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.

HowSimBiologyModels 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 speciesobjectcontained 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 (药物and/orDose) and reactions (剂量- >药物), 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, seeDosing Types.

You can also view this model as a regression function,y = f(k,u), whereyis the predicted value, given values of an inputu, and parameter valuesk. In SimBiology the model representsf, and the model is used to generate a regression function ify,k, anduare 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 (药物_CompartmentNameandDose_CompartmentName为每个舱)。
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 theDose_CompartmentName -> Drug_CompartmentNamereaction.
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 (infusionandzero-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 (`药物_CompartmentName`) in each compartment	None
SimBiology Model Builderapp —`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 (`药物_CompartmentName`) in each compartment	None
SimBiology Model Builderapp —`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 (`药物_CompartmentName`) in each compartment	None
SimBiology Model Builderapp —`zero-order` Command line —`ZeroOrder`	Assumes that the drug is added at a constant rate over fixed, but unknown duration.	The species`药物_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 Builderapp —`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 (`药物_CompartmentName`) for each compartment A parameter (`ka_CompartmentName`) representing the absorption rate of the drug A`MassActionreaction (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 Builderapp —`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`MassActionreaction (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. SeeIntercompartmental Clearance.
SimBiology Model Builderapp —`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`基于the initial values for`Cl_CompartmentName`and compartment volume A`MassActionreaction (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. SeeIntercompartmental Clearance.
SimBiology Model Builderapp —`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`),法律paramet动能ers`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. SeeIntercompartmental Clearance

SimBiology Model Builderapp —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)
AMassActionreaction (drug —> null)with forward rate parameter (ke_CompartmentName) specific to the compartment

Compartment volume
(Capacityproperty)
Elimination rate constant (ke_CompartmentName)
Inter-compartmental clearance (Q) when there is more than one compartment.
SeeIntercompartmental Clearance.

SimBiology Model Builderapp —Linear {Clearance, Volume}

Command line —'linear-clearance'

Assumes simple mass-action kinetics in the elimination of the drug. In the SimBiology model, similar toLinear {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)
AnInitialAssignmentrule that initializeske_CompartmentName基于the initial values forCl_CompartmentNameand compartment volume
AMassActionreaction (drug —> null)with forward rate parameter (ke_CompartmentName)

Compartment volume
(Capacityproperty)
Clearance (Cl_CompartmentName)
Inter-compartmental clearance (Q) when there is more than one compartment.
SeeIntercompartmental Clearance.

SimBiology Model Builderapp —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),法律paramet动能ersVm_CompartmentNameandKm_CompartmentName

Compartment volume
(Capacityproperty)
Parameter (Km_CompartmentName)
Parameter (Vm_CompartmentName)
Inter-compartmental clearance (Q) when there is more than one compartment.
SeeIntercompartmental 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,C1andC2, generates a reversible mass-action reactionC1。Drug_C1 < - > C2。药物. The forward rate parameter is the compartmental clearance,Q₁₂, divided by the volume ofC1. The reverse rate parameter isQ₁₂, divided by the volume ofC2.

The process of adding each pair of compartments in the chainC_mandC_ngenerates the following model components:

A parameterQ_mnrepresenting the compartmental clearance between those two compartments. This parameter is added to the list of parameters to be estimated (Estimatedproperty ofPKModelMapobject).
A parameter (kmn) representing the rate of transfer of the drug fromCmtoCn, wherek_mn= Q_mn/V_m.
A parameter (knm) representing the rate ofCntoCm, wherek_nm= Q_mn/V_n.
A reversible mass-action reaction between the two compartments,Cm.Drug_Cm <-> Cn.Drug_Cn, with forward rate parameterkmn, and reverse rate parameterknm.
An initial assignment rule that initializes the value of the parameterkmn, based on the initial values forCmandQmn.
An initial assignment rule that initializes the value of the parameterknm, based on the initial values forCnandQmn.

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 isonoroff, you must express dosing data in amount. By default,Unit Conversionisoff, so you must ensure that units for the data and the model are consistent with one another. IfUnit Conversionison, you must specify units.

Parameters in the model have default units. If unit conversion ison, 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 (CentralorPeripheral)	`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 conversiononoroff. For details, seeModel Simulation.

For details on dimensional analysis for reaction rates, seeHow 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 aPKModelDesignobject. ThePKModelDesignobject 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 namedCentral, withBolusfor theDosingTypeproperty,linear-clearancefor theEliminationTypeproperty, andtruefor theHasResponseVariableproperty.
```
pkc1 = addCompartment(pkm, 'Central', 'DosingType', 'Bolus', ... 'EliminationType', 'linear-clearance', ... 'HasResponseVariable', true);
```
For a description of otherDosingTypeandEliminationTypeproperty values, seeDosing TypesandElimination Types.
For a description of theHasResponseVariableproperty, seeHasResponseVariable. At least one compartment in a model must have a response. Although SimBiology supports multiple responses per compartment, when adding compartments to aPKModelDesignobject, 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 theHasLagproperty totrue:
```
pkc_lag = addCompartment(pkm, 'Central', 'DosingType', 'Bolus', ... 'EliminationType', 'linear-clearance', ... 'HasResponseVariable', true, 'HasLag', true);
```
Or after adding a compartment, set itsHasLagproperty totrue:
```
pkc1.HasLag = true;
```
Optionally, add a second compartment namedPeripheral, with no dosing, no elimination, and no time lag. Set theHasResponseVariableproperty totrue. 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 clearanceQ. 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 (pkc1orpkc2), to change compartment properties.
Construct a SimBiology model object.
```
[modelObj, PKModelMapObj] = pkm.construct
```
Theconstruct方法返回一个SimBiology model object (modelObj) and aPKModelMapobject (PKModelMapObj) that contains the mapping of the model components to the elements of the regression function.

Note

If you change thePKModelDesignobject, you must create a new model object using theconstructmethod. Changes to thePKModelDesigndo not automatically propagate to a previously constructed model object.
Perform parameter fitting usingNonlinear RegressionorNonlinear Mixed-Effects Modeling.

The model object and thePKModelMapobject are input arguments for thesbionlmefit,sbionlmefitsaandsbionlinfitfunctions used in parameter fitting.