A Theoretical Study on Modeling the Respiratory Tract With Ladder Networks by Means of Intrinsic Fractal Geometry

Abstract

Fractional order modeling of biological systems has received significant interest in the research community. Since the fractal geometry is characterized by a recurrent structure, the self-similar branching arrangement of the airways makes the respiratory system an ideal candidate for the application of fractional calculus theory. To demonstrate the link between the recurrence of the respiratory tree and the appearance of a fractional-order model, we develop an anatomically consistent representation of the respiratory system. This model is capable of simulating the mechanical properties of the lungs and we compare the model output with in vivo measurements of the respiratory input impedance collected in 20 healthy subjects. This paper provides further proof of the underlying fractal geometry of the human lungs, and the consequent appearance of constant-phase behavior in the total respiratory impedance.

Fractional Calculus: Quo Vadimus? (Where are we Going?)

“…; (3) Permeability of abstract concepts from FC into less abstract fields (e.g., medicine) implies surpassing ethical and moral prejudice; (4) Perhaps a platform to facilitate communication between these various sciences (and scientists) and a common language (i.e., clear definitions of fractal, fractional, etc) should be enforced. References: [31,32,33,34,35,36,13]. Related to the question "FC: Quo vadimus?…”

Phase Constancy in a Ladder Model of Neural Dynamics

“…In this paper, we make use of the theoretical basis developed in the past for self-similar structures [19], [18], [30]. Consider the generalized case shown in Fig.…”

“…If, in this network, we can express each compartment as a recurrent function of the first compartment, then the total impedance of such a network exhibits a phase constancy [19]. This phase constancy can be positive or negative, depending on the values of Zt and Zl as a function of the frequency.…”

“…In our previous work, we have shown that such self-similar structures naturally lead to the appearance of constant-phase behavior, a typical feature of systems whose time-domain response can be characterized by power law models or fractional derivatives [18], [19]. We suspect that the self-similar anatomy of neuron populations could be as well characterized by such ladder networks.…”

Fractal immunology and immune patterning: Potential tools for immune protection and optimization

“…To date, the most highly developed examples of fractal analysis are the applications for physiological systems such as the neurological , cardiovascular (Cheung et al, 2010), and respiratory systems (Ionescu et al, 2010) and for the analysis of cancers (Bedin et al, 2010). Additionally, fractals are significant in evaluating maturational and pathological changes affecting human gait (Hausdorff, 2007;Scafetta et al, 2009).…”