Hypo-elastic model for lung parenchyma

Abstract

A simple, isotropic, elastic constitutive model for the spongy tissue in lung is formulated from the theory of hypo-elasticity. The model is shown to exhibit a pressure dependent behavior that has been interpreted in the literature as indicating extensional anisotropy. In contrast, we show that this behavior arises naturally from an analysis of isotropic hypo-elastic invariants and is a result of non-linearity, not anisotropy. The response of the model is determined analytically for several boundary value problems used for material characterization. These responses give insight into both the material behavior as well as admissible bounds on parameters. The model predictions are compared with published experimental data for dog lung.

Viscoelastic Model for Lung Parenchyma for Multi-Scale Modeling of Respiratory System, Phase II: Dodecahedral Micro-Model

“…In the first annual report for this project [19], the authors derived a hypo-elastic theory for parenchyma, whose findings are published in [20]. The resulting model is characterized by four material parameters: the two Lamé constants, and , and their hypo-elastic analogs,˛andˇ, which are the so- called Fung constants.…”

“…The Poisson's ratio applicable to this BVP is very different from the one that arises from the simple extension of a uniform rod, which is given by Q D C˛ =4. C / [20,Eq. 35], where is the true stress, and D =2.…”

“…(20) allows the three, independent, line elements of Eq. (81) to be written in their deformed state as …”

“…Three, elastic, tangent responses have been established by applying this experimental protocol to our hypo-elastic material model for parenchyma [19,20].…”

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AbstractIn the first year of this contractual effort a hypo-elastic constitutive model was developed and shown to have great potential in modeling the elastic response of parenchyma [19,20]. This model resides at the macroscopic level of the continuum.

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