Journal of Applied Physiology, Vol 65, Issue 3 1400-1409, Copyright © 1988 by American Physiological Society

ARTICLES

A minimal mathematical model of human periodic breathing

D. W. Carley and D. C. Shannon
Pediatric Pulmonary Unit, Massachusetts General Hospital, Boston 02114.

Numerous mathematical models of periodic breathing (PB) currently exist. These models suggest mechanisms that may underlie many known causes of PB. However, each model that has been shown to simulate PB under reasonable conditions contains greater than 15 physiological parameters. Because some parameters exhibit a wide range of values in a population, such simulations cannot test a model's ability to account for the breathing patterns of individuals. Furthermore it is impractical to perform a direct experimental validation study that would require the estimation of each of 15 or more parameters for each subject. A minimal model of PB is presented that is suitable for direct validation. Analytic expressions are given that define the conditions for PB in terms of the following: 1) CO2 sensitivity, 2) Cardiac output, 3) Mixed venous CO2, 4) Circulation time, and 5) Mean lung volume for CO2. This model is shown to be consistent with previous models and experimental data regarding the degree of hypoxia or congestive heart failure required to produce PB. A quantitative measure of relative stability is defined as a metric of comparison to the human studies described in the accompanying paper (J. Appl. Physiol. 65: 1389-1399, 1988).

This article has been cited by other articles:

				C. H. Manisty, K. Willson, R. Wensel, Z. I. Whinnett, J. E. Davies, W. L. G. Oldfield, J. Mayet, and D. P. Francis Development of respiratory control instability in heart failure: a novel approach to dissect the pathophysiological mechanisms J. Physiol., November 15, 2006; 577(1): 387 - 401. [Abstract] [Full Text] [PDF]

				N. S. Cherniack and G. S. Longobardo Mathematical models of periodic breathing and their usefulness in understanding cardiovascular and respiratory disorders Exp Physiol, March 1, 2006; 91(2): 295 - 305. [Abstract] [Full Text] [PDF]

				A. Xie, J. B. Skatrud, D. S. Puleo, and J. A. Dempsey Influence of arterial O2 on the susceptibility to posthyperventilation apnea during sleep J Appl Physiol, January 1, 2006; 100(1): 171 - 177. [Abstract] [Full Text] [PDF]

				E. N. Bruce Assessing Respiratory Control during Spontaneous Breathing . Practice May Be More Difficult than Theory Am. J. Respir. Crit. Care Med., April 15, 2002; 165(8): 1033 - 1034. [Full Text] [PDF]

				J. G. Van den Aardweg and J. M. Karemaker Influence of Chemoreflexes on Respiratory Variability in Healthy Subjects Am. J. Respir. Crit. Care Med., April 15, 2002; 165(8): 1041 - 1047. [Abstract] [Full Text] [PDF]

				G. D. Pinna, R. Maestri, A. Mortara, M. T. L. Rovere, F. Fanfulla, and P. Sleight Periodic breathing in heart failure patients: testing the hypothesis of instability of the chemoreflex loop J Appl Physiol, December 1, 2000; 89(6): 2147 - 2157. [Abstract] [Full Text] [PDF]

				D. P. Francis, K. Willson, L. C. Davies, A. J.S. Coats, and M. Piepoli Quantitative General Theory for Periodic Breathing in Chronic Heart Failure and its Clinical Implications Circulation, October 31, 2000; 102(18): 2214 - 2221. [Abstract] [Full Text] [PDF]

				J. Trinder, J. A. Van Beveren, P. Smith, J. Kleiman, and A. Kay Correlation between ventilation and EEG-defined arousal during sleep onset in young subjects J Appl Physiol, December 1, 1997; 83(6): 2005 - 2011. [Abstract] [Full Text] [PDF]

				J. Lai and E. N. Bruce Ventilatory stability to transient CO2 disturbances in hyperoxia and normoxia in awake humans J Appl Physiol, August 1, 1997; 83(2): 466 - 476. [Abstract] [Full Text] [PDF]