Fractional-order Approach to Modeling and Characterizing the Complex and Frequency-dependent Apparent Arterial Compliance: In Human and Animal Validation

Abstract

Recently, experimental and theoretical studies have revealed the potential of fractional calculus to represent viscoelastic blood vessel and arterial biomechanical properties. This paper presents five fractional-order models to describe the dynamic relationship between aortic blood pressure and volume, representing the apparent vascular compliance. The proposed model employs fractional-order capacitor element (FOC) to lump the complex and frequency dependence characteristics of arterial compliance. FOC combines both resistive and capacitive properties, which the fractional differentiation order, alpha, can control. The proposed representations have been compared with generalized integer-order models of arterial compliance. All structures have been validated using different aortic pressure and flow rate waveforms collected from various human and animal species such as pigs and dogs. The results demonstrate that the fractional-order scheme can reconstruct the overall dynamic of the complex and frequency-dependent apparent compliance dynamic and reduce the complexity. The physiological relevance of the proposed models' parameters was assessed by evaluating the variance-based global sensitivity analysis. Moreover, the simplest fractional-order representation has been embed in a global arterial lumped parameter representation to develop a novel fractional-order modified arterial Windkessel. The introduced arterial model has been validated by applying real human and animal hemodynamic data and shows an accurate reconstruction of the proximal blood pressure. The novel proposed paradigm confers a potential to be adopted in clinical practice and basic cardiovascular mechanics research.