Fractional-order Modeling of the Complex and Frequency-dependent Arterial Compliance: In Human and Animal Validation

Recently, experimental and theoretical studies have recognized the power of fractional calculus to perceive viscoelastic blood vessel structure and bio-mechanical properties. This work presents five fractional-order model representations to describe the dynamic relationship between the aortic blood pressure input and blood volume. Each configuration incorporates a fractional-order capacitor element (FOC) to lump the apparent arterial compliance's complex and frequency dependence properties. FOC combines both resistive and capacitive attributes within a single component, which can be controlled through the fractional differentiation order factor, alpha. Besides, the equivalent capacitance of FOC is by its very nature frequency-dependent, compassing the complex properties using only a few parameters. The proposed representations have been compared with generalized integer-order models of arterial compliance. Both model's structures have been applied and validated using different aortic pressure and flow rate data acquired from various species such as humans, pigs, and dogs. The results have shown that the fractional-order framework is able to 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 as well as the models' calibration were assessed by evaluating a variance-based global sensitivity analysis. The results show that this new paradigm confers a prominent potential to be adopted in clinical practice and basic cardiovascular mechanics research.