Abstract
The consequences of requiring a general linear model of respiratory mechanics to inspire a fixed volume in a fixed time in a way that minimizes various measures of muscular energy expenditure are examined. For such a model no volume profile minimizes the time-integral of the applied pressure developed by the respiratory muscles, although this integral is not independent of the profile. Minimizing the mechanical work done by the respiratory muscles, on the other hand, requires that the inspiratory flow be constant. These results support the hypothesis that neither the pressure integral nor the mechanical work are individually minimized over an inspiration by an animal or man at rest. Minimization of a weighted sum of the pressure integral and the work done may be a more physiologically reasonable criterion by which the respiratory muscles direct inspiration. This combined cost function predicts a non-constant optimum velocity profile.
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References
Bates JHT, Milic-Emili J (1985) Breathing patterns and the concepts of minimum respiratory work and minimum effort. To appear in: von Euler C (ed) 10th Nobel Conference on “Neurobiology of the Control of Breathing”, Stockholm, Sept. 4–6. Raven Press, New York
Bates JHT, Rossi A, Milic-Emili J (1985a) Analysis of the behaviour of the respiratory system with constant inspiratory flow. J Appl. Physiol 58:1840–1848
Bates JHT, Decramer M, Chartrand D, Zin WA, Boddener A, Milic-Emili J (1985b) Volume-time profile during relaxed expiration in the normal dog. J Appl Physiol 59:732–737
Bracewell RN (1978) The Fourier transform and its applications, 2nd ed McGraw-Hill, New York
Collett PW, Perry C, Engel LA (1985) Pressure-time product, flow, and oxygen cost of resistive breathing in humans. J Appl Physiol 58:1263–1272
Fixley MS, Roussos CS, Murphy B, Martin RR, Engel LA (1978) Flow dependence of gas distribution and the pattern of inspiratory muscle contraction. J Appl Physiol 45:733–741
Hämäläinen RP (1983) Optimization of respiratory airflow. In: Whipp BJ, Wiberg DM (eds) Modelling and control of breathing. Elsevier, New York, pp 181–188
Hämäläinen RP, Viljanen AA (1978) Modelling the respiratory airflow pattern by optimization c iteria. Biol Cybern 29:143–149
Hatze H (1976) The complete optimization of a human motion. Math Biosci 28:99–135
Hildebrandt J (1970) Pressure-volume data of cat lung interpreted by a plastoelastic, linear viscoelastic model. J Appl Physiol 28:365–372
Jackson AC, Tabrizi M, Kotlikoff MI, Voss JR (1984) Airway pressures in an asymmetrically branched airway model of the dog respiratory system. J Appl Physiol 57:1222–1230
Lafortuna CL, Minetti AE, Mognoni P (1984) Inspiratory flow pattern in humans. J Appl Physiol 57:1111–1119
Roussos Ch, Campbell EJM (1986) Respiratory muscle energetics. In: Fishman A, Mead J, Macklem PT (eds) Handbook of physiology. American Physiological Society, Bethesda (in press)
Ruttimann UE, Yamamoto WS (1972) Respiratory airflow patterns that satisfy power and force criteria of optimality. Ann Biomed Eng 1:146–159
Stein RB (1982) What muscle variable(s) does the nervous system control in limb movements? Behav Brain Sci 5:535–577
Swan GW (1984) Applications of optimal control theory in biomedicine. Dekker, New York
Yamashiro SM, Grodins FS (1971) Optimal regulation of respiratory airflow. J Appl Physiol 30:597–602
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Bates, J.H.T. The minimization of muscular energy expenditure during inspiration in linear models of the respiratory system. Biol. Cybern. 54, 195–200 (1986). https://doi.org/10.1007/BF00356858
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DOI: https://doi.org/10.1007/BF00356858