Simulator module

class Patient(patient_characteristic: list, co_base: float = 6.5, map_base: float = 90, model_propo: str = 'Schnider', model_remi: str = 'Minto', ts: float = 1, hill_param: list | None = None, random_PK: bool = False, random_PD: bool = False, co_update: bool = False, save_data_bool: bool = True)

Bases: object

Define a Patient class able to simulate Anesthesia process.

Parameters:

Patient_characteristic: list

Patient_characteristic = [age (yr), height(cm), weight(kg), gender(0: female, 1: male)]

co_basefloat, optional

Initial cardiac output. The default is 6.5L/min.

map_basefloat, optional

Initial Mean Arterial Pressure. The default is 90mmHg.

model_propostr, optional

Name of the Propofol PK Model. The default is ‘Schnider’.

model_remistr, optional

Name of the Remifentanil PK Model. The default is ‘Minto’.

tsfloat, optional

Samplling time (s). The default is 1.

BIS_paramlist, optional

Parameter of the BIS model (Propo Remi interaction) list [C50p_BIS, C50r_BIS, gamma_BIS, beta_BIS, E0_BIS, Emax_BIS]. The default is None.

random_PKbool, optional

Add uncertainties in the Propodfol and Remifentanil PK models. The default is False.

random_PDbool, optional

Add uncertainties in the BIS PD model. The default is False.

co_updatebool, optional

Turn on the option to update PK parameters thanks to the CO value. The default is False.

save_data_boolbool, optional

Save all interns variable at each sampling time in a data frame. The default is True.

Attributes:

agefloat

Age of the patient (yr).

heightfloat

Height of the patient (cm).

weightfloat

Weight of the patient (kg).

genderbool

0 for female, 1 for male.

co_basefloat

Initial cardiac output (L/min).

map_basefloat

Initial mean arterial pressure (mmHg).

tsfloat

Sampling time (s).

model_propostr

Name of the propofol PK model.

model_remistr

Name of the remifentanil PK model.

hill_paramlist

Parameter of the BIS model (Propo Remi interaction) list [C50p_BIS, C50r_BIS, gamma_BIS, beta_BIS, E0_BIS, Emax_BIS].

random_PKbool

Add uncertainties in the Propodfol and Remifentanil PK models.

random_PDbool

Add uncertainties in the BIS PD model.

co_updatebool

Turn on the option to update PK parameters thanks to the CO value.

save_data_boolbool

Save all interns variable at each sampling time in a data frame.

lbmfloat

Lean body mass (kg).

propo_pkCompartmentModel

6-comparments model for Propofol.

remi_pkCompartmentModel

5-comparments model for Remifentanil.

nore_pkCompartmentModel

1-comparments model for Norepinephrine.

bis_pdBIS_model

Surface-response model for bis computation.

tol_pdTOL_model

Hierarchical model for TOL computation.

hemo_pdHemo_PD_model

Hemodynamic model for CO and MAP computation.

datapd.DataFrame

Dataframe containing all the intern variables at each sampling time.

bisfloat

Bispectral index (%).

tolfloat

Tolerance of laryngospie probability (0-1).

cofloat

Cardiac output (L/min).

mapfloat

Mean arterial pressure (mmHg).

blood_volumefloat

Blood volume (L).

bis_noise_stdfloat

Standard deviation of the BIS noise.

co_noise_stdfloat

Standard deviation of the CO noise.

map_noise_stdfloat

Standard deviation of the MAP noise.

add_noise()

Add noise on the outputs of the model (except TOL).

The MAP and CO noises are considered white noise while the BIS noise is filtered. The filter of the BIS noise is a second order low pass filter with a cut-off frequency of 0.03 Hz.

blood_loss(fluid_rate: float = 0)

Actualize the patient parameters to mimic blood loss.

Parameters:

fluid_ratefloat, optional

Fluid rates from blood volume (mL/min), negative is bleeding while positive is a transfusion. The default is 0.

Returns:

None.

find_bis_equilibrium_with_ratio(bis_target: float, rp_ratio: float = 2) → tuple[float, float]

Find the input of Propofol and Remifentanil to meet the BIS target at the equilibrium with a fixed ratio between drugs rates.

Solve the optimization problem:

\[J = (bis - bis_{target})^2\]

Where \(bis\) is the BIS computed from the pharmacodynamic model. And with the constraints:

\[u_{propo} = u_{remi} * rp_{ratio}\]

\[A_{propo} x_{propo} + B_{propo} u_{propo} = 0\]

\[A_{remi} x_{remi} + B_{remi} u_{remi} = 0\]

Parameters:

bis_targetfloat

BIS target (%).

rp_ratiofloat

remifentanil over propofol rates ratio. The default is 2.

Returns:

u_propofloat:

Propofol infusion rate (mg/s).

u_remifloat:

Remifentanil infusion rate (µg/s).

find_equilibrium(bis_target: float, tol_target: float, map_target: float) → tuple[float, float, float]

Find the input to meet the targeted outputs at the equilibrium.

Solve the optimization problem to find the equilibrium input for BIS - TOL:

\[min_{C_{p,es}, C_{r,es}} \frac{||BIS_{target} - BIS||^2}{100^2} + ||TOL_{target} - TOL||^2\]

Then compute the concentration of Noradrenaline to meet the MAP target.

Finally, compute the input of Propofol, Remifentanil and Noradrenaline to meet the targeted concentration.

Parameters:

bis_targetfloat

BIS target (%).

tol_targetfloat

TOL target ([0, 1]).

map_target:float

MAP target (mmHg).

Returns:

u_propofloat:

Propofol infusion rate (mg/s).

u_remifloat:

Remifentanil infusion rate (µg/s).

u_norefloat:

Norepinephrine infusion rate (µg/s).

full_sim(u_propo: list | None = None, u_remi: list | None = None, u_nore: list | None = None)

Simulate the patient model with the given inputs.

Parameters:

u_propolist

Propofol infusion rate (mg/s).

u_remilist

Remifentanil infusion rate (µg/s).

u_norelist

Norepinephrine infusion rate (µg/s).

Returns:

pandas.Dataframes

Dataframe with all the data.

init_dataframe()

Initilize the dataframe variable.

initialized_at_given_input(u_propo: float = 0, u_remi: float = 0, u_nore: float = 0)

Initialize the patient Simulator at the given input as an equilibrium point.

For each drug, the equilibrium state is computed from the input. Then this state is used to intitialze each drug pharmacokinetic model.

Parameters:

u_propofloat, optional

Propofol infusion rate (mg/s). The default is 0.

u_remifloat, optional

Remifentanil infusion rate (µg/s). The default is 0.

u_norefloat, optional

Norepinephrine infusion rate (µg/s). The default is 0.

Returns:

None.

initialized_at_maintenance(bis_target: float, tol_target: float, map_target: float) → tuple[float, float, float]

Initialize the patient model at the equilibrium point for the given output value.

Parameters:

bis_targetfloat

BIS target (%).

rass_targetfloat

RASS target ([0, -5]).

map_target:float

MAP target (mmHg).

Returns:

u_propofloat:

Propofol infusion rate (mg/s).

u_remifloat:

Remifentanil infusion rate (µg/s).

u_norefloat:

Norepinephrine infusion rate (µg/s).

one_step(u_propo: float = 0, u_remi: float = 0, u_nore: float = 0, blood_rate: float = 0, dist: list = [0, 0, 0], noise: bool = True) → tuple[float, float, float, float]

Simulate one step time of the patient.

Parameters:

u_propofloat, optional

Propofol infusion rate (mg/s). The default is 0.

u_remifloat, optional

Remifentanil infusion rate (µg/s). The default is 0.

u_norefloat, optional

Norepinephrine infusion rate (µg/s). The default is 0.

blood_ratefloat, optional

Fluid rates from blood volume (mL/min), negative is bleeding while positive is a transfusion. The default is 0.

distlist, optional

Disturbance vector on [BIS (%), MAP (mmHg), CO (L/min)]. The default is [0]*3.

noisebool, optional

bool to add measurement noise on the outputs. The default is True.

Returns:

bisfloat

Bispectral index(%).

cofloat

Cardiac output (L/min).

mapfloat

Mean arterial pressure (mmHg).

tolfloat

Tolerance of Laringoscopy index (0-1).

save_data(inputs: list = [0, 0, 0])

Save all current intern variable as a new line in self.dataframe.

PK models module

class CompartmentModel(Patient_characteristic: list, lbm: float, drug: str, model: str | None = None, ts: float = 1, random: bool = False, x0: list | None = None, opiate=True, measurement='arterial')

Bases: object

PKmodel class modelize the PK model of propofol or remifentanil drug. Simulate the drug distribution in the body.

Use a 6 compartement model for propofol, a 5 compartement model for remifentanil, and a 1 compartement model for norepinephrine. The model is a LTI model with the form:

\[x(k+1)= Ax(k) + Bu(k)\]

\[y(k) = Cx(k)\]

The state vector is the concentration of the drug in each compartement in the following order: blood, muscles, fat, BIS effect-site, MAP effect-site 1, MAP effect-site 2. The output of the model is the BIS effect-site concentration.

Parameters:

Patient_characteristic: list

Patient_characteristic = [age (yr), height(cm), weight(kg), gender(0: female, 1: male)]

lbmfloat

lean body mass index.

drugstr

can be “Propofol”, “Remifentanil” or “Norepinephrine”.

modelstr, optional

Could be “Schnider” [Schnider1999], “Marsh_initial”[Marsh1991], “Marsh_modified”[Struys2000], “Shuttler”[Schuttler2000] or “Eleveld”[Eleveld2018] for Propofol. “Minto”[Minto1997], “Eleveld”[Eleveld2017] for Remifentanil. only “Beloeil”[Beloeil2005] for Norepinephrine. The default is “Minto” for Remifentanil and “Schnider” for Propofol.

tsfloat, optional

Sampling time, in s. The default is 1.

randombool, optional

bool to introduce uncertainties in the model. The default is False.

x0list, optional

Initial concentration of the compartement model. The default is np.ones([4, 1])*1e-4.

opiatebool, optional

For Elelevd model for propofol, specify if their is a co-administration of opiate (Remifentantil) in the same time. The default is True.

measurementstr, optional

For Elelevd model for propofol, specify the measuremnt place for blood concentration. Can be either ‘arterial’ or ‘venous’. The default is ‘arterial’.

References

[Schnider1999]

T. W. Schnider et al., “The Influence of Age on Propofol Pharmacodynamics,” Anesthesiology, vol. 90, no. 6, pp. 1502-1516., Jun. 1999, doi: 10.1097/00000542-199906000-00003.

[Marsh1991]

B. Marsh, M. White, N. morton, and G. N. C. Kenny, “Pharmacokinetic model Driven Infusion of Propofol in Children,” BJA: British Journal of Anaesthesia, vol. 67, no. 1, pp. 41–48, Jul. 1991, doi: 10.1093/bja/67.1.41.

[Struys2000]

M. M. R. F. Struys et al., “Comparison of Plasma Compartment versus Two Methods for Effect Compartment–controlled Target-controlled Infusion for Propofol,” Anesthesiology, vol. 92, no. 2, p. 399, Feb. 2000, doi: 10.1097/00000542-200002000-00021.

[Schuttler2000]

J. Schüttler and H. Ihmsen, “Population Pharmacokinetics of Propofol: A Multicenter Study,” Anesthesiology, vol. 92, no. 3, pp. 727–738, Mar. 2000, doi: 10.1097/00000542-200003000-00017.

[Eleveld2018]

D. J. Eleveld, P. Colin, A. R. Absalom, and M. M. R. F. Struys, “Pharmacokinetic–pharmacodynamic model for propofol for broad application in anaesthesia and sedation” British Journal of Anaesthesia, vol. 120, no. 5, pp. 942–959, mai 2018, doi:10.1016/j.bja.2018.01.018.

[Minto1997]

C. F. Minto et al., “Influence of Age and Gender on the Pharmacokinetics and Pharmacodynamics of Remifentanil: I. Model Development,” Anesthesiology, vol. 86, no. 1, pp. 10–23, Jan. 1997, doi: 10.1097/00000542-199701000-00004.

[Eleveld2017]

D. J. Eleveld et al., “An Allometric Model of Remifentanil Pharmacokinetics and Pharmacodynamics,” Anesthesiology, vol. 126, no. 6, pp. 1005–1018, juin 2017, doi: 10.1097/ALN.0000000000001634.

[Beloeil2005]

H. Beloeil, J.-X. Mazoit, D. Benhamou, and J. Duranteau, “Norepinephrine kinetics and dynamics in septic shock and trauma patients,” BJA: British Journal of Anaesthesia, vol. 95, no. 6, pp. 782–788, Dec. 2005, doi: 10.1093/bja/aei259.

Attributes:

tsfloat

Sampling time, in s.

drugstr

can be “Propofol”, “Remifentanil” or “Norepinephrine”.

A_initlist

Initial value of the matrix A.

B_initlist

Initial value of the matrix B.

v1float

Volume of the first compartement.

continuous_syscontrol.StateSpace

Continuous state space model.

discrete_syscontrol.StateSpace

Discrete state space model.

xlist

State vector.

ylist

Output vector (hypnotic effect site concentration).

full_sim(u: list) → list

Simulate PK model with a given input.

Parameters:

ulist

Infusion rate (mg/s for Propofol, µg/s for Remifentanil and Norepinephrine).

Returns:

numpy array

List of the states value during the simulation. (µg/mL for Propofol and ng/mL for Remifentanil and Norepinephrine).

one_step(u: float) → list

Simulate one step of PK model.

\[x^+ = Ax + Bu\]

\[y = Cx\]

Parameters:

ufloat

Infusion rate (mg/s for Propofol, µg/s for Remifentanil).

Returns:

numpy array

Actual effect site concentration (µg/mL for Propofol and ng/mL for Remifentanil and Norepinephrine).

update_param_CO(CO_ratio: float)

Update PK coefficient with a linear function of Cardiac output value.

Parameters:

COfloat

Ratio of Current CO relatively to initial CO.

Returns:

None.

update_param_blood_loss(v_ratio: float)

Update PK coefficient to mimic a blood loss.

Update the blodd volume compartment

Parameters:

v_ratiofloat

blood volume as a fraction of init volume, 1 mean no loss, 0 mean 100% loss.

Returns:

None.

PD models module

class BIS_model(hill_model: str = 'Bouillon', hill_param: list | None = None, random: bool = False)

Bases: object

Surface Response model to link Propofol and Remifentanil blood concentration to BIS.

equation:

\[BIS = E0 + Emax * \frac{U^\gamma}{1+U^\gamma}\]

\[U = \frac{U_p + U_r}{1 - \beta \theta + \beta \theta^2}\]

\[U_p = \frac{C_{p,es}}{C_{p,50}}\]

\[U_r = \frac{C_{r,es}}{C_{r,50}}\]

\[\theta = \frac{U_p}{U_r+U_p}\]

Parameters:

hill_modelstr, optional

Only ‘Bouillon’ [Bouillon2004] is available. Ignored if hill_param is specified.

hill_paramlist, optional

Parameter of the Hill model (Propo Remi interaction) list [c50p_BIS, c50r_BIS, gamma_BIS, beta_BIS, E0_BIS, Emax_BIS]:

• c50p_BIS : Concentration at half effect for propofol effect on BIS (µg/mL)

• c50r_BIS : Concentration at half effect for remifentanil effect on BIS (ng/mL)

• gamma_BIS : slope coefficient for the BIS model,

• beta_BIS : interaction coefficient for the BIS model,

• E0_BIS : initial BIS,

• Emax_BIS : max effect of the drugs on BIS.

The default is None.

randombool, optional

Add uncertainties in the parameters. Ignored if Hill_cruv is specified. The default is False.

tsfloat, optional

Sampling time, in s. The default is 1.

References

[Bouillon2004]

T. W. Bouillon et al., “Pharmacodynamic Interaction between Propofol and Remifentanil Regarding Hypnosis, Tolerance of Laryngoscopy, Bispectral Index, and Electroencephalographic Approximate Entropy,” Anesthesiology, vol. 100, no. 6, pp. 1353–1372, Jun. 2004, doi: 10.1097/00000542-200406000-00006.

Attributes:

c50pfloat

Concentration at half effect for propofol effect on BIS (µg/mL).

c50rfloat

Concentration at half effect for remifentanil effect on BIS (ng/mL).

gammafloat

slope coefficient for the BIS model.

betafloat

interaction coefficient for the BIS model.

E0float

initial BIS.

Emaxfloat

max effect of the drugs on BIS.

hill_paramlist

Parameter of the Hill model (Propo Remi interaction) list [c50p_BIS, c50r_BIS, gamma_BIS, beta_BIS, E0_BIS, Emax_BIS]

c50p_initfloat

Initial value of c50p, used for blood loss modelling.

compute_bis(c_es_propo: float, c_es_remi: float) → float

Compute BIS function from Propofol and Remifentanil effect site concentration.

Parameters:

cepfloat

Propofol effect site concentration µg/mL.

cerfloat

Remifentanil effect site concentration ng/mL

Returns:

BISfloat

Bis value.

inverse_hill(BIS: float, c_es_remi: float = 0) → float

Compute Propofol effect site concentration from BIS and Remifentanil effect site concentration.

Parameters:

BISfloat

BIS value.

cerfloat, optional

Effect site Remifentanil concentration (ng/mL). The default is 0.

Returns:

cepfloat

Effect site Propofol concentration (µg/mL).

plot_surface()

Plot the 3D-Hill surface of the BIS related to Propofol and Remifentanil effect site concentration.

update_param_blood_loss(v_ratio: float)

Update PK coefficient to mimic a blood loss.

Update the c50p parameters thanks to the blood volume ratio. The values are estimated from [Johnson2003].

Parameters:

v_lossfloat

blood volume as a fraction of init volume, 1 mean no loss, 0 mean 100% loss.

Returns:

None.

References

[Johnson2003]

K. B. Johnson et al., “The Influence of Hemorrhagic Shock on Propofol: A Pharmacokinetic and Pharmacodynamic Analysis,” Anesthesiology, vol. 99, no. 2, pp. 409–420, Aug. 2003, doi: 10.1097/00000542-200308000-00023.

class Hemo_PD_model(nore_param: list | None = None, propo_param: list | None = None, remi_param: list | None = None, random: bool = False, co_base: float = 6.5, map_base: float = 90)

Bases: object

Modelize the effect of Propofol, Remifentanil, Norepinephrine on Mean Arterial Pressure and Cardiac Output.

Use the addition of sigmoid curve to model the effect of each drugs on MAP and CO. The following articles are used to define the parameters of the model:

• Norepinephrine to MAP: [Beloeil2005]

• Noepinephrine to CO: [Monnet2011]

• Propofol to MAP: [Jeleazcov2011]

• Propofol to CO: [Fairfield1991]

• Remifentanil to MAP: [Standing2010]

• Remifentanil to CO: [Chanavaz2005]

Parameters:

nore_paramlist, optional

List of hill curve parameters for Norepinephrine action [Emax_map, c50_map, gamma_map, Emax_co, c50_co, gamma_co]. The default is None.

propo_paramlist, optional

List of hill curve parameters for Propofol action [emax_SAP, emax_DAP, c50_map_1, c50_map_2, gamma_map_1, gamma_map_2, Emax_co, c50_co, gamma_co]. The default is None.

remi_paramlist, optional

List of hill curve parameters for Relifentanil action [Emax_map, c50_map, gamma_map, Emax_co, c50_co, gamma_co]. The default is None.

randombool, optional

Add uncertainties in the parameters. The default is False.

co_base: float, optional

Baseline Cardiac output (L/min). The default is 6.5 L/min.

map_base: float, optional

Baseline mean arterial pressure (mmHg). The default is 90mmHg.

References

[Beloeil2005]

H. Beloeil, J.-X. Mazoit, D. Benhamou, and J. Duranteau, “Norepinephrine kinetics and dynamics in septic shock and trauma patients,” BJA: British Journal of Anaesthesia, vol. 95, no. 6, pp. 782–788, Dec. 2005, doi: 10.1093/bja/aei261.

[Monnet2011]

X. Monnet, J. Jabot, J. Maizel, C. Richard, and J.-L. Teboul, “Norepinephrine increases cardiac preload and reduces preload dependency assessed by passive leg raising in septic shock patients” Critical Care Medicine, vol. 39, no. 4, p. 689, Apr. 2011, doi: 10.1097/CCM.0b013e318206d2a3.

[Jeleazcov2011]

C. Jeleazcov, M. Lavielle, J. Schüttler, and H. Ihmsen, “Pharmacodynamic response modelling of arterial blood pressure in adult volunteers during propofol anaesthesia,” BJA: British Journal of Anaesthesia, vol. 115, no. 2, pp. 213–226, Aug. 2015, doi: 10.1093/bja/aeu553.

[Fairfield1991]

J. E. Fairfield, A. Dritsas, and R. J. Beale, “HAEMODYNAMIC EFFECTS OF PROPOFOL: INDUCTION WITH 2.5 MG KG-1,” British Journal of Anaesthesia, vol. 67, no. 5, pp. 618–620, Nov. 1991, doi: 10.1093/bja/67.5.618.

[Standing2010]

J. F. Standing, G. B. Hammer, W. J. Sam, and D. R. Drover, “Pharmacokinetic–pharmacodynamic modeling of the hypotensive effect of remifentanil in infants undergoing cranioplasty,” Pediatric Anesthesia, vol. 20, no. 1, pp. 7–18, 2010, doi: 10.1111/j.1460-9592.2009.03174.x.

[Chanavaz2005]

C. Chanavaz et al., “Haemodynamic effects of remifentanil in children with and without intravenous atropine. An echocardiographic study,” BJA: British Journal of Anaesthesia, vol. 94, no. 1, pp. 74–79, Jan. 2005, doi: 10.1093/bja/aeh293.

Attributes:

co_basefloat

Baseline cardiac output.

map_basefloat

Baseline mean arterial pressure.

emax_nore_mapfloat

Maximal effect of Norepinephrine on MAP.

c50_nore_mapfloat

Concentration of Norepinephrine that produce half of the maximal effect on MAP.

gamma_nore_mapfloat

Slope of the sigmoid curve for Norepinephrine effect on MAP.

emax_nore_cofloat

Maximal effect of Norepinephrine on CO.

c50_nore_cofloat

Concentration of Norepinephrine that produce half of the maximal effect on CO.

gamma_nore_cofloat

Slope of the sigmoid curve for Norepinephrine effect on CO.

emax_propo_SAPfloat

Maximal effect of Propofol on SAP.

emax_propo_DAPfloat

Maximal effect of Propofol on DAP.

emax_propo_cofloat

Maximal effect of Propofol on CO.

c50_propo_map_1float

Concentration of Propofol that produce half of the maximal effect on MAP.

c50_propo_map_2float

Concentration of Propofol that produce half of the maximal effect on MAP.

gamma_propo_map_1float

Slope of the sigmoid curve for Propofol effect on MAP.

gamma_propo_map_2float

Slope of the sigmoid curve for Propofol effect on MAP.

c50_propo_cofloat

Concentration of Propofol that produce half of the maximal effect on CO.

gamma_propo_cofloat

Slope of the sigmoid curve for Propofol effect on CO.

emax_remi_mapfloat

Maximal effect of Remifentanil on MAP.

emax_remi_cofloat

Maximal effect of Remifentanil on CO.

c50_remi_mapfloat

Concentration of Remifentanil that produce half of the maximal effect on MAP.

gamma_remi_mapfloat

Slope of the sigmoid curve for Remifentanil effect on MAP.

c50_remi_cofloat

Concentration of Remifentanil that produce half of the maximal effect on CO.

gamma_remi_cofloat

Slope of the sigmoid curve for Remifentanil effect on CO.

mapfloat

Mean arterial pressure.

cofloat

Cardiac output.

compute_hemo(c_es_propo: list, c_es_remi: float, c_es_nore: float) → tuple[float, float]

Compute current MAP and CO using addition of hill curv, one for each drugs.

Parameters:

c_es_propolist

Propofol concentration on both hemodynamic effect site concentration µg/mL.

c_es_remifloat

Remifentanil hemodynamic effect site concentration µg/mL.

c_es_norefloat

Norepinephrine hemodynamic effect site concentration µg/mL.

Returns:

mapfloat

Mean arterial pressure (mmHg), without blood loss.

cofloat

Cardiac output (L/min), without blood loss.

class TOL_model(model: str = 'Bouillon', model_param: list | None = None, random: bool = False)

Bases: object

Hierarchical model to link druf effect site concentration to Tolerance of Laringoscopy.

The equation are:

\[postopioid = preopioid * \left(1 - \frac{C_{r,es}^{\gamma_r}}{C_{r,es}^{\gamma_r} + (C_{r,50} preopioid)^{\gamma_r}}\right)\]

\[TOL = \frac{C_{p,es}^{\gamma_p}}{C_{p,es}^{\gamma_p} + (C_{p,50} postopioid)^{\gamma_p}}\]

Parameters:

modelstr, optional

Only ‘Bouillon’ is available. Ignored if model_param is specified. The default is ‘Bouillon’.

model_paramlist, optional

Model parameters, model_param = [c50p, c50p, gammaP, gammaR, Preopioid intensity]. The default is None.

randombool, optional

Add uncertainties in the parameters. Ignored if model_param is specified. The default is False.

Attributes:

c50pfloat

Concentration at half effect for propofol effect on BIS (µg/mL).

c50rfloat

Concentration at half effect for remifentanil effect on BIS (ng/mL).

gamma_pfloat

Slope of the Hill function for propofol effect on TOL.

gamma_rfloat

Slope of the Hill function for remifentanil effect on TOL.

pre_intensityfloat

Preopioid intensity.

compute_tol(c_es_propo: float, c_es_remi: float) → float

Return TOL from Propofol and Remifentanil effect site concentration.

Compute the output of the Hirarchical model to predict TOL from Propofol and Remifentanil effect site concentration. TOL = 1 mean very relaxed and will tolerate laryngoscopie while TOL = 0 mean fully awake and will not tolerate.

Parameters:

cepfloat

Propofol effect site concentration µg/mL.

cerfloat

Remifentanil effect site concentration ng/mL

Returns:

TOLfloat

TOL value.

plot_surface()

Plot the 3D-Hill surface of the BIS related to Propofol and Remifentanil effect site concentration.

fsig(x, c50, gam)

Disturbances module

compute_disturbances(time: float, dist_profil: str = 'realistic', start_step: float = 600, end_step: float = 1200) → list

Give the value of the distubance profil for a given time.

Parameters:

timefloat

Time: in seconde.

dist_profilstr, optional

disturbance profil, can be: ‘realistic’, ‘simple’, ‘step’ or “null”. The default is ‘realistic’.

start_stepfloat, optional

start time of the step distuebance (seconds). The default is 600s.

end_stepfloat, optional

End time of the step distuebance (seconds). The default is 1200s.

Returns:

list

dist_bis, dist_map, dist_co: respectively the additive disturbance to add to the BIS, MAP and CO signals.

Metrics module

compute_control_metrics(time: list, bis: list, phase: str = 'maintenance', start_step: float = 600, end_step: float = 1200)

Compute metrics for closed loop anesthesia.

This function compute the control metrics initially proposed in [Ionescu2008].

Parameters:

timelist

List of time value.

bislist

List of BIS value over time.

tsfloat, optional

Sampling time in second. The default is 1.

phasestr, optional

Control phase, can be “maintenance”, ‘induction” or “total”. The default is ‘maintenance’.

start_step: float, optional

Start time of the step disturbance, for maintenance and total phase. The default is 600s.

end_step: float, optional

End time of the step disturbance, for maintenance and total phase. The default is 1200s.

Returns:

TTfloat

Observed time-to-target (in minute) required for reaching first time the target interval of [55,45] BIS values.

BIS_NADIR: float

for “induction” or “total” phase. The lowest observed BIS value during induction phase.

ST10: float

for “induction” or “total” phase. Settling time (in minute) on the reference BIS value, defined within ± 5BIS(i.e., between 45 and 55 BIS)and stay within this BIS range.

ST20: float

for “induction” or “total” phase. Settling time (in minute) on the reference BIS value, defined within ± 10BIS(i.e., between 40 and 60 BIS) and stay within this BIS range.

US: float

for “induction” or “total” phase. Undershoot, defined as the BIS value that exceeds the limit of the defined BIS interval, namely, the 45 BIS value.

TTpfloat

Time to target (in minute) after the positive step disturbance.

BIS_NADIRp: float

for “maintenance” or “total” phase. Minimum BIS vamue after the positive step disturbance.

TTpn: float

for “maintenance” or “total” phase. Time to target (in minute) after the negative step disturbance.

BIS_NADIRn: float

for “maintenance” or “total” phase. Maximum BIS vamue after the negative step disturbance.

References

[Ionescu2008]

C. M. Ionescu, R. D. Keyser, B. C. Torrico, T. D. Smet, M. M. Struys, and J. E. Normey-Rico, “Robust Predictive Control Strategy Applied for Propofol Dosing Using BIS as a Controlled Variable During Anesthesia,” IEEE Transactions on Biomedical Engineering, vol. 55, no. 9, pp. 2161–2170, Sep. 2008, doi: 10.1109/TBME.2008.923142.