Fractional-order Modeling of the Arterial Compliance: An Alternative Surrogate Measure of the Arterial Stiffness

TL;DR

This paper introduces a fractional-order circuit model for arterial compliance that captures elastic and viscous properties, showing strong correlation with hemodynamic measures and promising as an alternative measure of arterial stiffness.

Contribution

It presents a novel fractional-order capacitor-based model for arterial compliance, providing a new approach to assess arterial stiffness using fractional calculus.

Findings

Model fits well with in-silico data from over 4,000 subjects.

Strong correlations between fractional-order parameters and hemodynamic indices.

Potential of fractional-order models as alternative tools for arterial stiffness analysis.

Abstract

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 a novel lumped-parameter equivalent circuit models of the apparent arterial compliance using a fractional-order capacitor (FOC). FOC, which generalizes capacitors and resistors, displays a fractional-order behavior that can capture both elastic and viscous properties through a power-law formulation. The proposed framework describes the dynamic relationship between the blood pressure input and blood volume, using linear fractional-order differential equations. The results show that the proposed models present reasonable fit performance with in-silico data of more than 4,000 subjects. Additionally, strong correlations have been identified between the fractional-order parameter estimates and the central hemodynamic determinants as well as pulse wave velocity indexes. Therefore, fractional-order based paradigm of arterial compliance shows prominent potential as an alternative tool in the analysis of arterial stiffness.