Simulator module

class Patient(patient_characteristic: list, co_base: float = 6.5, map_base: float = 90, model_propo: str = 'Schnider', model_remi: str = 'Minto', model_bis: str = 'Bouillon', 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.
model_bisstr: Name of the BIS PD 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).

Simulate the patient model with the given inputs.

Parameters:

u_proponumpy array, optional: Propofol infusion rate (mg/s).
u_reminumpy array, optional: Remifentanil infusion rate (µg/s).
u_norenumpy array, optional: Norepinephrine infusion rate (µg/s).
x0_proponumpy array, optional: Initial state of the propofol PK model. The default is zeros.
x0_reminumpy array, optional: Initial state of the remifentanil PK model. The default is zeros.
x0_norenumpy array, optional: Initial state of the norepinephrine PK model. The default is zeros.

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, remifentanil or norepinephrine 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’.

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).

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.

full_sim(u: list, x0: array | None = None) → list

Simulate PK model with a given input.

Parameters:

ulist: Infusion rate (mg/s for Propofol, µg/s for Remifentanil and Norepinephrine).
x0numpy array, optional: Initial state. The default is None.

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

‘Bouillon’ [Bouillon2004] and ‘Aubouin’ [Aubouin2023] are available. Ignored if hill_param is specified. Default is ‘Bouilllon’.

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.

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.

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.

[Aubouin2023]

A. Aubouin et al., “Comparison of Multiple Kalman Filter and Moving Horizon Estimator for the Anesthesia Process” draft 2023.

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.

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.

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.

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 (s).
bislist: List of BIS value over time.
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:

dfpd.DataFrame

Dataframe containing the computed metrics: TT : float

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.

intergal_absolut_error(time: list, bis: list, bis_target: float = 50)

Compute the integral of the absolute error.

This function compute the integral of the absolute error between the BIS value and the target value.

Parameters:

timelist: List of time value (s).
bislist: List of BIS value over time.
bis_targetfloat, optional: Target BIS value. The default is 50.

Returns:

IAEfloat: Integral of the absolute error.

new_metrics_induction(time: list, bis: list)

Compute new metrics for induction of closed loop anesthesia.

This function compute new metrics for closed loop anesthesia.

Parameters:

timelist: List of time value (s).
bislist: List of BIS value over time.

Returns:

dfpd.DataFrame

Dataframe containing the computed metrics: IAE : float

Integral of the absolute error.

Sleep_Timefloat: Time to reach BIS < 60 and stay below 60 (minutes).
Low BIS timefloat: Time passed with BIS < 40 (seconds).
Lowest BISfloat: Lowest BIS value.
Settling timefloat: Time to reach BIS < 60 and stay within [40, 60] (minutes).

new_metrics_maintenance(time: list, bis: list)

Compute new metrics for maintenance of closed loop anesthesia.

Parameters:

timelist: List of time value (s).
bislist: List of BIS value over time.

Returns:

dfpd.DataFrame

Dataframe containing the computed metrics: IAE : float

Integral of the absolute error.

Time out of rangefloat: Time passed with BIS out of [40, 60] (seconds).
Lowest BISfloat: Lowest BIS value.
Highest BISfloat: Highest BIS value.

TCI controller module

class TCIController(patient_info: list, drug_name: str, model_used: str, drug_concentration: float = 10, maximum_rate: float = 500, sampling_time: float = 1, control_time: float = 10, target_compartement: str = 'effect_site')

Bases: object

Implement the control algorithm coded in the TCI device Orchestra PRIMUS, from [Shafer1992].

Warning: This code has been retro enginering and does not came from an official source.

Parameters:

patient_infolist: Patient information = [age (yr), height (cm), weight (kg), gender( 0= female, 1 = male)].
drug_namestr: Can be either ‘Propofol’ or ‘Remifentanil’.
drug_concentrationfloat: drug concentration in the seringue (mg/ml for Propofol and µg/ml for remifentanil).
model_usedstr: Could be “Minto”, “Eleveld” for Remifentanil, “Schnider”, “Marsh_initial”, “Marsh_modified”, “Shuttler” or “Eleveld” for Propofol.
maximum_ratefloat: Maximum drug rate in ml/hr.
sampling_timefloat, optional: Sampling time of the model for the calculs. The default is 1s.
control_timefloat, optional: Sampling time of the controller, must be a multiple of the sampling time. The default is 10s.
target_compartementstr, optional: Can be either “plasma” or “effect_site”. The default is ‘effect_site’.

Attributes:

sampling_timefloat: Sampling time of the model for the calculs.
control_timefloat: Sampling time of the controller.
drug_concentrationfloat: drug concentration in the seringue (mg/ml for Propofol and µg/ml for remifentanil).
target_idint: index of the target compartment in the state vector.
infusion_maxfloat: Maximum drug rate in mg/s or µg/s.
Adnp.array: Discretized state matrix of the mode with the sampling time of the model.
Bdnp.array: Discretized input matrix of the model.
Ad_controlnp.array: Discretized state matrix of the model with the sampling time of the controller.
Bd_controlnp.array: Discretized input matrix of the model with the sampling time of the controller.
Celist: List of the effect site concentration after a 10s infusion.
infusion_ratefloat: Last control move chosen.
xnp.array: Array to store the patient state at simulation time.
targetfloat: Target concentration.

References

[Shafer1992]

1. Shafer and K. M. Gregg, “Algorithms to rapidly achieve and maintain stable drug concentrations at the site of drug effect with a computer-controlled infusion pump,”0 Journal of Pharmacokinetics and Biopharmaceutics, vol. 20, no. 2, pp. 147–169, Apr. 1992, doi: 10.1007/BF01070999.

one_step(target: float = 0) → float

Implement one_step of the model. It must be called each sampling time.

Parameters:

targetfloat, optional: target concentration (µg/ml for propofol, ng/ml for Remifentanil). The default is 0.

Returns:

infusion rate: float: infusion rate in ml/hr.