A model for the distribution and transport of CO2 in the body and the ventilatory response to CO2

CO2 rebreathing model in COPD: blood-to-gas equilibration

Rebreathing in a closed system can be used to estimate mixed venous PCO2 (PvCO2) and cardiac output, but these estimates are affected by VA/Q heterogeneity. The purpose of this study was to validate a mathematical model of CO2 exchange during CO2 rebreathing in 29 patients with chronic obstructive pulmonary disease (COPD), with baseline arterial PCO2 (PaCO2) ranging from 28 to 60 mmHg. Rebreathing increased end-tidal PCO2 (PETCO2) by 20 mmHg over 2.2 min. This model employed baseline values for inspired (bag) PCO2, estimated PvCO2, distribution of ventilation and blood flow in one high VA/Q and one low VA/Q compartment, the ventilation increase and conservation of mass equations to simulate time courses of PICO2, PETCO2, PvCO2, and PaCO2. Measured PICO2 and PETCO2 during rebreathing differed by an average (SEM) of 1.4 (0.4) mmHg from simulated values. By end of rebreathing, predicted PvCO2 was lower than measured and predicted PaCO2, indicating gas to blood CO2 flux. Estimates of the ventilatory response to CO2, quantified as the slope (S) of the ventilation increase versus PETCO2, were inversely related to gas-to-blood PCO2 disequilibria due to VA/Q heterogeneity and buffer capacity (BC), but not airflow limitation. S may be corrected for these artifacts to restore S as a more valid noninvasive index of central CO2 responsiveness. We conclude that a rebreathing model incorporating baseline VA/Q heterogeneity and BC can simulate gas and blood PCO2 in patients with COPD, where VA/Q variations are large and variable.

Partial CO2 rebreathing indirect Fick technique for non-invasive measurement of cardiac output

OBJECTIVE

Evaluation in animals of a non-invasive and continuous cardiac output monitoring system based on partial carbon-dioxide (CO2) rebreathing indirect Fick technique.

METHODS

We have developed a non-invasive cardiac output (NICO) monitoring system, based on the partial rebreathing method. The partial rebreathing technique employs a differential form of the Fick equation for calculating cardiac output (QT) using non-invasive measurements. Changes in CO2 elimination (deltaVCO2) and partial pressure of end-tidal CO2 (deltaPETCO2) in response to a brief period of partial rebreathing are used to measure pulmonary capillary blood flow (Q(PCBF)). A non-invasive estimate of anatomic and intrapulmonary shunt fraction (Q(S)/Q(T)), based on oxygen saturation from pulse oximetry (SpO2) and inspired oxygen concentration (FIO2), is added to compute total cardiac output [Q(T) = Q(PCBF)/(1 - Q(S)/Q(T))]. The performance of the NICO was compared with iced 5% dextrose bolus thermodilution cardiac output (TDco) measurements in 6 dogs. Cardiac output was varied using dobutamine, and halothane, and by clamping of the inferior vena cava. Two hundred and forty-six (n = 246) paired measurements of TDco and NICO over a range of cardiac outputs (TDco range = 0.60-8.87 l/min) were compared using Bland-Altman analysis and weighted correlation coefficient.

RESULTS

The Bland-Altman technique yielded a NICO precision of +/- 0.70 l/min (13.8%) with a mean bias of -0.07 l/min (-1.4%) compared to TDco. The weighted correlation coefficient between TDco and NICO values was: r = 0.93 (n = 246).

CONCLUSION

The partial CO2 rebreathing technique for measurement of cardiac output is non-invasive, automated, and based on the well accepted Fick principle. The limits of agreement between NICO and TDco is within the recommended value for NICO to be a clinically acceptable method for cardiac output measurement. The results of this canine study show that NICO performed as well, and in some cases better, than other currently available non-invasive cardiac output techniques over a wide range of cardiac outputs.

Alignment of ventilation and gas fraction for breath-by-breath respiratory gas exchange calculations in exercise

The effects of correct alignment of the ventilation and fractional gas concentration during breath-by-breath calculation of oxygen uptake (VO2) have been examined during exercise in four subjects, at each of 50, 100, 150, and 200 W. Data were analyzed using lagtimes in the range of 200 to 400 msec to align ventilation with gas fraction. VO2 was markedly affected by lagtime. Calculated values of VO2 at 200 W ranged from 1953 +/- 55 (mean +/- SEM), to 2583 +/- 29, to 2843 +/- 28 ml.min-1 with lagtimes of 200, 310, and 400 msec, respectively. Mean values from a mixing box system did not differ significantly from the mean of the breath-by-breath data collection with a lagtime of 310 msec. Additional computations have shown that temperature correction can markedly affect calculated ventilatory volumes and N2 balance. VO2 was not changed because of the compensation from the calculated effects of changes in lung gas stores.

CO2 control of the respiratory system: plant dynamics and stability analysis

A stability analysis of respiratory chemical control is developed using a mathematical model of CO2 mass transport dynamics. Starting with a 3-compartment model of CO2 stores that distinguishes alveolar, muscle, and other tissue, model reduction techniques are applied to obtain a first-order representation of the respiratory plant. This model contains an effective tissue volume for CO2, whose derived value is much smaller than previously predicted. To investigate oscillatory instabilities, a controller which incorporates only peripheral chemoreceptor responses was added to the first-order plant model. An explicit stability index (SI) is obtained analytically from a linearized version of this model. SI varies directly with the controller gain and circulation delay time and inversely with the effective tissue volume and inspired CO2 concentration. Numerical simulations using the first-order nonlinear model show that SI is a good predictor of system stability. According to the linearized model, the system is stable for SI less than 1; from the nonlinear model, the system is stable for SI less than 1.1. For typical normal adults, the SI value is well within the stable region.

Rate of elimination of excess CO2 in humans

This study examined the ability of the respiratory system of awake normal subjects to correct an acute disturbance in body CO2 stores produced by rebreathing. Thirteen subjects, after 10 min of O2 breathing, rebreathed CO2 for 4 min in order to increase CO2 stores. The rate of CO2 elimination (VelCO2) after rebreathing was measured breath by breath for the next 10 min. The VelCO2 was highest immediately after the end of rebreathing and then decreased non-linearly toward the pre-rebreathing level as stored CO2 decreased. The time for 90% of this change in VelCO2 to occur (T90) was measured as an index of the rate of correction of body CO2 imbalance. The T90 was independent of the peak PCO2 obtained by rebreathing, and changes in CO2 storage did not produce significant changes in T90. The value of T90 was 120 +/- 48 sec (mean +/- SD) and there was a significant negative correlation between T90 and the slope of the ventilatory response to CO2 among subjects (r = -0.864, P less than 0.001). These results suggest that the capacity to eliminate the acutely stored CO2 in awake normal subjects is dependent on the ventilatory response to CO2. The data were further analyzed by using a mathematical model. Mathematical analysis confirmed the inverse relationship between CO2 sensitivity and T90. Model simulations also suggested that the restoration speed of CO2 balance under hyperoxic conditions is affected by brain blood flow but mainly determined by the sensitivity of central chemoreceptors.

[Mathematical simulation of the respiratory system (author's transl)]

The respiratory system is described as a feedback control system. The controller consists of the peripheral chemoreceptors and the central chemosensitive structures, the respiratory centre in the medulla oblongata and the thorax-lung pump which they drive. The controlled system is comprised of three compartments (lung, brain and the remaining tissue) connected by the blood circulation. The controlled values are arterial pH and arterial O2 partial pressure and cerebral extracellular pH. Earlier models have been improved by: (1) the dead space description, (2) the thermodynamic formulation of the CO2 dissociation equation and the simple but accurate O2 dissociation equation of the blood, (3) the alteration of the CO2 dissociation equation for the brain and the remaining tissue to accommodate recent results, (4) the application of the one-receptor-theory of central chemosensitivity, (5) the pH dependence of brain circulation, (6) the bicarbonate exchange between blood and extracellular fluid of the brain and (7) the introduction of variable circulation times. Respiratory and metabolic disturbances of the respiratory system are analyzed. The mathematical formulation of the respiratory system is a differential difference equation system. In the steady state the experimental results are reproduced fairly well. A slight discrepancy is found in the simulation of metabolic acidosis. Apparently we have assumed the sensitivity of the peripheral chemoreceptors to be too large so that the respiratory response is not correctly predicted. In the numerical solution there is an overshoot in the on-transient and a damped oscillation in the off-transient of the alveolar CO2 partial pressure during respiratory acidosis. We have varied the parameters to make deviations small. The best agreement seems to result, if the central threshold is near the normal extracellular pH of the brain. A further deviation from experimental findings is that the cerebral CO2 and H+ concentration, the blood circulation of the brain, the alveolar O2 partial tension and the ventilation show a slight oscillation in the off-transient. Except for these discrepancies the experimental results, especially the stability of the extracellular pH of the brain, are reproduced fairly well. During hypoxia there are deviations form the experimental results if the central residual activity is constant and the central threshold deviates from the normal extracellular pH of the brain. But if the central residual activity is pH dependent and if the central threshold is equal to the normal extracellular pH of the brain, then the time course of VE and the other variables agree fairly well with experimental results. There is also a good correspondence between the theoretical and experimental data during hyperoxia. During metabolic acidosis the time constant of the bicarbonate exchange between blood and extracellular fluid of the brain is important. If a time constant of one minute is assumed, then the predicted and the experimental results correspond sufficiently well.