Fractional-order model representations of apparent vascular compliance as an alternative in the analysis of arterial stiffness: an in-silico study

Abstract

Abstract Objective. Recent studies have demonstrated the advantages of fractional-order calculus tools for probing the viscoelastic properties of collagenous tissue, characterizing the arterial blood flow and red cell membrane mechanics, and modeling the aortic valve cusp. In this article, we present novel lumped-parameter equivalent circuit models for apparent arterial compliance using a fractional-order capacitor (FOC). FOCs, which generalize capacitors and resistors, display a fractional-order behavior that can capture both elastic and viscous properties through a power-law formulation. Approach. The proposed framework describes the dynamic relationship between the blood-pressure input and the blood volume, using linear fractional-order differential equations. Main results. The results show that the proposed models present a reasonable fit with the in-silico data of more than 4000 subjects. Additionally, strong correlations have been identified between the fractional-order parameter estimates and the central hemodynamic determinants as well as the pulse-wave velocity indexes. Significance. Therefore, the fractional-order-based paradigm for arterial compliance shows notable potential as an alternative tool in the analysis of arterial stiffness.