Data-driven identification and comparison of full multivariable models for propofol–remifentanil induced general anesthesia

Erhan Yumuk*, Dana Copot, Clara M. Ionescu, Martine Neckebroek

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


In this paper, we present results with clinical data to enable a 2x2 input–output multivariable patient model for hypnosis and analgesia. Nonlinear multi-drug interaction models are identified from data recorded from 70 patients undergoing surgery during total intravenous anesthesia (TIVA) with several medical monitors for variables such as Bispectral Index, Nociception level (Medasense), skin conductance (Medstorm) and advanced spectral analysis conductance (AnspecPro). Bispectral index measures the depth of hypnosis (lack of consciousness), while nociception related indices from Medasense, Medstorm, and AnspecPro devices measure levels related to analgesia (lack of reaction to noxious stimuli). A comparison is given among three response surface model (RSM) structures – Minto, Greco, and Reduced Greco – for hypnotic and analgesic states during Propofol–Remifentanil interaction. The identified models capture the pharmacodynamic properties of dose–effect concentrations of Propofol/Remifentanil while the pharmacokinetic part of the patient model is calculated from patient's biometric values using Schnider/Minto (SM), and Eleveld/Eleveld (EE) models. In presence of strict clinical protocols delivering data under poor identifiability conditions, we propose two methods of identification: (i) based on steady-state gains, and (ii) using all available data which includes part of the dynamic transient. The model parameters are optimized with Genetic Algorithm based on a goodness of fit performance measure complemented with root mean square error. The results suggest that the EE model combination is advantageous for Bispectral index pharmacokinetic modeling at the cost of numerical complexity, therefore reducing the uncertainty left to be identified in the pharmacodynamic part of the patient model. By contrast, the SM model combination is less computationally demanding and provides some improvement in the RSM accuracy for nociception level indicators. The comparison of three devices for nociception levels evaluation suggests that clinical data captured with the Medasense monitor provides best fitted RSMs with the Reduced Greco RSM structure, despite having fewer parameters.

Original languageEnglish
Article number103243
JournalJournal of Process Control
Publication statusPublished - Jul 2024
Externally publishedYes

Bibliographical note

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© 2024 The Authors


  • Closed loop control of anesthesia
  • Depth of anesthesia
  • Multivariable control
  • Multivariable models
  • Nonlinear gain
  • Response surface models


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