Reactance and elastance as measures of small airways response to bronchodilator in asthma

Bronchodilation alters both respiratory system resistance (Rrs) and reactance (Xrs) in asthma, but how changes in Rrs and Xrs compare, and respond differently in health and asthma, in reflecting the contributions from the large and small airways has not been assessed. We assessed reversibility using spirometry and oscillometry in healthy and asthma subjects. Using a multibranch airway-tree model with the mechanics of upper airway shunt, we compared the effects of airway dilation and small airways recruitment to explain the changes in Rrs and Xrs. Bronchodilator decreased Rrs by 23.0 (19.0)% in 18 asthma subjects and by 13.5 (19.5)% in 18 healthy subjects. Estimated respiratory system elastance (Ers) decreased by 23.2 (21.4)% in asthma, with no significant decrease in healthy subjects. With the use of the model, airway recruitment of 15% across a generation of the small airways could explain the changes in Ers in asthma with no recruitment in healthy subjects. In asthma, recruitment accounted for 40% of the changes in Rrs, with the remaining explained by airway dilation of 6.8% attributable largely to the central airways. Interestingly, the same dilation magnitude explained the changes in Rrs in healthy subjects. Shunt only affected Rrs of the model. Ers was unaltered in health and unaffected by shunt in both groups. In asthma, Ers changed comparably to Rrs and could be attributed to small airways, while the change in Rrs was split between large and small airways. This implies that in asthma Ers sensed through Xrs may be a more effective measure of small airways obstruction and recruitment than Rrs.NEW & NOTEWORTHY This is the first study to quantify to relative contributions of small and large airways to bronchodilator response in healthy subjects and patients with asthma. The response of the central airways to bronchodilator was similar in magnitude in both study groups, whereas the response of the small airways was significant among patients with asthma. These results suggest that low-frequency reactance and derived elastance are both sensitive measures of small airway function in asthma.

Effects of airway tree asymmetry on the emergence and spatial persistence of ventilation defects

Asymmetry and heterogeneity in the branching of the human bronchial tree are well documented, but their effects on bronchoconstriction and ventilation distribution in asthma are unclear. In a series of seminal studies, Venegas et al. have shown that bronchoconstriction may lead to self-organized patterns of patchy ventilation in a computational model that could explain areas of poor ventilation [ventilation defects (VDefs)] observed in positron emission tomography images during induced bronchoconstriction. To investigate effects of anatomic asymmetry on the emergence of VDefs we used the symmetric tree computational model that Venegas and Winkler developed using different trees, including an anatomic human airway tree provided by M. Tawhai (University of Auckland), a symmetric tree, and three trees with intermediate asymmetry (Venegas JG, Winkler T, Musch G, Vidal Melo MF, Layfield D, Tgavalekos N, Fischman AJ, Callahan RJ, Bellani G, Harris RS. Nature 434: 777-782, 2005 and Winkler T, Venegas JG. J Appl Physiol 103: 655-663, 2007). Ventilation patterns, lung resistance (RL), lung elastance (EL), and the entropy of the ventilation distribution were compared at different levels of airway smooth muscle activation. We found VDefs emerging in both symmetric and asymmetric trees, but VDef locations were largely persistent in asymmetric trees, and bronchoconstriction reached steady state sooner than in a symmetric tree. Interestingly, bronchoconstriction in the asymmetric tree resulted in lower RL (∼%50) and greater EL (∼%25). We found that VDefs were universally caused by airway instability, but asymmetry in airway branching led to local triggers for the self-organized patchiness in ventilation and resulted in persistent locations of VDefs. These findings help to explain the emergence and the persistence in location of VDefs found in imaging studies.

Airway resistance variability and response to bronchodilator in children with asthma

Variability of airway function is a feature of asthma, spanning timescales from months to seconds. Short-term variation in airway resistance (R(rs)) is elevated in asthma and is thought to be due to increased variation in the contractile activation of airway smooth muscle. If true, then variation in R(rs) should decrease in response to bronchodilators, but this has not been investigated. Using the forced oscillation technique, R(rs) and the variation in R(rs) from 4-34 Hz were measured in 39 children with well-controlled mild-to-moderate asthma and 31 healthy controls (7-13 yrs) before and after an inhaled bronchodilator (200 microg salbutamol) or placebo. In agreement with other findings, baseline R(rs) at all frequencies and the sd of R(rs) (R(rs) sd) below 14 Hz were found to be elevated in asthma while neither forced expiratory volume in one second nor the mean forced expiratory flow between 25 and 75% of forced vital capacity were different compared with controls. The present authors found that R(rs) sd changed the most of any measurement in asthma, and this was the only measurement that changed significantly more in children with asthma following bronchodilator administration. The present results show that like airway narrowing, short-term airway variability of resistance may be a characteristic feature of asthma that may be useful for monitoring response to therapy.

Scaling the microrheology of living cells

We report a scaling law that governs both the elastic and frictional properties of a wide variety of living cell types, over a wide range of time scales and under a variety of biological interventions. This scaling identifies these cells as soft glassy materials existing close to a glass transition, and implies that cytoskeletal proteins may regulate cell mechanical properties mainly by modulating the effective noise temperature of the matrix. The practical implications are that the effective noise temperature is an easily quantified measure of the ability of the cytoskeleton to deform, flow, and reorganize.

Measurement of cell microrheology by magnetic twisting cytometry with frequency domain demodulation

Magnetic twisting cytometry (MTC) (Wang N, Butler JP, and Ingber DE, Science 260: 1124-1127, 1993) is a useful technique for probing cell micromechanics. The technique is based on twisting ligand-coated magnetic microbeads bound to membrane receptors and measuring the resulting bead rotation with a magnetometer. Owing to the low signal-to-noise ratio, however, the magnetic signal must be modulated, which is accomplished by spinning the sample at approximately 10 Hz. Present demodulation approaches limit the MTC range to frequencies <0.5 Hz. We propose a novel demodulation algorithm to expand the frequency range of MTC measurements to higher frequencies. The algorithm is based on coherent demodulation in the frequency domain, and its frequency range is limited only by the dynamic response of the magnetometer. Using the new algorithm, we measured the complex modulus of elasticity (G*) of cultured human bronchial epithelial cells (BEAS-2B) from 0.03 to 16 Hz. Cells were cultured in supplemented RPMI medium, and ferromagnetic beads (approximately 5 microm) coated with an RGD peptide were bound to the cell membrane. Both the storage (G', real part of G*) and loss (G", imaginary part of G*) moduli increased with frequency as omega(alpha) (2 pi x frequency) with alpha approximately equal to 1/4. The ratio G"/G' was approximately 0.5 and varied little with frequency. Thus the cells exhibited a predominantly elastic behavior with a weak power law of frequency and a nearly constant proportion of elastic vs. frictional stresses, implying that the mechanical behavior conformed to the so-called structural damping (or constant-phase) law (Maksym GN, Fabry B, Butler JP, Navajas D, Tschumperlin DJ, LaPorte JD, and Fredberg JJ, J Appl Physiol 89: 1619-1632, 2000). We conclude that frequency domain demodulation dramatically increases the frequency range that can be probed with MTC and reveals that the mechanics of these cells conforms to constant-phase behavior over a range of frequencies approaching three decades.

Homeokinesis and short-term variability of human airway caliber

We hypothesized that short-term variation in airway caliber could be quantified by frequency distributions of respiratory impedance (Zrs) measured at high frequency. We measured Zrs at 6 Hz by forced oscillations during quiet breathing for 15 min in 10 seated asthmatic patients and 6 normal subjects in upright and supine positions before and after methacholine (MCh). We plotted frequency distributions of Zrs and calculated means, skewness, kurtosis, and significance of differences between normal and log-normal frequency distributions. The data were close to, but usually significantly different from, a log-normal frequency distribution. Mean lnZrs in upright and supine positions was significantly less in normal subjects than in asthmatic patients, but not after MCh and MCh in the supine position. The lnZrs SD (a measure of variation), in the upright position and after MCh was significantly less in normal subjects than in asthmatic patients, but not in normal subjects in the supine position and after MCh in the supine position. We conclude that 1) the configuration of the normal tracheobronchial tree is continuously changing and that this change is exaggerated in asthma, 2) in normal lungs, control of airway caliber is homeokinetic, maintaining variation within acceptable limits, 3) normal airway smooth muscle (ASM) when activated and unloaded closely mimics asthmatic ASM, 4) in asthma, generalized airway narrowing results primarily from ASM activation, whereas ASM unloading by increasing shortening velocity allows faster caliber fluctuations, 5) activation moves ASM farther from thermodynamic equilibrium, and 6) asthma may be a low-entropy disease exhibiting not only generalized airway narrowing but also an increased appearance of statistically unlikely airway configurations.

Selected contribution: time course and heterogeneity of contractile responses in cultured human airway smooth muscle cells

We measured the time course and heterogeneity of responses to contractile and relaxing agonists in individual human airway smooth muscle (HASM) cells in culture. To this end, we developed a microrheometer based on magnetic twisting cytometry adapted with a novel optical detection system. Ferromagnetic beads (4.5 microm) coated with Arg-Gly-Asp peptide were bound to integrins on the cell surface. The beads were twisted in a sinusoidally varying magnetic field at 0.75 Hz. Oscillatory bead displacements were recorded using a phase-synchronized video camera. The storage modulus (cell stiffness; G'), loss modulus (friction; G"), and hysteresivity (eta; ratio of G" to G') could be determined with a time resolution of 1.3 s. Within 5 s after addition of histamine (100 microM), G' increased by 2.2-fold, G" increased by 3.0-fold, and eta increased transiently from 0.27 to 0.34. By 20 s, eta decreased to 0.25, whereas G' and G" remained above baseline. Comparable results were obtained with bradykinin (1 microM). These changes in G', G", and eta measured in cells were similar to but smaller than those reported for intact muscle strips. When we ablated baseline tone by adding the relaxing agonist dibutyryl cAMP (1 mM), G' decreased within 5 min by 3.3-fold. With relaxing and contracting agonists, G' could be manipulated through a contractile range of 7.3-fold. Cell populations exhibited a log-normal distribution of baseline stiffness (geometric SD = 2.8) and a heterogeneous response to both contractile and relaxing agonists, partly attributable to variability of baseline tone between cells. The total contractile range of the cells (from maximally relaxed to maximally stimulated), however, was independent of baseline stiffness. We conclude that HASM cells in culture exhibit a clear, although heterogeneous, response to contractile and relaxing agonists and express the essential mechanical features characteristic of the contractile response observed at the tissue level.

Mechanical properties of cultured human airway smooth muscle cells from 0.05 to 0.4 Hz

We investigated the rheological properties of living human airway smooth muscle cells in culture and monitored the changes in rheological properties induced by exogenous stimuli. We oscillated small magnetic microbeads bound specifically to integrin receptors and computed the storage modulus (G') and loss modulus (G") from the applied torque and the resulting rotational motion of the beads as determined from their remanent magnetic field. Under baseline conditions, G' increased weakly with frequency, whereas G" was independent of the frequency. The cell was predominantly elastic, with the ratio of G" to G' (defined as eta) being approximately 0. 35 at all frequencies. G' and G" increased together after contractile activation and decreased together after deactivation, whereas eta remained unaltered in each case. Thus elastic and dissipative stresses were coupled during changes in contractile activation. G' and G" decreased with disruption of the actin fibers by cytochalasin D, but eta increased. These results imply that the mechanisms for frictional energy loss and elastic energy storage in the living cell are coupled and reside within the cytoskeleton.

Role of ERK MAP kinases in responses of cultured human airway smooth muscle cells to IL-1beta

We have previously reported that interleukin (IL)-1beta causes beta-adrenergic hyporesponsiveness in cultured human airway smooth muscle cells by increasing cyclooxygenase-2 (COX-2) expression and prostanoid formation. The purpose of this study was to determine whether extracellular signal-regulated kinases (ERKs) are involved in these events. Levels of phosphorylated ERK (p42 and p44) increased 8.3- and 13-fold, respectively, 15 min after treatment with IL-1beta (20 ng/ml) alone. Pretreating cells with the mitogen-activated protein kinase kinase inhibitor PD-98059 or U-126 (2 h before IL-1beta treatment) decreased ERK phosphorylation. IL-1beta (20 ng/ml for 22 h) alone caused a marked induction of COX-2 and increased basal PGE(2) release 28-fold (P < 0.001). PD-98059 (100 microM) and U-126 (10 microM) each decreased COX-2 expression when administered before IL-1beta treatment. In control cells, PD-98059 and U-126 had no effect on basal or arachidonic acid (AA; 10 microM)-stimulated PGE(2) release, but both inhibitors caused a significant decrease in bradykinin (BK; 1 microM)-stimulated PGE(2) release, consistent with a role for ERK in the activation of phospholipase A(2) by BK. In IL-1beta-treated cells, prior administration of PD-98059 caused 81, 92 and 40% decreases in basal and BK- and AA-stimulated PGE(2) release, respectively (P < 0.01), whereas administration of PD-98059 20 h after IL-1beta resulted in only 38 and 43% decreases in basal and BK-stimulated PGE(2) release, respectively (P < 0.02) and had no effect on AA-stimulated PGE(2) release. IL-1beta attenuated isoproterenol-induced decreases in human airway smooth muscle stiffness as measured by magnetic twisting cytometry, and PD-98059 or U-126 abolished this effect in a concentration-dependent manner. These results are consistent with the hypothesis that ERKs are involved early in the signal transduction pathway through which IL-1beta induces PGE(2) synthesis and beta-adrenergic hyporesponsiveness and that ERKs act by inducing COX-2 and activating phospholipase A(2).

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

We have developed a model of forces developed in lung tissue in which the stress-bearing units are heterogeneous. Each element of the fiber network is composed of an idealized elastin and collagen element in parallel. Elastin is represented by linear springs and collagen by stiff strings that extend without resistance until taut. The model can quantitatively account for the nonlinear shape of the length-tension curve of lung tissue strips when the knee lengths of the collagen fibers are distributed according to an inverse power law. The novel feature of this model is that as macroscopic strain increases the load is carried by progressively fewer elements with progressively higher forces, and preferential pathways of force transmission emerge within the matrix. The topology of these self-organizing pathways of force transmission takes the rough appearance of cracks, but, unlike real cracks, they represent the locus of force concentration rather than force release.

Nonparametric block-structured modeling of lung tissue strip mechanics

Very large amplitude pseudorandom uniaxial perturbations containing frequencies between 0.125 and 12.5 Hz were applied to five dog lung tissue strips. Three different nonlinear block-structured models in nonparametric form were fit to the data. These models consisted of (1) a static nonlinear block followed by a dynamic linear block (Hammerstein model); (2) the same blocks in reverse order (Wiener model); and (3) the blocks in parallel (parallel model). Both the Hammerstein and Wiener models performed well for a given input perturbation, each accounting for greater than 99% of the measured stress signal variance. However, the Wiener and parallel model parameters showed some dependence on the strain amplitude and the mean stress. In contrast, a single Hammerstein model accounted for the data at all strain amplitudes and operating stresses. A Hammerstein model featuring a fifth-order polynomial static nonlinearity and a linear impulse response function of 1 s duration accounted for the most output variance (99.84%+/-0.13%, mean+/-standard deviations for perturbations of 50% strain at 1.5 kPa stress). The static nonlinear behavior of the Hammerstein model also matched the quasistatic stress-strain behavior obtained at the same strain amplitude and operating stress. These results show that the static nonlinear behavior of the dog lung tissue strip is separable from its linear dynamic behavior.

Nonparametric block-structured modeling of rat lung mechanics

The quasistatic and dynamic pressure volume characteristics of the lungs were measured in five anesthetized, paralyzed open-chest rats. Psuedo-random volume perturbations over a frequency range of 0.25 to 25 Hz and having peak-peak amplitudes of 1 to 4 ml were applied after the lungs were allowed to expire against 0.2, 0.4, 0.6, and 0.8 kPa positive end-expiratory pressure (PEEP). The lung mechanics were partitioned in two ways: a linear dynamic block followed by a static nonlinearity (Wiener model) and a static nonlinearity ahead of a linear dynamic block (Hammerstein model). It was found that a Hammerstein model featuring a third-order polynomial static nonlinearity and a linear impulse response function of 1-sec duration accounted for the greatest amount of the output variance (98.8 +/- 0.6%, mean +/- SD from perturbations of 4 ml amplitude and PEEP = 0.8 kPa). The static nonlinear behavior matched the measured quasistatic pressure volume behavior obtained at the same amplitude and at the same level of PEEP, provided that all direct current gain of the model was located within the static nonlinearity. Under these conditions, the linear resistance was inversely dependent on the PEEP, whereas little PEEP or amplitude dependence of the linear compartment elastance was observed. Thus, of the two block-structured models tested, the Hammerstein model accounted better for the large amplitude nonlinear mechanical behavior. However, neither model could account for the dependence of the linear block resistance on PEEP.

A distributed nonlinear model of lung tissue elasticity

We present a theory relating the static stress-strain properties of lung tissue strips to the stress-bearing constituents, collagen and elastin. The fiber pair is modeled as a Hookean spring (elastin) in parallel with a nonlinear string element (collagen), which extends to a maximum stop length. Based on a series of fiber pairs, we develop both analytical and numerical models with distributed constituent properties that account for nonlinear tissue elasticity. The models were fit to measured stretched stress-strain curves of five uniaxially stretched tissue strips, each from a different dog lung. We found that the distributions of stop length and spring stiffness follow inverse power laws, and we hypothesize that this results from the complex fractal-like structure of the constituent fiber matrices in lung tissue. We applied the models to representative pressure-volume (PV) curves from patients with normal, emphysematous, and fibrotic lungs. The PV curves were fit to the equation V = A--Bexp(-KP), where V is volume, P is transpulmonary pressure, and A, B, and K are constants. Our models lead to a possible mechanistic explanation of the shape factor K in terms of the structural organization of collagen and elastin fibers.

Dynamic viscoelastic nonlinearity of lung parenchymal tissue

To investigate the contribution of nonlinear tissue viscoelasticity to the dynamic behavior of lung, time and frequency responses of isolated parenchymal strips of degassed dog lungs were investigated. The strips were subjected to loading and unloading stretch steps for 60 s and to sinusoidal oscillations (0.03-3 Hz) of different stretch amplitudes (delta lambda = 0.05, 0.1, and 0.2) and at different operating stresses (T(o) = 0.5, 1, and 2 kPa). Elastance (E) increased linearly with the logarithm of frequency (approximately 10% per frequency decade), and resistance (R) decreased hyperbolically with frequency. Both E and R varied little with delta lambda but they increased proportionally with T(o). Hysteresivity (eta = R x 2 pi x frequency/E) ranged from 0.07 to 0.10. In agreement with the frequency response, the magnitude of the unit step response increased with T(o) and was higher when loading than when unloading, and the stress relaxation ratio (approximately 0.10) did not vary greatly with T(o) or with delta lambda. The time and frequency behavior of the strips were interpreted in terms of the quasilinear viscoelastic model of Navajas et al. (J. Appl. Physiol. 73:2681-2692, 1992). The model explains most of the dependencies of step and oscillatory responses on the measurement conditions, in particular the proportional dependence of E and R on T(o). According to the model, about two-thirds of energy dissipated during oscillation arises from tissue viscoelasticity. The remaining dissipated energy could be accounted for by plasticity. Thus the effect of nonlinear elasticity on the dynamic behavior of lung tissue can be empirically described by a simple quasilinear model characterized by only two parameters.

Lung tissue rheology and 1/f noise

The mechanical properties of lung tissue are important contributors to both the elastic and dissipative properties of the entire organ at normal breathing frequencies. A number of detailed studies have shown that the stress adaptation in the tissue of the lung following a step change in volume is very accurately described by the function t-k, for some small positive constant k. We applied step increases in length to lung parenchymal strips and found the ensuing stress recovery to be extremely accurately described by t-k over almost 3 decades of time, despite the quasi-static stress-length characteristics of the strips being highly nonlinear. The corresponding complex impedance of lung tissue was found to have a magnitude that varied inversely with frequency. We note that this is highly reminiscent of a phenomenon known as 1/f noise, which has been shown to occur ubiquitously throughout the natural world. 1/f noise has been postulated to be a reflection of the complexity of the system that produces it, something like a central limit theorem for dynamic systems. We have therefore developed the hypothesis that the t-k nature of lung tissue stress adaptation follows from the fact that lung tissue itself is composed of innumerable components that interact in an extremely rich and varied manner. Thus, although the constant k is no doubt determined by the particular constituents of the tissue, we postulate that the actual functional form of the stress adaptation is not.

Temporal dynamics of pulmonary response to intravenous histamine in dogs: effects of dose and lung volume

We measured tracheal pressure (Ptr) and tracheal flow (V) in open-chest anesthetized paralyzed dogs. The lungs were maintained at a fixed volume (initial positive end-expiratory pressure 0.5 kPa) for 80 s while small-amplitude oscillations in V at 1 and 6 Hz were applied simultaneously at the tracheal opening. A bolus of histamine was given intravenously at the start of the oscillation period. The time course of lung elastic recoil pressure (Pel) was obtained by passing a running average over Ptr to smooth out its oscillations. The oscillations themselves were separated into their 1- and 6-Hz components, as were those in V. By fitting models to the 1- and 6-Hz components of Ptr and V by recursive least squares, we obtained time courses of lung resistance at 6 Hz (RL6), dynamic lung elastance at 1 Hz (EL1), and the difference between dynamic lung resistance at 1 and 6 Hz (RL1-RL6). In four dogs we studied the effects of histamine doses of 0.05, 1.0, and 20 mg. We found that Pel increased quickly and plateaued, RL6 continued to increase throughout the oscillation period, and EL1 exhibited features of both Pel and RL6. Furthermore, the ratio of RL1-RL6 to EL1 was qualitatively similar in time course to Pel. We explain these varied time courses in terms of the development of regional ventilation inhomogeneity throughout the lung as the reaction to histamine develops. In four dogs we also studied the effects of reducing the initial positive end-expiratory pressure by 0.25 kPa and found that the changes in RL6, EL1, and RL1-RL6 were greatly magnified, presumably because of the reduced forces of parenchymal interdependence.