A distributed nonlinear model of lung tissue elasticity

Abstract

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.