Modeling of the lung impedance using a fractional order ladder network with constant phase elements

The self similar branching arrangement of the airways makes the respiratory system an ideal candidate for the application of fractional calculus theory. The fractal geometry is typically characterized by a recurrent structure. This study investigates the identification of a model for the respiratory tree by means of its electrical equivalent based on intrinsic morphology. Measurements were obtained from seven volunteers, in terms of their respiratory impedance by means of its complex representation for frequencies below 5 Hz. A parametric modeling is then applied to the complex valued data points. Since at low-frequency range the inertance is negligible, each airway branch is modeled by using gamma cell resistance and capacitance, the latter having a fractional-order constant phase element (CPE), which is identified from measurements. In addition, the complex impedance is also approximated by means of a model consisting of a lumped series resistance and a lumped fractional-order capacitance. The results reveal that both models characterize the data well, whereas the averaged CPE values are supraunitary and subunitary for the ladder network and the lumped model, respectively.

Fractional generalization of memristor and higher order elements

Fractional calculus generalizes integer order derivatives and integrals. Memristor systems generalize the notion of electrical elements. Both concepts were shown to model important classes of phenomena. This paper goes a step further by embedding both tools in a generalization considering complex-order objects. Two complex operators leading to real-valued results are proposed. The proposed class of models generate a broad universe of elements. Several combinations of values are tested and the corresponding dynamical behavior is analyzed.

A theoretical study on modelling the respiratory tract with ladder networks by means of intrinsic fractal geometry

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.

Nonlinear Dynamics for Local Fractional Burgers Equation Arising in Fractal Flow

The local fractional Burgers’ equation (LFBE) is investigated from the point of view of local fractional conservation laws envisaging a nonlinear local fractional transport equation with a linear non-differentiable diffusion term. The local fractional derivative transformations and the LFBE conversion to a linear local fractional diffusion equation are analyzed.

Fate Hazardous elements in soils surrounding a coal-fired power plant complex

Proceedings of the 13th International UFZ-Deltares Conference on Sustainable Use and Management of Soil, Sediment and Water Resources - 9–12 June 2015 • Copenhagen, Denmark

Trace Elements in Ambient Air at Porto Metropolitan Area—Checking for Compliance with New European Union (Eu) Air Quality Standards

Because of the scientific evidence showing that arsenic (As), cadmium (Cd), and nickel (Ni) are human genotoxic carcinogens, the European Union (EU) recently set target values for metal concentration in ambient air (As: 6 ng/m3, Cd: 5 ng/m3, Ni: 20 ng/m3). The aim of our study was to determine the concentration levels of these trace elements in Porto Metropolitan Area (PMA) in order to assess whether compliance was occurring with these new EU air quality standards. Fine (PM2.5) and inhalable (PM10) air particles were collected from October 2011 to July 2012 at two different (urban and suburban) locations in PMA. Samples were analyzed for trace elements content by inductively coupled plasma–mass spectrometry (ICP-MS). The study focused on determination of differences in trace elements concentration between the two sites, and between PM2.5 and PM10, in order to gather information regarding emission sources. Except for chromium (Cr), the concentration of all trace elements was higher at the urban site. However, results for As, Cd, Ni, and lead (Pb) were well below the EU limit/target values (As: 1.49 ± 0.71 ng/m3; Cd: 1.67 ± 0.92 ng/m3; Ni: 3.43 ± 3.23 ng/m3; Pb: 17.1 ± 10.1 ng/m3) in the worst-case scenario. Arsenic, Cd, Ni, Pb, antimony (Sb), selenium (Se), vanadium (V), and zinc (Zn) were predominantly associated to PM2.5, indicating that anthropogenic sources such as industry and road traffic are the main source of these elements. High enrichment factors (EF > 100) were obtained for As, Cd, Pb, Sb, Se, and Zn, further confirming their anthropogenic origin.