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Frequency Domain: Parametric Model Selection and Evaluation

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Part of the book series: Series in BioEngineering ((SERBIOENG))

Abstract

This chapter provides the reader with insight for selecting the best candidate model to characterize the impedance and further validation in clinical studies. An analysis of the modeling performance of several candidate fractional-order models on the respiratory impedance is necessary, in order to decide which model is most suitable in the frequency range of interest. The models are presented on an evolutionary basis from the most simple to the most complex representation. The model delivering the least modeling errors and having the least number of parameters is then selected as the best candidate to model the input impedance in various frequency range intervals. Once the selection is performed, the ability of the FO model in classifying between healthy and pathologic patient data needs to be assessed. The investigated clinical groups are twofold: (i) adults and (ii) children. In the adult group are healthy volunteers and patients a priori diagnosed with chronic obstructive pulmonary disease and with kyphoscoliosis. In the children group are healthy volunteers, and patients a priori diagnosed with asthma and with cystic fibrosis. All the measurements have been performed using the forced oscillation lung function test.

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References

  1. Barnes PJ (2000) Chronic obstructive pulmonary disease. N Engl J Med 343(4):269–280

    Article  Google Scholar 

  2. Bates J (2009) Lung mechanics—an inverse modeling approach. Cambridge University Press, Cambridge

    Book  Google Scholar 

  3. Beaulieu A, Bosse D, Micheau P, Avoine O, Praud J, Walti H (2012) Measurement of fractional order model parameters of respiratory mechanical impedance in total liquid ventilation. IEEE Trans Biomed Eng 59(2):323–331

    Article  Google Scholar 

  4. Brennan S, Hall G, Horak F, Moeller A, Pitrez P, Franzmann A, Turner S, de Klerk 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

    Article  Google Scholar 

  5. Busse W, Lemanske R (2001) Asthma New Engl J Med 344(5):350–362

    Article  Google Scholar 

  6. Cavalcanti J, Lopes A, Jansen J, Melo P (2006) Detection of changes in respiratory mechanics due to increasing degrees of airway obstruction in asthma by the forced oscillation technique. Respir Med 100:2207–2219

    Article  Google Scholar 

  7. Duarte F, Tenreiro Machado JA, Duarte G (2010) Dynamics of the Dow Jones and the NASDAQ stock indexes. Nonlinear Dyn 61(4):691–705

    Article  MATH  Google Scholar 

  8. 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. Clin Respir Physiol 21:171–178

    Google Scholar 

  9. Farre R, Peslin R, Oostveen E, Suki B, Duvivier C, Navajas D (1989) Human respiratory impedance from 8 to 256 Hz corrected for upper airway shunt. J Appl Physiol 67:1973–1981

    Google Scholar 

  10. Fredberg J, Stamenovic D (1989) On the imperfect elasticity of lung tissue. J Appl Physiol 67:2408–2419

    Google Scholar 

  11. Frey U, Suki B, Kraemer R, Jackson A (1997) Human respiratory input impedance between 32 and 800 Hz, measured by interrupter technique and forced oscillations. J Appl Physiol 82:1018–1023

    Article  Google Scholar 

  12. Frey U, Schibler A, Kraemer R (1995) Pressure oscillations after flow interruption in relation to lung mechanics. Respir Physiol 102:225–237

    Article  Google Scholar 

  13. Frey U, Silverman M, Kraemer R, Jackson A (1998) High-frequency respiratory impedance measured by forced oscillation technique in infants. Am J Respir Crit Care Med 158:363–370

    Article  Google Scholar 

  14. Gillis H, Lutchen KR (1999) How heterogeneous bronchconstriction affects ventilation and pressure distributions in human lungs: a morphometric model. Ann Biomed Eng 27:14–22

    Article  Google Scholar 

  15. Habib R, Chalker R, Suki B, Jackson A (1994) Airway geometry and wall mechanical properties estimated from sub-glottal input impedance in humans. J Appl Physiol 77(1):441–451

    Google Scholar 

  16. Hanifi A, Goplen N, Matin M, Salters R, Alam R (2012) A linear parametric approach for analysis of mouse respiratory impedance. IEEE Trans Biomed Circuits Syst 6(3):287–294

    Article  Google Scholar 

  17. Hantos Z, Daroczy B, Suki B, Galgoczy G, Csendes T (1986) Forced oscillatory impedance of the respiratory system at low frequencies. J Appl Phys 60(1):123–132

    Google Scholar 

  18. Hantos Z, Daroczy B, Suki B, Nagy S, Fredberg J (1992) Input impedance and peripheral inhomogeneity of dog lungs. J Appl Phys 72(1):168–178

    Article  Google Scholar 

  19. Hantos Z, Adamicz A, Govaerts E, Daroczy B (1992) Mechanical impedances of lungs and chest wall in the cat. J Appl Phys 73(2):427–433

    Google Scholar 

  20. Hlastala M, Robertson T (1998) Complexity in structure and function of the lung. In: Lung biology in health and disease series, vol 121. Dekker, New York

    Google Scholar 

  21. Hogg J, Chu F, Utokaparch S et al. (2004) The nature of small airway obstruction in chronic obstructive pulmonary disease. N Engl J Med 350(26):2645–2653

    Article  Google Scholar 

  22. Horsfield K, Dart G, Olson D, Cumming G (1971) Models of the human bronchial tree. J Appl Physiol 31:207–217

    Google Scholar 

  23. Hou C, Gheorghiu S, Coppens MS, Huxley VH, Pfeifer P (2005) Gas diffusion through the fractal landscape of the lung. In: Losa, Merlini, Nonnenmacher (ed) Fractals in biology and medicine, vol IV. Birkhauser, Berlin

    Google Scholar 

  24. Ionescu C, Muntean I, Tenreiro-Machado J, De Keyser R, Abrudean M (2009) A theoretical study on modelling the respiratory tract with ladder networks by means of intrinsic fractal geometry. IEEE Trans Biomed Eng. doi:10.1109/TBME.2009.2030496

    Google Scholar 

  25. Ionescu C, Derom E, De Keyser R (2009) Assessment of respiratory mechanical properties with constant-phase models in healthy and COPD lungs. Comput Methods Programs Biomed. doi:10.1016/j.cmpb.2009.06.006

    Google Scholar 

  26. Ionescu C, Machado JT, De Keyser R (2011) Fractional-order impulse response of the respiratory system. Comput Math Appl 62(3):845–854

    Article  MATH  Google Scholar 

  27. Ionescu C, De Keyser R, Sabatier J, Oustaloup A, Levron F (2011) Low frequency constant-phase behaviour in the respiratory impedance. Biomed Signal Process Control 6:197–208

    Article  Google Scholar 

  28. Jabloński I, Mroczka J (2009) Frequency domain identification of the respiratory system model during the interrupter technique. Measurement 42:390–398

    Article  Google Scholar 

  29. Jabloński I, Polak A, Mroczka J (2011) Preliminary study on the accuracy of respiratory input impedance measurement using the interrupter technique. Comput Methods Programs Biomed 101:115–125

    Article  Google Scholar 

  30. Jesus I, Tenreiro Machado JA (2008) Development of fractional order capacitors based on electrolyte processes. Nonlinear Dyn. doi:10.1007/s11071-008-9377-8

    MathSciNet  Google Scholar 

  31. Lutchen KR, Gillis H (1997) The relation between airway morphometry and lung resistance and elastance during constriction: a modeling study. J Appl Physiol 83(4)

    Google Scholar 

  32. Losa G, Merlini D, Nonnenmacher T, Weibel E (2005) Fractals in biology and medicine, vol IV. Birkhauser, Basel

    Book  Google Scholar 

  33. Mandelbrot B (1983) The fractal geometry of nature. Freeman, New York

    Google Scholar 

  34. McCool F, Rochester D (2008) Non-muscular diseases of the chest wall. In: Fishman A (ed) Fishman’s pulmonary disease and disorders, vol II. McGraw-Hill Medical, New York, pp 1541–1548

    Google Scholar 

  35. Monje CA, Chen YQ, Vinagre B, Xue D, Feliu V (2010) Fractional order systems and controls—fundamentals and applications. Advanced industrial control series. Springer, Berlin. ISBN 978-1-84996-334-3

    Book  MATH  Google Scholar 

  36. Northrop R (2002) Non-invasive measurements and devices for diagnosis. CRC Press, Boca Raton

    Google Scholar 

  37. Oustaloup A (1995) La derivation non-entière. Hermes, Paris (in French)

    MATH  Google Scholar 

  38. Pasker H, Peeters M, Genet P, Nemery N, Van De Woestijne K (1997) Short-term ventilatory effects in workers exposed to fumes containing zinc oxide: comparison of forced oscillation technique with spirometry. Eur Respir J 10:523–1529

    Article  Google Scholar 

  39. Peslin R, Duvivier C, Jardin P (1984) Upper airway walls impedance measured with head plethysmograph. J Appl Physiol: Respir, Environ Exercise Physiol 57(2):596–600

    Google Scholar 

  40. Reyes-Melo M, Martinez-Vega J, Guerrero-Salazar C, Ortiz-Mendez U (2004) Application of fractional calculus to modelling of relaxation phenomena of organic dielectric materials. In: IEEE proc int conf on solid dielectrics. 6 p

    Google Scholar 

  41. Rogers D, Doull I (2005) Physiological principles of airway clearance techniques used in the physiotherapy management of cystic fibrosis. Curr Pediatr 15:233–238

    Article  Google Scholar 

  42. Romero PV, Sato J, Shardonofsky F, Bates J (1990) High frequency characteristics of respiratory mechanics determined by flow interruption. J Appl Physiol 69:1682–1688

    Google Scholar 

  43. Suki B, Yuan H, Zhang Q, Lutchen K (1992) Partitioning of lung tissue response and inhomogeneous airway constriction at the airway opening. J Appl Phys 82:1349–1359

    Google Scholar 

  44. Suki B, Barabasi A, Lutchen K (1994) Lung tissue viscoelasticity: a mathematical framework and its molecular basis. J Appl Physiol 76(6):2749–2759

    Google Scholar 

  45. Suki B, Bates J (2011) Lung tissue mechanics as an emergent phenomenon. J Appl Physiol 110:1111–1118

    Article  Google Scholar 

  46. Thamrin C, Finucane K, Singh B, Hantos Z, Sly P (2007) Volume dependence of high-frequency respiratory mechanics in healthy adults. Ann Biomed Eng 36(1):162–170

    Article  Google Scholar 

  47. Thamrin C, Albu G, Sly P, Hantos Z (2009) Negative impact of the noseclip on high-frequency respiratory impedance measurements. Respir Physiol Neurobiol 165:115–118

    Article  Google Scholar 

  48. Thorpe CW, Bates J (1997) Effect of stochastic heterogeneity on lung impedance during acute bronchoconstriction: a model analysis. J Appl Physiol 82:1616–1625

    Google Scholar 

  49. Vignola A, Paganin F, Capieu L, Scichilone N, Bellia M, Maakel L, Bellia V, Godard P, Bousquet J, Chanez P (2004) Airway remodeling assessed by sputum and high-resolution computer tomography in asthma and COPD. Eur Respir J 24:910–917

    Article  Google Scholar 

  50. Yuan H, Kononov S, Cavalcante F, Lutchen K, Ingenito E, Suki B (2000) Effects of collagenase and elastase on the mechanical properties of lung tissue strips. J Appl Physiol 89(3):3–14

    Google Scholar 

  51. Weibel ER (1963) Morphometry of the human lung. Springer, Berlin

    Google Scholar 

  52. Weibel ER (2005) Mandelbrot’s fractals and the geometry of life: a tribute to Benoit Mandelbrot on his 80th birthday. Losa, Merlini, Nonnenmacher (eds) Fractals in biology and medicine, vol IV. Birkhauser, Berlin

    Google Scholar 

  53. West B, Barghava V, Goldberger A (1986) Beyond the principle of similitude: renormalization of the bronchial tree. J Appl Physiol 60:1089–1097

    Google Scholar 

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Ionescu, C.M. (2013). Frequency Domain: Parametric Model Selection and Evaluation. In: The Human Respiratory System. Series in BioEngineering. Springer, London. https://doi.org/10.1007/978-1-4471-5388-7_7

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  • DOI: https://doi.org/10.1007/978-1-4471-5388-7_7

  • Publisher Name: Springer, London

  • Print ISBN: 978-1-4471-5387-0

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