Arterial Viscoelastic Model using Lumped Parameter Circuit With Fractional-Order Capacitor

Cardiovascular diseases are deemed to be the underlying source of mortality globally. Modeling the systemic arterial system is of a vital importance in the diagnosis and assessment of cardiac pathophysiology. In this work, we explore the fractional viscoelastic properties of the arterial blood vessel, and present a fractional-order lumped parameter model. We refer to this model as arterial fractional order visco-elastic (AFV) model. A novel feature of this characterization is that the ideal analog parameter displaying the arterial compliance in the well-known windkessel model, has been replaced by a fractional order element (Fractional Capacitor). It displays the complex and frequency dependent total arterial compliance by combining both resistive and capacitive properties that exhibit the fractional viscoelastic behavior of the vessel wall. The contribution of both characteristics is controlled by a fractional differentiation order parameter (a) enabling an accurate and real physiological description. The proposed model offers a pioneer way for the better interpretation of the viscoelastic effect on the arterial hemodynamic. In addition, it can be investigated as a reliable computer-based simulation platform for cardiac pathophysiology diagnosis and treatment.