We thank Dr. Looke for his interest in our recently published article.1Space constraints preclude a full description of the in silico and animal studies that we performed before introduction of our controller in the operating room. We followed these different steps: the State Entropy (SE) and the Response Entropy were recorded simultaneously in surgical patients anesthetized using a target-controlled infusion of propofol and remifentanil; a controller guided by the entropy monitor similar to the controller developed for the Bispectral monitor was developed and implemented2; the controller was tuned during laboratory simulation; to obtain the agreement of the relevant French regulatory office for the clinical study, a risk assessment was performed and followed by an open-loop pilot study in swine3; fine-tuning was tested in a previous pilot study in 10 subjects.
However, simulation studies cannot evaluate the controller's performance in surgical patients. In fact, simulation can only determine whether the controller respects command such as to administer or to stop a bolus of propofol. For example, in the same patient a bolus of 20 mg propofol has virtually no effect before induction, yet can reduce SE in the same patient when anesthetized. Furthermore, SE can increase when noxious surgical stimuli are applied to the patient without any change in the control status. And finally, although simulation studies are necessary for administrative clearance, there is little relationship between performance in silico or in animal studies and performance in anesthetized surgical patients because the transfer function remains unknown. Thus, a controller's performance can only be evaluated clinically in comparison with a suitable control group.
Since 2004, we have evaluated the performance of our controller guided by the Bispectral monitor in different circumstances such as a pediatric patient,4a patient suffering from gigantism,5or lung transplantation with or without cardiopulmonary bypass, including the controller behavior during a cardiac arrest.6Our controller has been used in a large population of patients in various clinical situations in various European countries and in Africa.7We have reported 3,742 h of anesthesia using the automated controller in 1,494 patients in whom the controller made automatically 217,074 target modifications of propofol or remifentanil.8In this study, the occurrence of drug overdosing accompanied by burst suppression was 0.6 ‰ after a target modification by the controller. Currently, we have two ongoing two prospective clinical trials (NCT 00896714 and 01198639) in which we have included more than 4,000 patients without untoward effects. These clinical data were obtained without the use of a sophisticated algorithm but using a discrete robust Proportional Integral-Derivative controller (see appendix) and we make the assumption that clinical studies are more relevant than in silico studies.
We agree that anesthesia is not limited to a drug delivery device and that clinicians must maintain cardiopulmonary homeostasis, prevent recall, and limit movement. However, a teletherapeutic system for anesthesia has previously been described9for propofol administration or tracheal intubation.10Technical innovation can improve patient safety and will modify our role in the operating room. Finally, the relevant question is not simulation or laboratory evaluation, but whether patient outcome is improved by automated control. Our study shows that at least intermediate variables are improved by automated control.
The controller has a cascade structure including two controllers with a Proportional Integral-Derivative (PID) algorithm and a target-controlled infusion system for the administration of intravenous anesthetic agents. The three PID elements produce outputs with the following nature:
P element: proportional to the current error which is the “present” error.
I element: proportional to the integral of the error up to the instant t, which is the accumulation of the “past” error.
D element: proportional to the derivative of the error at the instant t, which is the prediction of the “future” error.
Thus, the PID controller takes the present, the past, and the future of the error into consideration. In continuous time, the PID controller is described by the following equation:
When implemented digitally and in discrete time (i.e. , the controller's output is kept constant during two consecutive sampling instants) the PID is implemented as:
In these two equations, u (t ) is the output of the controller, the control error is e (t ) = y sp −y (t ) where y sp is the setpoint, y (t ) is the controlled output. The PID tuning parameters are the controller's gain Kc , the integral or reset time Ti , and the derivative time Td whereas Ts represents the sampling interval for the digital PID controller.
The closed-loop controller manipulates the target concentration of propofol or remifentanil for the effect site compartment to maintain a SE at a target of 50. The algorithm consists of two terms: a feedback components or amplification of the feedback and a so-called feedforward component described as follows:
Feedback Term or Amplification of the feedback:
With e (t ) = SE sp −SE (T ), the Index Error corresponds to −e (t ) the feedback term is expressed as:
with AFB = Amplification of the Feedback.
The minimal interval T (s ) between two consecutive controls is set equal to the time to peak effect of propofol and remifentanil. This delay is modified by the activation of feedforward.
With u (t ) = Ce (t ), y (t ) = SE (t ) and ysp = SEsp the feedback term can then be written as:
Comparing equations (2)and (3), it is obvious that the feedback controller is then an integral controller; note that the gain, though, is a function of u (t −Ts ) where
A feedforward term was implemented, which can amplify the concentration corrections (every 5 s). This function is activated during the maintenance phase. The condition can be expressed as e (t ) + 2e (t − 1) +e (t − 2) > 10 when sampling every 5 s (compare with the derivative term in the PID). The correction is performed immediately with
Finally, the controller calculates the SE “error” (difference between the set point of 50 and the actual SE value), allowing the titration until the target level of SE = 50 was obtained. The SE “error” is used to calculate new concentrations that are proportional to error size, sign (positive or negative), and actual drug concentration.