Human Hypertension Blood Flow Model Using Fractional Calculus

Mohamed A Bahloul; Yasser Aboelkassem; Taous-Meriem Laleg-Kirati

doi:10.3389/fphys.2022.838593

Human Hypertension Blood Flow Model Using Fractional Calculus

Front Physiol. 2022 Mar 22:13:838593. doi: 10.3389/fphys.2022.838593. eCollection 2022.

Authors

Mohamed A Bahloul¹, Yasser Aboelkassem^{2

3}, Taous-Meriem Laleg-Kirati^{1

4}

Affiliations

¹ Computer, Electrical, and Mathematical Sciences, and Engineering Division (CEMSE), King Abdullah University of Science and Technology (KAUST), Thuwal, Saudi Arabia.
² College of Innovation and Technology, University of Michigan, Flint, MI, United States.
³ Michigan Institute for Data Science, University of Michigan, Ann Arbor, MI, United States.
⁴ National Institute for Research in Digital Science and Technology (INRIA), Paris, France.

Abstract

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.

Keywords: Windkessel model; blood flow; fractional calculus; hypertension; vascular compliance.