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

We investigated the contributions of the connective tissue fiber network and interstitial cells to parenchymal mechanics in a surfactant-free system. In eight strips of uniform dimension from guinea pig lung, we assessed the storage (G') and loss (G") moduli by using pseudo-random length oscillations containing a specially designed set of seven frequencies from 0.07 to 2.4 Hz at baseline, during methacholine (MCh) challenge, and after death of the interstitial cells. Measurements were made at mean forces of 0.5 and 1 g and strain amplitudes of 5, 10, and 15% and were repeated 12 h later in the same, but nonviable samples. The results were interpreted using a linear viscoelastic model incorporating both tissue damping (G) and stiffness (H). The G' and G" increased linearly with the logarithm of frequency, and both G and H showed negative strain amplitude and positive mean force dependence. After MCh challenge, the G' and G" spectra were elevated uniformly, and G and H increased by < 15%. Tissue stiffness, strain amplitude, and mean force dependence were virtually identical in the viable and nonviable samples. The G and hence energy dissipation were approximately 10% smaller in the nonviable samples due to absence of actin-myosin cross-bridge cycling. We conclude that the connective tissue network may also dominate parenchymal mechanics in the intact lung, which can be influenced by the tone or contraction of interstitial cells.

During a bronchial challenge, much of the observed response of lung tissues is an artifactual consequence of inhomogeneous airway constriction. Inhomogeneities, in the sense of time constant inequalities, are an inherently linear phenomenon. Conversely, if lung tissues respond to a bronchoagonist, they become more nonlinear. On the basis of these distinct responses, we present an approach to separate real tissue changes from airway inhomogeneities. We developed a lung model that includes airway inhomogeneities in the form of a continuous distribution of airway resistances and nonlinear viscoelastic tissues. Because time domain data are dominated by nonlinearities, whereas frequency domain data are most sensitive to inhomogeneities, we apply a combined time-frequency domain identification scheme. This model was tested with simulated data from a morphometrically based airway model mimicking gross peripheral airway inhomogeneities and shown capable of recovering all tissue parameters to within 15% error. Application to our previously measured data suggests that in dogs during histamine infusion 1) the distribution of airway resistances increases widely and 2) lung tissues do respond but less so than previously reported. This approach, then, is unique in its ability to differentiate between airway and tissue responses to an agonist from a single broadband measurement made at the airway opening.

Lung parenchyma is a soft biological material composed of many interacting elements such as the interstitial cells, extracellular collagen-elastin fiber network, and proteoglycan ground substance. The mechanical behavior of this delicate structure is complex showing several mild but distinct types of nonlinearities and a fractal-like long memory stress relaxation characterized by a power-law function. To characterize tissue nonlinearity in the presence of such long memory, we investigated the robustness and predictive ability of several nonlinear system identification techniques on stress-strain data obtained from lung tissue strips with various input wave forms. We found that in general, for a mildly nonlinear system with long memory, a nonparametric nonlinear system identification in the frequency domain is preferred over time-domain techniques. More importantly, if a suitable parametric nonlinear model is available that captures the long memory of the system with only a few parameters, high predictive ability with substantially increased robustness can be achieved. The results provide evidence that the first-order kernel of the stress-strain relationship is consistent with a fractal-type long memory stress relaxation and the nonlinearity can be described as a Wiener-type nonlinear structure for displacements mimicking tidal breathing.

We present a combined theoretical and numerical procedure for sensitivity analyses of lung mechanics models that are nonlinear in both state variables and parameters. We apply the analyses to a recently proposed nonlinear lung model which incorporates a wide range of potential nonlinear identification conditions including nonlinear viscoelastic tissues, airway inhomogeneities via a parallel airway resistance distribution function, and a nonlinear block-structure paradigm. Additionally, we examine a system identification procedure which fits time- and frequency-domain data simultaneously. Model nonlinearities motivate sensitivity analyses involving numerical approximation of sensitivity coefficients. Examination of the normalized sensitivity coefficients provides direct insight on the relative importance of each model parameter, and hence the respective mechanism. More formal quantification of parameter uniqueness requires approximation of the paired and multidimensional parameter confidence regions. Combined with parameter estimation, we use the sensitivity analyses to justify tissue nonlinearities in modeling of lung mechanics for healthy and airway constricted conditions, and to justify both airway inhomogeneities and tissue nonlinearities during bronchoconstriction. The tools in this paper are general and can be applied to a wide class of nonlinear models.