PhysiPKPD

Getting started...

...with a new project

1. Download (or copy contents of) get_physipkpd.py and helpers_for_get_and_add.py to local files in the same directory.
2. Run

python get_physipkpd.py --dir path/to/project/dir --studio

• The --studio flag downloads a PhysiPKPD-enabled version of PhysiCell-Studio to help build the model

3. Follow output for next steps

...adding PhysiPKPD to an existing project

1. Download (or copy contents of) add_physipkpd.py and helpers_for_get_and_add.py to local files in the same directory.
2. Run

python add_physipkpd.py path/to/project/dir --studio

• The --studio flag downloads a PhysiPKPD-enabled version of PhysiCell-Studio to help build the model

3. Follow output for next steps

Note: This script will perform the steps below, except updates to the configuration file. Specifically, it will...

• add lines to your project's main.cpp, custom.h, custom.cpp, and Makefile
• add PhysiPKPD to your project's addons if it does not exist already
• create a new copy of the PhysiPKPD-enabled studio at the same directory level as your project

...by downloading PhysiPKPD and adding to a working PhysiCell directory

1. Download the repository and unzip the file.
2. Move the folder PhysiPKPD/addons/PhysiPKPD into PhysiCell/addons/
3. Move the folder PhysiPKPD/sample_projects_phsyipkpd into PhysiCell
4. Open PhysiCell/sample_projects/Makefile-default (the one that make reset will put it in the main PhysiCell directory)
5. Add the text from PhysiCell/addons/PhysiPKPD/Makefile-PhysiPKPD_Addendum to PhysiCell/sample_projects/Makefile-default (anywhere should work, perhaps best around line 195 at the end of the other sample projects)

...by cloning the repository

1. Fork this repository to your own GitHub account.
2. Clone the resulting forked repository onto your machine.
3. Copy all the PhysiCell files in your PhysiCell directory except addons
4. Copy the subfolders in PhysiCell/addons into your cloned directory's addons folder
5. Continue from #4 above.

Congratulations! You're ready to try out PhysiPKPD!

Running the sample projects

There are 5 sample projects currently distributed with PhysiPKPD. They highlight some of the possible behaviors achievable with PhysiPKPD. To run one of these samples, do the following:

1. make reset to make sure you have the newly edited Makefile in your top directory
2. Make your preferred sample project:
   • make pkpd-proliferation-sample
   • make pkpd-apoptosis-sample
   • make pkpd-necrosis-sample
   • make pkpd-motility-sample
   • make pkpd-combo-sample
   • make pkpd-confluence-start-sample (currently deprecated)
3. Compile your model: make
4. Run your model
   • On Mac: ./pkpd_sample ./config/pkpd_model.xml
   • On Windows: pkpd_sample.exe .\config\pkpd_model.xml
5. Look at the snapshots in output/ and the living cell counts in output/cell_counts.csv

Making your own project

There are two template projects available. Load one with make pkpd-template or make pkpd-template-sbml. The former sets up a model with two PKPD substrates, one with a dosing schedule defined by a CSV file. The latter sets up a model with two PKPD substrates, one defined by an SBML model.

Adding PhysiPKPD to an existing project

To add PhysiPKPD to an existing project, take the following steps:

1. In main.cpp...
   • add setup_pharmacodynamics(); as a new line after setup_tissue();
   • add PK_model( PhysiCell_globals.current_time ); immediately before microenvironment.simulate_diffusion_decay( diffusion_dt );
   • add PD_model( PhysiCell_globals.current_time ); immediately after microenvironment.simulate_diffusion_decay( diffusion_dt );
2. In custom_modules/custom.h...
   • add #include "../addons/PhysiPKPD/src/PhysiPKPD.h" to the top
3. In the configuration file, e.g., config/PhysiCell_settings.xml...
   • add a PK element to every PK substrate (microenvironment_setup//variable) (see PK Templates)
   • add a PD element to every cell_definition that will be affected by a PD substrate; add a substrate block within this PD element for each PD substrate affecting the given cell definition (see PD Templates)
   • add S_damage to every cell_definition//custom_data for every PD substrate S (even those unaffected by S because PhysiCell requires all cells to have the same custom data)
4. In Makefile...
   • add a line PhysiPKPD_OBJECTS := PhysiPKPD_PK.o PhysiPKPD_PD.o
   • add $(PhysiPKPD_OBJECTS) to the list of PhysiCell_OBJECTS
   • define PhysiPKPD_PK.o and PhysiPKPD_PD.o with the following lines

PhysiPKPD_PK.o: ./addons/PhysiPKPD/src/PhysiPKPD_PK.cpp
	$(COMPILE_COMMAND) -c ./addons/PhysiPKPD/src/PhysiPKPD_PK.cpp

PhysiPKPD_PD.o: ./addons/PhysiPKPD/src/PhysiPKPD_PD.cpp
	$(COMPILE_COMMAND) -c ./addons/PhysiPKPD/src/PhysiPKPD_PD.cpp

5. Ensure Dirichlet conditions are enabled for any PK substrates.
6. Ensure cell types that are affected by a PD substrate have a nonzero uptake rate for that substrate.
7. Ensure rules are enabled and set in the rules CSV file for any PD substrates.

Pharmacokinetics

PK models are added as microenvironment_setup//variable//PK element, i.e., at the same level as Dirichlet_options, of a substrate, S. An enabled="true" attribute is required to turn on the PK model.

PK models

There are four available model's: Constant, 1C, 2C, and SBML¹. An example template for each is provided below. For each model, the circulation_concentration of the PK model is what interacts with the microenvironment. Specifically, any Dirichlet node for S is set as circulation_concentration x biot_number. The biot_number is thus just the factor dropoff in substrate concentration from the blood to the perivascular niche.

Model	Description	Specification
Constant	Piecewise constant circulation compartment	Constant
1-compartment	Circulation compartment with linear elimination	1C
2-compartment	1C plus a periphery compartment with linear intercompartmental clearance rates	2C
SBML-defined	Any SBML-defined model. Place the file in the ./config/ folder. PhysiPKPD will look for the species named circulation_concentration to use for updating Dirichlet nodes	SBML

Table: PK model specifications

Parameter	Description	If Missing
model	Defines the PK model used for the substrate	Error
biot_number	Ratio of substrate concentration on boundary of microenvironment (Dirichlet condition) and concentration in systemic circulation	Set to 1.0

Table: XML elements for all PK models

Constant model

The Constant model fixes the circulation compartment concentration at user-specified times and values. The times and values must be supplied in a CSV (see below).

1C model

The 1C model is a 1-comparment model defined by

$$ \begin{aligned} C' & = - \lambda C \end{aligned} $$

where $\lambda$ is the elimination rate of the circulation_concentration, $C$.

2C model

The 2C model is a 2-comparment model defined by

$$ \begin{aligned} C' & = \frac{k_{21}}{R}P - k_{12}C - \lambda C \\ P' & = k_{12}RC - k_{21}P \end{aligned} $$

where $\lambda$ and $C$ are as above, $P$ is the concentration in a peripheral compartment, though not the PhysiCell microenvironment. The intercompartmental clearance rates, $k_{12}$ and $k_{21}$, define the exchange rate between these compartments while $R$ is the ratio of the compartmental volumes: $V_C/V_P$.

Parameter	Models	Description	If Missing
elimination_rate $(\lambda)$	1C,2C	Linear elimination rate in central compartment (in mintues-1)	Error
volume_ratio $(R = V_1/V_2 = V_C/V_P)$	2C	Ratio of central compartment to periphery compartment	Error for 2C
k12 $(k_{12})$	2C	Rate of change in concentration in central compartment due to distribution (in minutes-1)	Error for 2C
k21 $(k_{21})$	double	Rate of change in concentration in periphery compartment due to redistribution (in minutes-1)	Error for 2C

Table: PK parameters for `1C` and `2C` models

SBML model

Any SBML-defined ODE with one state variable named circulation_concentration can be used for a PK model as well. Place the file in the ./config/ folder. If sbml_filename is not set, PhysiPKPD will look for ./config/PK_default.xml to apply.

Parameter	Description	If Missing
sbml_filename	Filename of SBML file, e.g. PK_default.xml	Set to PK_default.xml

Table: PK parameters for `SBML` models

Dosing schedules

Every PK model requires a dosing schedule to achieve nonzero circulation_concentration. For SBML models, these must be set as events in the SBML file. For 1C and 2C models, these can be set either with parameters of a CSV file. This is set with the schedule element and its attribute format, set to either parameters or csv. See the 1C template for an example using parameters, and see the 2C template for an example using csv.

For Constant models, use a CSV in the same format as the 1C and 2C models, i.e., times in column one and values in column two. In this case, the values are what the circulation compartment concentration is set to rather than the amount added to that compartment. It will remain at that value indefinitely, so to turn "off" the substrate, add a (time, value) pair of (t_off, 0).

Dosing parameters

Two types of doses can be set this way, loading doses and regular doses. The number of loading doses, loading_doses, determines how many loading doses are given before regular doses. The total number of doses, loading and regular, is set by total_doses. Loading doses are given first, then regular doses. If loading_doses $>$ total_doses, then total_doses of loading doses are given and no regular doses. The time between any consecutive doses, loading or regular, is dose_interval. The units attribute of dose_interval can be set to min, hours, or days. If none is supplied, min is used. The time of the first dose is given by first_dose_time which can also use the units attribute exactly like dose_interval. The dose given on a loading dose is set by loading_dose and on a regular dose by regular_dose.

Parameter	Description	If Missing
total_doses	Total number of doses to give including loading doses	Error
loading_doses	Number of loading doses to give before switching to regular doses	Set to 0
regular_dose	Increase in concentration in central compartment after a regular dose	If total_doses>loading_doses, throws an error
loading_dose	Increase in concentration in central compartment after a loading dose	If loading_doses>0, throws an error
first_dose_time	Time of first dose if given at fixed time (in units="units")	Set to current_time
dose_interval	Time between successive doses, loading or regular (in units="units")	If total_doses>1, throws an error

Table: Dosing parameters

Dosing by CSV

If the format attribute in schedule is set to "csv", PhysiPKPD will look for the file ./config/S_dose_schedule.csv to define the dosing schedule. Alternatively, you can specify the path similar to the cell_positions and cell_rules files by supplying a folder and filename (see the 2C template). This file consists of two columns: time of dose (min), dose amount. No header row is needed.

PhysiCell PK parameters

You can also set the following parameters in microenvironment_setup for each substrate:

Parameter	Description
diffusion_coefficient	Diffusion rate in the microenvironment
decay_rate	Rate of decay in the microenvironment

Table: PK parameters in PhysiCell

Pharmacodynamics

PD models are added as cell_definition//PD element, i.e., at the same level as custom_data. Within this element, multiple cell_definition//PD//substrate elements define which substrates affect the given cell type. Each substrate includes the attribute name="S" to set the substrate. See templates here.

PD models

Two similar models are supplied for PD, both using the principle of Area Under the Curve or AUC. One uses the AUC of the internalized concentration, AUC, and the other uses the AUC of the internalized amount, AUC_amount. PhysiPKPD will turn on track_internalized_substrates for you if it detects a PD model. When using AUC, PhysiPKPD divides the internalized amount that PhysiCell tracks by the cell's current volume to determine the initial condition for $A$. Both update according to the following differential equation:

$$ \begin{aligned} A' & = -mA \\ D' & = A - r_1D - r_0 \end{aligned} $$

where $A$ is the internalized quantity, amount or concentration, and $D$ is the accumulated damage or AUC². The internalized quantity, $A$, is metabolized at a rate $m$, damage is repaired with linear rate $r_1$ and constant rate $r_0$.

Parameter	Description	If Missing
model	Defines the PD model used for the substrate	Set to AUC
metabolism_rate $(m)$	Rate of elimination of S from inside a cell (in minutes-1)	Error
linear_repair_rate $(r_1)$	First-order elimination rate of damage from S (in minutes-1)	Error
constant_repair_rate $(r_0)$	Zero-order elimination rate of damage from S (in damage per minute)	Error

Table: XML elements for all PD models

Let us know if you would like to see a different PD model included. Unlike PK dynamics, integration with SBML solvers is not implemented.

The damage variable, S_damage

If a substrate, S, affects any cell type via a PD model, every cell type must include custom_data//S_damage in its custom_data. This is where the damage, $D$, above is stored and accessed for affecting cell behavior.

Mechanisms of action

The effect of the PD model on the cell type is no longer defined by PhysiPKPD. Instead, you must supply rules that define how each cell type is affected by each PD substrate, if at all. The intention of PhysiPKPD is that users will use the signal custom:S_damage to alter cell phenotype via the rules. We recommend using PhysiCell-Studio to help generate a rules file.

Optional PD parameters

Setting PD timesteps

By default, PhysiPKPD uses the mechanics_dt set in the configuration file to determine how often to update each PD model. You can change this by adding a PD//substrate//dt element with the desired time in minutes. For precomputation purposes, see below, this time step must be a multiple of diffusion_dt.

Precomputation

PhysiPKPD currently requires all PD models to use precomputation, which speeds up calculations. This relies on two assumptions: homogeneity of response to S within a given cell type and that the same amount of simulation time passes between updates. The latter is assured by having the time step be a multiple of diffusion_dt. The former is currently imposed by how PhysiPKPD uses the PD parameters uniformly for all cells within a cell type. If you want these parameters to vary by cells within a cell type, that is not currently supported.

Parameter	Description	If Missing
dt	Sets the time interval between PD updates (in minutes)	Set to mechanics_dt
precompute	Boolean for precomputations	Must be true

Table: Optional XML elements for all PD models

Templates

PK templates

Place any of the following within the variable element:

<microenvironment_setup>
   <variable name="PKPD_D1" units="dimensionless" ID="0">
      ...
      </Dirichlet_options>

      <--! Place PK model here -->

   </variable>
   ...
</microenvironment_setup>

Constant template

<PK enabled="true">
    <model>Constant</model>
    <schedule format="csv" />
    <biot_number>1</biot_number>
</PK>

1C template

<PK enabled="true">
    <model>1C</model>
    <schedule format="parameters">
        <total_doses>4</total_doses>
        <loading_doses>0</loading_doses>
        <first_dose_time units="min">180</first_dose_time>
        <dose_interval units="min">360</dose_interval>
        <regular_dose>500</regular_dose>
        <loading_dose>1000</loading_dose>
    </schedule>
    <elimination_rate units="1/min">0.0027</elimination_rate>
    <biot_number>1</biot_number>
</PK>

2C template

<PK enabled="true">
    <model>2C</model>
    <schedule format="csv>
        <folder>./config</folder>
        <filename>S_dose_schedule.csv</filename>
    </schedule>
    <elimination_rate units="1/min">0.0027</elimination_rate>
    <k12 units="1/min">0.0048</k12>
    <k21 units="1/min">.0048</k21>
    <volume_ratio>1</volume_ratio>
    <biot_number>1</biot_number>
</PK>

SBML template

<PK enabled="true">
    <model>SBML</model>
    <sbml_filename>PK_default.xml</sbml_filename>
    <biot_number>1</biot_number>
</PK>

PD template

Place the following within the cell_definition element:

<cell_definitions>
   <cell_definition name="PKPD_cell" ID="0">
      ...
      </phenotype>

      <--! Place PD model(s) here -->

      </cell_definition>
   ...
</cell_definitions>

<PD>
    <substrate name="PKPD_D1">
        <model>AUC</model>
        <metabolism_rate>0.05</metabolism_rate>
        <constant_repair_rate>5e3</constant_repair_rate>
        <linear_repair_rate>2e-2</linear_repair_rate>
        <precompute>true</precompute>
        <dt>0.1</dt>
    </substrate>
    <substrate name="PKPD_D2">
        <model>AUC</model>
        <metabolism_rate>0.05</metabolism_rate>
        <constant_repair_rate>5e3</constant_repair_rate>
        <linear_repair_rate>2e-2</linear_repair_rate>
        <precompute>true</precompute>
        <dt>0.1</dt>
    </substrate>
</PD>

Footnotes

1. To use an SBML-defined PK model, you must have libRoadRunner installed. If you can run the sample_projects_intracellular/ode projects, you are ready to run these PhysiPKPD models. ↩

2. Because $D$ is measuring the AUC, the coefficient for $A$ in $D'$ is fixed to $1$. That is, $D$ has units amount x min or concentration x min, depending on the model used. ↩