Create Pharmacokinetic Models

Ways to Create or Import Pharmacokinetic Model

To start modeling, you can:

Create a PK model using a model construction wizard that lets you specify the number of compartments, the route of administration, and the type of elimination.
Extend any model to build higher fidelity models.
Build or load your own model. Load a SimBiology^® project or SBML model.

How SimBiology Models Represent Pharmacokinetic Models

The following figure compares a model as typically represented in pharmacokinetics with the same model shown in the SimBiology model diagram. For this comparison, assume that you are modeling administration of a drug using a two-compartment model with any dosing input and linear elimination kinetics. (The model structure remains the same with any dosing type.)

Note the following:

SimBiology represents the concentration or amount of a drug in a given compartment or volume by a species object contained within the compartment.
SimBiology represents the exchange or flow of the drug between compartments and the elimination of the drug by reactions.
SimBiology represents intercompartmental clearance by a parameter (Q) which specifies the clearance between the compartments.
SimBiology drives the dosing schedule with a combination of species (Drug and/or Dose) and reactions (Dose -> Drug), depending on whether the administration into the compartment follows bolus, zero-order, infusion, or first-order dosing kinetics. For more information on the components added and parameters estimated, see Dosing Types.

You can also view this model as a regression function, y = f(k,u), where y is the predicted value, given values of an input u, and parameter values k. In SimBiology the model represents f, and the model is used to generate a regression function if y, k, and u are identified in the model.

Dosing Types

When creating models, SimBiology creates the following model components for each compartment in the model, regardless of the dosing type:

Two species (Drug_CompartmentName and Dose_CompartmentName) for each compartment.
A reaction (Dose_CompartmentName -> Drug_CompartmentName) for each compartment, governed by mass action kinetics.
A parameter (ka_CompartmentName) for each compartment, representing the absorption rate of the drug when absorption follows first-order kinetics. This is the forward rate parameter for the Dose_CompartmentName -> Drug_CompartmentName reaction.
A parameter (Tk0_CompartmentName) for each compartment, representing the duration of drug absorption when absorption follows zero-order kinetics.
A parameter (TLag_CompartmentName) for each compartment, representing the time lag for any dose that targets that compartment and also that is specified as having a time lag.

For dosing types that have a fixed infusion or absorption duration (infusion and zero-order), you can use overlapping doses. The doses are additive.

The following table describes the dosing types, the default parameters to estimate, and lists the model components created and used for dosing.

Dosing Type	Description	SimBiology Model Components Used	Default Parameters to Estimate
`''`(empty character vector)	No dose	The species (`Drug_CompartmentName`) in each compartment	None
SimBiology Model Builder app — `bolus` Command line — `Bolus`	Assumes that the drug amount is increased instantly at the dose time. In the SimBiology model, the initial concentration of the drug is based on dose amount and volume of the compartment containing the drug.	The species (`Drug_CompartmentName`) in each compartment	None
SimBiology Model Builder app — `infusion` Command line — `Infusion`	Assumes that the infused drug amount increases at a constant known absorption (or infusion) rate over a known duration. The imported data set must contain the rate and not an infusion duration. SimBiology uses this information to change the species concentration at the constant rate over the duration specified in the data set.	The species (`Drug_CompartmentName`) in each compartment	None
SimBiology Model Builder app — `zero-order` Command line — `ZeroOrder`	Assumes that the drug is added at a constant rate over fixed, but unknown duration.	The species `Drug_CompartmentName` in each compartment The parameter (`Tk0_CompartmentName`) in each compartment that has zero-order dosing. This parameter represents the duration of drug absorption	`Tk0_CompartmentName` (absorption duration)
SimBiology Model Builder app — `first-order` Command line — `FirstOrder`	Assumes that the rate at which the drug is absorbed is not constant. In the SimBiology model, absorption rate is assumed to be governed by mass-action kinetics.	A species (`Dose_CompartmentName`) representing the dose amount before it is absorbed A species (`Drug_CompartmentName`) for each compartment A parameter (`ka_CompartmentName`) representing the absorption rate of the drug A `MassAction` `reaction (Dose_CompartmentName —> Drug_CompartmentName)` with forward rate parameter (`ka_CompartmentName`)	`ka_CompartmentName` (absorption rate)

Elimination Types

Elimination Type Description SimBiology Model Components Created Default Parameters to Estimate

Elimination Type	Description	SimBiology Model Components Created	Default Parameters to Estimate
SimBiology Model Builder app — `Linear {Elimination Rate, Volume}` Command line — `'linear'`	Assumes simple mass-action kinetics in the elimination of the drug. In the SimBiology model, elimination is specified by mass-action kinetics with the elimination rate constant specified by the forward rate parameter (`ke`).	A parameter representing the elimination rate (`ke_CompartmentName`) A `MassAction` `reaction (drug —> null)` with forward rate parameter (`ke_CompartmentName`) specific to the compartment	Compartment volume (`Capacity` property) Elimination rate constant (`ke_CompartmentName`) Inter-compartmental clearance (`Q`) when there is more than one compartment. See Intercompartmental Clearance.
SimBiology Model Builder app — `Linear {Clearance, Volume}` Command line — `'linear-clearance'`	Assumes simple mass-action kinetics in the elimination of the drug. In the SimBiology model, similar to `Linear {Elimination Rate, Volume}`. But, in addition, this option lets you specify the model in terms of clearance (`Cl`) where, `Cl = ke * volume`).	A parameter representing the clearance (`Cl_CompartmentName`) A parameter representing the elimination rate constant (`ke_CompartmentName`) An `InitialAssignment` rule that initializes `ke_CompartmentName` based on the initial values for `Cl_CompartmentName` and compartment volume A `MassAction` `reaction (drug —> null)` with forward rate parameter (`ke_CompartmentName`)	Compartment volume (`Capacity` property) Clearance (`Cl_CompartmentName`) Inter-compartmental clearance (`Q`) when there is more than one compartment. See Intercompartmental Clearance.
SimBiology Model Builder app — `Enzymatic (Michaelis-Menten)` Command line — `'enzymatic'`	Assumes that elimination is governed by Michaelis-Menten kinetics.	Parameter representing the Michaelis constant, (`Km_CompartmentName`) A parameter for maximum velocity (`Vm_CompartmentName` A reaction with Michaelis-Menten kinetics (`drug -> null`), with kinetic law parameters `Vm_CompartmentName` and `Km_CompartmentName`	Compartment volume (`Capacity` property) Parameter (`Km_CompartmentName`) Parameter (`Vm_CompartmentName`) Inter-compartmental clearance (`Q`) when there is more than one compartment. See Intercompartmental Clearance

SimBiology Model Builder app — Linear {Elimination Rate, Volume}

Command line — 'linear'

Assumes simple mass-action kinetics in the elimination of the drug. In the SimBiology model, elimination is specified by mass-action kinetics with the elimination rate constant specified by the forward rate parameter (ke).

A parameter representing the elimination rate (ke_CompartmentName)
A MassAction reaction (drug —> null) with forward rate parameter (ke_CompartmentName) specific to the compartment

Compartment volume
(Capacity property)
Elimination rate constant (ke_CompartmentName)
Inter-compartmental clearance (Q) when there is more than one compartment.
See Intercompartmental Clearance.

SimBiology Model Builder app — Linear {Clearance, Volume}

Command line — 'linear-clearance'

Assumes simple mass-action kinetics in the elimination of the drug. In the SimBiology model, similar to

Linear {Elimination Rate,
                  Volume}

. But, in addition, this option lets you specify the model in terms of clearance (Cl) where,

Cl = ke *
                  volume

A parameter representing the clearance (Cl_CompartmentName)
A parameter representing the elimination rate constant (ke_CompartmentName)
An InitialAssignment rule that initializes ke_CompartmentName based on the initial values for Cl_CompartmentName and compartment volume
A MassAction reaction (drug —> null) with forward rate parameter (ke_CompartmentName)

Compartment volume
(Capacity property)
Clearance (Cl_CompartmentName)
Inter-compartmental clearance (Q) when there is more than one compartment.
See Intercompartmental Clearance.

SimBiology Model Builder app — Enzymatic (Michaelis-Menten)

Command line — 'enzymatic'

Assumes that elimination is governed by Michaelis-Menten kinetics.

Parameter representing the Michaelis constant, (Km_CompartmentName)
A parameter for maximum velocity (Vm_CompartmentName
A reaction with Michaelis-Menten kinetics (drug -> null), with kinetic law parameters Vm_CompartmentName and Km_CompartmentName

Compartment volume
(Capacity property)
Parameter (Km_CompartmentName)
Parameter (Vm_CompartmentName)
Inter-compartmental clearance (Q) when there is more than one compartment.
See Intercompartmental Clearance

Intercompartmental Clearance

The compartments created when you generate a SimBiology model form a chain and each pair of linked compartments are connected by a transport reaction similar to linear elimination. The addition of two compartments, C1 and C2, generates a reversible mass-action reaction C1.Drug_C1 <-> C2.Drug. The forward rate parameter is the compartmental clearance, Q₁₂, divided by the volume of C1. The reverse rate parameter is Q₁₂, divided by the volume of C2.

The process of adding each pair of compartments in the chain C_m and C_n generates the following model components:

A parameter Q_mn representing the compartmental clearance between those two compartments. This parameter is added to the list of parameters to be estimated (Estimated property of PKModelMap object).
A parameter (kmn) representing the rate of transfer of the drug from Cm to Cn, where k_mn = Q_mn/V_m.
A parameter (knm) representing the rate of Cn to Cm, where k_nm = Q_mn/V_n.
A reversible mass-action reaction between the two compartments, Cm.Drug_Cm <-> Cn.Drug_Cn, with forward rate parameter kmn, and reverse rate parameter knm.
An initial assignment rule that initializes the value of the parameter kmn, based on the initial values for Cm and Qmn.
An initial assignment rule that initializes the value of the parameter knm, based on the initial values for Cn and Qmn.

Unit Conversion for Imported Data

Unit conversion converts the matching physical quantities to one consistent unit system in order to resolve them. This conversion is in preparation for correct simulation, but SimBiology returns the physical quantities in the model in units that you specify.

Regardless of whether unit conversion is on or off, you must express dosing data in amount. By default, Unit Conversion is off, so you must ensure that units for the data and the model are consistent with one another. If Unit Conversion is on, you must specify units.

Parameters in the model have default units. If unit conversion is on, you can change the units as long as the dimensions are consistent. These default units, which you might use to specify the values for the initial guess, are as follows.

Physical Quantity or Model Parameter	Unit
Central or peripheral compartment volume (Central or Peripheral)	`liter`
First-order elimination rate (ke)	`1/second`
Michaelis constant (Km)	`milligram/liter`
Maximum reaction-velocity, Michaelis-Menten kinetics (Vm)	`milligram/second`
Clearance (Cl)	`liter/second`
Absorption duration (Tk0)	`second`
Absorption rate (ka)	`1/second`

Use the configuration settings options to turn unit conversion on or off. For details, see Model Simulation.

For details on dimensional analysis for reaction rates, see How Reaction Rates Are Evaluated.

Create a Pharmacokinetic Model Using the Command Line

To create a PK model with the specified number of compartments, dosing type, and method of elimination:

Create a PKModelDesign object. The PKModelDesign object lets you specify the number of compartments, route of administration, and method of elimination, which SimBiology uses to construct the model object with the necessary compartments, species, reactions, and rules.
```
pkm = PKModelDesign;
```
Add a compartment specifying the compartment name, and optionally, the type of dosing, and the method of elimination. Also specify whether the data contains a response variable measured in this compartment and whether the dose(s) have time lags. For example, specify a compartment named Central, with Bolus for the DosingType property, linear-clearance for the EliminationType property, and true for the HasResponseVariable property.
```
pkc1 = addCompartment(pkm, 'Central', 'DosingType', 'Bolus', ...
                     'EliminationType', 'linear-clearance', ...
                     'HasResponseVariable', true);
```
For a description of other DosingType and EliminationType property values, see Dosing Types and Elimination Types.
For a description of the HasResponseVariable property, see HasResponseVariable. At least one compartment in a model must have a response. Although SimBiology supports multiple responses per compartment, when adding compartments to a PKModelDesign object, you are limited to one response per compartment.
Note
To add a compartment that has a time lag associated with any dose that targets it, set the HasLag property to true:
```
pkc_lag = addCompartment(pkm, 'Central', 'DosingType', 'Bolus', ...
                        'EliminationType', 'linear-clearance', ...
                        'HasResponseVariable', true, 'HasLag', true);
```
Or after adding a compartment, set its HasLag property to true:
```
pkc1.HasLag = true;
```
Optionally, add a second compartment named Peripheral, with no dosing, no elimination, and no time lag. Set the HasResponseVariable property to true. If you are using the tobramycin data set [1], skip this step and use only one compartment.
```
pkc2 = addCompartment(pkm, 'Peripheral', 'HasResponseVariable', true);
```
The model construction process adds the necessary parameters, including a parameter representing intercompartmental clearance Q. You can add more compartments by repeating this step. The addition of each compartment creates a chain of compartments in the order of compartment addition, with a bidirectional flow of the drug between compartments in the model.
Use the handle to the compartment (pkc1 or pkc2), to change compartment properties.
Construct a SimBiology model object.
```
[modelObj, PKModelMapObj] = pkm.construct
```
The construct method returns a SimBiology model object (modelObj) and a PKModelMap object (PKModelMapObj) that contains the mapping of the model components to the elements of the regression function.
Note
If you change the PKModelDesign object, you must create a new model object using the construct method. Changes to the PKModelDesign do not automatically propagate to a previously constructed model object.
Perform parameter fitting using Nonlinear Regression or Nonlinear Mixed-Effects Modeling.

The model object and the PKModelMap object are input arguments for the sbionlmefit, sbionlmefitsa and sbionlinfit functions used in parameter fitting.