Key result
Fractional-order Windkessel models successfully captured the real dynamics of the aortic input impedance modulus and monitored changes across various arterial physiological states better than classical models.
Why the study?
To develop a fractional order generalization of the classical Windkessel arterial model to describe aortic input impedance as an assessment of left ventricular afterload.
Fractional-order Windkessel models provide a more accurate mathematical representation of arterial viscoelasticity and left ventricular afterload compared to classical integer-order models.
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.
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Bahloul et al. (2019) studied Arterial hemodynamics (n=3,325). Fractional-order Windkessel models (FWK2 and FWK3) vs. Classical Windkessel models (WK2 and WK3) was evaluated on Aortic input impedance modulus representation. Fractional-order Windkessel models successfully captured the real dynamics of the aortic input impedance modulus and monitored changes across various arterial physiological states better than classical models.
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