New approach for the control of anesthesia based on dynamics decoupling

Zabi, Saïd; Queinnec, Isabelle; Tarbouriech, Sophie; García, Germain; Mazerolles, Michel

doi:10.1016/j.ifacol.2015.10.192

Cited by 12 publications

(21 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…As an RMC, we shall consider the widely used compartmental model describing the dynamics of the drug in the human body (see the works of Ionescu et al and Zabi et al and the references therein). In this model, the two states following dynamics is used to represent the unknown functions Φ and F

{\overset{ξ}{true}}_{1} = k_{12} x_{2} - k_{21} ξ_{1}

{\overset{ξ}{true}}_{2} = k_{13} x_{2} - k_{31} ξ_{2}

normalΦ = - false(k_{10} + k_{12} + k_{13} false) x_{2} + k_{21} ξ_{1} + k_{31} ξ_{2},

where the coefficients k i j are given by nominal expressions that depend on the gender ( G ), age ( A ), height ( H ), and weight ( W ) of the patient

k_{i j}^{nom} : = F_{i j} false(G, A, H, W false) .

…”

Section: Resultsmentioning

confidence: 99%

Feedback law with probabilistic certification for Propofol‐based control of BIS during anesthesia

Alamir

Fiacchini

Queinnec

et al. 2018

Intl J Robust & Nonlinear

Self Cite

View full text Add to dashboard Cite

Summary This paper proposes a new control strategy for Propofol injection during anesthesia in patients undergoing surgery and where the Bispectral Index (BIS) is considered to be the regulated variable. The proposed control shows the nice feature of being completely independent of the knowledge of the pharmacokinetics that govern the diffusion of the drug. This paper also proposes a certification framework that gives a probabilistic guarantee regarding the containment of the BIS inside the desired interval as well as for the time needed for the BIS to be steered to this interval. Moreover, this certification is given for realistic (and hence very high) level of uncertainties on the parameters that define the unknown‐to‐the‐controller dynamics. This last feature is checked using a widely employed model.

show abstract

{\overset{ξ}{true}}_{1} = k_{12} x_{2} - k_{21} ξ_{1}

{\overset{ξ}{true}}_{2} = k_{13} x_{2} - k_{31} ξ_{2}

normalΦ = - false(k_{10} + k_{12} + k_{13} false) x_{2} + k_{21} ξ_{1} + k_{31} ξ_{2},

where the coefficients k i j are given by nominal expressions that depend on the gender ( G ), age ( A ), height ( H ), and weight ( W ) of the patient

k_{i j}^{nom} : = F_{i j} false(G, A, H, W false) .

…”

Section: Resultsmentioning

confidence: 99%

Feedback law with probabilistic certification for Propofol‐based control of BIS during anesthesia

Alamir

Fiacchini

Queinnec

et al. 2018

Intl J Robust & Nonlinear

Self Cite

View full text Add to dashboard Cite

show abstract

“…Given the sigmoid describing the relation between the BIS and the effect site concentration, it follows that for the BIS equal to 50% of BIS 0 the effect site concentration must be equal to EC 50 . The values of the other variables can then be deduced from the unique equilibrium point of system (1) (see Zabi et al (2015)). …”

Section: Equilibrium Pointmentioning

confidence: 99%

“…The slow states can be considered as disturbances. The stability of the full strategy will be guaranteed as soon as the switch occurs once the trajectory of the system has entered an invariant domain around the equilibrium (Zabi et al (2015)). …”

Section: Computation Algorithmmentioning

confidence: 99%

“…In a precedent paper (Zabi et al (2015)), we developed a new strategy for the robust control of anesthesia for the maintenance phase taking into account the saturation of the actuator, the multiple time scale dynamics in the anesthesia model and the variability of the patient. In the continuation of our work, this paper address the problem of control of the induction phase using the optimal control.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Time-optimal control for the induction phase of anesthesia

et al. 2017

Self Cite

View full text Add to dashboard Cite

This paper deals with the control of the induction phase of anesthesia. The objective during this first phase is to bring the patient from its awake state to a final state corresponding to some given depth of anesthesia, measured by the BIS (Bispectral index), within a minimum time. This optimal time control strategy is addressed by means of the maximum principle of Pontryagin. Furthermore, since the anesthesia model presents multiple time scale dynamics that can be split in two groups : fast and slow and since the BIS is a direct function of the fast ones, we only consider the optimal control of fast states. The final state of the slow dynamics is let free. The synthesis approach of the optimal control is detailed then tested in the case of a nominal patient.

show abstract

“…A first direction could be to adapt the conditions provided in [14] to our current problem. Due to the difficulties encountered to deal with the nonlinearities appearing in the conditions, we decided here to propose an alternative route by providing analysis conditions based on tools issued from [18] and [19], by using the toolbox SATAW-Tool 2 .…”

Section: Computational Issuesmentioning

confidence: 99%

Control of Anesthesia Based on Singularly Perturbed Model

et al. 2017

Self Cite

View full text Add to dashboard Cite

This paper deals with the control of anesthesia taking into account the positivity together with the upper limitation constraints of the variables and the target interval tolerated for the depth of anesthesia during a surgery. Due to the presence of multiple time scale dynamics in the anesthesia model, the system is re-expressed through a singularly perturbed system allowing to decouple the fast dynamics from the slow ones. Differently from general approaches for singularly perturbed systems, the control objective is then to control and accelerate the fast system without interest in modifying the slow dynamics. Thus, a structured state feedback control is proposed through quasi-LMI (linear matrix inequalities) conditions. The characterization of domains of stability and invariance for the system is provided. Associated convex optimization issues are then discussed. Finally, the theoretical conditions are evaluated on a simulated patient case.

show abstract

New approach for the control of anesthesia based on dynamics decoupling

Cited by 12 publications

References 12 publications

Feedback law with probabilistic certification for Propofol‐based control of BIS during anesthesia

Feedback law with probabilistic certification for Propofol‐based control of BIS during anesthesia

Time-optimal control for the induction phase of anesthesia

Control of Anesthesia Based on Singularly Perturbed Model

Contact Info

Product

Resources

About