Abstract
This contribution presents novel concepts for analysis of pressure–volume curves, which offer information about the time domain dynamics of the respiratory system. The aim is to verify whether a mapping of the respiratory diseases can be obtained, allowing analysis of (dis)similarities between the dynamical pattern in the breathing in children. The groups investigated here are children, diagnosed as healthy, asthmatic, and cystic fibrosis. The pressure–volume curves have been measured by means of the noninvasive forced oscillation technique during breathing at rest. The geometrical fractal dimension is extracted from the pressure–volume curves and a power-law behavior is observed in the data. The power-law model coefficients are identified from the three sets and the results show that significant differences are present between the groups. This conclusion supports the idea that the respiratory system changes with disease in terms of airway geometry, tissue parameters, leading in turn to variations in the fractal dimension of the respiratory tree and its dynamics.
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References
Baker G.L., Gollub J.B., (1996) Chaotic Dynamics: An Introduction, 2nd ed. Cambridge, England: Cambridge University Press.
Birch M., MacLeod D., Levine M., (2001) An analogue instrument for the measurement of respiratory impedance using the forced oscillation technique, Phys Meas 22:323-339
Blom J., (2004) Monitoring of respiration and circulation, CRC Press.
Brennan S., Hall G., Horak F., Moeller A., Pitrez P., Franzamann A., Turner S., de Clerck N., Franklin P., Winfield K., Balding E., Stick S., Sly P., (2005) Correlation of forced oscillation technique in preschool children with cystic fibrosis with pulmonary inflammation, Thorax 60:159-163
Busse W., Lemanske R., (2001) Asthma, New Engl J Med, 344(5): 350-362
De Geeter N., Ionescu C., De Keyser R., (2009) A mechanical model of soft biological tissue - an application to lung parenchyma, In: Proceedings of the 31st Annual Int Conf of the IEEE Engineering in Medicine and Biology Society, Minneapolis, USA, 2-6 September, ISBN 978-1-4244-3296-7, 2863-2866
Duiverman E., Clement J., Van de Woestijne K., Neijens H., van den Bergh A., Kerrebijn K., (1985) Forced oscillation technique: reference values for resistance and reactance over a frequency spectrum of 2-26 Hz in healthy children aged 2.3-12.5 years, Clinical Resp Physiol 21:171-178
Elizur A., Cannon C., Ferkol T., (2008) Airway inflammation in cystic fibrosis, Chest 133(2):489-495
Ionescu C., Segers P., De Keyser R., (2009) Mechanical properties of the respiratory system derived from morphologic insight, IEEE Trans Biomed Eng 56(4):949-959
Ionescu C. , Muntean I., Machado J.T., De Keyser R., Abrudean M., (2010) A theoretical study on modelling the respiratory tract with ladder networks by means of intrinsic fractal geometry, IEEE Trans Biomed Eng 57(2):246-253
Ionescu C., Kosinsky W., De Keyser R., (2010) Viscoelasticity and fractal structure in a model of human lungs, Archives of Mechanics 62(1): 21-48
Ionescu C., (2009) Fractional-order models for the respiratory system, Doctoral Thesis, ISBN 978-90-8578-318-3
Ljung L., (1999) System identification: theory for the user, Prentice Hall
Moon F.C., (1987) Chaotic Vibration, New York: John Wiley,
Monje A. , Chen Y., Vinagre B., Xue D., Feliu V., (2010) Fractional order systems and controls, Springer-Verlag
Northrop R., (2002) Non-invasive instrumentation and measurement in medical diagnosis, CRC Press
Oostveen E.,Macleod D. , Lorino H., Farré R., Hantos Z., Desager K., Marchal F., (2003) The forced oscillation technique in clinical practice: methodology, recommendations and future developments, Eur Respir J 22:1026-1041
Podlubny I., (2002) Geometrical and physical interpretation of fractional integration and fractional differentiation, Journal of Fractional Calculus and Applied Analysis 5(4):357-366
Tenreiro Machado J. A., (1997) Analysis and Design of Fractional-Order Digital Control Systems, Journal Systems Analysis-Modelling-Simulation, Gordon and Breach Science Publishers 27:107-122
Tenreiro Machado J. A., (2003) A Probabilistic Interpretation of the Fractional-Order Differentiation, Journal of Fractional Calculus and Applied Analysis 6(1):73-80
West B., (2010) Fractal physiology and the fractional calculus: a perspective, Frontiers in Fractal Physiology 1(12):1-17 (open source: www.frontiersin.org)
Acknowledgements
C. Ionescu gratefully acknowledges the children from primary school in Zwijnaarde who volunteered to perform lung function testing in our laboratory. We also acknowledge the technical assistance provided at University Hospital Antwerp, Belgium, to measure asthma and CF diagnosed children. J. Tenreiro Machado would like to acknowledge FCT, FEDER, POCTI, POSI, POCI, POSC, POTDC, and COMPETE for their support to R&D Projects and GECAD Unit.
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Ionescu, C.M., Machado, J.T. (2011). Intrinsic Fractal Dynamics in the Respiratory System by Means of Pressure–Volume Loops. In: Nonlinear and Complex Dynamics. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-0231-2_18
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DOI: https://doi.org/10.1007/978-1-4614-0231-2_18
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