  In this paper, a new fractional order generalization of the classical
Windkessel arterial model is developed to describe the aortic input impedance
as an assessment of the left ventricular after-load. The proposed models embeds
fractional-order capacitor to describe the total arterial compliance. In this
paper, we report our investigations on fractional calculus tools and
demonstrate that fractional-order impedance can be used to determine the
vascular properties and studying its dynamic effects. We conceived two
fractional-order lumped parametric models: the fractional-order two-element
Windkessel model and the fractional-order three-element Windkessel model. We
compared these models to the classical Windkessel one using in-silico ascending
aortic blood pressure and flow database of 3325 virtual subjects. Results
showed that the proposed fractional-order models overcame the limitations of
the standard arterial Windkessel model and captured very well the real dynamic
of the aortic input impedance modulus. We also demonstrated that the proposed
models could monitor the changes in the aortic input impedance for various
arterial physiological states. Therefore, our models provide a new tool for
"hemodynamic inverse problem" solving and offer a new, innovative way to better
understand the viscoelastic effect, in terms of resistive behavior of the
arterial motions.
