Anesthesia is a controlled medical procedure in which drugs are administered to induce a
temporary loss of consciousness, pain sensation, and other physiological functions, thereby
enabling the safe performance of surgical or diagnostic interventions. A central objective of
general anesthesia is to maintain an appropriate depth, which encompasses hypnosis (loss of
consciousness), analgesia (pain relief), and muscle relaxation. The depth of hypnosis is
commonly monitored using the EEG-based bispectral index (BIS), which ranges from 0 to
100. Values between 40 and 60 are generally regarded as optimal, while higher values may
indicate inadequate anesthesia and the risk of awakening, and lower values suggest
excessively deep anesthesia or even suppression of brain activity.
To improve the understanding and management of anesthesia, mathematical models are often
employed to describe drug distribution within the body (pharmacokinetics) and their effects
(pharmacodynamics). Such models allow for simulations and predictions of a patient’s
response to anesthetic drugs. Among the most widely used agents is propofol, a fast-acting
anesthetic commonly administered in total intravenous anesthesia. In this context, target
controlled infusion algorithms are frequently applied. These rely on pharmacokinetic models
(such as the Schnider model) to calculate the infusion rate required to achieve the desired
effect-site concentration, namely in the brain.
The aim of this thesis is to investigate the flexibility of the Schnider model, which is widely
used in clinical practice in target-controlled infusion (TCI) pumps for calculating drug
infusion profiles. By varying all parameters in both the pharmacokinetic and
pharmacodynamic models, we sought to evaluate how well the Bispectral Index (BIS) values
can be matched with actual patient data. Through this model-fitting procedure, we aimed to
demonstrate that, in the case of our measurements, certain parameters can be neglected,
thereby simplifying the classical pharmacokinetic model scheme while maintaining the
dynamics defined by the original Schnider model.
To achieve this goal, we used two mathematical models: one describing the pharmacokinetics
of propofol in the effect-site compartment, and the other describing the pharmacodynamics of
propofol on the BIS index as a function of the effect-site concentration. Both models were
optimized against our measurement data and implemented and simulated in the MATLAB
environment.
Our simulations showed that by removing certain pharmacokinetic parameters, it is possible
to eliminate one compartment representing poorly perfused tissues in the human body,
without disturbing the overall system dynamics. This indicates that the original Schnider
pharmacokinetic model is overparameterized in the context of the studied population, which
opens the possibility for its simplification in specific clinical or research scenarios.
The results of this research contribute to a better understanding of the complexity and
limitations of the Schnider model and suggest opportunities for its adaptation or simplification
based on specific clinical data. In the future, such simplifications could support more efficient
individualization of anesthesia or the use of real-time anesthesia control systems.
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