Arterial viscoelasticity: a fractional derivative model

Abstract

Arteries are viscoelastic materials. Viscoelastic laws are fully characterized by measuring a complex modulus. Arterial mechanics can be described using stress-strain dynamic measurements applied to the particular cylindrical geometry. Most materials show an energy loss per cycle that increases steadily with frequency. By contrast, the frequency modulus response in arteries presents a frequency independence describing a plateau above a corner frequency near 4Hz. Traditional methods to fit this response include several spring and dashpot elements to model integer order differential equations in time domain. Recently, fractional derivative models proved to be efficient to describe rheological tissues, reducing the number of parameters and showing a natural power-law response. In this work a fractional derivative model with 4-parameter was selected to describe the arterial wall mechanics in-vivo. Strain and stress were measured simultaneously in an anaesthetized sheep. A fractional model was applied. The order resulted alpha=0.12, confirming the manifest elastic response of the aorta. The fractional derivative model proved to naturally mimic the elastic modulus spectrum with only 4 parameters and a reasonable small computational effort.