Assessment of Fractional-Order Arterial Windkessel as a Model of Aortic Input Impedance

A Description of the Isothermal Ageing Creep Process in Polymethyl Methacrylate Using Fractional Differential Models

Fractional differential viscoelastic models can describe complex material behaviours and fit experimental data well; however, the physical significance of model parameters is difficult to express. In this study, the fractional differential Maxwell, Kelvin, and Zener models were used to fit the short-term creep compliance curves of polymethyl methacrylate at different ageing times. The model fits were in good agreement with the experimental data. As the ageing time increased, the fractional differential Zener model showed a relative increase in the modulus parameter of the spring and a relative decrease in the modulus parameter reflecting the viscosity of the spring-pot, which indicated that physical ageing made the material more elastic. The relaxation time of the material increased, which indicated that the physical ageing reduced the free volume of the material, hindered the movement of molecules/segments, and increased the time required for the material to reach equilibrium. The fractional order of the model decreased, which reflected the phenomenon that physical ageing reduced the creep compliance of the material. Using the relaxation time as the time scale, the creep curves at different ageing times under the same stress level could be superimposed, naturally presenting the time-ageing time equivalence principle.

Fractional-Order Modeling of Arterial Compliance in Vascular Aging: A Computational Biomechanical Approach for Investigating Cardiovascular Dynamics

Goal: The goal of this study is to investigate the application of fractional-order calculus in modeling arterial compliance in human vascular aging. Methods: A novel fractional-order modified arterial Windkessel model that incorporates a fractional-order capacitor (FOC) element is proposed to capture the complex and frequency-dependent properties of arterial compliance. The model's performance is evaluated by verifying it using data collected from three different human subjects, with a specific focus on aortic pressure and flow rates. Results: The results show that the FOC model accurately captures the dynamics of arterial compliance, providing a flexible means to estimate central blood pressure distribution and arterial stiffness. Conclusions: This study demonstrates the potential of fractional-order calculus in advancing the modeling and characterization of arterial compliance in human vascular aging. The proposed FOC model can improve our understanding of the physiological changes in arterial compliance associated with aging and help to identify potential interventions for age-related cardiovascular diseases.

Human Hypertension Blood Flow Model Using Fractional Calculus

The blood flow dynamics in human arteries with hypertension disease is modeled using fractional calculus. The mathematical model is constructed using five-element lumped parameter arterial Windkessel representation. Fractional-order capacitors are used to represent the elastic properties of both proximal large arteries and distal small arteries measured from the heart aortic root. The proposed fractional model offers high flexibility in characterizing the arterial complex tree network. The results illustrate the validity of the new model and the physiological interpretability of the fractional differentiation order through a set of validation using human hypertensive patients. In addition, the results show that the fractional-order modeling approach yield a great potential to improve the understanding of the structural and functional changes in the large and small arteries due to hypertension disease.

Towards Characterization of the Complex and Frequency-dependent Arterial Compliance based on Fractional-order Capacitor

Arterial compliance is a vital determinant of the ventriculo-arterial coupling dynamic. Its variation is detrimental to cardiovascular functions and associated with heart diseases. Accordingly, assessment and measurement of arterial compliance are essential in the diagnosis and treatment of chronic arterial insufficiency. Recently, experimental and theoretical studies have recognized the power of fractional calculus to perceive viscoelastic blood vessel structure and biomechanical properties. This paper 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 unified component, which can be controlled through the fractional differentiation order factor, α. Besides, the equivalent capacitance of FOC is by its very nature frequency-dependent, compassing the complex properties using only a few numbers of parameters. The proposed representations have been compared with generalized integer-order models of arterial compliance. Both models 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 accurately reconstruct the dynamic of the complex and frequency-dependent apparent compliance dynamic and reduce the complexity. It seems that this new paradigm confers a prominent potential to be adopted in clinical practice and basic cardiovascular mechanics research.

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

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 thein-silicodata 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.

Fractional-Order SEIQRDP Model for Simulating the Dynamics of COVID-19 Epidemic

Goal: Coronavirus disease (COVID-19) is a contagious disease caused by a newly discovered coronavirus, initially identified in the mainland of China, late December 2019. COVID-19 has been confirmed as a higher infectious disease that can spread quickly in a community population depending on the number of susceptible and infected cases and also depending on their movement in the community. Since January 2020, COVID-19 has reached out to many countries worldwide, and the number of daily cases remains to increase rapidly. Method: Several mathematical and statistical models have been developed to understand, track, and forecast the trend of the virus spread. Susceptible-Exposed-Infected-Quarantined-Recovered-Death-Insusceptible (SEIQRDP) model is one of the most promising epidemiological models that has been suggested for estimating the transmissibility of the COVID-19. In the present study, we propose a fractional-order SEIQRDP model to analyze the COVID-19 pandemic. In the recent decade, it has proven that many aspects in many domains can be described very successfully using fractional order differential equations. Accordingly, the Fractional-order paradigm offers a flexible, appropriate, and reliable framework for pandemic growth characterization. In fact, due to its non-locality properties, a fractional-order operator takes into consideration the variables' memory effect, and hence, it takes into account the sub-diffusion process of confirmed and recovered cases. Results-The validation of the studied fractional-order model using real COVID-19 data for different regions in China, Italy, and France show the potential of the proposed paradigm in predicting and understanding the pandemic dynamic. Conclusions: Fractional-order epidemiological models might play an important role in understanding and predicting the spread of the COVID-19, also providing relevant guidelines for controlling the pandemic.