We thank Drs. Overdyk and Hillmann for their interest in our study on the dynamic modeling of the respiratory effects of remifentanil and propofol in humans.1
In their comments, they raise an important issue—incorporation of airway collapse in the pharmacodynamic model. Although we certainly considered obstructive apnea, we intentionally did not incorporate in our current model a component that accounts for airway patency. The reason for this decision was simply that airway collapse did not play a role in the respiratory responses observed in our cohort of young healthy volunteers. The subjects inhaled and exhaled through a mask placed over nose and mouth, held in position by one of the investigators, and aimed at keeping the airway open. Furthermore, we controlled for airway patency by two distinct measures. We continuously observed the thoracic and abdominal movement of subjects and monitored pulse transit time. Pulse transit time is a noninvasive measure that gives an indication of respiratory effort.2The low values of end-tidal Pco2observed close to apnea are not the result of airway obstruction, but rather very low tidal volumes with open airways.
Overdyk and Hillmann's comments suggest that some aspects of our model deserve additional explanation. First, they state that end-tidal carbon dioxide (ETco2) is an input for the model. This supposition is incorrect. Instead, ETco2and measured minute ventilation are bivariate model outputs. We refer readers to equations 3 and 4 in our model.1Remifentanil concentration and propofol are the model inputs.
Second, Overdyk and Hillmann state that our model does not incorporate a controller and a plant. In our second figure,1we presented both elements; the controller is highlighted, and the top part (i.e ., carbon dioxide kinetics) is the plant. Because we have a medical audience, we decided not to use wording specific to engineering when defining the plant part of our model. Interested readers may wish to refer to Lennart Ljung's System Identification: Theory for the User (Englewood Cliffs, NJ, Prentice-Hall, 1987).
Third, we do take CO2kinetics into account and, consequently, Pco2is a dependent variable.
Finally, we measured arterial carbon concentrations at various time points during our experiments (data not shown). Although the values we observed were somewhat higher than ETco2values, they closely followed patterns observed for end-tidal Pco2. We refer readers to the first equation and figure 2 of our original article.1Our model was based on end-tidal Pco2for various reasons. It is an easily measured variable and, consequently, may be used clinically as well.
The use of arterial lines for repetitive arterial carbon dioxide measurements is sometimes problematic.3See, for example, reference 3, where we acknowledge the discussion we had with our ethics committee regarding placement of arterial lines in healthy volunteers.3In addition, using arterial Pco2as a model output requires frequent sampling, which has stimulatory effects on breathing.4To the best of our knowledge, there are no studies with arterial sampling regimens that come close to the frequency of that used in our most recent study.1We submit that, relative to sparse (e.g ., two or three times per min) arterial carbon dioxide measurements, the use of frequent ETco2data points increases the reliability of model parameter estimates. Our model enables realistic simulations of the ventilatory effects of opioids and sedatives with ETco2as output.
As stated previously,4breathing in the perioperative patient is under the influence of many factors, including respiratory drive, arousal state, and the functionality of pharyngeal dilating muscles. Opioids, anesthetics, and sedatives have an effect on all three elements. In our most recent study,1we explored their effect on the ventilatory drive only. The effect of these agents on changes in arousal state and upper-airway patency requires further investigation.
*Leiden University Medical Center, Leiden, The Netherlands. firstname.lastname@example.org