Cardiovascular Circulatory System and Left Carotid Model: A Fractional Approach to Disease Modeling

Abstract

Cardiovascular diseases (CVDs) remain the leading cause of death worldwide, according to recent reports from the World Health Organization (WHO). This fact encourages research into the cardiovascular system (CVS) from multiple and different points of view than those given by the medical perspective, highlighting among them the computational and mathematical models that involve experiments much simpler and less expensive to be performed in comparison with in vivo or in vitro heart experiments. However, the CVS is a complex system that needs multidisciplinary knowledge to describe its dynamic models, which help to predict cardiovascular events in patients with heart failure, myocardial or valvular heart disease, so it remains an active area of research. Firstly, this paper presents a novel electrical model of the CVS that extends the classic Windkessel models to the left common carotid artery motivated by the need to have a more complete model from a medical point of view for validation purposes, as well as to describe other cardiovascular phenomena in this area, such as atherosclerosis, one of the main risk factors for CVDs. The model is validated by clinical indices and experimental data obtained from clinical trials performed on a pig. Secondly, as a first step, the goodness of a fractional-order behavior of this model is discussed to characterize different heart diseases through pressure–volume (PV) loops. Unlike other models, it allows us to modify not only the topology, parameters or number of model elements, but also the dynamic by tuning a single parameter, the characteristic differentiation order; consequently, it is expected to provide a valuable insight into this complex system and to support the development of clinical decision systems for CVDs.

Privacy Preservation of Nabla Discrete Fractional-Order Dynamic Systems

“…Fractional calculus is a generalization of classical calculus that extends derivatives and integrals from integer to non-integer orders. Due to their non-locality and hereditary properties, fractional calculus and fractional systems have drawn much attention and have been extensively studied in many fields, including signal processing [1], soft robots [2], medical science [3], economics [4], biology [5], and so on. Notably, its application in modeling various system dynamics and engineering scenarios demonstrates superior efficiency over traditional integer-order methods, particularly within the domain of control systems [6][7][8].…”

“…The observability matrix O L has rank n. 3 The observability Gramian matrix R O (k) = ∑ k s=1 F T A,α (s)C T CF A,α (s) has rank n.…”

Heart Rhythm Analysis Using Nonlinear Oscillators with Duffing-Type Connections

“…Mathematical modeling of the heart has been widely explored for different purposes [27][28][29][30][31]. Hodgkin and Huxley proposed the first model of electrical signal propagation through a wide variety of excitable cells around the 1950s [32] Later, FitzHugh and Nagumo provided a qualitative description of the Hodgkin-Huxley model, which led to a better understanding of its behavior [33].…”

Fractional-Order Model-Free Predictive Control for Voltage Source Inverters

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