Arterial to end-tidal CO₂ gradients during isocapnic hyperventilation

Abstract

Isocapnic hyperventilation (ICHV) is occasionally used to maintain the end-expired CO₂ partial pressure (P_ETCO₂) when the inspired CO₂ (P_ICO₂) rises. Whether maintaining P_ETCO₂ with ICHV during an increase of the P_ICO₂ also maintains arterial PCO₂ (P_aCO₂) remains poorly documented. 12 ASA PS I–II subjects undergoing a robot-assisted radical prostatectomy (RARP) (n = 11) or cystectomy (n = 1) under general endotracheal anesthesia with sevoflurane in O₂/air (40% inspired O₂) were enrolled. P_ICO₂ was sequentially increased from 0 to 0.5, 1.0, 1.5 and 2% by adding CO₂ to the inspiratory limb of the circle system, while increasing ventilation to a target P_ETCO₂ of 4.7–4.9% by adjusting respiratory rate during controlled mechanical ventilation. P_a-ETCO₂ gradients were determined after a 15 min equilibration period at each P_ICO₂ level and compared using ANOVA. Mean (standard deviation) age, height, and weight were 66 (6) years, 171 (6) cm, and 75 (8) kg, respectively. Capnograms were normal and hemodynamic parameters remained stable. P_ETCO₂ could be maintained within 4.7–4.9% in all subjects at all times except in 1 subject with 1.5% P_ICO₂ and 5 subjects with 2.0% P_ICO₂; data from the one subject in whom both 1.5 and 2.0% P_ICO₂ resulted in P_ETCO₂ > 5.1% were excluded from analysis. P_a-ETCO₂ gradients did not change when P_ICO₂ increased. The effect of a modest rise of P_ICO₂ up to 1.5% on P_ETCO₂ during RARP can be readily overcome by increasing ventilation without altering the P_a-ETCO₂ gradients. At higher P_ICO₂, airway pressures may become a limiting factor, which requires further study.

Appendix A

The relationship between ventilation, CO₂ elimination, P_ICO₂ and P_ETCO₂ can be derived by considering CO₂ mass balances in the lung: the amount of exhaled CO₂ has to be the same as the amount of CO₂ entering the lungs (See Eq. 1). If it is assumed that in- and expired MV are the same, if f_VD is defined as apparatus plus anatomical dead space, and if partial pressures in the formula below are expressed in fraction of 1 atm, these mass balances are described as:

Equation 1. CO₂ mass balances in the lung.

The amount of exhaled CO₂ (= amount leaving the Y-piece of the circle breathing system; left hand side of equation) is the sum of the amount contained in the apparatus and anatomical dead space (with concentration P_ICO₂, expressed in fraction) plus the part of exhaled MV that does take place in gas exchange (with concentration P_ETCO₂, expressed in fraction). The amount of CO₂ entering the lungs (right hand side of equation) is the sum of VCO₂ and the amount of inhaled CO₂. VCO₂ is the amount of CO₂ entering the alveoli from the mixed venous blood, which itself is the sum of endogenous CO₂ production and any exogenous CO₂ load (e.g. resorption from a capnopneumoperitoneum). The amount of inhaled CO₂ is the product of MV and P_ICO₂, expressed in fraction. Equation [Eq. 1] can be rearranged as follows, starting by dividing all parameters by MV:

$$\begin{aligned}{\text{f}}_{{{\text{VD}}}} *{\text{ P}}_{{\text{I}}} {\text{CO}}_{{2}} + \, \left( {{1} - {\text{f}}_{{{\text{VD}}}} } \right) \, *{\text{ P}}_{{{\text{ET}}}} {\text{CO}}_{{2}} = \, \left( {{\text{VCO}}_{{2}} /{\text{ MV}}} \right) \, +{\text{ P}}_{{\text{I}}} {\text{CO}}_{{2}}\\ - {\text{ P}}_{{\text{I}}} {\text{CO}}_{{2}} + {\text{ f}}_{{{\text{VD}}}} *{\text{ P}}_{{\text{I}}} {\text{CO}}_{{2}} + \, \left( {{1} - {\text{f}}_{{{\text{VD}}}}} \right) \, * {\text{ P}}_{{{\text{ET}}}} {\text{CO}}_{{2}} = {\text{ VCO}}_{{2}} /{\text{ MV}}\\ - \, \left( {{1 } - {\text{ f}}_{{{\text{VD}}}} } \right) \, *{\text{ P}}_{{\text{I}}} {\text{CO}}_{{2}} + \, \left( {{1} - {\text{f}}_{{{\text{VD}}}} } \right) \, *{\text{ P}}_{{{\text{ET}}}} {\text{CO}}_{{2}} = {\text{ VCO}}_{{2}} /{\text{ MV}}\\ \left( {{1} - {\text{f}}_{{{\text{VD}}}} } \right) \, * \, \left( {{\text{P}}_{{{\text{ET}}}} {\text{CO}}_{{2}} - {\text{ P}}_{{\text{I}}} {\text{CO}}_{{2}} } \right) \, = {\text{ VCO}}_{{2}} /{\text{ MV}}\\{P}_{{{\text{ET}}}} {\text{CO}}_{{2}} - {\text{ P}}_{{\text{I}}} {\text{CO}}_{{2}} = \, \left( {{\text{VCO}}_{{2}} /{\text{ MV}}} \right)/\left( {{1} - {\text{f}}_{{{\text{VD}}}} } \right)\end{aligned}$$

(2)

Rearranging Eq. 2 explains how ventilation has to be adjusted to keep P_ETCO₂ constant (isocapnia) when P_ICO₂ increases:

$${\text{P}}_{{{\text{ET}}}} {\text{CO}}_{{2}} = \left( {{\text{VCO}}_{{2}} /{\text{MV}}} \right)/\left( {{1} - {\text{f}}_{{{\text{VD}}}} } \right) + {\text{P}}_{{\text{I}}} {\text{CO}}_{{2}}$$

$${\text{P}}_{{{\text{ET}}}} {\text{CO}}_{2} = \frac{{{\text{VCO}}_{2} }}{{{\text{MV*}}\left( {1 - {\text{f}}_{{{\text{VD}}}} } \right)}} + {\text{P}}_{{\text{I}}} {\text{CO}}_{2}$$

(3)

When the increase in P_ICO₂ is small (e.g. 0.1%), it can be ignored because the additive effect of a rise of P_ICO₂ of that order of magnitude on P_ETCO₂ is clinically irrelevant. The effect of a modest rise in P_ICO₂ on P_ETCO₂ can be curtailed by increasing MV. The extent to which MV has to be increased to maintain P_ETCO₂ with various P_ICO₂ concentrations can be derived by rearranging the above equation:

$${\text{MV}} = \frac{{{\text{VCO}}_{2} }}{{\left( {{\text{P}}_{{{\text{ET}}}} {\text{CO}}_{2} - {\text{P}}_{{\text{I}}} {\text{CO}}_{2} } \right)\left( {1 - {\text{f}}_{{{\text{VD}}}} } \right)}}$$

(4)

Equation 4 illustrates that the increase in MV required to maintain P_ETCO₂ varies in a non-linear manner with P_ICO₂.