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

Abstract

Rebreathing in a closed system can be used to estimate mixed venous $P_{{\rm CO}_{2}}\;(P\bar{v}_{{\text{CO}}_2})$ and cardiac output, but these estimates are affected by $\dot{V}_{\rm A}/\dot{Q}$ 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 $P_{{\rm CO}_{2}}\;(\hbox{Pa}_{{\rm CO}_{2}})$ ranging from 28 to 60 mmHg. Rebreathing increased end-tidal $P_{{\rm CO}_{2}}\;(\hbox{PET}_{{\rm CO}_{2}})$ by 20 mmHg over 2.2 min. This model employed baseline values for inspired (bag) $P_{{\rm CO}_{2}},$ estimated $P\bar{v}_{{\text{CO}}_2},$ distribution of ventilation and blood flow in one high $\dot{V}_{\rm A}/\dot{Q}$ and one low $\dot{V}_{\rm A}/\dot{Q}$ compartment, the ventilation increase and conservation of mass equations to simulate time courses of $\hbox{PI}_{{\rm CO}_{2}},\hbox{PET}_{{\rm CO}_{2}},\; P\bar{v}_{{\text{CO}}_{2}}$ and $\hbox{Pa}_{{\rm CO}_{2}}.$ Measured $\hbox{PI}_{{\rm CO}_{2}}$ and $\hbox{PET}_{{\rm CO}_{2}}$ during rebreathing differed by an average (SEM) of 1.4 (0.4) mmHg from simulated values. By end of rebreathing, predicted $P\bar{v}_{{\text{CO}}_2}$ was lower than measured and predicted $\hbox{Pa}_{{\rm CO}_{2}},$ indicating gas to blood CO₂ flux. Estimates of the ventilatory response to CO₂, quantified as the slope (S) of the ventilation increase versus $\hbox{PET}_{{\rm CO}_{2}},$ were inversely related to gas-to-blood $P_{{\rm CO}_{2}}$ disequilibria due to $\dot{V}_{\rm A}/\dot{Q}$ 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 $\dot{V}_{\rm A}/\dot{Q}$ heterogeneity and BC can simulate gas and blood $P_{{\rm CO}_{2}}$ in patients with COPD, where $\dot{V}_{\rm A}/\dot{Q}$ variations are large and variable.