Parametric and Nonparametric Nonlinear System Identification of Lung Tissue Strip Mechanics

Abstract

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.

Biomechanics of the Aging Lung Parenchyma

“…Additionally, subtle changes in the coupling between viscous and elastic stresses appear to be a manifestation of ECM remodeling in the parenchyma [1,21,43,45,51,71,112]. The nonlinear viscoelastic stress-strain [95,123,162] or pressure-flow [106,136,140,144,163] relations carry significantly more information about the structure and composition of the parenchyma as well as the processes within the ECM than the incremental modulus around a fixed operating point. The incremental analysis is limited to obtaining the values of the moduli as a function of σ 0 or P tp while ignoring all higher order components in Eq.…”

“…5.7. Unfortunately, the full nonlinear analysis remains highly complicated and only a few studies have utilized it in the lung [94,95,136,140,162]. Nonlinear properties of the tissue can also be extracted from forced oscillatory data when large oscillatory amplitudes are employed [163].…”

A Recruitment Model of Quasi-Linear Power-Law Stress Adaptation in Lung Tissue

“…For a single Maxwell body having constant dashpot resistance (R) and spring constant (E), the decay in stress following a step increase in strain is exponential with time-constant R/E. However, when a strip of pre-conditioned lung tissue is subjected to a sudden step in strain, the logarithm of stress relative to initial stress (S), plotted against the logarithm of time (t) describes an almost perfect straight line over many decades of t. 6,15,31 In other words,…”

“…Conventional Maxwell body models also run into difficulties when they try to account for the nonlinear rheological behavior of lung parenchyma, which exhibits the curious attribute of being confined to the tissue's static stress-strain properties. 9,12,20,31 Fung called this phenomenon quasi-linear viscoelasticity, 11,12 yet its mechanistic basis remains obscure.…”

Dynamic nonlinearity of lung tissue: frequency dependence and harmonic distortion

“…The study of harmonic distortion of output and input signals of lung parenchyma strips submitted to sinusoidal deformation constitutes a simple and model-independent method to assess the degree of nonlinearity in a nondimensional way, (21,28,31,35). Furthermore, the harmonic distortion approach avoids the intrinsic complexity of other nonlinear models (17,18,20,31,34,35).Studies show that harmonic distortion (HD) can be used to determine nonlinear lung behavior as a function of strain amplitude and operational stress (14, 21, 33). However, no studies have been performed to determine the effects of frequency on harmonic distortion of lung tissue submitted to sinusoidal input.…”