title: Assessing composition and structure of soft biphasic media from Kelvin-Voigt fractional derivative model parameters.
abstract: Kelvin-Voigt fractional derivative (KVFD) model parameters have been used to describe viscoelastic properties of soft tissues. However, translating model parameters into a concise set of intrinsic mechanical properties related to tissue composition and structure remains challenging. This paper begins by exploring these relationships using a biphasic emulsion materials with known composition. Mechanical properties are measured by analyzing data from two indentation techniques - ramp-stress relaxation and load-unload hysteresis tests. Material composition is predictably correlated with viscoelastic model parameters. Model parameters estimated from the tests reveal that elastic modulusE0closely approximates the shear modulus for pure gelatin. Fractional-order parameterαand time constantτvary monotonically with the volume fraction of the material's fluid component.αcharacterizes medium fluidity and the rate of energy dissipation, andτis a viscous time constant. Numerical simulations suggest that the viscous coefficientηis proportional to the energy lost during quasi-static force-displacement cycles,EA. The slope ofEAversusηis determined byαand the applied indentation ramp timeTr. Experimental measurements from phantom and ex vivo liver data show close agreement with theoretical predictions of theη-EArelation. The relative error is less than 20% for emulsions 22% for liver. We find that KVFD model parameters form a concise features space for biphasic medium characterization that described time-varying mechanical properties.
authors.affiliation: Key Laboratory of Biomedical Information Engineering, Ministry of Education, School of Life Science and Technology, Xi'an JiaoTong University, Xianning West Road No.28, Xi'an, Shaanxi, 710049, P. R. China; Department of Bioengineering and Beckman Institute for Advanced Science and Technology, University of Illinois at Urbana-Champaign, Urbana IL, 61801, USA.
authors.forename: Hong Mei
authors.initials: HM
authors.lastname: Zhang
authors.affiliation: Department of Bioengineering and Beckman Institute for Advanced Science and Technology, University of Illinois at Urbana-Champaign, Urbana IL, 61801, USA.
authors.forename: Yue
authors.initials: Y
authors.lastname: Wang
authors.affiliation: Department of Physiology and Biomedical Engineering, Mayo Clinic College of Medicine, Rochester, MN, USA.
authors.forename: Mostafa
authors.initials: M
authors.lastname: Fatemi
authors.affiliation: Department of Bioengineering and Beckman Institute for Advanced Science and Technology, University of Illinois at Urbana-Champaign, Urbana IL, 61801, USA.
authors.forename: Michael F
authors.initials: MF
authors.lastname: Insana
keywords: Ex vivo liver; KVFD; gelatin emulsions; indentation; viscoelastic modeling