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In this paper, a new fractional order generalization of the classicalWindkessel arterial model is developed to describe the aortic input impedanceas an assessment of the left ventricular after-load. The proposed models embedsfractional-order capacitor to describe the total arterial compliance. In thispaper, we report our investigations on fractional calculus tools anddemonstrate that fractional-order impedance can be used to determine thevascular properties and studying its dynamic effects. We conceived twofractional-order lumped parametric models: the fractional-order two-elementWindkessel model and the fractional-order three-element Windkessel model. Wecompared these models to the classical Windkessel one using in-silico ascendingaortic blood pressure and flow database of 3325 virtual subjects. Resultsshowed that the proposed fractional-order models overcame the limitations ofthe standard arterial Windkessel model and captured very well the real dynamicof the aortic input impedance modulus. We also demonstrated that the proposedmodels could monitor the changes in the aortic input impedance for variousarterial physiological states. Therefore, our models provide a new tool for"hemodynamic inverse problem" solving and offer a new, innovative way to betterunderstand the viscoelastic effect, in terms of resistive behavior of thearterial motions.

Fractional Order Models of Arterial Windkessel as an Alternative in the Analysis of the Left Ventricular Afterload