Assessing composition and structure of soft biphasic media from Kelvin-Voigt fractional derivative model parameters

Hongmei Zhang, Yue Wang, Mostafa Fatemi, Michael F. Insana

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


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 modulus E 0 closely approximates the shear modulus for pure gelatin. Fractional-order parameter α and time constant τ vary monotonically with the volume fraction of the material's fluid component. α characterizes medium fluidity and the rate of energy dissipation, and τ is a viscous time constant. Numerical simulations suggest that the viscous coefficient η is proportional to the energy lost during quasi-static force-displacement cycles, E A. The slope of E A versus η is determined by α and the applied indentation ramp time T r. Experimental measurements from phantom and ex vivo liver data show close agreement with theoretical predictions of the relation. 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.

Original languageEnglish (US)
Article number035703
JournalMeasurement Science and Technology
Issue number3
StatePublished - Jan 17 2017

ASJC Scopus subject areas

  • Instrumentation
  • Engineering (miscellaneous)
  • Applied Mathematics


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