Numerical identification method for the non-linear viscoelastic compressible behavior of soft tissue using uniaxial tensile tests and image registration – Application to rat lung parenchyma

Abstract

This paper presents an improved identification method of the constitutive properties of lung parenchyma. We aim to determine the non-linear viscoelastic behavior of lung parenchyma with a particular focus on the compressible properties - i.e. the ability to change volume. Uniaxial tensile tests are performed on living precision-cut rat lung slices. Image registration is used to compute the displacement field at the surface of the sample. The constitutive model consists of a hyperelastic potential split into volumetric and isochoric contributions and a viscous contribution. This allows for the description of the experimentally observed hysteresis loop. The identification is performed numerically: each test is simulated using the realistic geometry of the sample; the difference between the measured and computed displacements is minimized with an optimization algorithm. We compare several hyperelastic potentials and we can determine the most suitable law for rat lung parenchyma. An exponential potential or a polynomial potential with a first order term and a third or higher order term give similarly satisfactory results. The identified parameters are: for the volumetric contribution: κ=7.25e4Pa, for the exponential form: k1=4.34e3Pa, k2=5.92, for the polynomial form: C1=2.87e3Pa, C3=3.83e4Pa. The identification of the time parameter for the viscous contribution shows that it depends on the loading frequency (0.2Hz: τ=0.257s, 0.4Hz: τ=0.123s, 0.8Hz: τ=0.050s). Adding a viscous contribution significantly increases the accuracy of the identification.

Differential Regulation of Lung Endothelial Permeability <b><i>in Vitro</i></b> and <b><i>in Situ</i></b>

“…However, at this stiffness the response to thrombin is weak [129] and reversible [130]. The estimates of the stiffness of normal lungs range from 0.5 kPa as determined by atomic force microscopy [131] to 5 kPa based on uniaxial tension tests or model-based calculations [132,133,134]. However, none of these estimates refers to the stiffness of pulmonary vessels, which remains unknown.…”

Isotropic incompressible hyperelastic models for modelling the mechanical behaviour of biological tissues: a review

“…The Yeoh model was applied successfully for the characterisations of human breast tissue [85], porcine muscular tissue [67], rat lung parenchyma [5,93], porcine and rat brain [52,53], and porcine liver [62]. Zaeimdar [122] applied this model together with the Mooney-Rivlin and the Neo-Hookean models through compression of eight animal tissues (chicken breast, cow fat, cow muscle, veal kidney, veal liver, pig fat, pig muscle, sheep brain) and found that the Yeoh model is the best one in capturing nonlinearity of these tissues.…”

“…The effect of compressibility must be included in the model elucidation in order to provide an accurate description of this tissue behaviour. The most recent results of modelling rat lung parenchyma could be found in [5,93]. Rausch et al [93] combined and recombined established strain energy functions, compared the best fits of the tested strain energy functions, and found the optimal combination, which describes lung parenchyma tissue in the best way.…”

“…Rausch et al [93] combined and recombined established strain energy functions, compared the best fits of the tested strain energy functions, and found the optimal combination, which describes lung parenchyma tissue in the best way. Bel-Brunon et al [5] considered in their study not only the compressibility but also the viscous contribution and determined the most suitable constitutive law for rat lung parenchyma. Thus, not pure hyperelastic models, but different kinds of combinations of the strain energy functions with compressibility and viscosity contributions could describe lung tissue behaviour adequately.…”

“…The assumption of isotropy, but not the incompressibility, for lung tissue is confirmed by [102,108]. A constitutive model for describing the material behaviour of such an isotropic compressible material should consist of a hyperelastic potential split into volumetric contribution, considering compressibility of the material and isochoric contribution, neglecting effects of compressibility [5,93]. The isochoric contribution can be modelled as an incompressible material, and here and after we mean only the isochoric contribution when we talk about lung tissue.…”