A mathematical analysis of carbon dioxide respiration in man

Chilton, A. B.; Stacy, Ralph W.

doi:10.1007/bf02477818

Cited by 39 publications

(14 citation statements)

References 2 publications

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“…(1989) described the difficulty of interpreting and distinguishing different phases of a single breath diagram of spontaneously breathing humans with most severe COPD. Several explanations for the blurring of the transition between phase II and III and increased phase III slopes have been debated in humans: sequential or out‐of‐phase emptying of different parallel lung regions, each containing different gas concentrations of the measured gas (West et al., 1957); continuing evolution of gas from the blood into a contracting alveolar volume (Chilton and Stacey, 1952; DuBois et al., 1981); and the presence of longitudinal gas concentration gradients in the airways due to a combination of factors such as gas convection, molecular diffusion, airway geometry and gas evolution from the blood (Cumming et al., 1967; Scherer et al., 1972, 1988). Thus, the division of the volumetric capnogram into strict definitions of phases I, II and III is arbitrary to some extent as the expirogram is a continuous curve influenced by both convection and diffusion (Fletcher et al., 1986).…”

Section: Discussionmentioning

confidence: 99%

Statistical Shape Analysis of Volumetric Capnograms: Evaluation of a New Approach for the Assessment of Pulmonary Function in Horses with Chronic Obstructive Pulmonary Disease

Herholz¹,

Straub²,

Moens³

et al. 2001

Journal of Veterinary Medicine Series A

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The shape of the volumetric capnogram is modified by airway obstruction, and the evaluation of this deformation could allow an indirect measurement of bronchial patency. The study included 35 horses; five horses without evidence of pulmonary disease (group I) and 30 horses suffering from different degrees of chronic obstructive pulmonary disease (COPD) (groups II-IV). Data of recorded CO2 and volume curves were off-line plotted and statistically analysed using regression analysis. Analyses were performed separately for fractions 25-95% (VTE25-95), 25-50% (VTE25-50) and 50-95% (VTE50-95) of expiratory tidal volume. For VTE25-95 estimates of linear and quadratic regression parameters were significantly different between groups. For VTE25-50 linear terms were significant in all clinical groups and decreased considerably from group I to group IV. Linear and quadratic terms for VTE50-95 were significant in all clinical groups and increased with the severity of COPD. The difference of total expiratory CO2 volume was significant between all groups. Statistical analysis of the volumetric capnogram is a precise method for description of shape deformities of the single breath diagram for CO2 (SBD-CO2) in horses with COPD and global models including phase II and III of the SBD-CO2 are helpful in the detection of pulmonary function impairment. However, although the model of the statistical shape analysis of the SBD-CO2 is precise, it may not necessarily be a useful test to discriminate horses with minor, moderate and severe COPD for clinical use.

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Section: Discussionmentioning

confidence: 99%

Statistical Shape Analysis of Volumetric Capnograms: Evaluation of a New Approach for the Assessment of Pulmonary Function in Horses with Chronic Obstructive Pulmonary Disease

Herholz¹,

Straub²,

Moens³

et al. 2001

Journal of Veterinary Medicine Series A

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“…The derivation of PV, CO, from asymptotic rise of PET,CO, during rebreathing from a bag initially containing a low CO, concentration was theoretically established by Chilton & Stacy (1952). The asymptote may be obtained graphically (Jernerus, Lundin & Thomson, 1963) or mathematically by least squares regression analysis (Wise & Defares, 1972).…”

Section: Discussionmentioning

confidence: 99%

Comparison of Two Rebreathing Methods for the Determination of Mixed Venous Partial Pressure of Carbon Dioxide during Exercise

Heigenhauser

Jones

1979

Clinical Science

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1. Duplicate measurements were made of mixed venous Pco, (PV, co,) by two rebreathing methods during steady-state exercise at three power outputs in seven subjects. One method employed a high initial bag CO, concentration to obtain equilibrium of CO, in the lung-bag system before recirculation (equilibrium method); in the other, a low initial bag CO, concentration was used and a statistical method was applied to alveolar Pco, rneasurements before recirculation, to obtain the asymptote from the exponential rise in end-tidal Pco, during rebreathing (exponential method).2. The reproducibility was similar; SD of duplicate determinations of PV, co, was 0-15 kPa (1 -1 mmHg) for the equilibrium method and 0.20 kPa (1 -5 mmHg) for the exponential method. Measurements of PV,co, by the exponential method were systematically lower than the equilibrium method.When the equilibrium PC,co, was corrected for the alveolar-arterial ('downstream') Pco, difference, using published values, PV, co, was similar for both methods. 3.As an alveolar to arterial Pco, difference did not appear to exist with the exponential method, it is concluded that the previously described disequilibrium between alveolar and arterial Pco, during rebreathing in exercise is mainly related to prevention of net CO, movement from the pulmonary capillary blood in the equilibrium method, and is not present when continuous CO, evolution occurs in the exponential method.

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“…In general, the more parameters one attempts to estimate the larger will be the variance of each parameter estimate. Simulation studies of mathematical models of varying complexity have been performed in the past [24][25][26][27][28][29]. Using these results as a basis, Dresdner et al [30] modeled the CO2 exchange system and compared simulation results with measured data from a mechanically ventilated subject.…”

Section: Introductionmentioning

confidence: 99%

A deep breath method for noninvasive estimation of cardiopulmonary parameters

Mitchell

1988

J Clin Monit Comput

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A specific ventilation pattern incorporating a single deep breath is used to demonstrate the possibility of estimating six cardiopulmonary parameters by measuring respiratory flow and expired oxygen and carbon dioxide concentrations at the mouth. Equations are derived from both alternating and continuous ventilation models of gas exchange which allow the six parameter estimates to be computed. The results indicate that pulmonary capillary blood flow, functional residual capacity, equivalent lung volume, mixed venous PO2 and PCO2, and pulmonary tissue plus capillary blood volume can be estimated in subjects with normal gas exchange. The use of a mechanical ventilator to provide a uniform ventilation pattern before and after the ventilator induced deep breath is the key to the methods simplicity. This allowed parameter estimates to be obtained which could then be analyzed for accuracy and precision. The feasibility of estimating these parameters, demonstrated by the present study, suggests that a recursive least squares estimation procedure could be used to recover the time variation of each parameter during exercise stress testing of subjects with normal or nearly normal gas exchange.

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A mathematical analysis of carbon dioxide respiration in man

Cited by 39 publications

References 2 publications

Statistical Shape Analysis of Volumetric Capnograms: Evaluation of a New Approach for the Assessment of Pulmonary Function in Horses with Chronic Obstructive Pulmonary Disease

Statistical Shape Analysis of Volumetric Capnograms: Evaluation of a New Approach for the Assessment of Pulmonary Function in Horses with Chronic Obstructive Pulmonary Disease

Comparison of Two Rebreathing Methods for the Determination of Mixed Venous Partial Pressure of Carbon Dioxide during Exercise

A deep breath method for noninvasive estimation of cardiopulmonary parameters

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