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

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Abstract
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.
Keywords
Constant phase element (CPE), forced oscillations, fractal structure, frequency response, ladder network, respiratory impedance, INPUT IMPEDANCE, MECHANICAL-PROPERTIES, RESPIRATORY SYSTEM, GEOMETRY, WALL, CAT

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Chicago
Ionescu, Clara-Mihaela, JA Tenreiro Machado, and Robain De Keyser. 2011. “Modeling of the Lung Impedance Using a Fractional-order Ladder Network with Constant Phase Elements.” Ieee Transactions on Biomedical Circuits and Systems 5 (1): 83–89.
APA
Ionescu, C.-M., Machado, J. T., & De Keyser, R. (2011). Modeling of the lung impedance using a fractional-order ladder network with constant phase elements. IEEE TRANSACTIONS ON BIOMEDICAL CIRCUITS AND SYSTEMS, 5(1), 83–89.
Vancouver
1.
Ionescu C-M, Machado JT, De Keyser R. Modeling of the lung impedance using a fractional-order ladder network with constant phase elements. IEEE TRANSACTIONS ON BIOMEDICAL CIRCUITS AND SYSTEMS. 2011;5(1):83–9.
MLA
Ionescu, Clara-Mihaela, JA Tenreiro Machado, and Robain De Keyser. “Modeling of the Lung Impedance Using a Fractional-order Ladder Network with Constant Phase Elements.” IEEE TRANSACTIONS ON BIOMEDICAL CIRCUITS AND SYSTEMS 5.1 (2011): 83–89. Print.
@article{1193508,
  abstract     = {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.},
  author       = {Ionescu, Clara-Mihaela and Machado, JA Tenreiro and De Keyser, Robain},
  issn         = {1932-4545},
  journal      = {IEEE TRANSACTIONS ON BIOMEDICAL CIRCUITS AND SYSTEMS},
  keywords     = {Constant phase element (CPE),forced oscillations,fractal structure,frequency response,ladder network,respiratory impedance,INPUT IMPEDANCE,MECHANICAL-PROPERTIES,RESPIRATORY SYSTEM,GEOMETRY,WALL,CAT},
  language     = {eng},
  number       = {1},
  pages        = {83--89},
  title        = {Modeling of the lung impedance using a fractional-order ladder network with constant phase elements},
  url          = {http://dx.doi.org/10.1109/TBCAS.2010.2077636},
  volume       = {5},
  year         = {2011},
}

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