These modeling approaches are considered high-dimensional paradigms as they involve more than one dimension along with the time scale to describe the complex geometries of the arterial network. On the other hand, the microscale models are generally considered more insightful as they provide a precise estimate of cardiovascular function and accurately represent local as well as global arterial biomechanical properties. In addition, it is less insightful in terms of physiological interpretability, ( Zhou et al., 2019). This class is considered computationally simple but less accurate than the microscale models. Accordingly, they are commonly explored to describe the global cardiovascular functions and biomechanical properties ( Shi et al., 2011 Malatos et al., 2016). Typically this class used ordinary differential equations (ODEs) to describe the arterial hemodynamic as a function of time only. The macro-scale class is considered a low dimensional strategy that usually implicates the well-known lumped parametric, the arterial Windkessel, ( Frank, 1899). In the open literature, the arterial hemodynamics and mechanic modeling approaches are classified into two main classes: macro and micro modeling methods. Commonly, these approaches involve a compromise between precision and complexity. Over the last century, various physics-driven and data-driven modeling methods and diverse numerical computational approaches have been developed to characterize vascular biomechanics and arterial hemodynamics. Accordingly, deep understanding and analysis of the pathological mechanisms of hypertension vascular remodeling hold high significance for diagnosing CVDs and is crucial for the clinical treatment of hypertension ( Li et al., 2017). In particular, they observe that the vascular remodeling in resistive arteries is firmly associated with the progression and severity of hypertension's disease. Several clinical studies in-patient and experimental researches have revealed the marked correlation between vascular remodeling and the pathophysiology of hypertension. However, in hypertensive states, this adaptive response does not lead to normal hemodynamic control but instead inducts irregular vascular changes, defined as, vascular remodeling ( Brown et al., 2018). In a normotensive state, any variation of the hemodynamic induces structural and functional adaptations within the different cell types and layers of the vascular wall. The primary pathological sign of high blood pressure is reduced vascular compliance due to structural remodeling and functional modifications in the arteries. In fact, hypertension is considered chronic pathology that can only be regulated with medication however, it cannot be cured definitely. Although the reduction in hypertension can restrain the onset of CVDs, current treatments techniques are only partially effective. A key risk factor for CVDs is high blood pressure, known as hypertension. This number is expected to reach 23.6 million by 2030 ( Mensah et al., 2019). 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.Ĭardiovascular diseases (CVDs) are the leading cause of death worldwide, responsible for more than 17.9 million deaths in 2019 that representing 32% of global mortality. 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. The proposed fractional model offers high flexibility in characterizing the arterial complex tree network. 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 mathematical model is constructed using five-element lumped parameter arterial Windkessel representation. The blood flow dynamics in human arteries with hypertension disease is modeled using fractional calculus. 4National Institute for Research in Digital Science and Technology (INRIA), Paris, France.3Michigan Institute for Data Science, University of Michigan, Ann Arbor, MI, United States.2College of Innovation and Technology, University of Michigan, Flint, MI, United States.1Computer, Electrical, and Mathematical Sciences, and Engineering Division (CEMSE), King Abdullah University of Science and Technology (KAUST), Thuwal, Saudi Arabia.Bahloul 1 Yasser Aboelkassem 2,3 * Taous-Meriem Laleg-Kirati 1,4
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