of regional deposition using reusable parts. During ventilation, nebulized ~3-micron-sized fluid droplets were delivered into the model. Regional delivery, quantified by precision weighing individual airways, was highly reproducible. A successful strategy to control regional deposition was achieved by combining an inspiratory wave form with a "breath hold" pause after each inspiration. Specifically, the second generation of the tree was successfully targeted, and deposition was increased by up to four times in generation 2 when compared to a ventilation without the breath hold (p < 0.0001). Breath hold was also demonstrated to facilitate deposition into blocked regions of the model, which mimic airway closure during an asthma that receive no flow during inhalation. Additionally, visualization experiments demonstrated that in the absence of fluid flow, the deposition of 3-micron water droplets is dominated by gravity, which, to our knowledge, has not been confirmed under standard laboratory conditions.

A High-Throughput System for Cyclic Stretching of Precision-Cut Lung Slices During Acute Cigarette Smoke Extract Exposure

Rationale

Precision-cut lung slices (PCLSs) are a valuable tool in studying tissue responses to an acute exposure; however, cyclic stretching may be necessary to recapitulate physiologic, tidal breathing conditions.

Objectives

To develop a multi-well stretcher and characterize the PCLS response following acute exposure to cigarette smoke extract (CSE).

Methods

A 12-well stretching device was designed, built, and calibrated. PCLS were obtained from male Sprague-Dawley rats (N = 10) and assigned to one of three groups: 0% (unstretched), 5% peak-to-peak amplitude (low-stretch), and 5% peak-to-peak amplitude superimposed on 10% static stretch (high-stretch). Lung slices were cyclically stretched for 12 h with or without CSE in the media. Levels of Interleukin-1β (IL-1β), matrix metalloproteinase (MMP)-1 and its tissue inhibitor (TIMP1), and membrane type-MMP (MT1-MMP) were assessed via western blot from tissue homogenate.

Results

The stretcher system produced nearly identical normal Lagrangian strains (E_xx and E_yy, p > 0.999) with negligible shear strain (E_xy < 0.0005) and low intra-well variability 0.127 ± 0.073%. CSE dose response curve was well characterized by a four-parameter logistic model (R² = 0.893), yielding an IC₅₀ value of 0.018 cig/mL. Cyclic stretching for 12 h did not decrease PCLS viability. Two-way ANOVA detected a significant interaction between CSE and stretch pattern for IL-1β (p = 0.017), MMP-1, TIMP1, and MT1-MMP (p < 0.001).

Conclusion

This platform is capable of high-throughput testing of an acute exposure under tightly-regulated, cyclic stretching conditions. We conclude that the acute mechano-inflammatory response to CSE exhibits complex, stretch-dependence in the PCLS.

Tracking respiratory mechanics around natural breathing rates via variable ventilation

Measuring respiratory resistance and elastance as a function of time, tidal volume, respiratory rate, and positive end-expiratory pressure can guide mechanical ventilation. However, current measurement techniques are limited since they are assessed intermittently at non-physiological frequencies or involve specialized equipment. To this end, we introduce ZVV, a practical approach to continuously track resistance and elastance during Variable Ventilation (VV), in which frequency and tidal volume vary from breath-to-breath. ZVV segments airway pressure and flow recordings into individual breaths, calculates resistance and elastance for each breath, bins them according to frequency or tidal volume and plots the results against bin means. ZVV's feasibility was assessed clinically in five human patients with acute lung injury, experimentally in five mice ventilated before and after lavage injury, and computationally using a viscoelastic respiratory model. ZVV provided continuous measurements in both settings, while the computational study revealed <2% estimation errors. Our findings support ZVV as a feasible technique to assess respiratory mechanics under physiological conditions. Additionally, in humans, ZVV detected a decrease in resistance and elastance with time by 12.8% and 6.2%, respectively, suggesting that VV can improve lung recruitment in some patients and can therefore potentially serve both as a dual diagnostic and therapeutic tool.

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.

The effect of mechanical or electrical stimulation on apnea length in mice

Premature birth is a leading cause of infant mortality which is often attributed to irregular breathing and apnea of prematurity. A common treatment for apnea is caffeine to stimulate the brain's respiratory center. However, caffeine's long term effect on infant development is not fully comprehended. We hypothesized that noninvasive localized body stimulation regularizes breathing pattern. We investigated the impact of electrical or mechanical stimulation on breathing in mice. After the mice were ventilated for 28 s to induce apnea, mice were taken off the ventilator while receiving mechanical, electrical, or no stimulation in a randomized order. Both stimuli targeted the diaphragm area through a custom-built belt with vibrating motors or adhesive electrodes. After each apnea cycle, the time to take the first breath (T) was recorded. The electrical stimulation given at 4.5, 8.3, 16.7 V (pulse rate = 3 Hz, pulse width = 120 μs) showed no reduction in T. Electrical stimulation at pulse rates of 10 or 20 Hz (16.7 V, pulse width 260 μs) showed a detrimental effect increasing T by ~ 7% compared to control values (p = 0.005, p = 0.038 respectively). High and medium intensity mechanical stimulations significantly reduced T by 11.74 (p < 10^-13) and by 17.08% (p < 10^-8), respectively. Further reducing the amplitude of vibrations did not affect T. When the probe was attached to the ankles, only the high intensity vibrations resulted in a decrease in T (p < 10^-13). Mechanical vibrations, applied at various intensities and locations, could be used to treat irregular breathing and apnea in infants.

Blood pressure-induced physiological strain variability modulates wall structure and function in aorta rings

Vascular smooth muscle cells respond to mechanical stretch by reorganizing their cytoskeletal and contractile elements. Recently, we showed that contractile forces in rat aorta rings were maintained when the rings were exposed to 4 h of physiological variability in cycle-by-cycle strain, called variable stretch (VS), mimicking beat-to-beat blood pressure variability. Contractility, however, was reduced when the aorta was exposed to monotonous stretch (MS) with an amplitude equal to the mean peak strain of VS.

OBJECTIVE

Here we reanalyzed the data to obtain wall stiffness as well as added new histologic and inhibitor studies to test the effects of VS on the extracellular matrix.

MAIN RESULTS

The results demonstrate that while the stiffness of the aorta did not change during 4 h MS or VS, nonlinearity in mechanical behavior was slightly stronger following MS. The inhibitor studies also showed that mitochondrial energy production and cytoskeletal organization were involved in this fluctuation-driven mechanotransduction. Reorganization of β-actin in the smooth muscle layer quantified from immunohistochemically labeled images correlated with contractile forces during contraction. Histologic analysis of wall structure provided evidence of reorganization of elastin and collagen fibers following MS but less so following VS. The results suggested that the loss of muscle contraction in MS was compensated by reorganization of fiber structure leading to similar wall stiffness as in VS.

SIGNIFICANCE

We conclude that muscle tone modulated by variability in stretch plays a role in maintaining aortic wall structural and mechanical homeostasis with implications for vascular conditions characterized by a loss or an increase in blood pressure variability.

Design and nonlinear modeling of a sensitive sensor for the measurement of flow in mice

OBJECTIVE

While many studies rely on flow and pressure measurements in small animal models of respiratory disease, such measurements can however be inaccurate and difficult to obtain. Thus, the goal of this study was to design and implement an easy-to-manufacture and accurate sensor capable of monitoring flow.

APPROACH

We designed and 3D printed a flowmeter and utilized parametric (resistance and inertance) and nonparametric (polynomial and Volterra series) system identification to characterize the device. The sensor was tested in a closed system for apparent flow using the common mode rejection ratio (CMRR). The sensor properly measured tidal volumes and respiratory rates in spontaneously breathing mice. The device was used to evaluate a ventilator's ability to deliver a prescribed volume before and after lung injury.

MAIN RESULTS

The parametric and polynomial models provided a reasonable prediction of the independently measured flow (Adjusted coefficient of determination [Formula: see text]  =  0.9591 and 0.9147 respectively), but the Volterra series of the 1st, 2nd, and 3rd order with a memory of six time points provided better fits ([Formula: see text]  =  0.9775, 0.9787, and 0.9954, respectively). At and below the mouse breathing frequency (1-5 Hz), CMRR was higher than 40 dB. Following lung injury, the sensor revealed a significant drop in delivered tidal volume.

SIGNIFICANCE

We demonstrate that the application of nonparametric nonlinear Volterra series modeling in combination with 3D printing technology allows the inexpensive and rapid fabrication of an accurate flow sensor for continuously measuring small flows in various physiological conditions.

Optimization of Variable Ventilation for Physiology, Immune Response and Surfactant Enhancement in Preterm Lambs

Preterm infants often require mechanical ventilation due to lung immaturity including reduced or abnormal surfactant. Since cyclic stretch with cycle-by-cycle variability is known to augment surfactant release by epithelial cells, we hypothesized that such in vivo mechanotransduction improves surfactant maturation and hence lung physiology in preterm subjects. We thus tested whether breath-by-breath variability in tidal volume (V_T) in variable ventilation (VV) can be tuned for optimal performance in a preterm lamb model. Preterm lambs were ventilated for 3 h with conventional ventilation (CV) or two variants of VV that used a maximum V_T of 1.5 (VV1) or 2.25 (VV2) times the mean V_T. V_T was adjusted during ventilation to a permissive pCO₂ target range. Respiratory mechanics were monitored continuously using the forced oscillation technique, followed by postmortem bronchoalveolar lavage and tissue collection. Both VVs outperformed CV in blood gas parameters (pH, SaO₂, cerebral O₂ saturation). However, only VV2 lowered PaCO₂ and had a higher specific respiratory compliance than CV. VV2 also increased surfactant protein (SP)-B release compared to VV1 and stimulated its production compared to CV. The production and release of proSP-C however, was increased with CV compared to both VVs. There was more SP-A in both VVs than CV in the lung, but VV2 downregulated SP-A in the lavage, whereas SP-D significantly increased in CV in both the lavage and lung. Compared to CV, the cytokines IL-1β, and TNFα decreased with both VVs with less inflammation during VV2. Additionally, VV2 lungs showed the most homogeneous alveolar structure and least inflammatory cell infiltration assessed by histology. CV lungs exhibited over-distension mixed with collapsed and interstitial edematous regions with occasional hemorrhage. Following VV1, some lambs had normal alveolar structure while others were similar to CV. The IgG serum proteins in the lavage, a marker of leakage, were the highest in CV. An overall combined index of performance that included physiological, biochemical and histological markers was the best in VV2 followed by VV1. Thus, VV2 outperformed VV1 by enhancing SP-B metabolism resulting in open alveolar airspaces, less leakage and inflammation and hence better respiratory mechanics.