» Download Article

Authors
Ionescu, Clara; Oustaloup, Alain; Levron, Françoıs; Melchior, Pierre; Sabatier, Jocelyn; De Keyser, Robin M.C.

Identifier
10.3182/20090706-3-FR-2004.00165

Index Terms
Biological Systems; Model Validation; Frequency Domain Identification

Abstract
The respiratory system has specific geometrical and material properties, which allow researchers to classify it as a typical fractal structure. Hitherto, only material properties in animal and human lung parenchyma have been investigated, assuming a power-law behavior of the viscoelastic properties in soft biological tissue. Consequently, lumped, fractional-order parametric models have been used to characterize such power-law behavior, in both healthy and pathologic lungs. This paper attempts to verify if the appearance of the fractional-order operator is also related to the underlying geometry and structure of the respiratory tree. Typical morphologic values are used in an electrical equivalent, based on our previous results. Simulation results show that the dichotomous and recursive, fractal-like properties of the respiratory system lead naturally to the appearance of the fractional-order operators.

References

Adolfsson K., Enelund M., Olsson P. (2005) “On the fractional order model of viscoelasticity”, Mechanics of Time-dependent materials, Springer, 9, 15–34
Eke A., Herman P., Kocsis L., Kozak L. (2002) “Fractal characterization of complexity in temporal physiological signals”, Physiol. Meas., 23, R1-R38
Fitzpatrick M.F., McLean H., Urton A.M., Tan A., O’Donnell D., Driver H.S. (2003) “Effect of nasal or oral route on upper airway resistance during sleep”, Eur Resp J, 22: 827-832
Ghista D.N., Loh K.M., Damodaran M. (2006) “Lung ventilation modeling and assessment“, in Human Respiration: Anatomy and Physiology, Mathematical Modeling, Numerical Simulation and Applications, WIT Press Series: Advances in Bioengineering, Vol 3, chapter 4, 95-115
Hantos Z., Daroczy B., Suki B., Nagy S., Fredberg J. (1992a) “Input impedance and peripheral inhomogeneity of dog lungs”, J Appl. Phys., 72(1), 168-178
Hantos Z., Adamicz A., Govaerts E., Daroczy B. (1992b) “Mechanical impedances of lungs and chest wall in the cat”, J Appl. Phys., 73(2), 427-433
Hou C., Gheorgiu S., Coppens M.S., Huxley V.H., Pfeifer P., (2005) “Gas diffusion through the fractal landscape of the lung”, in Fractals in Biology and Medicine, vol IV, Eds: Losa G., Merlini D., Nonnenmacher T., Weibel E.R., Berlin: Birkhaüser, 17-30
Ionescu C., De Keyser R., (2008) “Parametric models for characterizing the respiratory input impedance”, J Med Eng & Tech, 32(4): 315-324
Ionescu C., De Keyser R, (2009) “Relations between fractional order model parameters and lung pathology in COPD”, IEEE Trans Biomed Engineering, in press (Vol 56, April 2009)
Ionescu C., Segers P., De Keyser R., (2009) “Mechanical properties of the respiratory system derived from morphologic insight”, IEEE Trans Biomed Engineering, in press (Vol 56, April 2009)
Mandelbrot B. (1983) “The fractal geometry of nature”, NY: Freeman &Co
Mauroy B. (2005) “3D hydrodynamics in the upper human bronchial tree: interplay between geometry and flow distribution”, in Fractals in Biology and Medicine, vol IV, Eds: Losa G., Merlini D., Nonnenmacher T., Weibel E.R., Berlin: Birkhaüser, 43-54
Oustaloup A. (1995) “La derivation non-entière” (in French), Hermes, Paris
Oustaloup A, Levron F, Mathieu B, Nanot F, (2000) “Frequency-based complex noninteger differentiator: characterization and synthesis“, IEEE Trans on Circuits and Systems – part I, vol. 47, 25-39
Oustaloup A., Sabatier J., (1995) “Recursive distributed parameters systems and non integer derivation”, European Conf on Circuit Theory and Design (ECCTD’95), Istanbul, Turkey
Relton F. (1965) Applied Bessel functions, New York, Dover
Sabatier J. (1998) “La derivation non-entiere en modelisation des systemes a parameters distribues recursif et en commande robuste des procedes non-stationaire“, Doctoral Thesis (in French), University of Bordeaux, LAPS, France, 1998 (see Chapter 2, Annexes 2-3)
Sauret V., Halson P., Brown I., Fleming J., Bailey A. (2002) “Study of the three-dimentional geometry of the central conducting airways in man using computed tomographic (CT) images”, Journal of Anatomy, 200, 123-134
Sommacal L., Melchior P., Dossat A., Petit J., Cabelguen J-M, Oustaloup A., Ijspeert A., (2007) Improvement of the muscle fractional multimodel for low-rate stimulation, Biomedical Signal Processing and Control, 2(3), 226-233
Sommacal L., Melchior P., Oustaloup A., Cabelguen J-M, Ijspeert A., (2008) Fractional multimodels of the frog gastrocnemius muscle, Journal of Vibration and Control, 14(9-10), 1415-1430
Yuan H., Kononov S., Cavalcante F.,, Lutchen K., Ingenito E., Suki B. (1997) “Effects of collagenase and elastase on the mechanical properties of lung tissue strips”, J Appl. Phys., 89, 3-14
Weibel E.R. (1963) “Morphometry of the human lung”, Berlin: Springer
Weibel E.R. (2005) “Mandelbrot’s fractals and the geometry of life: a tribute to Benoît Mandelbrot on his 80th birthday”, in Fractals in Biology and Medicine, vol IV, Eds: Losa G., Merlini D., Nonnenmacher T., Weibel E.R., Berlin: Birkhaüser, 3-16