Graphical model interface

Note:The graphical model interface is a free-form model building interface. It is much more sophisti­cated than the built-in model, which means user error is more likely. It is recommended for advanced users.

To use the graphical editor to create the structural model:

Click Edit as Graphical.

In the displayed dialog, click Yes to confirm using the graphical editor.

If Closed form? is currently checked, a second dialog is presented notifying the user that closed-form will not be used. This is because graphical models are built with differential equa­tions. Click Yes to continue.

Model_panel_1.png 

Example of a one-compartment, 1st order absorption PK model

When the graphical editor is in use, the Edit as Graphical button changes to Use Builtin. Click this button to return to the built-in model interface.

The Main Mappings, Dosing, Parameters, and Parameters.Mappings panels and all tabs except the Structure tab work the same in the Graphical model as they do in the built-in model. If no model ele­ments are selected in the Model panel then the Structure tab displays the model parameters, state­ments, and scale control. Use the pointer to move the slider Slider_2.png right or left to adjust the graphical model scale, which makes the model picture larger or smaller. If a compartment is selected, then the compartment type and type-specific settings are displayed in the Structure tab.

Users can specify the model using the Model toolbox or the right-click menu. The right-click Insert menu allows users to insert compartments, flows, observations, PD blocks, structural parameters, and other model elements. Users can also cut, copy, paste, and manipulate model elements. (The dif­ference between Replace and Insert is that the former replaces the selected objects in the diagram with the contents of the clipboard while trying to retain wire and flow connections. The latter just cop­ies the contents of the clipboard into the diagram.)

Insertable model elements

Compartment

Absorption (Add_Absorption_Compartment_button.png)

Absorption compartment options

 

Central (Add_Central_Compartment_button.png)

Central compartment options

 

Peripheral (Add_Peripheral_Compartment_button.png)

Peripheral compartment options

 

Elimination (Add_Elimination_Compartment_button.png)

Elimination compartment options

Flow (Add_PK_Flow_button.png)

 

PK Flow

Observation

Continuous (Add_Continuous_Observation_button.png)

Continuous observation block

 

Categorical

Categorical observation block

 

Event

Event observation block

 

Count

Count observation block

 

LL

Log-likelihood observation block

PD

Emax (Add_PD_Emax_Block_button.png)

Emax block

 

Linear

Linear block

 

Indirect

Indirect block

 

Effect Cpt

Effect compartment block

Parameter

 

Parameter block

Procedure

 

Procedure block

Expression

 

Expression block

Annotation

 

Annotation block

PBPK

 

Vascular flow

Caution:When switching from a PK/Emax, or PK/Indirect built-in to a Graphical model, verify the tab set­tings. In particular, the Freeze PK? checkbox, when checked in the built-in model, can become unchecked when switching to Graphical.

Absorption compartment options

This PK compartment is used as an input site for doses following a first-order input function. By default, flows connecting an absorption compartment to another compartment use a first-order func­tion. That function can be changed by specifying PK flow options in the Structure tab. Connect an absorption compartment to another compartment via a PK flow to create a 1st-order absorption PK model.

Caution:Be careful not to use the same names for the volume and concentration parameters in different compartments.

Central compartment options

Central compartments can be connected to other PK compartments, including at least one elimination compartment (unless no drug leaves the body), by using a PK flow. Any number of central and periph­eral compartments can be connected together, with one exception: if a set of PK compartments using volume parameters are connected by PK flows parameterized in microconstants, there can be only one central compartment.

Central_Compartment_Structural_tab.png 

Note:Option 2 requires the dosing data to be in separate columns in the input dataset. Option split requires the data to be in the same column.

If 1, 2, or split dose points are selected, users can add time delay parameters, bioavailability expressions, add infusions, and specify zero-order absorption options. For 2 or split, these parameters can be set for each dose point by selecting the Dosept 1 and Dosept 2 tabs.

Dose_point_options.png 

A dosing parameter rate, such as Aa Rate or A1 Rate, is added to the contexts in the Main Mappings panel.

A Duration? checkbox is also added in the Structure tab. Checking this box causes the con­text A1 or Aa Rate to change to A1 or Aa Duration.

No: There is no zero-order input.

Rate: The drug is introduced into the system at a constant rate. Enter the zero-order rate expression in the field, either as a parameter or a numeric value.

Duration: The drug is introduced over a finite period of time, or duration. Enter the zero-order duration expression in the field, either as a parameter or a numeric value.

Peripheral compartment options

Peripheral compartments can be connected to other PK compartments, including central and elimina­tion compartments, by using a PK flow. If there is only one central compartment, the volumes of the peripheral compartments are determined by their surrounding constraints, or flow parameters.

Elimination compartment options

The elimination compartment (which is shown as a urinecpt code statement) can be connected to any other PK compartment via a PK flow. The only difference between urinecpt and deriv is that urinecpt is ignored when determining a steady-state condition.

    urinecpt(A0=(A1*Ke)
      ,fe=Fe
     )

     observe(UrineObs=A0+eps, doafter={A0=0; })

PK Flow

Use a PK flow to represent a mass flow between PK compartments. To connect two PK compart­ments with a flow:

Note that lag time for an absorption model is indicated in the absorption or central compartments.

Different types of default PK flows are added depending on which compartments they connect:

If the absorption compartment is connected to a central, peripheral, or elimination compart­ment, the default PK flow is a micro parameter, one-way flow. The default parameter name for the PK flow changes depending on the direction on which the flow moves, and on which com­partments are being connected. For example, if the flow moves from the absorption compart­ment to another compartment, the parameter name for the forward movement (Kfwd) is Ka. The default parameter name for any backward PK flow is K12.

The default PK flow between the central or peripheral compartments and the elimination com­partment is named CL, and it is a clearance/volume parameter, one-way flow.

The default PK flow between the central and peripheral compartments is named Q, and it is a clearance/volume parameter, with a two-way flow.

To specify PK flow options

Micro: Enter a variable name for the flow into the second compartment in the Kfwd field or use the default. If the 2Way checkbox is also checked, enter a variable name for the flow back into the first compartment in the Kbak field.

Clearance/Volume: Enter a variable name for the clearance in the CL field or use the default.

Saturating: Enter variable names in the Vmax field for the maximum metabolic rate and in the Km field for the fractional metabolic rate or use the defaults.

Diagonal: Draws the diagonal flow.

Horizontal First: Draws the flow horizontally from the first compartment.

Vertical First: Draws the flow vertically from the first compartment.

Continuous observation block

The Continuous Observation block links a model variable such as excreted amount, or plasma con­centration, to observed data. The observations are normally distributed around the value of the model variable with some standard deviation prescribed by the error model. When estimating model param­eters, the likelihood of an observation is obtained from the normal distribution. When simulating data, the observations are generated by sampling values from the standard normal distribution and apply­ing them to the terms in the error model.

Connector_line_between_CObs_and_central_compartment.png 

To delete a connection

To specify continuous observation options

Categorical observation block

Use the Categorical Observation block to model multinomial data. The data should be given as inte­ger (whole) number values, such as 0, 1, 2, etc. A key feature of the Categorical Observation block is the ability to use model variables to affect the probability of observing data in a particular category. For instance, the Categorical Observation block could be used to link the probability of a patient reporting adverse effects of a given type to the administered dose or even drug concentration.

The default settings for the Categorical Observation block give a 50% chance of a zero or one output when the input value is zero. The probability of a one output increases as the input value increases from zero.

The Categorical Observation block can be connected to any PK compartment, observation block, PD block, or parameter block. See the Continuous Observation block section for instructions on adding and deleting a connection.

To specify categorical observation options

Logit: the inverse of the sigmoid function. p=ei+o/(1+ei+o)

Probit: the inverse cumulative distribution function. p=G(i+o) where G is the cumulative nor­mal distribution.

Log-log: the logarithmic function. p=exp(–e–i+o)

CLog-log: complementary logarithmic function. p=i+o (truncated to the interval [0,1])

Event observation block

An Event block represents an unscheduled event. Observations take the form of indicator variables for the event: 1 if the event occurs at the time of the observation, or 0 (zero) if the event has not yet occurred at the time of the observation.

The likelihood of the observation is determined by integrating the hazard over the length of the sam­pling interval, so that at the end of the interval the expected number of events are computed. The expected, or mean, number of events is made the mean of a Poisson distribution. A sample is taken at random from that Poisson distribution at each sampling interval to say how many, if any, events occurred.

The number of events during each sampling interval, which is only one if a probability is entered, is added to the N output variable of the event block.

An event block represents an unscheduled event. One record is created in the results for each evalu­ation period during which the event is triggered. Each record indicates the time, the censor value (one for event occurrence; zero for right-censored), and a sequence number showing the total number of events having occurred for a given subject.

Note:Censor values in the results are zero for censored events and one for non-censored event records, where the event happened.

The Event Observation block can be connected to any PK compartment, observation block, PD block, or parameter block. See the Continuous Observation block section for instructions on adding and deleting a connection.

To specify event observation block options

For more information on the use of the Event Observation block see “Event statement for Survival models”.

Make sure the Model Text tab shows an entry for the observation in the Column Definition Text field. It is displayed as obs([block name]<-[“column name”]). If there is no entry, type it in the User-Provided Extra Column Definition Text field.

Count observation block

With the exception of the Cnt field versus the Evt field, the options are the same as for the Event observation block.

For more information on the use of the Count Observation block see “Count statement for Count mod­els”.

Log-likelihood observation block

With the exception of the LL field versus the Evt field, the options are the same as for the Event observation block.

For more information on the use of the Count Observation block see “LL statement for Log Likelihood models”.

Emax block

The Emax block represents an Emax or a sigmoidal Emax model, where the output is the effect level as a function of drug concentration. The baseline effect level (E0) is always zero.

The Emax block contains five input nodes and one output node.

Emax_block.png 

The input nodes are made available depending on the options that are selected in the Structure tab. If an input node cannot be used, it is marked with an X.

Emax_block_with_input_nodes_disabled.png 

The input nodes on the Emax block can be connected to output nodes on PK compartments, observa­tion blocks, PD blocks, and parameter blocks.

Once an output node is connected its name cannot be changed.

To specify Emax block options

The structural parameters EC50 and Emax change to IC50 (concentration producing 50% of maximal inhibition) and E0 (baseline effect).

C: Drug concentration in plasma, or another input variable.

EC50: Input level that achieves 50% of predicted maximum effect in an Emax model.

IC50: Input level required to produce 50% of the maximal inhibition.

first (E0): Baseline effect.

EMax: Maximum drug effect.

IMax: Maximum drug inhibition (requires that both Baseline and Inhibitory checkboxes be checked).

Gam: Shape parameter.

Linear block

The Linear block provides a simple linear model in the form of: Output=A*Input+B.

The Linear block contains four input nodes and one output node. The input nodes are made available depending on the options that are selected in the Structural tab. If an input node cannot be used, it is marked with an X.

The input nodes on the Linear block can be connected to output nodes on PK compartments, obser­vation blocks, PD blocks, and parameter blocks. Once an output node is connected its name cannot be changed.

To specify Linear block options

C: drug concentration in plasma, or another input variable.

Alpha: coefficient for zero-order term.

Beta: coefficient for first-order term (if order >=1).

Gam: coefficient for second-order term (if order=2).

Indirect block

PK/PD models with stimulation or inhibition of the indirect response formation or degradation can be created using this block.

To specify Indirect block options

Stim. Limited (limited stimulation of input)

Stim. Infinite (infinite stimulation of input)

Inhib. Limited (limited inhibition of input)

Inhib. Inverse (inverse inhibition of input)

Stim. Linear (linear stimulation of input)

Stim. Log Linear (logarithmic and linear stimulation of input)

Use the Indirect menu options to select a model in which the response formation (build-up) or degra­dation (loss) is stimulated or inhibited by increased concentrations. The default response setting is the build-up of the response, or the production of the response.

Build-up: Changes the statement for the Ke parameter to Kin.

Loss: Changes the statement for the Ke parameter to include Kin-Kout, where Kin is the zero-order input rate constant and Kout is the first output rate constant.

no Exponent: Removes the exponent from the effect statement.

Exponent: Adds the exponent Gamma to the effect statement.

Kin: Zero-order turnover rate for the production of a response.

Kout: Fractional turnover rate.

Emax: Maximum drug induced effect.

Imax: Maximum drug induced inhibition.

EC50: Concentration at 50% of maximal effect.

IC50: Concentration producing 50% of maximal inhibition.

Gam: Exponent parameter.

Effect compartment block

This block represents an effect site for a PK/PD model with a delay between the central and effect-site concentrations, that is, plots of plasma concentration versus effect level show a counter-clock­wise hysteresis. See Sheiner, Stanski, Vozeh, Miller and Ham (1979). Simultaneous modeling of pharmacokinetics and pharmacodynamics: application to d-tubocurarine. Clin Pharm Ther 25:358–71 for more about modeling data with a hysteresis in the concentration-effect plot.

The Effect Compartment block contains two input nodes and one output node. The input nodes are made available depending on the options that are selected in the Structural tab. If an input node can­not be used, it is marked with an X.

The input nodes on the Effect Compartment block can be connected to output nodes on PK compart­ments, observation blocks, PD blocks, and parameter blocks.

Once an output node is connected its name cannot be changed.

To specify Effect compartment block options

Ke0 is the exit rate constant from the effect compartment.

Parameter block

The Parameter block is used to add extra structural parameters to a model.

The Parameter block’s input nodes are labeled S1, S2, and so forth depending on how many Param­eter blocks are added to the model. The output node is labeled based on the name given to the parameter.

The input node on the Parameter block can be connected to output nodes on PK compartments, observation blocks, PD blocks, and other parameter blocks. Once an output node is connected its name cannot be changed.

Procedure block

Use Procedure blocks to write continuous functions, including differential equations, and logical state­ments. Within a Procedure block, functions in the Code tab are executed in the order they are listed, one or more times at each simulation step. For that reason, Procedure blocks are not suitable for counting, storing model status across time, or performing computations at specific times during simu­lation.

Procedure_block_options.png 

To specify Procedure block options

Note:Sequence blocks cannot be entered in a procedure block when working with the graphical model. They can be entered in the textual model, however.

Expression block

Each Expression block's value is set by the expression entered in the Contents tab. Note that this can only be an expression; no statements, such as assignments (using the “=” sign), or PML code can be included. An expression is any combination of numbers, identifiers, and operators representing a sin­gle value. It includes no “=” sign representing assignment.

An expression can contain:

conditional operators (e.g., (cond) ? actionA:actionB)

logical operators (e.g., &&, ||, !)

comparison operators (e.g., >=, <=, !=, ==, >, <)

These are all at a lesser level of precedence than arithmetic operators. So, for example, “a+b>c” means “(a+b)>c”.

Expression_block_options.png 

To specify Expression block options

Annotation block

The Annotation block is used to add notes to a model.

Vascular flow

Use a vascular flow to represent blood flow in physiologically-based PK models. Use this flow to con­nect PK compartments representing organs or other areas into circuits of blood flow. The flow rate between organs is represented by the variable Q.

Note:A Vascular Flow should connect a central or a peripheral compartment. It should not be used to connect an elimination or an absorption compartment.

To specify Vascular Flow options

Diagonal: Draws the diagonal flow.

Horizontal First: Draws the flow horizontally from the first compartment.

Vertical First: Draws the flow vertically from the first compartment.

Textual model interface

To use the textual editor to create the structural model

Click Edit as Textual to use PML (Phoenix Modeling Language) code to create the model.

In the displayed dialog, click Yes to confirm using the textual editor.

When using the textual editor, the Edit as Textual button changes to either Use Builtin or Use Graphical, depending on the mode you were in before switching to the textual editor. Click this button to return to the previous mode.

The mappings panel switches to the Model panel and the model text is displayed. It represents the model as it currently exists and allows users to edit the structural model using PML code. The PML examples illustrate the use of PML to create various models and describes the use of the available statements and functions.

While typing, the text editor will provide hints for adding parameters. Type the parameter and its fol­lowing comma to see the hint for the next parameter.

When in text model mode, some Phoenix Model Object option tabs change:

The General tab displays PML errors and warnings as model code is entered in the Model panel.

The Parameters tab displays only the parameter names. Bounds and initial values should be entered in the fixef statements in the PML code.

The Input Options tab is where infusion information is specified.

The Model Text tab displays only the column definition. The model code is now only dis­played in the Model panel.

Note:When doing a Profile of a Textual model, avoid deleting fixef parameters as this can lead to extra copies of fixed effects appearing in the “Fixed Eff” list.

 


Last modified date:6/26/19
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