Mathematical Models in Respiratory Mechanics

  • W. A. Zin
  • R. F. M. Gomes


The respiratory system, as well as its pulmonary and chest wall components, is comprised of a multitude of elements. The undisputed necessity to interpret the meaning of measurable variables such as volume, airflow, and pressure under both physiological and pathological conditions has imposed the need for relatively simple models that should be able to describe as accurately as possible the mechanical behaviour of the system. The components of such models and their associated parameters should have reasonable physiological counterparts, naturally.


Respiratory System Breathing Frequency Central Airway Electrical Representation Respiratory Impedance 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Sharp JT, Henry JP, Sweany SK, Meadows WR, Pietras RJ (1964) Total respiratory inertance and its gas and tissue components in normal and obese men. J Appl Physiol 43:503–509Google Scholar
  2. 2.
    Hantos Z, Daroczy B, Klebniczki J, Dombos K, Nagy S (1982) Parameter estimation of transpulmonary mechanics by a nonUnear inertive model. J Appl Physiol 52:955–963PubMedGoogle Scholar
  3. 3.
    Bates JHT, Shardonofsky R, Stewart DE (1989) The low-frequency dependence of respiratory system resistance and elastance in normal dogs. Respir Physiol 78:369–382PubMedCrossRefGoogle Scholar
  4. 4.
    Mead J, Whittenberger JL (1953) Physical properties of human lungs measured during spontaneous respiration. J Appl Physiol 5:779–796Google Scholar
  5. 5.
    Zin WA, Pengelly LD, Milic-Emili J (1982) Single-breath method for measurement of respiratory mechanics in anesthetized animals. J Appl Physiol 52:1266–1271PubMedGoogle Scholar
  6. 6.
    Hughes R, May AJ, Widdicombe JG (1959) Stress relaxation in rabbits’ lungs. J Physiol (Lond) 146:85–97Google Scholar
  7. 7.
    Don HF, Robson JG (1965) The mechanics of the respiratory system during anesthesia. Anesthesiol 26:168–178CrossRefGoogle Scholar
  8. 8.
    Bates JHT, Rossi A, Mihc-Emili J (1985) Analysis of the behavior of the respiratory system with constant inspiratory flow. J Appl Physiol 58:1840–1848PubMedGoogle Scholar
  9. 9.
    Bates JHT, Decramer M, Chartrand D, Zin WA, Böddener A, Milic-Emili J (1985) The volume-time profile during relaxed expiration in the normal dog. J Appl Physiol 59:732–737PubMedGoogle Scholar
  10. 10.
    Chelucci GL, Brunet F, Dall’Ava-Santucci J, Dhainaut JF, Paccaly D, Armaganidis A, Milic-Emili J, Lockhart A (1991) A single-compartment model cannot describe passive expiration in intubated, paralysed humans. Eur Respir J 4:458–464PubMedGoogle Scholar
  11. 11.
    Barnas GM, Yoshino K, Loring SH, Mead J (1987) Impedance and relative displacements of relaxed chest wall up to 4 Hz. J Appl Physiol 62:71–81PubMedGoogle Scholar
  12. 12.
    Brusasco V, Warner DO, Beck KC, Rodarte JR, Rehder K (1989) Partitioning of pulmonary resistance in dogs: effects of tidal volume and frequency. J Appl Physiol 66:1190–1197PubMedCrossRefGoogle Scholar
  13. 13.
    Hantos Z, Daroczy B, Suki B, Galgoczy G, Csendes T (1986) Forced oscillatory impedance of the respiratory system at low frequencies. J Appl Physiol 60:123–132PubMedCrossRefGoogle Scholar
  14. 14.
    Hantos Z, Daroczy B, Suki B, Nagy S (1987) Low-frequency respiratory mechanical impedance in the rat. J Appl Physiol 63:36–43PubMedGoogle Scholar
  15. 15.
    Otis AB, McKerrow CB, Bartlett RA, Mead J, Mcllroy MB, Selverstone NJ, Radford EP (1956) Mechanical factors in the distribution of pulmonary ventilation. J Appl Physiol 8: 427–444PubMedGoogle Scholar
  16. 16.
    Bates JHT, Baconnier P, Milic-Emili J (1988) A theoretical analysis of interrupter technique for measuring respiratory mechanics. J Appl Physiol 64:2204–2214PubMedGoogle Scholar
  17. 17.
    Mead J (1969) Contribution of comphance of airways to frequency-dependent behavior of lungs. J Appl Physiol 26:670–673PubMedGoogle Scholar
  18. 18.
    Eyles JG, Pimmel RL (1981) Estimating respiratory mechanical parameters in parallel compartment models. IEEE Trans Biomed Eng 28:313–317PubMedCrossRefGoogle Scholar
  19. 19.
    Peslin R (1986) Methods for measuring total respiratory impedance by forced oscillations. Bull Eur Physiopathol Respir 22:621–631PubMedGoogle Scholar
  20. 20.
    Michaelson ED, Grassman ED, Peters WR (1975) Pulmonary mechanics by spectral analysis of forced random noise. J Clin Invest 56:1210–1230PubMedCrossRefGoogle Scholar
  21. 21.
    Lorino AM, Lorino H, Harf A (1994) A synthesis of the Otis, Mead, and Mount mechanical respiratory models. Respir Physiol 97:123–133PubMedCrossRefGoogle Scholar
  22. 22.
    Bates JHT, Ludwig MS, Sly PD, Brown K, Martin JG, Fredberg JJ (1988) Interrupter resistance elucidated by alveolar pressure measurement in open-chest normal dogs. J Appl Physiol 65:408–414PubMedGoogle Scholar
  23. 23.
    Saldiva PHN, Zin WA, Santos RLB, Eidelman DH, Milic-Emili J (1992) Alveolar pressure measurement in open-chest rats. J Appl Physiol 72:302–306PubMedGoogle Scholar
  24. 24.
    Mount LE (1955) The ventilation flow-resistance and compliance of rat lungs. J Physiol (Lond) 127:157–167Google Scholar
  25. 25.
    Bates JHT, Brown KA, Kochi T (1989) Respiratory mechanics in the normal dog determined by expiratory flow interruption. J Appl Physiol 67:2276–2285PubMedGoogle Scholar
  26. 26.
    Hildebrandt J (1970) Pressure-volume data of cat lung interpreted by a plastoelastic, linear viscoelastic model. J Appl Physiol 28:365–372PubMedGoogle Scholar
  27. 27.
    Fredberg JJ, Stamenovic D (1989) On the imperfect elasticity of lung tissue. J Appl Physiol 67:2408–2419PubMedGoogle Scholar
  28. 28.
    Sharp JT, Johnson FN, Goldberg NB, van Lith P (1967) Hysteresis and stress adaptation in the human respiratory system. J Appl Physiol 23:487–497PubMedGoogle Scholar
  29. 29.
    Similowski T, Bates JHT (1991) Two-compartment modelling of respiratory system mechanics at low frequencies: gas redistribution of tissue rheology? Eur Respir J 4:353–358PubMedGoogle Scholar
  30. 30.
    Navajas D, Farre R, Cannet J, Roger M, Sanchis J (1990) Respiratory input impedance in anesthetized paralyzed patients. J Appl Physiol 69:1372–1379PubMedGoogle Scholar
  31. 31.
    Shardonofsky F, Sato J, Bates JHT (1990) Quasi-static pressure-volume hysteresis in the canine respiratory system in vivo. J Appl Physiol 68:2230–2236PubMedGoogle Scholar
  32. 32.
    Hildebrandt J (1969) Dynamic properties of air-filled excised cat lung determined by liquid plethysmography. J Appl Physiol 27:246–250PubMedGoogle Scholar
  33. 33.
    Hildebrandt J (1969) Comparison of mathematical models for cat lung and viscoelastic balloon derived by Laplace transform methods from près sure-volume data. Bull Math Biophys 31:651–667PubMedCrossRefGoogle Scholar
  34. 34.
    Rohrer R (1915) Der Strömungswiderstand in den menschlichen Atemwegen und der Einfluss der unregelmässigen Verzweigung des Bronchialsystems auf den Atmungsverlauf in verschiedenen Lungenbezirken. Arch Ges Physiol 162:225–300CrossRefGoogle Scholar
  35. 35.
    Suki B, Bates JHT (1991) A nonlinear viscoelastic model of lung tissue mechanics. J Appl Physiol 71:826–833PubMedGoogle Scholar
  36. 36.
    Hantos Z, Daroczy B, Suki B, Nagy S, Rredberg JJ (1992) Input impedance and peripheral inhomogeneity of dog lungs. J Appl Physiol 72:168–178PubMedCrossRefGoogle Scholar
  37. 37.
    Lutchen KR, Suki B, Zhang Q, Petak R, Caroczy B, Hantos Z (1994) Airway and tissue mechanics during physiological breathing and bronchoconstriction in dogs. J Appl Physiol 77:373–385PubMedGoogle Scholar
  38. 38.
    Rotger M, Peslin R, Navajas D, Rarré R (1995) Lung and respiratory impedance at low frequency during mechanical ventilation in rabbits. J Appl Physiol 78:2153–2160.PubMedGoogle Scholar

Copyright information

© Springer-Verlag Italia, Milano 1996

Authors and Affiliations

  • W. A. Zin
  • R. F. M. Gomes

There are no affiliations available

Personalised recommendations