Three-Element Fractional-Order Viscoelastic Arterial Windkessel Model

Abstract

Arterial hemodynamic assessment has always been essential for clinical Cardiovascular System (CVS) diagnosis. Using Windkessel (WK) lumped parametric model as non-invasive measurement tool provides the potential of achieving a very convenient, computational inexpensive and accurate prediction of the arterial parameters. Many versions of WK models have been proposed and extensively studied, over the last century. In general, they can be classified into two categories: elastic and viscoelastic models. Recently, several studies have discussed the potential of describing the arterial wall viscoelasticity using fractional order models, reducing the number of parameters and exposing a natural response. Hence, a key missing item in the arterial Windkessel modeling is a fractional-order analog component that can provide a reliable, realistic and reduced representation of the fractional viscoelasticity behavior. In this paper, we present, for the first time, a three-element fractional-order viscoelastic Windkessel model. The proposed model incorporates a fractional-order capacitor that substitutes the ideal capacitor of standard three-elements WK model. The latter non-ideal element combines both resistive and capacitive properties which displays viscoelastic behavior of the arterial vessel. The contribution of both properties is controlled by the fractional differentiation order α enabling an accurate and reliable physiological description.