# Mathematical method to build an empirical model for inhaled anesthetic agent wash-in

Jan FA Hendrickx1*, Harry Lemmens2, Sofie De Cooman3, André AJ Van Zundert4, René EJ Grouls5, Eric Mortier6 and Andre M De Wolf7

### Author affiliations

1 Department of Anesthesiology, Intensive Care and Pain Therapy, Onze Lieve Vrouwziekenhuis, Aalst, Belgium

2 Department of Anesthesia, Stanford School of Medicine, Stanford, California, USA

3 Department of Anesthesiology, Sint-Jan Hospital, Brussels, Belgium

4 Department of Anesthesiology, Intensive Care and Pain Therapy, Catharina Hospital, Eindhoven, The Netherlands

5 Department of Clinical Pharmacy, Catharina Hospital, Eindhoven, The Netherlands

6 Department of Anesthesiology, University of Ghent, Ghent, Belgium

7 Department of Anesthesiology, Northwestern University Medical School, Chicago, Illinois, USA

For all author emails, please log on.

BMC Anesthesiology 2011, 11:13  doi:10.1186/1471-2253-11-13

Published: 24 June 2011

### Abstract

#### Background

The wide range of fresh gas flow - vaporizer setting (FGF - FD) combinations used by different anesthesiologists during the wash-in period of inhaled anesthetics indicates that the selection of FGF and FD is based on habit and personal experience. An empirical model could rationalize FGF - FD selection during wash-in.

#### Methods

During model derivation, 50 ASA PS I-II patients received desflurane in O2 with an ADU® anesthesia machine with a random combination of a fixed FGF - FD setting. The resulting course of the end-expired desflurane concentration (FA) was modeled with Excel Solver, with patient age, height, and weight as covariates; NONMEM was used to check for parsimony. The resulting equation was solved for FD, and prospectively tested by having the formula calculate FD to be used by the anesthesiologist after randomly selecting a FGF, a target FA (FAt), and a specified time interval (1 - 5 min) after turning on the vaporizer after which FAt had to be reached. The following targets were tested: desflurane FAt 3.5% after 3.5 min (n = 40), 5% after 5 min (n = 37), and 6% after 4.5 min (n = 37).

#### Results

Solving the equation derived during model development for FD yields FD=-(e(-FGF*-0.23+FGF*0.24)*(e(FGF*-0.23)*FAt*Ht*0.1-e(FGF*-0.23)*FGF*2.55+40.46-e(FGF*-0.23)*40.46+e(FGF*-0.23+Time/-4.08)*40.46-e(Time/-4.08)*40.46))/((-1+e(FGF*0.24))*(-1+e(Time/-4.08))*39.29). Only height (Ht) could be withheld as a significant covariate. Median performance error and median absolute performance error were -2.9 and 7.0% in the 3.5% after 3.5 min group, -3.4 and 11.4% in the 5% after 5 min group, and -16.2 and 16.2% in the 6% after 4.5 min groups, respectively.

#### Conclusions

An empirical model can be used to predict the FGF - FD combinations that attain a target end-expired anesthetic agent concentration with clinically acceptable accuracy within the first 5 min of the start of administration. The sequences are easily calculated in an Excel file and simple to use (one fixed FGF - FD setting), and will minimize agent consumption and reduce pollution by allowing to determine the lowest possible FGF that can be used. Different anesthesia machines will likely have different equations for different agents.