TMDD

Running

The structsearch tool is available both in Pharmpy/pharmr.

The code to initiate structsearch for a TMDD model in Python/R is stated below:

PythonR

from pharmpy.modeling import read_model
from pharmpy.tools read_modelfit_results, run_structsearch

start_model = read_model('path/to/model')
start_model_results = read_modelfit_results('path/to/model')

res = run_structsearch(type='tmdd',
                        model=start_model,
                        results=start_model_results)

Arguments

The arguments of the structsearch tool for TMDD models are listed below.

Mandatory

Argument	Description
type	Type of model. In this case “tmdd”.
model	PK start model.
results	ModelfitResults of the start model.

Optional

Argument	Description
strictness	Strictness criteria for model selection. Default is “minimization_successful or (rounding_errors and sigdigs>= 0.1)”. Optional.
extra_model	Extra model for TMDD structsearch. Optional. If specified, 8 additional QSS models will be generated.
extra_model_results	ModelfitResults object for the extra model for TMDD structsearch. Optional if extra_model is not specified.
dv_types	Dictionary of DV types for multiple DVs (e.g. dv_types = {‘target’: 2}). Allowed keys are: ‘drug’, ‘target’, ‘complex’, ‘drug_tot’ and ‘target_tot’. Optional. Default is None which means that all observations are treated as drug observations.

Models

Implemented target mediated drug disposition (TMDD) models are:

• Full model

• Irreversible binding approximation (IB)

• Constant total receptor approximation (CR)

• Irreversible binding and constant total receptor approximation (CR+IB)

• Quasi steady-state approximation (QSS)

• Wagner

• Michaelis-Menten approximation (MMAPP)

Full model:

\[\frac {dA_{\text{central}}}{dt} = k_{\text{off}} \cdot A_{\text{complex}}(t) \ + \biggl(- \frac{\text{Cl}}{\text{V}} \ - \frac{k_{\text{on}} \cdot A_{\text{target}}(t)}{\text{V}} \biggl) \cdot A_{\text{central}}(t)\]

\[\frac {dA_{\text{target}}}{dt} = - k_{\text{deg}} \cdot A_{\text{target}}(t) \ + k_{\text{off}} \cdot A_{\text{complex}}(t) \ - \frac{k_{\text{on}} \cdot A_{\text{central}}(t) \cdot A_{\text{target}}(t)}{\text{V}} \ + k_{\text{syn}} \cdot \text{V}\]

\[\frac {dA_{\text{complex}}}{dt} = \frac{k_{\text{on}} \cdot A_{\text{central}}(t) \ \cdot A_{\text{target}}(t)}{\text{V}} + ( - k_{\text{int}} - k_{\text{off}}) \cdot A_{\text{complex}}(t)\]

IB model:

\[\frac {dA_{\text{central}}}{dt} = \biggl(- \frac{\text{Cl}}{\text{V}} \ - \frac{k_{\text{on}} \cdot A_{\text{target}}(t)}{\text{V}} \biggl) \cdot A_{\text{central}}(t)\]

\[\frac {dA_{\text{target}}}{dt} = - k_{\text{deg}} \cdot A_{\text{target}}(t) \ - \frac{k_{\text{on}} \cdot A_{\text{central}}(t) \cdot A_{\text{target}}(t)}{\text{V}} \ + k_{\text{syn}} \cdot \text{V}\]

\[\frac {dA_{\text{complex}}}{dt} = \frac{k_{\text{on}} \cdot A_{\text{central}}(t) \ \cdot A_{\text{target}}(t)}{\text{V}} - k_{\text{int}} \cdot A_{\text{complex}}(t)\]

CR model:

\[\frac {dA_{\text{central}}}{dt} = k_{\text{off}} \cdot A_{\text{complex}}(t) \ + \biggl( - \frac{\text{Cl}}{\text{V}} - k_{\text{on}} \cdot R_0 \ + \frac{k_{\text{on}} \cdot A_{\text{complex}}(t)}{\text{V}} \biggl) \cdot A_{\text{central}}(t)\]

\[\frac {dA_{\text{complex}}}{dt} = \biggl( k_{\text{on}} \cdot R_0 - \frac{ k_{\text{on}} \ \cdot A_{\text{complex}}(t)}{\text{V}} \biggl) \cdot A_{\text{central}}(t) + \ (- k_{\text{int}} - k_{\text{off}}) \cdot A_{\text{complex}}(t)\]

CR + IB model:

\[\frac {dA_{\text{central}}}{dt} = \biggl(- \frac{\text{Cl}}{\text{V}} - k_{\text{on}} \cdot R_0 \ - \frac{k_{\text{on}} \cdot A_{\text{complex}}(t)}{\text{V}} \biggl) \cdot A_{\text{central}}(t)\]

\[\frac {dA_{\text{complex}}}{dt} = \biggl( k_{\text{on}} \cdot R_0 - \frac{ k_{\text{on}} \ \cdot A_{\text{complex}}(t)}{\text{V}} \biggl) \cdot A_{\text{central}}(t) \ - k_{\text{int}} \cdot A_{\text{complex}}(t)\]

QSS model:

\[\frac {dA_{\text{central}}}{dt} = - \frac{Cl \cdot \text{LAFREE} \cdot A_{\text{central}}(t)}{V} \ - \frac{Cl \cdot \text{LAFREE}}{V} - \frac{k_{\text{int}} \cdot \ \text{LAFREE} \cdot A_{\text{target}}(t)}{k_{\text{D}} + \text{LAFREE}}\]

\[\frac {dA_{\text{target}}}{dt} = k_{\text{syn}} \cdot V + \biggl( -k_{\text{deg}} \ - \frac{\text{LAFREE} \cdot (k_{\text{int}} - k_{\text{deg}})}{k_{\text{D}} + \text{LAFREE}} \biggl) \ \cdot A_{\text{target}}(t)\]

Wagner model:

\[\frac {dA_{\text{central}}}{dt} = - \frac{Cl \cdot \text{LAFREE}}{V} \ + k_{\text{int}} \cdot \text{LAFREE} - k_{\text{int}} \cdot A_{\text{central}}(t)\]

MMAPP model:

\[\frac {dA_{\text{central}}}{dt} = \Biggl( - \frac{Cl}{V} - \frac{k_{\text{int}} \cdot \ A_{\text{target}}(t)}{ V \cdot \Bigl( k_{\text{MC}} + \frac{A_{\text{central}}(t)}{V} \Bigl) } \Biggl) \ \cdot A_{\text{entral}}(t)\]

\[\frac {dA_{\text{target}}}{dt} = -k_{\text{deg}} \cdot A_{\text{target}}(t) + k_{\text{syn}} \ - \frac{(k_{\text{kint}} - k_{\text{deg}}) \cdot A_{\text{central}}(t) \cdot A_{\text{target}}(t)}{V \ \cdot \biggl( k_{\text{MC}} + \frac{A_{\text{central}}(t)}{V} \biggl)}\]

DV types

The dv_types argument is a dictionary specifiying the DVs. If dv_types is not specified then all observations are treated as drug observations. There are five types implemented: ‘drug’ (free drug), ‘target’, ‘complex’, ‘drug_tot’ (total drug) and ‘target_tot’ (total target). Only ‘drug’ and ‘drug_tot’ can have dv=1.

Example 1:

dv_types = {'drug':1, 'target':2, 'complex':3}

In this case the drug has dv=1, the target has dv=2 and complex has dv=3:

Example 2:

dv_types = {'target':2, 'complex':3}

This is equivalent to the previous example. Per default drug has dv=1.

Example 3:

dv_types = {'target_tot':3, 'complex':2}

The dv types can be arranged in any possible order.

Structsearch workflow

There are two workflows for the structsearch tool for TMDD models, depending on whether the tool is used separately or inside the AMD tool. If used as a standalone tool, the structsearch workflow is as follows:

1. Create 8 QSS models for the input model and optionally additional 8 QSS models for the extra model if specified.

2. Find best QSS model of the 8(16) QSS models

3. Create 4 full models, 2 CR+IB models, 1 Wagner model, 2 CR models, 2 IB models and 1 MMAPP model. Use parameter estimates from the best QSS model as initial estimates for the generated models.

4. Find the best model of these 12 models.

When used inside the AMD tool:

1. Perform modelsearch

2. Get the final model of the modelsearch and a model with the same features as the final model but with one less peripheral compartment if one such model exists.

3. Create 8 QSS models for the final model and 8 QSS models for the final model minus one compartment if it exists. Otherwise only 8 QSS models are created.

4. Find best QSS model of the 8(16) QSS models

5. Create 4 full models, 2 CR+IB models, 1 Wagner model, 2 CR models, 2 IB models and 1 MMAPP model. Use parameter estimates from the best QSS model as initial estimates for the generated models.

6. Find the best model of these 12 models.

Results

The results object contains various summary tables which can be accessed in the results object, as well as files in .csv/.json format. The name of the selected best model (based on the input selection criteria) is also included.

Below is an example for a TMDD run.

PythonR

res = run_structsearch(type='tmdd',
                        model=start_model,
                        results=start_model_results)

The summary_tool table contains information such as which feature each model candidate has, the difference to the start model (in this case comparing BIC), and final ranking:

	description	n_params	d_params	dbic	bic	rank	parent_model
model
structsearch_run1	FULL1	13	1	14.679076	4243.302405	1.0	QSS2
structsearch_run2	FULL2	13	1	14.679069	4243.302412	2.0	QSS2
structsearch_run5	CR1	12	0	10.987197	4246.994284	3.0	QSS2
QSS2	QSS2	12	0	0.000000	4257.981481	4.0	QSS2
structsearch_run11	WAGNER	11	-1	-31.897162	4289.878642	5.0	QSS2
structsearch_run9	CR+IB1	11	-1	-97.201724	4355.183204	6.0	QSS2
structsearch_run7	IB1	12	0	-97.201728	4355.183209	7.0	QSS2
structsearch_run12	MMAPP	12	0	-103.284581	4361.266061	8.0	QSS2
structsearch_run3	FULL3	13	1	NaN	NaN	NaN	QSS2
structsearch_run4	FULL4	13	1	NaN	NaN	NaN	QSS2
structsearch_run6	CR2	12	0	NaN	NaN	NaN	QSS2
structsearch_run8	IB2	12	0	NaN	NaN	NaN	QSS2
structsearch_run10	CR+IB2	11	-1	NaN	NaN	NaN	QSS2

Examples

Run TMDD for multiple DVs:

PythonR

from pharmpy.modeling import read_model
from pharmpy.tools read_modelfit_results, run_structsearch

start_model = read_model('path/to/model')
start_model_results = read_modelfit_results('path/to/model')

res = run_structsearch(type='tmdd',
                        model=start_model,
                        results=start_model_results,
                        dv_types={'drug': 1, 'target': 2, 'complex': 3})

Note: “drug” can be omitted in dv_types. In this case it will be set to 1.