A two-compartment fractional derivative model for Propofol diffusion in anesthesia

Fractional-Order Closed-Loop Model Reference Adaptive Control for Anesthesia

“…In reference [17], the authors present the relationship between the diffusion process and fractional-order models. Also, the introduction of fractional-order pharmacokinetic models are presented in references [15,16,18,19] which represent the experimental data in a more precise way, thanks to the t −α decay of the fractional operators, and with this, a new line of investigation was opened ion the area of drug delivery systems.…”

“…Then, all the signals in the closed-loop system given by (16), (17), (22), and (23) are bound, ∀t ≥ 0. Futhermore, the tracking error is e → 0 when t → ∞.…”

Bridging the gap between modelling and control of anesthesia: An ambitious ideal

“…It is possible to derive further the model from (6) in its Laplace equivalent, as indicated in [27]. This result has regained the attention of the research community and current efforts are being directed towards providing pharmacokinetic models with fractional order differ-integrals [11], [28], [29], [30], [31], [32], [33], and their equivalent Laplace models of non-integer order, coined in the literature as FOIMs (fractional order impedance models) [34].…”

“…The parameters K ij for ij, denote the drug transfer frequency from the i-th to the j − th compartment and U (t) [mg/s] is the infusion rate of the analgesic drug into the first compartment. The parameters K ij of the PK models depend on age, weight, height and gender and can be calculated for Propofol as in [32], [33]. Standard arguments imply that the equations which are determined by the mass balance in compartments have the following form [29], [30].…”

Relation between fractional order models and diffusion in the body

“…The first compartment represents the place where the drug is applied (plasma) and the second compartment represents the target organ (muscle). The basic idea behind this model can be used to model the diffusion process in the human body by a multi-compartmental model (Dokoumetzidis and Macheras (2009);Popovic et al (2010); Copot et al (2013)). The model is formulated while maintaining the mass balance principles.…”