Assessment of Fractional-Order Arterial Windkessel as a Model of Aortic Input Impedance
Mohamed A. Bahloul, Taous‐Meriem Laleg‐Kirati
Abstract
<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Goal:</i> Fractional-order Windkessel model is proposed to describe the aortic input impedance. Compared with the conventional arterial Windkessel, the main advantage of the proposed model is the consideration of the viscoelastic nature of the arterial wall using the fractional-order capacitor (FOC). <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Methods:</i> The proposed model, along with the standard two-element Windkessel, three-element Windkessel, and the viscoelastic Windkessel models, are assessed and compared using in-silico data. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Results:</i> The results show that the fractional-order model fits better the moduli of the aortic input impedance and fairly approximates the phase angle. In addition, by its very nature, the pseudo-capacitance of FOC makes the proposed model's dynamic compliance complex and frequency-dependent. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Conclusions:</i> The analysis of the proposed fractional-order model indicates that fractional-order impedance yields a powerful tool for a flexible characterization of the arterial hemodynamics.