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Respiratory mechanics by least squares fitting in mechanically ventilated patients: Applications during paralysis and during pressure support ventilation



To evaluate a least squares fitting technique for the purpose of measuring total respiratory compliance (Crs) and resistance (Rrs) in patients submitted to partial ventilatory support, without the need for esophageal pressure measurement.


Prospective, randomized study.


A general ICU of a University Hospital.


11 patients in acute respiratory failure, intubated and assisted by pressure support ventilation (PSV).


Patients were ventilated at 4 different levels of pressure support. At the end of the study, they were paralyzed for diagnostic reasons and submitted to volume controlled ventilation (CMV).

Measurements and results

A least squares fitting (LSF) method was applied to measure Crs and Rrs at different levels of pressure support as well as in CMV. Crs and Rrs calculated by the LSF method were compared to reference values which were obtained in PSV by measurement of esophageal pressure, and in CMV by the application of the constant flow, end-inspiratory occlusion method. Inspiratory activity was measured by P0.1. In CMV, Crs and Rrs measured by the LSF method are close to quasistatic compliance (−1.5±1.5 ml/cmH2O) and to the mean value of minimum and maximum end-inspiratory resistance (+0.9±2.5 cmH2O/(l/s)). Applied during PSV, the LSF method leads to gross underestimation of Rrs (−10.4±2.3 cmH2O/(l/s)) and overestimation of Crs (+35.2±33 ml/cmH2O) whenever the set pressure support level is low and the activity of the respiratory muscles is high (P0.1 was 4.6±3.1 cmH2O). However, satisfactory estimations of Crs and Rrs by the LSF method were obtained at increased pressure support levels, resulting in a mean error of −0.4±6 ml/cmH2O and −2.8±1.5 cmH2O/(l/s), respectively. This condition was coincident with a P0.1 of 1.6±0.7 cmH2O.


The LSF method allows non-invasive evaluation of respiratory mechanics during PSV, provided that a near-relaxation condition is obtained by means of an adequately increased pressure support level. The measurement of P0.1 may be helpful for titrating the pressure support in order to obtain the condition of near-relaxation.

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  1. 1.

    Rossi A, Gottfried SB, Higgs BD, Zocchi L, Grassino A, Milic-Emili J (1985) Respiratory mechanics in mechanically ventilated patients with respiratory failure. J Appl Physiol 58:1840–1848

  2. 2.

    von Neergaard K, Wirz K (1927) Die Messung der Strömungswiderstände in den Atemwegen des Menschen, insbesondere bei Asthma und Emphysem. Z Klin Med 105:51–82

  3. 3.

    Mead J, Whittenberger Jl (1953) Physical properties of human lungs measured during spontaneous respiration. J Appl Physiol 12:779–796

  4. 4.

    Jonson B, Nordström L, Olsson SG, Akerback D (1975) Monitoring of ventilation and lung mechanics during automatic ventilation. A new device. Bull Eur Physiopathol Respir 11:729–743

  5. 5.

    Anthonisen NR (1986) Tests of mechanical function. In: Fishman AP (ed) Handbook of physiology: the respiratory system, vol III. Mechanics of breathing. American Physiological Society, Washington DC, p 764

  6. 6.

    Rossi A, Gottfried SB, Zocchi L, Higgs BD, Lennox S, Calverley PMA, Begin P, Grassino A, Milic-Emili J (1985) Measurement of static compliance of the total respiratory system in patients with acute respiratory failure during mechanical ventilation. The effect of intrinsic pulmonary end-expiratory pressure. Am Rev Respir Dis 131:672–677

  7. 7.

    Wald A, Jason D, Murphy TW, Mazzia VDB (1969) A computer system for respiratory parameters. Comput Biomed Res 2:411–429

  8. 8.

    Uhl RR, Lewis FJ (1974) Digital computer calculation of human pulmonary mechanics using a least square fit technique. Comput Biomed Res 7:489–495

  9. 9.

    Brunner JX, Wolff G (1988) Pulmonary function indices in critical care patients. Springer, Berlin Heidelberg, pp 18–26

  10. 10.

    Eberhard L, Guttmann J, Wolff G, Bertschmann W, Minzer A, Kohl HJ, Zeravik J, Adolph M, Eckart J (1992) Intrinsic PEEP monitored in the ventilated ARDS patient with a mathematical method. J Appl Physiol 73:479–485

  11. 11.

    Bertschmann V, Guttmann J, Zeravik J, Eberhard L, Adolph M, Wolff g (1990) Atemzugsweise Bestimmung von Compliance und Resistance am Beatmeten. Intensivmedizin 27:42–47

  12. 12.

    Guttmann J, Eberhard L, Wolff G, Bertschmann W, Zeravik J, Adolph M (1992) Maneuver free determination of compliance and resistance in ventilated ARDS patients. Chest 102:1235–1242

  13. 13.

    Gillard C, Flemale A, Dierckx JP, Themelin G (1990) Measurement of effective elastance of the total respiratory system in ventilated patients by a computed method. Intensive Care Med 16:189–195

  14. 14.

    Brunner J, Wolff G (1985) A simple method for estimating compliance. Crit Care Med 13:675–678

  15. 15.

    Brochard L, Harf A, Lorino H, Lemaire F (1989) Inspiratory pressure support prevents diaphragmatic fatigue during weaning from mechanical ventilation. Am Rev Respir Dis 139:513–521

  16. 16.

    Baydur A, Behrakis PK, Zin WA, Jaeger M, Milic-Emili J (1982) A simple method for assessing the validity of the esophageal balloon technique. Am Rev Respir Dis 126:788–791

  17. 17.

    Rohrer F, Nakasone K, Wirz K (1925) Physiologie der Atembewegung. Handbuch der normalen und pathologischen Physiologie, vol 2, Springer, Berlin, pp 70–127

  18. 18.

    Otis AB, Fenn WO, Rahn H (1950) The mechanics of breathing in man. J Appl Physiol 2:592–607

  19. 19.

    Marini JJ, Crooke PS III, Truwit JD (1989) Determinants and limits of pressure-preset ventilation. A mathematical model of pressure control. J Appl Physiol 67:1081–1092

  20. 20.

    Iotti G, Braschi A (1990) Respiratory mechanics in chronic obstructive pulmonary disease. In: Vincent JL (ed) Update in intensive care and emergency medicine 10: Update 1990. Springer, Berlin Heidelberg, pp 223–230

  21. 21.

    D'Angelo E, Calderini E, Torri G, Robatto FM, Bono D, Milic-Emili J (1989) Respiratory mechanics in anesthetized paralyzed humans: effects of flow, volume, and time. J Appl Physiol 67:2556–2564

  22. 22.

    Kochi T, Okubo S, Zin WA, Milic-Emili J (1988) Flow and volume dependence of pulmonary mechanics in anesthetized cats. J Appl Physiol 64:441–450

  23. 23.

    Brenner M, Mukai DS, Russell JE, Spiritus EM, Wilson AF (1990) A new method for measurement of airway occlusion pressure. Chest 98:421–427

  24. 24.

    Bland JM, Altman DG (1986) Statistical methods for assessing agreement between two methods of clinical measurement. Lancet 8:307–310

  25. 25.

    Similowski T, Levy P, Corbeil C, Albala M, Pariente R, Derenne JP, Bates JHT, Jonson B, Milic-Emili J (1989) Viscoelastic behaviour of lung and chest wall in dogs determined by flow interruption. J Appl Physiol 67:2219–2229

  26. 26.

    Younes M, Riddle W, Polacheck J (1981) A model for the relation between respiratory neural and mechanical outputs. III. Validation. J Appl Physiol 51:990–1001

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Author information

Correspondence to G. A. Iotti.

Additional information

Supported by a grant provided by IRCCS Policlinico S. Matteo, Pavia, Italy; technical support provided by Hamilton Bonaduz AG, Bonaduz, Switzerland

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Iotti, G.A., Braschi, A., Brunner, J.X. et al. Respiratory mechanics by least squares fitting in mechanically ventilated patients: Applications during paralysis and during pressure support ventilation. Intensive Care Med 21, 406–413 (1995). https://doi.org/10.1007/BF01707409

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Key words

  • Respiratory mechanics
  • Respiratory resistance
  • Respiratory compliance
  • Mechanical ventilation
  • Pressure support ventilation