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

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 =7.25e4 Pa, for the exponential form: k1=4.34e3 Pa, k2=5.92, for the polynomial form: C1=2.87e3 Pa, C3=3.83e4 Pa. The identification of the time parameter for the viscous contribution shows that it depends on the loading frequency (0.2 Hz: τ =0.257 s, 0.4 Hz: τ =0.123 s, 0.8 Hz: τ =0.050 s). Adding a viscous contribution significantly increases the accuracy of the identification.