Modelling lung tissue theology
A model was developed to account for the static elastic behaviour of the lung tissue strip in terms of distributions of collagen and elastin fibers. Distributions of collagen fiber lengths and elastin fiber stiffnesses were determined by fitting the model to data from dog lung tissue strips. These distributions followed 1/f power-laws for more than 95% of the data. Computer simulations of two dimensional tissue strip models with 1/f distributions of collagen fiber lengths also predicted realistic stress-strain curves. The simulations illustrated the gradual development of geometric and stress heterogeneity throughout the tissue as the collagen fibers were recruited during stretch. This model suggests a mechanistic basis for the shape of the pressure-volume curve of whole lung. It also indicates how this curve may be affected by changes in tissue collagen and elastin similar to the changes occurring in the diseases of pulmonary emphysema and fibrosis. Nonparametric block-structured nonlinear models for describing both the static and dynamic stress-strain behaviour of the lung were applied to dog lung tissue strips and to whole rat lungs in vivo. Both the Wiener and Hammerstein models accounted for more than 99% of the tissue strip data, although the Hammerstein model was more consistently accurate across a range of perturbation amplitudes and operating stresses. Plastic dissipation of energy within the lung tissue strip was estimated at less than 20% of the total dissipation during slow sinusoidal cycling. The Hammerstein model was also the best of those investigated for describing the rat lung data in vivo, although there were dependencies of the model parameters on perturbation amplitude and operating point that indicate that a more complicated model is required for the whole lung. Finally, construction of a fiber recruitment model for the dynamic mechanical behaviour of lung tissue strips was attempted. However accurate reproduction of measured behaviour was not achieved, indicating that lung tissue dynamics arise from processes independent of fiber recruitment and may originate from the ensemble behaviour of its many constituents interacting as a complex dynamic system.
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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. © 1999 Biomedical Engineering Society.
PAC99: 8719Rr, 8710+e
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