Standard Model Generators

pysb-pkpd includes functions to quickly generate standard one-, two-, and three-compartment PK/PD models.

Model Generators

• pkpd.standard.one_compartment_model - Generate a standard one-compartment PK model with an optional PD model as a function of drug concentration in the model CENTRAL compartment. The PK model includes drug clearance from the CENTRAL compartment. API Reference
• pkpd.standard.two_compartment_model - Generate a standard two-compartment PK model with an optional PD model as a function of drug concentration in the model CENTRAL compartment. The PK model includes two comparments (CENTRAL and PERIPHERAL), drug clearance from the CENTRAL compartment, and drug distribution/re-distribution between the CENTRAL and PERIPHERAL compartments. API Reference
• pkpd.standard.three_compartment_model - Generate a standard three-compartment PK model with an optional PD model as a function of drug concentration in the model CENTRAL compartment. The PK model includes three comparments (CENTRAL, PERIPHERAL, and DEEPPERIPHERAL), drug clearance from the CENTRAL compartment, and drug distribution/re-distribution between the CENTRAL and PERIPHERAL compartments and the CENTRAL and DEEPPERIPHERAL compartments. API Reference

Dose routes and parameters

The dose route is specified with the dose_route input argument with optional parameters specified via the dose_parameters argument. The options are:

• 'iv-bolus', no special parameters. Instantaneous IV bolus. Example: dose_route='iv-bolus'.
• iv-infusion, no special parameters. Constant zero-order IV infusion. Note that in this case the dose amount is the infusion rate (amount/time). Example: dose_route='iv-infusion'
• oral with dose_parameters 'ka' (1st-order rate constant) and 'f' (bioavailibility fraction). Linear absorption to model oral or sub-cutaneous depot dose. The dose_parameters are passed in as dictionary. Example: dose_route='oral' with dose_parameters={'ka': 0.01, 'f': 0.75}.

Setting the PD model

PD models are specified with the optional pd_model input argument which takes a nested dictionary. The outer dictionary key specifies the model type while the inner dictionary specifies the model parameters and their values. The options are:

• 'emax' model with parameters 'emax' and 'ec50'. Example input: pd_model={'emax':{'emax': 2.0, 'ec50':52.4}}
• 'sigmoidal-emax' with parameters 'emax', 'ec50', and 'n'. Example input: pd_model={'sigmoidal-emax':{'emax': 2.0, 'ec50':52.4, 'n':1.1}}
• 'linear' with parameters 'slope' and 'intercept'. Example input: pd_model={'linear':{'slope': 1.4, 'intercept':0.43}}
• 'log-linear' with parameters 'slope' and 'intercept'. Example input: pd_model={'log-linear':{'slope': 1.4, 'intercept':0.43}}
• 'fixed' with parameters 'e_fixed' and 'c_threshold'. Example input: pd_model={'fixed':{'e_fixed': 4.7, 'c_threshold':100.0}}

The associated equations for each PD model are shown in the PD macros descriptions.

Example

One-compartment model with oral administration and an Emax PD model:

model = one_compartment_model(
    100.0,  # mg
    dose_route="oral",
    dose_parameters={
        'ka': 1e-1, # min^-1
         'f': 0.95,
    },
    volume_distribution=10.0,  # L
    clearance=0.750,  # L/min
    pd_model={
        "emax": {
            "emax": 2.2,
            "ec50": 50.0,  # mg
        }
    },
)