How do changes in exhaled CO₂ measure changes in cardiac output? A numerical analysis model

Abstract

Objective: In a previous study in anesthetized animals, the slope of percent decreases in exhaled CO₂ versus percent decreases in cardiac output (Q(T) inflation of vena cava balloons) was 0.73. To examine the mechanisms underlying this exhaled CO₂-Q(T) relationship, an iterative numerical analysis computer model of non-steady state CO(2) kinetics was developed.

Methods: The model consisted of a large peripheral tissue compartment connected by venous return and [Formula: see text] to a small central pulmonary compartment. Equations were developed to describe the movement of CO₂ in this system. Decreases in Q(T) were accompanied by experimentally measured increases in alveolar dead space fraction (VD: (alv)/VT: (alv)), generated by decreased pulmonary vascular pressure during the Q(T) decrease.

Results: When the model was perturbed by a 40% decrease in Q(T) and an increase in VD: (alv)/VT: (alv) from 5 to 20.6%, average alveolar expired P(CO₂) (PAE(CO₂)) decreased from 37.5 to 29.4 mm Hg, similar to the animal experiments. Due to the high peripheral tissue compliance for CO₂, the computer model demonstrated that, after a decrease in Q(T), at least 1 h was required for compartment CO₂ stores to approach a new equilibrium state.

Conclusions: The numerical analysis computer model helps to delineate the mechanisms underlying how decreased Q(T) resulted in decreased exhaled CO₂. The model permitted deconvolution of the effects of simultaneous variables and the interrogation of parameters that would be difficult to measure in actual experiments.