Model Library

The model library contains a number of pharmacokinetic and pharmacodynamic models in SBML file format which have been used to model the PKPD of erlotinib.

Those SBML models can be passed to either a PharmacokineticModel or a PharmacodynamicModel for simulation or to learn the model parameters from data.

Functional classes

• ModelLibrary

Detailed API

class chi.library.ModelLibrary

Contains references to pharmacokinetic and pharmacodynamic models in SBML file format.

These models can be instantiated for simulation or inference with a MechanisticModel.

References

[1] (1,2,3)

Koch, G. et al. Modeling of tumor growth and anticancer effects of combination therapy. J Pharmacokinet Pharmacodyn 36, 179–197 (2009).

erlotinib_tumour_growth_inhibition_model()

This model is a combination of a ModelLibrary.one_compartment_pk_model() and a tumour_growth_inhibition_model_koch_reparametrised().

one_compartment_pk_model(elimination_rate=True)

Returns an instantiation of a 1-compartment PK model.

In this model the distribution of the drug is modelled by one compartment with a linear elimination rate \(k_e\)

\[\frac{\text{d}A}{\text{d}t} = -k_e A \quad C = \frac{A}{V}.\]

Here, \(A\) and \(C\) are the amount and the concentration of the drug in the body, respectively. \(V\) is the effective volume of distribution of the drug in the compartment.

This model may be interpreted as modelling the blood plasma concentration of the drug, with the assumption that the clearance of the drug through the liver may be approximated by an exponential decay with the rate \(k_e\).

The drug may be either directly administered to \(A\) or indirectly through a dosing compartment.

Parameters:

elimination_rate (bool) – If True, the model uses the elimination rate \(k_e\) as a parameter. If False, the model uses the clearance \(CL\) as a parameter, which is related to the elimination rate by \(CL = k_e V\).

Return type:

chi.PKPDModel

tumour_growth_inhibition_model_koch()

Returns the absolute path to a SBML file, specifying the tumour growth inhibition pharmacodynamic model introduced by Koch et al. in [1].

In this model the tumour growth inhibition is modelled by an empirical model of the tumour volume \(V_T\) over time

\[\frac{\text{d}V_T}{\text{d}t} = \frac{2\lambda_0\lambda_1 V_T} {2\lambda_0V_T + \lambda_1} - \kappa C V_T.\]

Here, the tumour growth in absence of the drug is assumed to grow exponentially at rate \(2\lambda_0\) for tumour volumes below some critical volume \(V_{\text{crit}}\). For volumes beyond \(V_{\text{crit}}\) the growth dynamics is assumed to slow down and transition to a linear growth at rate \(\lambda_0\). The tumour growth inhibitory effect of the compound is modelled proportionally to its concentration \(C\) and the current tumour volume. The proportionality factor \(\kappa\) can be interpreted as the potency of the drug.

Note that the critical tumour volume \(V_{\text{crit}}\) at which the growth dynamics transitions from exponential to linear growth is given by the two growth rates

\[V_{\text{crit}} = \frac{\lambda _1}{2\lambda _0}.\]

Return type:

chi.SBMLModel

tumour_growth_inhibition_model_koch_reparametrised()

Returns the absolute path to a SBML file, specifying the tumour growth inhibition pharmacodynamic model introduced by Koch et al. in [1] with modified parametrisation.

In this model the tumour growth inhibition is modelled by an empirical model of the tumour volume \(V_T\) over time

\[\frac{\text{d}V_T}{\text{d}t} = \frac{\lambda V_T} {V_T / V_{\text{crit}} + 1} - \kappa C V_T.\]

Here, the tumour growth in absence of the drug is assumed to grow exponentially at rate \(\lambda\) for tumour volumes below some critical volume \(V_{\text{crit}}\). For volumes beyond \(V_{\text{crit}}\) the growth dynamics is assumed to slow down and transition to a linear growth at rate \(\lambda V_{\text{crit}}\). The tumour growth inhibitory effect of the compound is modelled proportionally to its concentration \(C\) and the current tumour volume. The proportionality factor \(\kappa\) can be interpreted as the potency of the drug.

Note that this parameterisation of the model is related to the original parametersation in [1] by

\[V_{\text{crit}} = \frac{\lambda _1}{2\lambda _0} \quad \text{and} \quad \lambda = 2\lambda _1 .\]

Return type:

chi.SBMLModel

two_compartment_pk_model()

Returns an instantiation of a 2-compartment PK model.

In this model the distribution of the drug is modelled by twp compartments: 1. the central compartment; and 2. the peripheral compartment. The drug transtions between the two compartments at the inter-compartment clearance rate \(q\) and is eliminated from the central compartment at the clearance rate \(k_{cl}\).

\[\frac{\text{d}a_c}{\text{d}t} = -k_{cl} c_c - q c_c + q c_p \quad \frac{\text{d}a_p}{\text{d}t} = q c_c - q c_p,\]

where \(a_c\) denotes the drug amount in the central compartment and \(a_p\) the drug amount in the peripheral compartment. The concentrations \(c_c\) and \(c_p\) are given by \(c_c = \frac{a_c}{v_c}\) and \(c_p = \frac{a_p}{v_p}\), where \(v_c\) and \(v_p\) denote the effective volumes of distribution of the drug in the compartments. k_{cl} and q denote the clearance and inter-compartment clearance rates, respectively.

Return type:

chi.PKPDModel