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FRACTIONAL CALCULUS APPLIED TO MODEL ARTERIAL VISCOELASTICITY

2008; National University of the South; Volume: 38; Issue: 2 Linguagem: Inglês

1851-8796

Damián Craiem, Francisco J. Rojo, J. M. Atienza, Gustavo V. Guinea, Ricardo L. Armentano,

Rheology and Fluid Dynamics Studies

Arterial viscoelasticity can be de- scribed using stress-relaxation experiments. To fit these curves, models with springs and dashpots, based on differential equations, were widely studied. However, uniaxial tests in arteries show particular shapes with an initial steep decay and a slow asymp- totic relaxation. Recently, fractional order deriva- tives were used to conceive a new component called spring-pot that interpolates between pure elastic and viscous behaviors. In this work we modified a stan- dard linear solid model replacing a dashpot with a spring-pot of order α. We tested the fractional model in human arterial segments. Results showed an accu- rate relaxation response during 1-hour with least squares errors below 1%. Fractional orders α were 0.2-0.4, justifying the extra parameter. Moreover, the adapted parameters allowed us to predict fre- quency responses that were similar to reported Complex Elastic Moduli in arteries. Our results in- dicate that fractional models should be considered as real alternatives to model arterial viscoelasticity.