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

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 novel lumpedparameter equivalent circuit models of the apparent arterial compliance using a fractional-order capacitor (FOC). FOC, which generalizes capacitors and resistors, displays a fractionalorder 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 fractionalorder 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.

Human Hypertension Blood Flow Model Using Fractional Calculus

“…Bearing this in mind, recently, an alternative modeling approach of the apparent compliance was proposed in (Bahloul and Kirati, 2021 ) where fractional-order tools were investigated to represent the complex phenomena underlying the apparent arterial compliance. In (Bahloul and Kirati, 2021 ), the authors presented fractional-order models to describe the dynamic relationship between aortic blood pressure and volume, describing the apparent vascular compliance. The proposed model employs fractional-order capacitor elements to lump the complex and frequency dependence characteristics of arterial compliance.…”

“…In recent decades, fractional-order models have surfaced as potential techniques that compromise between accuracy and computational cost for large-scale problems in different fields (Bahloul and Kirati, 2021 ). In particular fractional-order differential equations have been considerably explored in modeling complex biological systems (Magin, 2006 ).…”

“…The proposed model employs fractional-order capacitor (FOC) element that combine the complex and frequency dependence characteristics of arterial compliance. The FOC modeling approach accounted for both resistive and capacitive properties allowing a reduced-order representation of the vascular compliance and stiffness (Bahloul and Kirati, 2021 ).…”

Fractional-Order Windkessel Boundary Conditions in a One-Dimensional Blood Flow Model for Fractional Flow Reserve (FFR) Estimation

“…Some examples are the model of blood flow in viscoelastic vessels [10,11] and the model of heat and mass transfer through an arterial segment, which takes into account the interaction with a magnetic field [12]. Fractional derivatives are used to obtain a more realistic prediction of pulse wave forms, which involves the development of parameter identification procedures [13,14]. The latter task has become especially relevant in recent years with the development of computer technology and increasing interest in inverse problems.…”

Parameter Sensitivity and Experimental Validation for Fractional-Order Dynamical Modeling of Neurovascular Coupling

“…For instance, the power-law behavior has been demonstrated in describing human soft tissues viscoelasticity and characterizing the elastic vascular arteries. In-vivo and in-vitro experimental studies have pointed that fractional-order calculus-based approaches are more decent to precisely represent the hemodynamic; the viscoelasticity properties of soft collagenous tissues in the vascular bed; the aortic blood flow; red blood cell (RBC) membrane mechanical properties and the heart valve cusp [16] – [19] . Consistent with the ability of fractional-order models to fit temporal dynamics, Belkhatir et al in [20] have shown that the fractional-order model can yield better fit to Blood-Oxygenation-Level-Dependant (BOLD) signals measured with fMRI when compared with the original integer-order NVC model proposed by Friston et al in [5] .…”