Comparison of pneumotachography and anemometery for flow measurement during mechanical ventilation with volatile anesthetics

Abstract

Volatile anesthetics alter the physical properties of inhaled gases, such as density and viscosity. We hypothesized that the use of these agents during mechanical ventilation would yield systematic biases in estimates of flow ($\dot{V}$) and tidal volume (V _T) for two commonly used flowmeters: the pneumotachograph (PNT), which measures a differential pressure across a calibrated resistive element, and the hot-wire anemometer (HWA), which operates based on convective heat transfer from a current-carrying wire to a flowing gas. We measured $\dot{V}$ during ventilation of a spring-loaded mechanical test lung, using both the PNT and HWA placed in series at the airway opening. Delivered V _T was estimated from the numerically-integrated $\dot{V}$. Measurements were acquired under baseline conditions with room air, and during ventilation with increasing concentrations of isoflurane, sevoflurane, and desflurane. We also evaluated a simple compensation technique for HWA flow, which accounted for changes in gas mixture density. We found that discrepancies in estimated V _T between the PNT and HWA occurred during ventilation with isoflurane (6.3 ± 3.0%), sevoflurane (10.0 ± 7.3%), and desflurane (25.8 ± 17.2%) compared to baseline conditions. The magnitude of these discrepancies increased with anesthetic concentration. A simple compensation factor based on density reduced observed differences between the flowmeters, regardless of the anesthetic or concentration. These data indicate that the choice and concentration of anesthetic agents are primary factors for differences in estimated V _T between the PNT and HWA. Such discrepancies may be compensated by accounting for alterations in gas density.

Appendix

Density (ρ) for a homogeneous gas is expressed as the mass contained within a given volume:

$$\rho = \frac{nM}{V}$$

(9)

where n is the number of moles in a given volume V, and M is the molecular weight of the particular gas species. For an ideal gas this expression can be re-written as:

$$\rho = \frac{PM}{{{\mathcal{R}}T}}$$

(10)

where P is absolute pressure, T is absolute temperature, and ${\mathcal{R}}$ is the universal gas constant. In a mixture of N ideal gases, the mole fraction (x _i ) of each species is given by the ratio of the number of moles of each species (n _i ) relative to the total number of moles ($n_{\text{mix}}$):

$$\begin{array}{*{20}c} {x_{i} = \frac{{n_{i} }}{{n_{\text{mix}} }}} & {\text{where}} & {n_{\text{mix}} = \mathop \sum \limits_{i = 1}^{N} n_{i} } \\ \end{array}$$

(11)

The gas mixture density ($\rho_{\text{mix}}$) is then given by modifying Eq. 9 to obtain:

$$\rho_{\text{mix}} = \frac{1}{V}\mathop \sum \limits_{i = 1}^{N} n_{i} M_{i} = \frac{{n_{\text{mix}} }}{V}\mathop \sum \limits_{i = 1}^{N} x_{i} M_{i}$$

(12)

where M _i is molecular weight of each species. Again assuming ideal gas behavior:

$$\rho_{\text{mix}} = \frac{P}{{{\mathcal{R}}T}}\mathop \sum \limits_{i = 1}^{N} x_{i} M_{i}$$

(13)

which is equivalent to the weighted average of individual species densities at the same reference temperature and pressure:

$$\rho_{\text{mix}} = \mathop \sum \limits_{i = 1}^{N} x_{i} \rho_{\text{i}}$$

(14)

Glossary

$\upmu$

Gas viscosity

$\uprho$

Gas density

$\uprho_{\text{mix}}$

Density of gas mixture

$\uprho_{\text{cal}}$

Density of gas used for calibration

n

Number of moles of gas

N

Number of ideal gas species in gas mixture

$n_{\text{mix}}$

Total number of moles of gas in mixture

P

Absolute pressure

M

Molecular weight of gas

T

Temperature of gas

V

Volume of gas

i

Gas species index

x _i

Molar fraction of gas species i

${\mathcal{R}}$

Universal gas constant

$\dot{V}$

Flow

$\dot{V}_{\text{PNT}}$

Flow estimated using PNT

$\dot{V}_{\text{HWA}}$

Flow estimated using HWA

$\dot{V}_{HWA}^{'}$

Compensated estimate of flow from the HWA

V _T

Tidal volume

V _{T, HWA}

Estimated tidal volume from the HWA

V _{T, PNT}

Estimated tidal volume from the PNT

PNT

Pneumotachograph

HWA

Hot-wire anemometer

MAC

Minimum alveolar concentrations

ANOVA

Analysis of variance

ΔP

Differential pressure across PNT resistive element

$C_{\text{m}}$

Coefficient from PNT mesh screen geometrical properties

$\upalpha$

Viscous resistance coefficient for PNT mesh screen

h

Heat transfer coefficient between gas and HWA wire

T _w

Temperature of HWA wire

T _g

Temperature of ambient gas

A _w

Surface area of heat exchange on HWA wire

R _w

Resistance of HWA wire

i _w

Current through the HWA wire

A, B

Calibration constants of King’s Law

A _cs

Cross-sectional area of the gas flow in HWA

d _w

Diameter of HWA wire

$C_{{{\text{w}}1}} ,C_{{{\text{w}}2}}$

Coefficients from HWA geometrical properties

k

Thermal conductivity of gas

c _p

Specific heat capacity