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## Introducing cell interactions & transformations

### Introduction

PhysiCell 1.10.0 introduces a number of new features designed to simplify modeling of complex interactions and transformations. This blog post will introduce the underlying mathematics and show a complete example. We will teach this and other examples in greater depth at our upcoming Virtual PhysiCell Workshop & Hackathon (July 24-30, 2022). (Apply here!!)

### Cell Interactions

In the past, it has been possible to model complex cell-cell interactions (such as those needed for microecology and immunology) by connecting basic cell functions for interaction testing and custom functions. In particular, these functions were used for the COVID19 Coalition’s open source model of SARS-CoV-2 infections and immune responses. We now build upon that work to standardize and simplify these processes, making use of the cell’s state.neighbors (a list of all cells deemed to be within mechanical interaction distance).

All the parameters for cell-cell interactions are stored in cell.phenotype.cell_interactions.

#### Phagocytosis

A cell can phagocytose (ingest) another cell, with rates that vary with the cell’s live/dead status or the cell type. In particular, we store:

• double dead_phagocytosis_rate  : This is the rate at which a cell can phagocytose a dead cell of any type.
• std::vector<double> live_phagocytosis_rates : This is a vector of phagocytosis rates for live cells of specific types. If there are cell definitions in the simulation, then there are n rates in this vector. Please note that the index for any cell type is its index in the list of cell definitions, not necessarily the ID of its cell definition. For safety, use one of the following to determine that index:
• find_cell_definition_index( int type_ID ) : search for the cell definition’s index by its type ID (cell.type)
• find_cell_definition_index( std::string type_name ) : search for the cell definition’s index by its human-readable type name (cell.type_name)

We also supply a function to help access these live phagocytosis rates.

• double& live_phagocytosis_rate( std::string type_name )   : Directly access the cell’s rate of phagocytosing the live cell type by its human-readable name. For example,
pCell->phenotype.cell_interactions.live_phagocytosis_rate( "tumor cell" ) = 0.01;

At each mechanics time step (with duration $$\Delta t$$, default 0.1 minutes), each cell runs through its list of neighbors. If the neighbor is dead, its probability of phagocytosing it between $$t$$ and $$t+\Delta t$$ is

$\verb+dead_phagocytosis_rate+ \cdot \Delta t$

If the neighbor cell is alive and its type has index j, then its probability of phagocytosing the cell between $$t$$ and $$t+\Delta t$$ is

$\verb+live_phagocytosis_rates[j]+ \cdot \Delta t$

PhysiCell’s standardized phagocytosis model does the following:

• The phagocytosing cell will absorb the phagocytosed cell’s total solid volume into the cytoplasmic solid volume
• The phagocytosing cell will absorb the phagocytosed cell’s total fluid volume into the fluid volume
• The phagocytosing cell will absorb all of the phagocytosed cell’s internalized substrates.
• The phagocytosed cell is set to zero volume, flagged for removal, and set to not mechanically interact with remaining cells.
• The phagocytosing cell does not change its target volume. The standard volume model will gradually “digest” the absorbed volume as the cell shrinks towards its target volume.

#### Cell Attack

A cell can attack (cause damage to) another live cell, with rates that vary with the cell’s type. In particular, we store:

• double damage_rate  : This is the rate at which a cell causes (dimensionless) damage to a target cell. The cell’s total damage is stored in cell.state.damage.  The total integrated attack time is stored in cell.state.total_attack_time.
• std::vector<double> attack_rates : This is a vector of attack rates for live cells of specific types. If there are cell definitions in the simulation, then there are n rates in this vector. Please note that the index for any cell type is its index in the list of cell definitions, not necessarily the ID of its cell definition. For safety, use one of the following to determine that index:
• find_cell_definition_index( int type_ID ) : search for the cell definition’s index by its type ID (cell.type)
• find_cell_definition_index( std::string type_name ) : search for the cell definition’s index by its human-readable type name (cell.type_name)

We also supply a function to help access these attack rates.

• double& attack_rate( std::string type_name )   : Directly access the cell’s rate of attacking the live cell type by its human-readable name. For example,
pCell->phenotype.cell_interactions.attack_rate( "tumor cell" ) = 0.01;

At each mechanics time step (with duration $$\Delta t$$, default 0.1 minutes), each cell runs through its list of neighbors. If the neighbor cell is alive and its type has index j, then its probability of attacking the cell between $$t$$ and $$t+\Delta t$$ is

$\verb+attack_rates[j]+ \cdot \Delta t$

To attack the cell:

• The attacking cell will increase the target cell’s damage by $$\verb+damage_rate+ \cdot \Delta t$$.
• The attacking cell will increase the target cell’s total attack time by $$\Delta t$$.

Note that this allows us to have variable rates of damage (e.g., some immune cells may be “worn out”), and it allows us to distinguish between damage and integrated interaction time. (For example, you may want to write a model where damage can be repaired over time.)

As of this time, PhysiCell does not have a standardized model of death in response to damage. It is up to the modeler to vary a death rate with the total attack time or integrated damage, based on their hypotheses. For example:

$r_\textrm{apoptosis} = r_\textrm{apoptosis,0} + \left( r_\textrm{apoptosis,max} – r_\textrm{apoptosis,0} \right) \cdot \frac{ d^h }{ d_\textrm{halfmax}^h + d^h }$

In a phenotype function, we might write this as:

void damage_response( Cell* pCell, Phenotype& phenotype, double dt )
{ // get the base apoptosis rate from our cell definition
Cell_Definition* pCD = find_cell_definition( pCell->type_name );
double apoptosis_0 = pCD->phenotype.death.rates[0];
double apoptosis_max = 100 * apoptosis_0;
double half_max = 2.0;
double damage = pCell->state.damage;
phenotype.death.rates[0] = apoptosis_0 +
(apoptosis_max -apoptosis_0) * Hill_response_function(d,half_max,1.0);
return;
}

#### Cell Fusion

A cell can fuse with another live cell, with rates that vary with the cell’s type. In particular, we store:

• std::vector<double> fusion_rates : This is a vector of fusion rates for live cells of specific types. If there are n cell definitions in the simulation, then there are n rates in this vector. Please note that the index i for any cell type is its index in the list of cell definitions, not necessarily the ID of its cell definition. For safety, use one of the following to determine that index:
• find_cell_definition_index( int type_ID ) : search for the cell definition’s index by its type ID (cell.type)
• find_cell_definition_index( std::string type_name ) : search for the cell definition’s index by its human-readable type name (cell.type_name)

We also supply a function to help access these fusion rates.

• double& fusion_rate( std::string type_name )   : Directly access the cell’s rate of fusing with the live cell type by its human-readable name. For example,
pCell->phenotype.cell_interactions.fusion_rate( "tumor cell" ) = 0.01;

At each mechanics time step (with duration $$\Delta t$$, default 0.1 minutes), each cell runs through its list of neighbors. If the neighbor cell is alive and its type has index j, then its probability of fusing with the cell between $$t$$ and $$t+\Delta t$$ is

$\verb+fusion_rates[j]+ \cdot \Delta t$

PhysiCell’s standardized fusion model does the following:

• The fusing cell will absorb the fused cell’s total cytoplasmic solid volume into the cytoplasmic solid volume
• The fusing cell will absorb the fused cell’s total nuclear volume into the nuclear solid volume
• The fusing cell will keep track of its number of nuclei in state.number_of_nuclei.  (So, if the fusing cell has 3 nuclei and the fused cell has 2 nuclei, then the new cell will have 5 nuclei.)
• The fusing cell will absorb the fused cell’s total fluid volume into the fluid volume
• The fusing cell will absorb all of the fused cell’s internalized substrates.
• The fused cell is set to zero volume, flagged for removal, and set to not mechanically interact with remaining cells.
• The fused cell will be moved to the (volume weighted) center of mass of the two original cells.
• The fused cell does change its target volume to the sum of the original two cells’ target volumes. The combined cell will grow / shrink towards its new target volume.

### Cell Transformations

A live cell can transform to another type (e.g., via differentiation). We store parameters for cell transformations in cell.phenotype.cell_transformations, particularly:

• std::vector<double> transformation_rates : This is a vector of transformation rates from a cell’s current to type to one of the other cell types. If there are cell definitions in the simulation, then there are n rates in this vector. Please note that the index for any cell type is its index in the list of cell definitions, not necessarily the ID of its cell definition. For safety, use one of the following to determine that index:
• find_cell_definition_index( int type_ID ) : search for the cell definition’s index by its type ID (cell.type)
• find_cell_definition_index( std::string type_name ) : search for the cell definition’s index by its human-readable type name (cell.type_name)

We also supply a function to help access these transformation rates.

• double& transformation_rate( std::string type_name )   : Directly access the cell’s rate of transforming into a specific cell type by searching for its human-readable name. For example,
pCell->phenotype.cell_transformations.transformation_rate( "mutant tumor cell" ) = 0.01;

At each phenotype time step (with duration $$\Delta t$$, default 6 minutes), each cell runs through the vector of transformation rates. If a (different) cell type has index j, then the cell’s probability transforming to that type between $$t$$ and $$t+\Delta t$$ is

$\verb+transformation_rates[j]+ \cdot \Delta t$

PhysiCell uses the built-in Cell::convert_to_cell_definition( Cell_Definition& ) for the transformation.

### Other New Features

This release also includes a number of handy new features:

After setting chemotaxis sensitivities in phenotype.motility and enabling the feature, cells can chemotax based on linear combinations of substrate gradients.

• std::vector<double> phenotype.motility.chemotactic_sensitivities is a vector of chemotactic sensitivities, one for each substrate in the environment. By default, these are all zero for backwards compatibility. A positive sensitivity denotes chemotaxis up a corresponding substrate’s gradient (towards higher values), whereas a negative sensitivity gives chemotaxis against a gradient (towards lower values).
• For convenience, you can access (read and write) a substrate’s chemotactic sensitivity via phenotype.motility.chemotactic_sensitivity(name) where name is the human-readable name of a substrate in the simulation.
• If the user sets cell.cell_functions.update_migration_bias = advanced_chemotaxis_function, then these sensitivities are used to set the migration bias direction via: $\vec{d}_\textrm{mot} = s_0 \nabla \rho_0 + \cdots + s_n \nabla \rho_n.$
• If the user sets cell.cell_functions.update_migration_bias = advanced_chemotaxis_function_normalized, then these sensitivities are used to set the migration bias direction via: $\vec{d}_\textrm{mot} = s_0 \frac{\nabla\rho_0}{|\nabla\rho_0|} + \cdots + s_n \frac{ \nabla \rho_n }{|\nabla\rho_n|}.$

We now allow more nuanced, type-specific adhesion strengths to allow differential adhesion (e.g,. heterotypic versus homotypic).
• cell.phenotype.mechanics.adhesion_affinities is a vector of adhesive affinities, one for each cell type in the simulation. By default, these are all one for backwards compatibility.
• For convenience, you can access (read and write) a cell’s adhesive affinity for a specific cell type via phenotype.mechanics.adhesive_affinity(name), where name is the human-readable name of a cell type in the simulation.
• The standard mechanics function (based on potentials) uses this as follows. If cell i has an cell-cell adhesion strength a_i and an adhesive affinity p_ij to cell type j , and if cell j has a cell-cell adhesion strength of a_j and an adhesive affinity p_ji to cell type i, then the strength of their adhesion is $\sqrt{ a_i p_{ij} \cdot a_j p_{ji} }.$ Notice that if $$a_i = a_j$$ and $$p_{ij} = p_{ji}$$, then this reduces to $$a_i a_{pj}$$.
• The standard elastic spring function (standard_elastic_contact_function) uses this as follows. If cell i has an elastic constant a_i and an adhesive affinity p_ij to cell type j , and if cell j has an elastic constant a_j and an adhesive affinity p_ji to cell type i, then the strength of their adhesion is $\sqrt{ a_i p_{ij} \cdot a_j p_{ji} }.$ Notice that if $$a_i = a_j$$ and $$p_{ij} = p_{ji}$$, then this reduces to $$a_i a_{pj}$$.

### A brief immunology example

We will illustrate the major new functions with a simplified cancer-immune model, where tumor cells attract macrophages, which in turn attract effector T cells to damage and kill tumor cells. A mutation process will transform WT cancer cells into mutant cells that can better evade this immune response.

#### The problem:

We will build a simplified cancer-immune system to illustrate the new behaviors.

• WT cancer cells: Proliferate and release a signal that will stimulate an immune response. Cancer cells can transform into mutant cancer cells. Dead cells release debris. Damage increases apoptotic cell death.
• Mutant cancer cells: Proliferate but release less of the signal, as a model of immune evasion. Dead cells release debris. Damage increases apoptotic cell death.
• Macrophages: Chemotax towards the tumor signal and debris, and release a pro-inflammatory signal. They phagocytose dead cells.
• CD8+ T cells: Chemotax towards the pro-inflammatory signal and cause damage to tumor cells. As a model of immune evasion, CD8+ T cells can damage WT cancer cells faster than mutant cancer cells.

We will use the following diffusing factors:

• Tumor signal: Released by WT and mutant cells at different rates. We’ll fix a 1 min$$^{-1}$$ decay rate and set the diffusion parameter to 10000 $$\mu m^2/$$min to give a 100 micron diffusion length scale.
• Pro-inflammatory signal: Released by macrophages. We’ll fix a 1 min$$^{-1}$$ decay rate and set the diffusion parameter to 10000 $$\mu;m^2/$$min to give a 100 micron diffusion length scale.
• Debris: Released by dead cells. We’ll fix a 0.01 min$$^{-1}$$ decay rate and choose a diffusion coefficient of 1 $$\mu;m^2/$$min for a 10 micron diffusion length scale.

In particular, we won’t worry about oxygen or resources in this model. We can use Neumann (no flux) boundary conditions.

#### Getting started with a template project and the graphical model builder

The PhysiCell Model Builder was developed by Randy Heiland and undergraduate researchers at Indiana University to help ease the creation of PhysiCell models, with a focus on generating correct XML configuration files that define the diffusing substrates and cell definitions. Here, we assume that you have cloned (or downloaded) the repository adjacent to your PhysiCell repository. (So that the path to PMB from PhysiCell’s root directory is ../PhysiCell-model-builder/).

Let’s start a new project (starting with the template project) from a command prompt or shell in the PhysiCell directory, and then open the model builder.

make template
make
python ../PhysiCell-model-builder/bin/pmb.py

#### Setting up the domain

Let’s use a [-400,400] x [-400,400] 2D domain, with “virtual walls” enabled (so cells stay in the domain). We’ll run for 5760 minutes (4 days), saving SVG outputs every 15 minutes.

#### Setting up diffusing substrates

Move to the microenvironment tab. Click on substrate and rename it to tumor signal . Set the decay rate to 0.1 and diffusion parameter to 10000. Uncheck the Dirichlet condition box so that it’s a zero-flux (Neumann) boundary condition.

Now, select tumor signal in the lefthand column, click copy, and rename the new substrate (substrate01) to pro-inflammatory signal with the same parameters.

Then, copy this substrate one more time, and rename it from name debris. Set its decay rate to 0.01, and its diffusion parameter to 1.

Let’s save our work before continuing. Go to File, Save as, and save it as PhysiCell_settings.xml in your config file. (Go ahead and overwrite.)

If model builder crashes, you can reopen it, then go to File, Open, and select this file to continue editing.

#### Setting up the WT cancer cells

Move to the cell types tab. Click on the default cell type on the left side, and rename it to WT cancer cell. Leave most of the parameter values at their defaults. Move to the secretion sub-tab (in phenotype). From the drop-down menu, select tumor signal. Let’s set a high secretion rate of 10.

We’ll need to set WT cells as able to mutate, but before that, the model builder needs to “know” about that cell type. So, let’s move on to the next cell type for now.

Setting up mutant tumor cells

Click the WT cancer cell in the left column, and click copy. Rename this cell type (for me, it’s cell_def03) to mutant cancer cell.  Click the secretion sub-tab, and set its secretion rate of tumor signal lower to 0.1.

#### Set the WT mutation rate

Now that both cell types are in the simulation, we can set up mutation. Let’s suppose the mean time to a mutation is 10000 minutes, or a rate of 0.0001 min$$^{-1}$$.

Click the WT cancer cell in the left column to select it. Go to the interactions tab. Go down to transformation rate, and choose mutant cancer cell from the drop-down menu. Set its rate to 0.0001.

#### Create macrophages

Now click on the WT cancer cell type in the left column, and click copy to create a new cell type. Click on the new type (for me cell_def04) and rename it to macrophage.

Click on cycle and change to a live cells and change from a duration representation to a transition rate representation. Keep its cycling rate at 0.

Go to death and change from duration to transition rate for both apoptosis and necrosis, and keep the death rates at 0.0

Now, go to the motility tab. Set the speed to 1 $$\mu m/$$min, persistence time to 5 min, and migration bias to 0.5. Be sure to enable motility. Then, enable advanced motility. Choose tumor signal from the drop-down and set its sensitivity to 1.0. Then choose debris from the drop-down and set its sensitivity to 0.1

Now, let’s make sure it secretes pro-inflammatory signal. Go to the secretion tab. Choose tumor signal from the drop-down, and make sure its secretion rate is 0. Then choose pro-inflammatory signal from the drop-down, set its secretion rate to 100, and its target value to 1.

Lastly, let’s set macrophages up to phagocytose dead cells. Go to the interactions tab. Set the dead phagocytosis rate to 0.05 (so that the mean contact time to wait to eat a dead cell is 1/0.05 = 20 minutes). This would be a good time to save your work.

Macrophages probably shouldn’t be adhesive. So go to the mechanics sub-tab, and set the cell-cell adhesion strength to 0.0.

#### Create CD8+ T cells

Select macrophage on the left column, and choose copy. Rename the new cell type to CD8+ T cell.  Go to the secretion sub-tab and make sure to set the secretion rate of pro-inflammatory signal to 0.0.

Now, let’s use simpler chemotaxis for these towards pro-inflammatory signal. Go to the motility tab. Uncheck advanced chemotaxis and check chemotaxis. Choose pro-inflammatory signal from the drop-down, with the towards option.

Lastly, let’s set these cells to attack WT and tumor cells. Go to the interactions tab. Set the dead phagocytosis rate to 0.

Now, let’s work on attack. Set the damage rate to 1.0. Near attack rate, choose WT tumor cell from the drop-down, and set its attack rate to 10 (so it attacks during any 0.1 minute interval). Then choose mutant tumor cell from the drop-down, and set its attack rate to 1 (as a model of immune evasion, where they are less likely to attack a non-WT tumor cell).

#### Set the initial cell conditions

Go to the user params tab. On number of cells, choose 50. It will randomly place 50 of each cell type at the start of the simulation.

That’s all! Go to File and save (or save as), and overwrite config/PhysiCell_settings.xml. Then close the model builder.

#### Testing the model

Go into the PhysiCell directory. Since you already compiled, just run your model (which will use PhysiCell_settings.xml that you just saved to the config directory). For Linux or MacOS (or similar Unix-like systems):

./project

Windows users would type project without the ./ at the front.

Take a look at your SVG outputs in the output directory. You might consider making an animated gif (make gif) or a movie:

make jpeg && make movie

Here’s what we have.

Promising! But we still need to write a little C++ so that damage kills tumor cells, and so that dead tumor cells release debris. (And we could stand to “anchor” tumor cells to ECM so they don’t get pushed around by the immune cells, but that’s a post for another day!)

#### Customizing the WT and mutant tumor cells with phenotype functions

First, open custom.h in the custom_modules directory, and declare a function for tumor phenotype:

void tumor_phenotype_function( Cell* pCell, Phenotype& phenotype, double dt );

Now, let’s open custom.cpp to write this function at the bottom. Here’s what we’ll do:

• If dead, set rate of debris release to 1.0 and return.
• Otherwise, we’ll set damage-based apoptosis.
• Get the base apoptosis rate
• Get the current damage
• Use a Hill response function with a half-max of 36, max apoptosis rate of 0.05 min$$^{-1}$$, and a hill power of 2.0

Here’s the code:

void tumor_phenotype_function( Cell* pCell, Phenotype& phenotype, double dt )
{
// find my cell definition
static Cell_Definition* pCD = find_cell_definition( pCell->type_name );

// find the index of debris in the environment
static int nDebris = microenvironment.find_density_index( "debris" );
static int nTS = microenvironment.find_density_index( "tumor signal" );

// if dead: release debris. stop releasing tumor signal
{
phenotype.secretion.secretion_rates[nDebris] = 1;
phenotype.secretion.saturation_densities[nDebris] = 1;

phenotype.secretion.secretion_rates[nTS] = 0;

// last time I'll execute this function (special optional trick)
pCell->functions.update_phenotype = NULL;
return;
}

// damage increases death

// find death model
static int nApoptosis =
phenotype.death.find_death_model_index( PhysiCell_constants::apoptosis_death_model );

double signal = pCell->state.damage; // current damage
double base_val = pCD->phenotype.death.rates[nApoptosis]; // base death rate (from cell def)
double max_val = 0.05; // max death rate (at large damage)

static double damage_halfmax = 36.0;
double hill_power = 2.0;

// evaluate Hill response function
double hill = Hill_response_function( signal , damage_halfmax , hill_power );
// set "dose-dependent" death rate
phenotype.death.rates[nApoptosis] = base_val + (max_val-base_val)*hill;

return;
}

Now, we need to make sure we apply these functions to tumor cell. Go to create_cell_types and look just before we display the cell definitions. We need to:

• Search for the WT tumor cell definition
• Set the update_phenotype function for that type to the tumor_phenotype_function we just wrote
• Repeat for the mutant tumor cell type.

Here’s the code:

...
/*
Put any modifications to individual cell definitions here.

This is a good place to set custom functions.
*/

cell_defaults.functions.update_phenotype = phenotype_function;
cell_defaults.functions.custom_cell_rule = custom_function;
cell_defaults.functions.contact_function = contact_function;

Cell_Definition* pCD = find_cell_definition( "WT cancer cell");
pCD->functions.update_phenotype = tumor_phenotype_function;

pCD = find_cell_definition( "mutant cancer cell");
pCD->functions.update_phenotype = tumor_phenotype_function;

/*
This builds the map of cell definitions and summarizes the setup.
*/

display_cell_definitions( std::cout );
return;
}

That’s it! Let’s recompile and run!

make && ./project

And here’s the final movie.

Much better! Now the

### Coming up next!

We will use the signal and behavior dictionaries to help us easily write C++ functions to modulate the tumor and immune cell behaviors.

Once ready, this will be posted at http://www.mathcancer.org/blog/introducing-cell-signal-and-behavior-dictionaries/.

Tags :

## PhysiCell Tools : PhysiCell-povwriter

As PhysiCell matures, we are starting to turn our attention to better training materials and an ecosystem of open source PhysiCell tools. PhysiCell-povwriter is is designed to help transform your 3-D simulation results into 3-D visualizations like this one:

PhysiCell-povwriter transforms simulation snapshots into 3-D scenes that can be rendered into still images using POV-ray: an open source software package that uses raytracing to mimic the path of light from a source of illumination to a single viewpoint (a camera or an eye). The result is a beautifully rendered scene (at any resolution you choose) with very nice shading and lighting.

If you repeat this on many simulation snapshots, you can create an animation of your work.

### What you’ll need

This workflow is entirely based on open source software:

• 3-D simulation data (likely stored in ./output from your project)
• PhysiCell-povwriter, available on GitHub at
• POV-ray, available at
• ImageMagick (optional, for image file conversions)
• mencoder (optional, for making compressed movies)

### Setup

#### Building PhysiCell-povwriter

After you clone PhysiCell-povwriter or download its source from a release, you’ll need to compile it. In the project’s root directory, compile the project by:

make

(If you need to set up a C++ PhysiCell development environment, click here for OSX or here for Windows.)

Next, copy povwriter (povwriter.exe in Windows) to either the root directory of your PhysiCell project, or somewhere in your path. Copy ./config/povwriter-settings.xml to the ./config directory of your PhysiCell project.

#### Editing resolutions in POV-ray

PhysiCell-povwriter is intended for creating “square” images, but POV-ray does not have any pre-created square rendering resolutions out-of-the-box. However, this is straightforward to fix.

1. Open POV-Ray
2. Go to the “tools” menu and select “edit resolution INI file”
3. At the top of the INI file (which opens for editing in POV-ray), make a new profile:
[1080x1080, AA]
Width=480
Height=480
Antialias=On

4. Make similar profiles (with unique names) to suit your preferences. I suggest one at 480×480 (as a fast preview), another at 2160×2160, and another at 5000×5000 (because they will be absurdly high resolution). For example:
[2160x2160 no AA]
Width=2160
Height=2160
Antialias=Off

You can optionally make more profiles with antialiasing on (which provides some smoothing for areas of high detail), but you’re probably better off just rendering without antialiasing at higher resolutions and the scaling the image down as needed. Also, rendering without antialiasing will be faster.

5. Once done making profiles, save and exit POV-Ray.
6. The next time you open POV-Ray, your new resolution profiles will be available in the lefthand dropdown box.

### Configuring PhysiCell-povwriter

Once you have copied povwriter-settings.xml to your project’s config file, open it in a text editor. Below, we’ll show the different settings.

#### Camera settings

<camera>
<distance_from_origin units="micron">1500</distance_from_origin>
<xy_angle>3.92699081699</xy_angle> <!-- 5*pi/4 -->
<yz_angle>1.0471975512</yz_angle> <!-- pi/3 -->
</camera>

For simplicity, PhysiCell-POVray (currently) always aims the camera towards the origin (0,0,0), with “up” towards the positive z-axis. distance_from_origin sets how far the camera is placed from the origin. xy_angle sets the angle $$\theta$$ from the positive x-axis in the xy-plane. yz_angle sets the angle $$\phi$$ from the positive z-axis in the yz-plane. Both angles are in radians.

#### Options

<options>
<use_standard_colors>true</use_standard_colors>
<nuclear_offset units="micron">0.1</nuclear_offset>
<cell_bound units="micron">750</cell_bound>
</options>

use_standard_colors (if set to true) uses a built-in “paint-by-numbers” color scheme, where each cell type (identified with an integer) gets XML-defined colors for live, apoptotic, and dead cells. More on this below. If use_standard_colors is set to false, then PhysiCell-povwriter uses the my_pigment_and_finish_function in ./custom_modules/povwriter.cpp to color cells.

The nuclear_offset is a small additional height given to nuclei when cropping to avoid visual artifacts when rendering (which can cause some “tearing” or “bleeding” between the rendered nucleus and cytoplasm). cell_bound is used for leaving some cells out of bound: any cell with |x|, |y|, or |z| exceeding cell_bound will not be rendered. threads is used for parallelizing on multicore processors; note that it only speeds up povwriter if you are converting multiple PhysiCell outputs to povray files.

#### Save

<save> <!-- done -->
<folder>output</folder> <!-- use . for root -->
<filebase>output</filebase>
<time_index>3696</time_index>
</save>

Use folder to tell PhysiCell-povwriter where the data files are stored. Use filebase to tell how the outputs are named. Typically, they have the form output########_cells_physicell.mat; in this case, the filebase is output. Lastly, use time_index to set the output number. For example if your file is output00000182_cells_physicell.mat, then filebase = output and time_index = 182.

Below, we’ll see how to specify ranges of indices at the command line, which would supersede the time_index given here in the XML.

#### Clipping planes

PhysiCell-povwriter uses clipping planes to help create cutaway views of the simulations. By default, 3 clipping planes are used to cut out an octant of the viewing area.

Recall that a plane can be defined by its normal vector and a point p on the plane. With these, the plane can be defined as all points satisfying

$\left( \vec{x} -\vec{p} \right) \cdot \vec{n} = 0$

These are then written out as a plane equation

$a x + by + cz + d = 0,$

where

$(a,b,c) = \vec{n} \hspace{.5in} \textrm{ and } \hspace{0.5in} d = \: – \vec{n} \cdot \vec{p}.$

As of Version 1.0.0, we are having some difficulties with clipping planes that do not pass through the origin (0,0,0), for which $$d = 0$$.

In the config file, these planes are written as $$(a,b,c,d)$$:

<clipping_planes> <!-- done -->
<clipping_plane>0,-1,0,0</clipping_plane>
<clipping_plane>-1,0,0,0</clipping_plane>
<clipping_plane>0,0,1,0</clipping_plane>
</clipping_planes>

Note that cells “behind” the plane (where $$( \vec{x} – \vec{p} ) \cdot \vec{n} \le 0$$) are rendered, and cells in “front” of the plane (where $$(\vec{x}-\vec{p}) \cdot \vec{n} > 0$$) are not rendered. Cells that intersect the plane are partially rendered (using constructive geometry via union and intersection commands in POV-ray).

#### Cell color definitions

Within <cell_color_definitions>, you’ll find multiple <cell_colors> blocks, each of which defines the live, dead, and necrotic colors for a specific cell type (with the type ID indicated in the attribute). These colors are only applied if use_standard_colors is set to true in options. See above.

The live colors are given as two rgb (red,green,blue) colors for the cytoplasm and nucleus of live cells. Each element of this triple can range from 0 to 1, and not from 0 to 255 as in many raw image formats. Next, finish specifies ambient (how much highly-scattered background ambient light illuminates the cell), diffuse (how well light rays can illuminate the surface), and specular (how much of a shiny reflective splotch the cell gets).

This is repeated to give the apoptotic and necrotic colors for the cell type.

<cell_colors type="0">
<live>
<cytoplasm>.25,1,.25</cytoplasm> <!-- red,green,blue -->
<nuclear>0.03,0.125</nuclear>
<finish>0.05,1,0.1</finish> <!-- ambient,diffuse,specular -->
</live>
<apoptotic>
<cytoplasm>1,0,0</cytoplasm> <!-- red,green,blue -->
<nuclear>0.125,0,0</nuclear>
<finish>0.05,1,0.1</finish> <!-- ambient,diffuse,specular -->
</apoptotic>
<necrotic>
<cytoplasm>1,0.5412,0.1490</cytoplasm> <!-- red,green,blue -->
<nuclear>0.125,0.06765,0.018625</nuclear>
<finish>0.01,0.5,0.1</finish> <!-- ambient,diffuse,specular -->
</necrotic>
</cell_colors>

Use multiple cell_colors blocks (each with type corresponding to the integer cell type) to define the colors of multiple cell types.

### Using PhysiCell-povwriter

#### Use by the XML configuration file alone

The simplest syntax:

physicell$./povwriter (Windows users: povwriter or povwriter.exe) will process ./config/povwriter-settings.xml and convert the single indicated PhysiCell snapshot to a .pov file. If you run POV-writer with the default configuration file in the povwriter structure (with the supplied sample data), it will render time index 3696 from the immunotherapy example in our 2018 PhysiCell Method Paper: physicell$ ./povwriter

povwriter version 1.0.0
================================================================================

Copyright (c) Paul Macklin 2019, on behalf of the PhysiCell project

Usage:
================================================================================
povwriter : run povwriter with config file ./config/settings.xml

povwriter FILENAME.xml : run povwriter with config file FILENAME.xml

povwriter x:y:z : run povwriter on data in FOLDER with indices from x
to y in incremenets of z

Example: ./povwriter 0:2:10 processes files:
./FOLDER/FILEBASE00000000_physicell_cells.mat
./FOLDER/FILEBASE00000002_physicell_cells.mat
...
./FOLDER/FILEBASE00000010_physicell_cells.mat
(See the config file to set FOLDER and FILEBASE)

povwriter x1,...,xn : run povwriter on data in FOLDER with indices x1,...,xn

Example: ./povwriter 1,3,17 processes files:
./FOLDER/FILEBASE00000001_physicell_cells.mat
./FOLDER/FILEBASE00000003_physicell_cells.mat
./FOLDER/FILEBASE00000017_physicell_cells.mat
(Note that there are no spaces.)
(See the config file to set FOLDER and FILEBASE)

Tutorial & documentation at http://MathCancer.org/blog/povwriter
================================================================================

Using config file ./config/povwriter-settings.xml ...
Using standard coloring function ...
Found 3 clipping planes ...
Found 2 cell color definitions ...
Processing file ./output/output00003696_cells_physicell.mat...
Matrix size: 32 x 66978
Creating file pov00003696.pov for output ...
Writing 66978 cells ...
done!

Done processing all 1 files!

The result is a single POV-ray file (pov00003696.pov) in the root directory.

Now, open that file in POV-ray (double-click the file if you are in Windows), choose one of your resolutions in your lefthand dropdown (I’ll choose 2160×2160 no antialiasing), and click the green “run” button.

You can watch the image as it renders. The result should be a PNG file (named pov00003696.png) that looks like this:

#### Using command-line options to process multiple times (option #1)

Now, suppose we have more outputs to process. We still state most of the options in the XML file as above, but now we also supply a command-line argument in the form of start:interval:end. If you’re still in the povwriter project, note that we have some more sample data there. Let’s grab and process it:

physicell$cd output physicell$ unzip more_samples.zip
Archive: more_samples.zip
inflating: output00000000_cells_physicell.mat
inflating: output00000001_cells_physicell.mat
inflating: output00000250_cells_physicell.mat
inflating: output00000300_cells_physicell.mat
inflating: output00000500_cells_physicell.mat
inflating: output00000750_cells_physicell.mat
inflating: output00001000_cells_physicell.mat
inflating: output00001250_cells_physicell.mat
inflating: output00001500_cells_physicell.mat
inflating: output00001750_cells_physicell.mat
inflating: output00002000_cells_physicell.mat
inflating: output00002250_cells_physicell.mat
inflating: output00002500_cells_physicell.mat
inflating: output00002750_cells_physicell.mat
inflating: output00003000_cells_physicell.mat
inflating: output00003250_cells_physicell.mat
inflating: output00003500_cells_physicell.mat
inflating: output00003696_cells_physicell.mat

physicell$ls citation and license.txt more_samples.zip output00000000_cells_physicell.mat output00000001_cells_physicell.mat output00000250_cells_physicell.mat output00000300_cells_physicell.mat output00000500_cells_physicell.mat output00000750_cells_physicell.mat output00001000_cells_physicell.mat output00001250_cells_physicell.mat output00001500_cells_physicell.mat output00001750_cells_physicell.mat output00002000_cells_physicell.mat output00002250_cells_physicell.mat output00002500_cells_physicell.mat output00002750_cells_physicell.mat output00003000_cells_physicell.mat output00003250_cells_physicell.mat output00003500_cells_physicell.mat output00003696.xml output00003696_cells_physicell.mat Let’s go back to the parent directory and run povwriter: physicell$ ./povwriter 0:250:3500

povwriter version 1.0.0
================================================================================

Copyright (c) Paul Macklin 2019, on behalf of the PhysiCell project

Usage:
================================================================================
povwriter : run povwriter with config file ./config/settings.xml

povwriter FILENAME.xml : run povwriter with config file FILENAME.xml

povwriter x:y:z : run povwriter on data in FOLDER with indices from x
to y in incremenets of z

Example: ./povwriter 0:2:10 processes files:
./FOLDER/FILEBASE00000000_physicell_cells.mat
./FOLDER/FILEBASE00000002_physicell_cells.mat
...
./FOLDER/FILEBASE00000010_physicell_cells.mat
(See the config file to set FOLDER and FILEBASE)

povwriter x1,...,xn : run povwriter on data in FOLDER with indices x1,...,xn

Example: ./povwriter 1,3,17 processes files:
./FOLDER/FILEBASE00000001_physicell_cells.mat
./FOLDER/FILEBASE00000003_physicell_cells.mat
./FOLDER/FILEBASE00000017_physicell_cells.mat
(Note that there are no spaces.)
(See the config file to set FOLDER and FILEBASE)

Tutorial & documentation at http://MathCancer.org/blog/povwriter
================================================================================

Using config file ./config/povwriter-settings.xml ...
Using standard coloring function ...
Found 3 clipping planes ...
Found 2 cell color definitions ...
Matrix size: 32 x 18317
Processing file ./output/output00000000_cells_physicell.mat...
Creating file pov00000000.pov for output ...
Writing 18317 cells ...
Processing file ./output/output00002000_cells_physicell.mat...
Matrix size: 32 x 33551
Creating file pov00002000.pov for output ...
Writing 33551 cells ...
Processing file ./output/output00002500_cells_physicell.mat...
Matrix size: 32 x 43440
Creating file pov00002500.pov for output ...
Writing 43440 cells ...
Processing file ./output/output00001500_cells_physicell.mat...
Matrix size: 32 x 40267
Creating file pov00001500.pov for output ...
Writing 40267 cells ...
Processing file ./output/output00003000_cells_physicell.mat...
Matrix size: 32 x 56659
Creating file pov00003000.pov for output ...
Writing 56659 cells ...
Processing file ./output/output00001000_cells_physicell.mat...
Matrix size: 32 x 74057
Creating file pov00001000.pov for output ...
Writing 74057 cells ...
Processing file ./output/output00003500_cells_physicell.mat...
Matrix size: 32 x 66791
Creating file pov00003500.pov for output ...
Writing 66791 cells ...
Processing file ./output/output00000500_cells_physicell.mat...
Matrix size: 32 x 114316
Creating file pov00000500.pov for output ...
Writing 114316 cells ...
done!

Processing file ./output/output00000250_cells_physicell.mat...
Matrix size: 32 x 75352
Creating file pov00000250.pov for output ...
Writing 75352 cells ...
done!

Processing file ./output/output00002250_cells_physicell.mat...
Matrix size: 32 x 37959
Creating file pov00002250.pov for output ...
Writing 37959 cells ...
done!

Processing file ./output/output00001750_cells_physicell.mat...
Matrix size: 32 x 32358
Creating file pov00001750.pov for output ...
Writing 32358 cells ...
done!

Processing file ./output/output00002750_cells_physicell.mat...
Matrix size: 32 x 49658
Creating file pov00002750.pov for output ...
Writing 49658 cells ...
done!

Processing file ./output/output00003250_cells_physicell.mat...
Matrix size: 32 x 63546
Creating file pov00003250.pov for output ...
Writing 63546 cells ...
done!

done!

done!

done!

Processing file ./output/output00001250_cells_physicell.mat...
Matrix size: 32 x 54771
Creating file pov00001250.pov for output ...
Writing 54771 cells ...
done!

done!

done!

done!

Processing file ./output/output00000750_cells_physicell.mat...
Matrix size: 32 x 97642
Creating file pov00000750.pov for output ...
Writing 97642 cells ...
done!

done!

Done processing all 15 files!

Notice that the output appears a bit out of order. This is normal: povwriter is using 8 threads to process 8 files at the same time, and sending some output to the single screen. Since this is all happening simultaneously, it’s a bit jumbled (and non-sequential). Don’t panic. You should now have created pov00000000.povpov00000250.pov, … , pov00003500.pov.

Now, go into POV-ray, and choose “queue.” Click “Add File” and select all 15 .pov files you just created:

Hit “OK” to let it render all the povray files to create PNG files (pov00000000.png, … , pov00003500.png).

#### Using command-line options to process multiple times (option #2)

You can also give a list of indices. Here’s how we render time indices 250, 1000, and 2250:

#### Creating an animated GIF with ImageMagick

Suppose you want to create an animated GIF based on your images. I suggest first converting to JPG (see above) and then using ImageMagick again. Here, I’m adding a 20 ms delay between frames:

physicell$magick convert -delay 20 *.jpg out.gif Here’s the result: #### Creating a compressed movie with Mencoder Syntax coming later. ### Closing thoughts and future work In the future, we will probably allow more control over the clipping planes and a bit more debugging on how to handle planes that don’t pass through the origin. (First thoughts: we need to change how we use union and intersection commands in the POV-ray outputs.) We should also look at adding some transparency for the cells. I’d prefer something like rgba (red-green-blue-alpha), but POV-ray uses filters and transmission, and we want to make sure to get it right. Lastly, it would be nice to find a balance between the current very simple camera setup and better control. Thanks for reading this PhysiCell Friday tutorial! Please do give PhysiCell at try (at http://PhysiCell.org) and read the method paper at PLoS Computational Biology. Share this: Tags : ## Setting up the PhysiCell microenvironment with XML As of release 1.6.0, users can define all the chemical substrates in the microenvironment with an XML configuration file. (These are stored by default in ./config/. The default parameter file is ./config/PhysiCell_settings.xml.) This should make it much easier to set up the microenvironment (previously required a lot of manual C++), as well as make it easier to change parameters and initial conditions. In release 1.7.0, users gained finer grained control on Dirichlet conditions: individual Dirichlet conditions can be enabled or disabled for each individual diffusing substrate on each individual boundary. See details below. This tutorial will show you the key techniques to use these features. (See the User_Guide for full documentation.) First, let’s create a barebones 2D project by populating the 2D template project. In a terminal shell in your root PhysiCell directory, do this: make template2D We will use this 2D project template for the remainder of the tutorial. We assume you already have a working copy of PhysiCell installed, version 1.6.0 or later. (If not, visit the PhysiCell tutorials to find installation instructions for your operating system.) You will need version 1.7.0 or later to control Dirichlet conditions on individual boundaries. You can download the latest version of PhysiCell at: ### Microenvironment setup in the XML configuration file Next, let’s look at the parameter file. In your text editor of choice, open up ./config/PhysiCell_settings.xml, and browse down to <microenvironment_setup>: <microenvironment_setup> <variable name="oxygen" units="mmHg" ID="0"> <physical_parameter_set> <diffusion_coefficient units="micron^2/min">100000.0</diffusion_coefficient> <decay_rate units="1/min">0.1</decay_rate> </physical_parameter_set> <initial_condition units="mmHg">38.0</initial_condition> <Dirichlet_boundary_condition units="mmHg" enabled="true">38.0</Dirichlet_boundary_condition> </variable> <options> <calculate_gradients>false</calculate_gradients> <track_internalized_substrates_in_each_agent>false</track_internalized_substrates_in_each_agent> <!-- not yet supported --> <initial_condition type="matlab" enabled="false"> <filename>./config/initial.mat</filename> </initial_condition> <!-- not yet supported --> <dirichlet_nodes type="matlab" enabled="false"> <filename>./config/dirichlet.mat</filename> </dirichlet_nodes> </options> </microenvironment_setup> Notice a few trends: • The <variable> XML element (tag) is used to define a chemical substrate in the microenvironment. The attributes say that it is named oxygen, and the units of measurement are mmHg. Notice also that the ID is 0: this unique integer identifier helps for finding and accessing the substrate within your PhysiCell project. Make sure your first substrate ID is 0, since C++ starts indexing at 0. • Within the <variable> block, we set the properties of this substrate: • <diffusion_coefficient> sets the (uniform) diffusion constant for the substrate. • <decay_rate> is the substrate’s background decay rate. • <initial_condition> is the value the substrate will be (uniformly) initialized to throughout the domain. • <Dirichlet_boundary_condition> is the value the substrate will be set to along the outer computational boundary throughout the simulation, if you set enabled=true. If enabled=false, then PhysiCell (via BioFVM) will use Neumann (zero flux) conditions for that substrate. • The <options> element helps configure other simulation behaviors: • Use <calculate_gradients> to control whether PhysiCell computes all chemical gradients at each time step. Set this to true to enable accurate gradients (e.g., for chemotaxis). • Use <track_internalized_substrates_in_each_agent> to enable or disable the PhysiCell feature of actively tracking the total amount of internalized substrates in each individual agent. Set this to true to enable the feature. • <initial_condition> is reserved for a future release where we can specify non-uniform initial conditions as an external file (e.g., a CSV or Matlab file). This is not yet supported. • <dirichlet_nodes> is reserved for a future release where we can specify Dirchlet nodes at any location in the simulation domain with an external file. This will be useful for irregular domains, but it is not yet implemented. Note that PhysiCell does not convert units. The units attributes are helpful for clarity between users and developers, to ensure that you have worked in consistent length and time units. By default, PhysiCell uses minutes for all time units, and microns for all spatial units. ### Changing an existing substrate Let’s modify the oxygen variable to do the following: • Change the diffusion coefficient to 120000 $$\mu\mathrm{m}^2 / \mathrm{min}$$ • Change the initial condition to 40 mmHg • Change the oxygen Dirichlet boundary condition to 42.7 mmHg • Enable gradient calculations If you modify the appropriate fields in the <microenvironment_setup> block, it should look like this: <microenvironment_setup> <variable name="oxygen" units="mmHg" ID="0"> <physical_parameter_set> <diffusion_coefficient units="micron^2/min">120000.0</diffusion_coefficient> <decay_rate units="1/min">0.1</decay_rate> </physical_parameter_set> <initial_condition units="mmHg">40.0</initial_condition> <Dirichlet_boundary_condition units="mmHg" enabled="true">42.7</Dirichlet_boundary_condition> </variable> <options> <calculate_gradients>true</calculate_gradients> <track_internalized_substrates_in_each_agent>false</track_internalized_substrates_in_each_agent> <!-- not yet supported --> <initial_condition type="matlab" enabled="false"> <filename>./config/initial.mat</filename> </initial_condition> <!-- not yet supported --> <dirichlet_nodes type="matlab" enabled="false"> <filename>./config/dirichlet.mat</filename> </dirichlet_nodes> </options> </microenvironment_setup> ### Adding a new diffusing substrate Let’s add a new dimensionless substrate glucose with the following: • Diffusion coefficient is 18000 $$\mu\mathrm{m}^2 / \mathrm{min}$$ • No decay rate • The initial condition is 1 (dimensionless) • Neumann (no flux) boundary conditions To add the new variable, I suggest copying an existing variable (in this case, oxygen) and modifying to: • change the name and units throughout • increase the ID by one • write in the appropriate initial and boundary conditions If you modify the appropriate fields in the <microenvironment_setup> block, it should look like this: <microenvironment_setup> <variable name="oxygen" units="mmHg" ID="0"> <physical_parameter_set> <diffusion_coefficient units="micron^2/min">120000.0</diffusion_coefficient> <decay_rate units="1/min">0.1</decay_rate> </physical_parameter_set> <initial_condition units="mmHg">40.0</initial_condition> <Dirichlet_boundary_condition units="mmHg" enabled="true">42.7</Dirichlet_boundary_condition> </variable> <variable name="glucose" units="dimensionless" ID="1"> <physical_parameter_set> <diffusion_coefficient units="micron^2/min">18000.0</diffusion_coefficient> <decay_rate units="1/min">0.0</decay_rate> </physical_parameter_set> <initial_condition units="dimensionless">1</initial_condition> <Dirichlet_boundary_condition units="dimensionless" enabled="false">0</Dirichlet_boundary_condition> </variable> <options> <calculate_gradients>true</calculate_gradients> <track_internalized_substrates_in_each_agent>false</track_internalized_substrates_in_each_agent> <!-- not yet supported --> <initial_condition type="matlab" enabled="false"> <filename>./config/initial.mat</filename> </initial_condition> <!-- not yet supported --> <dirichlet_nodes type="matlab" enabled="false"> <filename>./config/dirichlet.mat</filename> </dirichlet_nodes> </options> </microenvironment_setup> ### Controlling Dirichlet conditions on individual boundaries In Version 1.7.0, we introduced the ability to control the Dirichlet conditions for each individual boundary for each substrate. The examples above apply (enable) or disable the same condition on each boundary with the same boundary value. Suppose that we want to set glucose so that the Dirichlet condition is enabled on the bottom z boundary (with value 1) and the left and right x boundaries (with value 0.5) and disabled on all other boundaries. We modify the variable block by adding the optional Dirichlet_options block: <variable name="glucose" units="dimensionless" ID="1"> <physical_parameter_set> <diffusion_coefficient units="micron^2/min">18000.0</diffusion_coefficient> <decay_rate units="1/min">0.0</decay_rate> </physical_parameter_set> <initial_condition units="dimensionless">1</initial_condition> <Dirichlet_boundary_condition units="dimensionless" enabled="true">0</Dirichlet_boundary_condition> <Dirichlet_options> <boundary_value ID="xmin" enabled="true">0.5</boundary_value> <boundary_value ID="xmax" enabled="true">0.5</boundary_value> <boundary_value ID="ymin" enabled="false">0.5</boundary_value> <boundary_value ID="ymin" enabled="false">0.5</boundary_value> <boundary_value ID="zmin" enabled="true">1.0</boundary_value> <boundary_value ID="zmax" enabled="false">0.5</boundary_value> </Dirichlet_options> </variable> Notice a few things: 1. The Dirichlet_boundary_condition element has its enabled attribute set to true 2. The Dirichlet condition is set under any individual boundary with a boundary_value element. • The ID attribute indicates which boundary is being specified. • The enabled attribute allows the individual boundary to be enabled (with value given by the element’s value) or disabled (applying a Neumann or no-flux condition for this substrate at this boundary). • Any individual boundary indicated by a boundary_value element supersedes the value given by Dirichlet_boundary_condition for this boundary. ### Closing thoughts and future work In the future, we plan to develop more of the options to allow users to set set the initial conditions externally and import them (via an external file), and to allow them to set up more complex domains by importing Dirichlet nodes. More broadly, we are working to push more model specification from raw C++ to imported XML. It is our hope that this will vastly simplify model development, facilitate creation of graphical model editing tools, and ultimately broaden the class of developers who can use and contribute to PhysiCell. Thanks for giving it a try! Share this: Tags : ## User parameters in PhysiCell As of release 1.4.0, users can add any number of Boolean, integer, double, and string parameters to an XML configuration file. (These are stored by default in ./config/. The default parameter file is ./config/PhysiCell_settings.xml.) These parameters are automatically parsed into a parameters data structure, and accessible throughout a PhysiCell project. This tutorial will show you the key techniques to use these features. (See the User_Guide for full documentation.) First, let’s create a barebones 2D project by populating the 2D template project. In a terminal shell in your root PhysiCell directory, do this: make template2D We will use this 2D project template for the remainder of the tutorial. We assume you already have a working copy of PhysiCell installed, version 1.4.0 or later. (If not, visit the PhysiCell tutorials to find installation instructions for your operating system.) ### User parameters in the XML configuration file Next, let’s look at the parameter file. In your text editor of choice, open up ./config/PhysiCell_settings.xml, and browse down to <user_parameters>, which will have some sample parameters from the 2D template project. <user_parameters> <random_seed type="int" units="dimensionless">0</random_seed> <!-- example parameters from the template --> <!-- motile cell type parameters --> <motile_cell_persistence_time type="double" units="min">15</motile_cell_persistence_time> <motile_cell_migration_speed type="double" units="micron/min">0.5</motile_cell_migration_speed> <motile_cell_relative_adhesion type="double" units="dimensionless">0.05</motile_cell_relative_adhesion> <motile_cell_apoptosis_rate type="double" units="1/min">0.0</motile_cell_apoptosis_rate> <motile_cell_relative_cycle_entry_rate type="double" units="dimensionless">0.1</motile_cell_relative_cycle_entry_rate> </user_parameters> Notice a few trends: • Each XML element (tag) under <user_parameters> is a user parameter, whose name is the element name. • Each variable requires an attribute named “type”, with one of the following four values: • bool for a Boolean parameter • int for an integer parameter • double for a double (floating point) parameter • string for text string parameter While we do not encourage it, if no valid type is supplied, PhysiCell will attempt to interpret the parameter as a double. • Each variable here has an (optional) attribute “units”. PhysiCell does not convert units, but these are helpful for clarity between users and developers. By default, PhysiCell uses minutes for all time units, and microns for all spatial units. • Then, between the tags, you list the value of your parameter. Let’s add the following parameters to the configuration file: • A string parameter called motile_color that sets the color of the motile_cell type in SVG outputs. Please refer to the User Guide (in the documentation folder) for more information on allowed color formats, including rgb values and named colors. Let’s use the value darkorange. • A double parameter called base_cycle_entry_rate that will give the rate of entry to the S cycle phase from the G1 phase for the default cell type in the code. Let’s use a ridiculously high value of 0.01 min-1. • A double parameter called base_apoptosis_rate for the default cell type. Let’s set the value at 1e-7 min-1. • A double parameter that sets the (relative) maximum cell-cell adhesion sensing distance, relative to the cell’s radius. Let’s set it at 2.5 (dimensionless). (The default is 1.25.) • A bool parameter that enables or disables placing a single motile cell in the initial setup. Let’s set it at true. If you edit the <user_parameters> to include these, it should look like this: <user_parameters> <random_seed type="int" units="dimensionless">0</random_seed> <!-- example parameters from the template --> <!-- motile cell type parameters --> <motile_cell_persistence_time type="double" units="min">15</motile_cell_persistence_time> <motile_cell_migration_speed type="double" units="micron/min">0.5</motile_cell_migration_speed> <motile_cell_relative_adhesion type="double" units="dimensionless">0.05</motile_cell_relative_adhesion> <motile_cell_apoptosis_rate type="double" units="1/min">0.0</motile_cell_apoptosis_rate> <motile_cell_relative_cycle_entry_rate type="double" units="dimensionless">0.1</motile_cell_relative_cycle_entry_rate> <!-- for the tutorial --> <motile_color type="string" units="dimensionless">darkorange</motile_color> <base_cycle_entry_rate type="double" units="1/min">0.01</base_cycle_entry_rate> <base_apoptosis_rate type="double" units="1/min">1e-7</base_apoptosis_rate> <base_cell_adhesion_distance type="double" units="dimensionless">2.5</base_cell_adhesion_distance> <include_motile_cell type="bool" units="dimensionless">true</include_motile_cell> </user_parameters> ### Viewing the loaded parameters Let’s compile and run the project. make ./project2D At the beginning of the simulation, PhysiCell parses the <user_parameters> block into a global data structure called parameters, with sub-parts bools, ints, doubles, and strings. It displays these loaded parameters at the start of the simulation. Here’s what it looks like: shell$  ./project2D
Using config file ./config/PhysiCell_settings.xml ...
User parameters in XML config file:
Bool parameters::
include_motile_cell: 1 [dimensionless]

Int parameters::
random_seed: 0 [dimensionless]

Double parameters::
motile_cell_persistence_time: 15 [min]
motile_cell_migration_speed: 0.5 [micron/min]
motile_cell_apoptosis_rate: 0 [1/min]
motile_cell_relative_cycle_entry_rate: 0.1 [dimensionless]
base_cycle_entry_rate: 0.01 [1/min]
base_apoptosis_rate: 1e-007 [1/min]

String parameters::
motile_color: darkorange [dimensionless]

### Getting parameter values

Within a PhysiCell project, you can access the value of any parameter by either its index or its name, so long as you know its type. Here’s an example of accessing the base_cell_adhesion_distance by its name:

/* this directly accesses the value of the parameter */
double temp = parameters.doubles( "base_cell_adhesion_distance" );
std::cout << temp << std::endl;

/* this streams a formatted output including the parameter name and units */
std::cout << parameters.doubles[ "base_cell_adhesion_distance" ] << std::endl;

std::cout << parameters.doubles["base_cell_adhesion_distance"].name << " "

Notice that accessing by () gets the value of the parameter in a user-friendly way, whereas accessing by [] gets the entire parameter, including its name, value, and units.

You can more efficiently access the parameter by first finding its integer index, and accessing by index:

/* this directly accesses the value of the parameter */
int my_index = parameters.doubles.find_index( "base_cell_adhesion_distance" );
double temp = parameters.doubles( my_index );
std::cout << temp << std::endl;

/* this streams a formatted output including the parameter name and units */
std::cout << parameters.doubles[ my_index ] << std::endl;

std::cout << parameters.doubles[ my_index ].name << " "
<< parameters.doubles[ my_index ].value << " "
<< parameters.doubles[ my_index ].units << std::endl;

Similarly, we can access string and Boolean parameters. For example:

if( parameters.bools("include_motile_cell") == true )
{ std::cout << "I shall include a motile cell." << std::endl; }

int rand_ind = parameters.ints.find_index( "random_seed" );
std::cout << parameters.ints[rand_ind].name << " is at index " << rand_ind << std::endl;

std::cout << "We'll use this nice color: " << parameters.strings( "motile_color" );

### Using the parameters in custom functions

Let’s use these new parameters when setting up the parameter values of the simulation. For this project, all custom code is in ./custom_modules/custom.cpp. Open that source file in your favorite text editor. Look for the function called “create_cell_types“. In the code snipped below, we access the parameter values to set the appropriate parameters in the default cell definition, rather than hard-coding them.

// add custom data here, if any

/* for the tutorial */
cell_defaults.phenotype.cycle.data.transition_rate(G0G1_index,S_index) =
parameters.doubles("base_cycle_entry_rate");
cell_defaults.phenotype.death.rates[apoptosis_model_index] =
parameters.doubles("base_apoptosis_rate");

Next, let’s change the tissue setup (“setup_tissue“) to check our Boolean variable before placing the initial motile cell.

// now create a motile cell
/*  remove this conditional for the normal project */
if( parameters.bools("include_motile_cell") == true )
{
pC = create_cell( motile_cell );
pC->assign_position( 15.0, -18.0, 0.0 );
}

Lastly, let’s make use of the string parameter to change the plotting. Search for my_coloring_function and edit the source file to use the new color:

// if the cell is motile and not dead, paint it black

static std::string motile_color = parameters.strings( "motile_color" );  // tutorial

if( pCell->phenotype.death.dead == false && pCell->type == 1 )
{
output[0] = motile_color;
output[2] = motile_color;
}

Notice the static here: We intend to call this function many, many times. For performance reasons, we don’t want to declare a string, instantiate it with motile_color, pass it to parameters.strings(), and then deallocate it once done. Instead, we store the search statically within the function, so that all future function calls will have access to that search result.

And that’s it! Compile your code, and give it a go.

make
./project2D

This should create a lot of data in the ./output directory, including SVG files that color motile cells as darkorange, like this one below.

Now that this project is parsing the XML file to get parameter values, we don’t need to recompile to change a model parameter. For example, change motile_color to mediumpurple, set motile_cell_migration_speed to 0.25, and set motile_cell_relative_cycle_entry_rate to 2.0. Rerun the code (without compiling):

./project2D

And let’s look at the change in the final SVG output (output00000120.svg):

### More notes on configuration files

You may notice other sections in the XML configuration file. I encourage you to explore them, but the meanings should be evident: you can set the computational domain size, the number of threads (for OpenMP parallelization), and how frequently (and where) data are stored. In future PhysiCell releases, we will continue adding more and more options to these XML files to simplify setup and configuration of PhysiCell models.

When you’re setting your BioFVM / PhysiCell g++ development environment, you’ll need to add the compiler, MSYS, and your text editor (like Notepad++) to your system path. For example, you may need to add folders like these to your system PATH variable:

1. c:\Program Files\mingw-w64\x86_64-5.3.0-win32-seh-rt_v4_rev0\mingw64\bin\
3. C:\MinGW\msys\1.0\bin\

Here’s how to do that in various versions of Windows.

### Windows XP, 7, and 8

First, open up a text editor, and concatenate your three paths into a single block of text, separated by semicolons (;):

2. Type a semicolon, paste in the first path, and append a semicolon. It should look like this:
;c:\Program Files\mingw-w64\x86_64-5.3.0-win32-seh-rt_v4_rev0\mingw64\bin\;
3. Paste in the next path, and append a semicolon. It should look like this:
4. Paste in the last path, and append a semicolon. It should look something like this:

Lastly, add these paths to the system path:

1. Go the Start Menu, the right-click “This PC” or “My Computer”, and choose “Properties.”
2. Click on “Advanced system settings”
3. Click on “Environment Variables…” in the “Advanced” tab
4. Scroll through the “System Variables” below until you find Path.
5. Select “Path”, then click “Edit…”
6. At the very end of “Variable Value”, paste what you made in Notepad in the prior steps. Make sure to paste at the end of the existing value, rather than overwriting it!
7. Hit OK, OK, and OK to completely exit the “Advanced system settings.”

### Windows 10:

Windows 10 has made it harder to find these settings, but easier to edit them. First, let’s find the system path:

1. At the “run / search / Cortana” box next to the start menu, type “view advanced”, and you should see “view advanced system settings” auto-complete:
2. Click to enter the advanced system settings, then choose environment variables … at the bottom of this box, and scroll down the list of user variables to Path
3. Click on edit, then click New to add a new path. In the new entry (a new line), paste in your first new path (the compiler):
4. Repeat this for the other two paths, then click OK, OK, Apply, OK to apply the new paths and exit.

## Running the PhysiCell sample projects

### Introduction

In PhysiCell 1.2.1 and later, we include four sample projects on cancer heterogeneity, bioengineered multicellular systems, and cancer immunology. This post will walk you through the steps to build and run the examples.

If you are new to PhysiCell, you should first make sure you’re ready to run it. (Please note that this applies in particular for OSX users, as Xcode’s g++ is not compatible out-of-the-box.) Here are tutorials on getting ready to Run PhysiCell:

1. Setting up a 64-bit gcc environment in Windows.
2. Setting up gcc / OpenMP on OSX (MacPorts edition)
3. Setting up gcc / OpenMP on OSX (Homebrew edition)
Note: This is the preferred method for Mac OSX.
4. Getting started with a PhysiCell Virtual Appliance (for virtual machines like VirtualBox)
Note: The “native” setups above are preferred, but the Virtual Appliance is a great “plan B” if you run into trouble

Please note that we expect to expand this tutorial.

### Building, running, and viewing the sample projects

All of these projects will create data of the following forms:

1. Scalable vector graphics (SVG) cross-section plots through = 0.0 μm at each output time. Filenames will look like snapshot00000000.svg.
2. Matlab (Level 4) .mat files to store raw BioFVM data. Filenames will look like output00000000_microenvironment0.mat (for the chemical substrates) and output00000000_cells.mat (for basic agent data).
3. Matlab .mat files to store additional PhysiCell agent data. Filenames will look like output00000000_cells_physicell.mat.
4. MultiCellDS .xml files that give further metadata and structure for the .mat files. Filenames will look like output00000000.xml.

You can read the combined data in the XML and MAT files with the read_MultiCellDS_xml function, stored in the matlab directory of every PhysiCell download. (Copy the read_MultiCellDS_xml.m and set_MultiCelLDS_constants.m files to the same directory as your data for the greatest simplicity.)

(If you are using Mac OSX and PhysiCell version > 1.2.1, remember to set the PHYSICELL_CPP environment variable to be an OpenMP-capable compiler – rf. Homebrew setup.)

#### Biorobots (2D)

Type the following from a terminal window in your root PhysiCell directory:

make biorobots-sample
make
./biorobots
make reset # optional -- gets a clean slate to try other samples

Because this is a 2-D example, the SVG snapshot files will provide the simplest method of visualizing these outputs. You can use utilities like ImageMagick to convert them into other formats for publications, such as PNG or EPS.

#### Anti-cancer biorobots (2D)

make cancer-biorobots-sample
make
./cancer_biorobots
make reset # optional -- gets a clean slate to try other samples

#### Cancer heterogeneity (2D)

make heterogeneity-sample
make project
./heterogeneity
make reset # optional -- gets a clean slate to try other samples

#### Cancer immunology (3D)

make cancer-immune-sample
make
./cancer_immune_3D
make reset # optional -- gets a clean slate to try other samples

## Getting started with a PhysiCell Virtual Appliance

Note: This is part of a series of “how-to” blog posts to help new users and developers of BioFVM and PhysiCell. This guide is for for users in OSX, Linux, or Windows using the VirtualBox virtualization software to run a PhysiCell virtual appliance.

These instructions should get you up and running without needed to install a compiler, makefile capabilities, or any other software (beyond the virtual machine and the PhysiCell virtual appliance). We note that using the PhysiCell source with your own compiler is still the preferred / ideal way to get started, but the virtual appliance option is a fast way to start even if you’re having troubles setting up your development environment.

### What’s a Virtual Machine? What’s a Virtual Appliance?

A virtual machine is a full simulated computer (with its own disk space, operating system, etc.) running on another. They are designed to let a user test on a completely different environment, without affecting the host (main) environment. They also allow a very robust way of taking and reproducing the state of a full working environment.

A virtual appliance is just this: a full image of an installed system (and often its saved state) on a virtual machine, which can easily be installed on a new virtual machine. In this tutorial, you will download our PhysiCell virtual appliance and use its pre-configured compiler and other tools.

### What you’ll need:

• VirtualBox: This is a free, cross-platform program to run virtual machines on OSX, Linux, Windows, and other platforms. It is a safe and easy way to install one full operating (a client system) on your main operating system (the host system). For us, this means that we can distribute a fully working Linux environment with a working copy of all the tools you need to compile and run PhysiCell. As of August 1, 2017, this will download Version 5.1.26.
• PhysiCell Virtual Appliance: This is a single-file distribution of a virtual machine running Alpine Linux, including all key tools needed to compile and run PhysiCell. As of July 31, 2017, this will download PhysiCell 1.2.2 with g++ 6.3.0.
• A computer with hardware support for virtualization: Your CPU needs to have hardware support for virtualization (almost all of them do now), and it has to be enabled in your BIOS. Consult your computer maker on how to turn this on if you get error messages later.

### Main steps:

#### 2) Import the PhysiCell Virtual Appliance

Go the “File” menu and choose “Import Virtual Appliance”. Browse to find the .ova file you just downloaded.

Click on “Next,” and import with all the default options. That’s it!

#### 3) [Optional] Change settings

You most likely won’t need this step, but you can increase/decrease the amount of RAM used for the virtual machine if you select the PhysiCell VM, click the Settings button (orange gear), and choose “System”:We set the Virtual Machine to have 4 GB of RAM. If you have a machine with lots of RAM (16 GB or more), you may want to set this to 8 GB.

Also, you can choose how many virtual CPUs to give to your VM:

We selected 4 when we set up the Virtual Appliance, but you should match the number of physical processor cores on your machine. In my case, I have a quad core processor with hyperthreading. This means 4 real cores, 8 virtual cores, so I select 4 here.

Select the PhysiCell machine, and click the green “start” button. After the virtual machine boots (with the good old LILO boot manager that I’ve missed), you should see this:

#### 5) Test the compiler and run your first simulation

Notice that PhysiCell is already there on the desktop in the PhysiCell folder. Right-click, and choose “open terminal here.” You’ll already be in the main PhysiCell root directory.

Now, let’s compile your first project! Type “make template2D && make” And run your project! Type “./project” and let it go!Go ahead and run either the first few days of the simulation (until about 7200 minutes), then hit <control>-C to cancel out. Or run the whole simulation–that’s fine, too.

#### 6) Look at the results

We bundled a few tools to easily look at results. First, ristretto is a very fast image viewer. Let’s view the SVG files: As a nice tip, you can press the left and right arrows to advance through the SVG images, or hold the right arrow down to advance through quickly.

Now, let’s use ImageMagick to convert the SVG files into JPG file: call “magick mogrify -format jpg snap*.svg”

Next, let’s turn those images into a movie. I generally create moves that are 24 frames pers se, so that 1 second of the movie is 1 hour of simulations time. We’ll use mencoder, with options below given to help get a good quality vs. size tradeoff:

When you’re done, view the movie with mplayer. The options below scale the window to fit within the virtual monitor:

If you want to loop the movie, add “-loop 999” to your command.

#### 7) Get familiar with other tools

Use nano (useage: nano <filename>) to quickly change files at the command line. Hit <control>-O to save your results. Hit <control>-X to exit.  <control>-W will search within the file.

Use nedit (useage: nedit <filename> &) to open up one more text files in a graphical editor. This is a good way to edit multiple files at once.

Sometimes, you need to run commands at elevated (admin or root) privileges. Use sudo. Here’s an example, searching the Alpine Linux package manager apk for clang:

physicell:~$sudo apk search gcc [sudo] password for physicell: physicell:~$ sudo apk search clang
clang-analyzer-4.0.0-r0
clang-libs-4.0.0-r0
clang-dev-4.0.0-r0
clang-static-4.0.0-r0
emscripten-fastcomp-1.37.10-r0
clang-doc-4.0.0-r0
clang-4.0.0-r0
physicell:~/Desktop/PhysiCell$If you want to install clang/llvm (as an alternative compiler): physicell:~$ sudo apk add gcc
physicell:~$sudo apk search clang clang-analyzer-4.0.0-r0 clang-libs-4.0.0-r0 clang-dev-4.0.0-r0 clang-static-4.0.0-r0 emscripten-fastcomp-1.37.10-r0 clang-doc-4.0.0-r0 clang-4.0.0-r0 physicell:~/Desktop/PhysiCell$

Coming soon.

### Why both with zipped source, then?

Given that we can get a whole development environment by just downloading and importing a virtual appliance, why
bother with all the setup of a native development environment, like this tutorial (Windows) or this tutorial (Mac)?

One word: performance. In my testing, I still have not found the performance running inside a
virtual machine to match compiling and running directly on your system. So, the Virtual Appliance is a great
option to get up and running quickly while trying things out, but I still recommend setting up natively with
one of the tutorials I linked in the preceding paragraphs.

### What’s next?

In the coming weeks, we’ll post further tutorials on using PhysiCell. In the meantime, have a look at the
PhysiCell project website, and these links as well:

1. BioFVM on MathCancer.org: http://BioFVM.MathCancer.org
2. BioFVM on SourceForge: http://BioFVM.sf.net
3. BioFVM Method Paper in BioInformatics: http://dx.doi.org/10.1093/bioinformatics/btv730
4. PhysiCell on MathCancer.org: http://PhysiCell.MathCancer.org
5. PhysiCell on Sourceforge: http://PhysiCell.sf.net
6. PhysiCell Method Paper (preprint): https://doi.org/10.1101/088773

## MathCancer C++ Style and Practices Guide

As PhysiCell, BioFVM, and other open source projects start to gain new users and contributors, it’s time to lay out a coding style. We have three goals here:

1. Consistency: It’s easier to understand and contribute to the code if it’s written in a consistent way.
2. Readability: We want the code to be as readable as possible.
3. Reducing errors: We want to avoid coding styles that are more prone to errors. (e.g., code that can be broken by introducing whitespace).

So, here is the guide (revised June 2017). I expect to revise this guide from time to time.

### Place braces on separate lines in functions and classes.

I find it much easier to read a class if the braces are on separate lines, with good use of whitespace. Remember: whitespace costs almost nothing, but reading and understanding (and time!) are expensive.

#### DON’T

class Cell{
public:
double some_variable;
bool some_extra_variable;

Cell(); };

class Phenotype{
public:
double some_variable;
bool some_extra_variable;

Phenotype();
};

#### DO:

class Cell
{
public:
double some_variable;
bool some_extra_variable;

Cell();
};

class Phenotype
{
public:
double some_variable;
bool some_extra_variable;

Phenotype();
};

### Enclose all logic in braces, even when optional.

In C/C++, you can omit the curly braces in some cases. For example, this is legal

interaction = false;
force = 0.0; // is this part of the logic, or a separate statement?
error = false;

However, this code is ambiguous to interpret. Moreover, small changes to whitespace–or small additions to the logic–could mess things up here. Use braces to make the logic crystal clear:

#### DON’T

interaction = false;
force = 0.0; // is this part of the logic, or a separate statement?
error = false;

if( condition1 == true )
do_something1 = true;
elseif( condition2 == true )
do_something2 = true;
else
do_something3 = true;

#### DO

{
interaction = false;
force = 0.0;
}
error = false;

if( condition1 == true )
{ do_something1 = true; }
elseif( condition2 == true )
{ do_something2 = true; }
else
{ do_something3 = true; }

### Put braces on separate lines in logic, except for single-line logic.

This style rule relates to the previous point, to improve readability.

#### DON’T

interaction = false;
force = 0.0; }

if( condition1 == true ){ do_something1 = true; }
elseif( condition2 == true ){
do_something2 = true; }
else
{ do_something3 = true; error = true; }

#### DO

{
interaction = false;
force = 0.0;
}

if( condition1 == true )
{ do_something1 = true; } // this is fine
elseif( condition2 == true )
{
do_something2 = true; // this is better
}
else
{
do_something3 = true;
error = true;
}

See how much easier that code is to read? The logical structure is crystal clear, and adding more to the logic is simple.

### End all functions with a return, even if void.

For clarity, definitively state that a function is done by using return.

#### DON’T

void my_function( Cell& cell )
{
cell.phenotype.volume.total *= 2.0;
cell.phenotype.death.rates[0] = 0.02;
// Are we done, or did we forget something?
// is somebody still working here?
}

#### DO

void my_function( Cell& cell )
{
cell.phenotype.volume.total *= 2.0;
cell.phenotype.death.rates[0] = 0.02;
return;
}

### Use tabs to indent the contents of a class or function.

This is to make the code easier to read. (Unfortunately PHP/HTML makes me use five spaces here instead of tabs.)

#### DON’T

class Secretion
{
public:
std::vector<double> secretion_rates;
std::vector<double> uptake_rates;
std::vector<double> saturation_densities;
};

void my_function( Cell& cell )
{
cell.phenotype.volume.total *= 2.0;
cell.phenotype.death.rates[0] = 0.02;
return;
}

#### DO

class Secretion
{
public:
std::vector<double> secretion_rates;
std::vector<double> uptake_rates;
std::vector<double> saturation_densities;
};

void my_function( Cell& cell )
{
cell.phenotype.volume.total *= 2.0;
cell.phenotype.death.rates[0] = 0.02;
return;
}

### Use a single space to indent public and other keywords in a class.

This gets us some nice formatting in classes, without needing two tabs everywhere.

#### DON’T

class Secretion
{
public:
std::vector<double> secretion_rates;
std::vector<double> uptake_rates;
std::vector<double> saturation_densities;
}; // not enough whitespace

class Errors
{
private:
public:
std::string error_message;
int error_code;
}; // too much whitespace!

#### DO

class Secretion
{
private:
public:
std::vector<double> secretion_rates;
std::vector<double> uptake_rates;
std::vector<double> saturation_densities;
};

class Errors
{
private:
public:
std::string error_message;
int error_code;
};

### Avoid arcane operators, when clear logic statements will do.

It can be difficult to decipher code with statements like this:

phenotype.volume.fluid=phenotype.volume.fluid<0?0:phenotype.volume.fluid;

Moreover, C and C++ can treat precedence of ternary operators very differently, so subtle bugs can creep in when using the “fancier” compact operators. Variations in how these operators work across languages are an additional source of error for programmers switching between languages in their daily scientific workflows. Wherever possible (and unless there is a significant performance reason to do so), use clear logical structures that are easy to read even if you only dabble in C/C++. Compiler-time optimizations will most likely eliminate any performance gains from these goofy operators.

#### DON’T

// if the fluid volume is negative, set it to zero
phenotype.volume.fluid=phenotype.volume.fluid<0.0?0.0:pCell->phenotype.volume.fluid;

#### DO

if( phenotype.volume.fluid < 0.0 )
{
phenotype.volume.fluid = 0.0;
}

Here’s the funny thing: the second logic is much clearer, and it took fewer characters, even with extra whitespace for readability!

### Pass by reference where possible.

Passing by reference is a great way to boost performance: we can avoid (1) allocating new temporary memory, (2) copying data into the temporary memory, (3) passing the temporary data to the function, and (4) deallocating the temporary memory once finished.

#### DON’T

double some_function( Cell cell )
{
return = cell.phenotype.volume.total + 3.0;
}
// This copies cell and all its member data!

#### DO

double some_function( Cell& cell )
{
return = cell.phenotype.volume.total + 3.0;
}
// This just accesses the original cell data without recopying it.

### Where possible, pass by reference instead of by pointer.

There is no performance advantage to passing by pointers over passing by reference, but the code is simpler / clearer when you can pass by reference. It makes code easier to write and understand if you can do so. (If nothing else, you save yourself character of typing each time you can replace “->” by “.”!)

#### DON’T

double some_function( Cell* pCell )
{
return = pCell->phenotype.volume.total + 3.0;
}
// Writing and debugging this code can be error-prone.

#### DO

double some_function( Cell& cell )
{
return = cell.phenotype.volume.total + 3.0;
}
// This is much easier to write.

### Be careful with static variables. Be thread safe!

PhysiCell relies heavily on parallelization by OpenMP, and so you should write functions under the assumption that they may be executed many times simultaneously. One easy source of errors is in static variables:

#### DON’T

double some_function( Cell& cell )
{
static double four_pi = 12.566370614359172;
static double output;
output *= output;
output *= four_pi;
return output;
}
// If two instances of some_function are running, they will both modify
// the *same copy* of output

#### DO

double some_function( Cell& cell )
{
static double four_pi = 12.566370614359172;
double output;
output *= output;
output *= four_pi;
return output;
}
// If two instances of some_function are running, they will both modify
// the their own copy of output, but still use the more efficient, once-
// allocated copy of four_pi. This one is safe for OpenMP.

### Use std:: instead of “using namespace std”

PhysiCell uses the BioFVM and PhysiCell namespaces to avoid potential collision with other codes. Other codes using PhysiCell may use functions that collide with the standard namespace. So, we formally use std:: whenever using functions in the standard namespace.

#### DON’T

using namespace std;

cout << "Hi, Mom, I learned to code today!" << endl;
string my_string = "Cheetos are good, but Doritos are better.";
cout << my_string << endl;

vector<double> my_vector;
vector.resize( 3, 0.0 );

#### DO

std::cout << "Hi, Mom, I learned to code today!" << std::endl;
std::string my_string = "Cheetos are good, but Doritos are better.";
std::cout << my_string << std::endl;

std::vector<double> my_vector;
my_vector.resize( 3, 0.0 );

### Camelcase is ugly. Use underscores.

This is purely an aesthetic distinction, but CamelCaseCodeIsUglyAndDoYouUseDNAorDna?

#### DON’T

double MyVariable1;
bool ProteinsInExosomes;
int RNAtranscriptionCount;

void MyFunctionDoesSomething( Cell& ImmuneCell );

#### DO

double my_variable1;
bool proteins_in_exosomes;
int RNA_transcription_count;

void my_function_does_something( Cell& immune_cell );

### Use capital letters to declare a class. Use lowercase for instances.

To help in readability and consistency, declare classes with capital letters (but no camelcase), and use lowercase for instances of those classes.

#### DON’T

class phenotype;

class cell
{
public:
std::vector<double> position;
phenotype Phenotype;
};

class ImmuneCell : public cell
{
public:
std::vector<double> surface_receptors;
};

void do_something( cell& MyCell , ImmuneCell& immuneCell );

cell Cell;
ImmuneCell MyImmune_cell;

do_something( Cell, MyImmune_cell );

#### DO

class Phenotype;

class Cell
{
public:
std::vector<double> position;
Phenotype phenotype;
};

class Immune_Cell : public Cell
{
public:
std::vector<double> surface_receptors;
};

void do_something( Cell& my_cell , Immune_Cell& immune_cell );

Cell cell;
Immune_Cell my_immune_cell;

do_something( cell, my_immune_cell );


text:
# Generating expression trees in Rust

February 28, 2017

I’ve been writing a lot of Rust. Since \@Taneb persuaded me to try it the language has grown phenomenally on me. I’ve always shied away from getting too attached to tools and focused more on systems but for the first time since my early Ruby days I’ve become a language fanboy.

While building my Genetic Programming library I needed a convenient way to represent and generate syntax trees. More than anything I wanted users to write a minimum of code. I used an interesting but problematic Recursive Enum approach that’s worth discussing.

enum Equation {
Add(Box<Equation>, Box<Equation>), // l + r
Sub(Box<Equation>, Box<Equation>), // l - r
Mul(Box<Equation>, Box<Equation>), // l × r
Div(Box<Equation>, Box<Equation>), // l ÷ r
Float(f64), // n
}

This is a very neat representation of a syntax tree for basic mathematics. One can express math quite simply:

use Equation::*;

// (17.2 × 50.0) ÷ (9.0 - 1.5)
let eq =
Div(
box Mul(
box Float(17.2),
box Float(50.0)
),
Sub(
box Float(9.0),
box Float(1.5)
)
);

Now we want to evaluate a tree into an output f64. Here’s a simple recursion:

impl Equation {
fn eval(&self) -> f64 {
match *self {
Add(ref left, ref right) => left.eval() + right.eval(),
Sub(ref left, ref right) => left.eval() - right.eval(),
Mul(ref left, ref right) => left.eval() * right.eval(),
// In practice I tend to implement a protectedDiv which avoids NaN.
Div(ref left, ref right) => left.eval() / right.eval(),
Float(n) => n,
}
}
}

## Taking inputs

But the tree has a fixed value! That sucks. Let’s make it a real equation:

enum Equation {
Add(Box<Equation>, Box<Equation>), // l + r
Sub(Box<Equation>, Box<Equation>), // l - r
Mul(Box<Equation>, Box<Equation>), // l × r
Div(Box<Equation>, Box<Equation>), // l ÷ r
Float(f64), // n
Input,
}

impl Equation {
// Eval now takes an input!
fn eval(&self, input: f64) -> f64 {
match *self {
Add(ref left, ref right) => left.eval(input) + right.eval(input),
Sub(ref left, ref right) => left.eval(input) - right.eval(input),
Mul(ref left, ref right) => left.eval(input) * right.eval(input),
// In practice I tend to implement a protectedDiv which avoids NaN.
Div(ref left, ref right) => left.eval(input) / right.eval(input),
Float(n) => n,
Input => input,
}
}
}

## Going generic with Evaluable

We can implement a trait to represent an evaluable type and implement it this way. I’m considering an approach like this to genericise over tree-based genetic agents and other forms.

trait Evaluable {
type Input;
type Output;

fn eval(&self, input: Self::Input) -> Self::Output;
}

impl Evaluable for Equation {
type Input = f64;
type Output = f64;

fn eval(&self, input: f64) -> f64 {
match *self {
Add(ref left, ref right) => left.eval(input) + right.eval(input),
Sub(ref left, ref right) => left.eval(input) - right.eval(input),
Mul(ref left, ref right) => left.eval(input) * right.eval(input),
// In practice I tend to implement a protectedDiv which avoids NaN.
Div(ref left, ref right) => left.eval(input) / right.eval(input),
Float(n) => n,
Input => input,
}
}
}

## Generation

Say we implement a function to generate a random nonterminal and a function to generate a random terminal. A new type that chooses whether to generate a nonterminal or terminal can then control various properties of generated trees. The details are a bit too lengthy to put here but this is something that evco’s Tree and TreeGen quite carefully perform.

## Practical implementation

I find this approach very pretty but it’s quite unsuitable to expect other people to implement to use a library. It’s at least 50 ugly lines of code for users of my library to implement methods to generate the tree.

Having other people implement these methods also removes much hope of keeping things tail-recursive. Recursive datastructures are notorious for operations upon them blowing the stack and crashing the program.

I implemented tail-recursive iteration inside the library but it’s too complex for third-parties to replicate without risking bugs.

## Custom derive

One way around this issue of people having to implement tedious methods is a custom derivation (proc_macro_derive.) The macro could analyse the types in the tree, identify enum variants as terminal vs nonterminal, and generate the methods accordingly.

This has implementation questions. A typical program doesn’t want to be provided with a random f64 - it wants one in a particular range. So we could require users to implement new types to wrap that, or allow attributes to mark the range to use:

#[derive(GeneratableTree)]
enum Equation {
Add(Box<Equation>, Box<Equation>), // l + r
Sub(Box<Equation>, Box<Equation>), // l - r
Mul(Box<Equation>, Box<Equation>), // l × r
Div(Box<Equation>, Box<Equation>), // l ÷ r
#[evco(range = "-10..10")]
Float(f64), // n
}

## Alternative, better implementations

The biggest irritation with the datastructure is that accessing a particular node takes O(n) operations because you have to traverse the entire tree to find it.

One can take an approach like a B-tree to optimise searching for elements. Sadly this doesn’t suit evolutionary computation very much: mutation is about as common as accessing and trees cannot be rebalanced.

So it would be better to store trees as something other than a recursive datastructure where each node is in its own allocated memory.

## Heap

A common means of representing trees on a computer is a Heap datastructure. This structures nodes into an array thus getting better cache locality, quicker access times, etc. The problem is that the enum we have is inherently a recursive structure.

Let’s try this:

enum Equation {
Add(f64, f64), // l + r
Sub(f64, f64), // l - r
Mul(f64, f64), // l × r
Div(f64, f64), // l ÷ r
Float(f64), // n
}

We could build and evaluate variants as we go, using this and the heap. But how do we indicate stored data versus arguments? We could supply stored data as a reference maybe?

enum Equation {
Add(f64, f64), // l + r
Sub(f64, f64), // l - r
Mul(f64, f64), // l × r
Div(f64, f64), // l ÷ r
Float(&f64), // n
}

This isn’t very pretty. One option would be that f64 inherently is generated and Float becomes unnecessary.

## Types

A further issue to consider: none of this uses generic types. All this only passes around f64 and nothing else. I guess we could indicate return types by requiring mutable pointers? The code to make this work might be ugly but it’ll be custom derived after all.

This allows specifying return type of each node, but generation logic would have to specify the tree’s root node to get a consistent type out the top of the trees:

enum Equation {
Add(f64, f64, &mut f64), // l + r
Sub(f64, f64, &mut f64), // l - r
Mul(f64, f64, &mut f64), // l × r
Div(f64, f64, &mut f64), // l ÷ r
IfEq(f64, f64, &mut bool),
}

It’s a pain.

format: plain


text:
CoCalc Public Filesunits2021 / analytical_methods / lectures / graphical interpretation of partial derivaties.sagews
Author: Killian O'Brien
Views : 77
Compute Environment: Ubuntu 18.04 (Stable)

# Graphical interpretation of partial derivatives of a function of two variables

The interactive demo below shows the surface defined by the function $z=f(x,y)=\sin(xy)$ together with the cross-sectional curves through the surface parallel to the $x$ and $y$ axes and based at the base point $(x,y)=(a,b)$. Use the slider controls to set the values of $a$ and $b$ and observe the form of the cross-sectional curves and values of the partial derivatives.

f(x,y)=sin(x*y)
xlim = 5*pi/4 # limit for the x coordinate
ylim = 5*pi/4 # limit for the y coordinate

@interact
def demo(a = slider(-xlim,xlim,2*xlim/100,0), b = slider(-ylim,ylim,2*ylim/100,0)):
p=plot3d(f(x,y), (x, -xlim, xlim), (y, -ylim, ylim), opacity=0.8)
xslice=parametric_plot3d([x,b,f(x,b)],(x,-xlim,xlim),color='red', thickness=8)
yslice=parametric_plot3d([a,y,f(a,y)],(y,-ylim,ylim),color='green', thickness=8)

pnt=point((a,b,f(a,b)), color='black',size=10)

show('The surface defined by $z = f(x,y)$ with cross-sectional curves, from the base point $(a,b)=('+str(n(a,digits=3))+','+str(n(b,digits=3))+')$'+ ' in the $x$ and $y$ directions.')
show(p+xslice+yslice+pnt, spin=2.5)

fx=f.diff(x)
fy=f.diff(y)

p=plot(f(x,b),(x,-xlim,xlim),color='red', thickness=6, axes_labels=['$x$','$z$'])
q=plot(f(a,y),(y,-ylim,ylim),color='green', thickness=6,  axes_labels=['$y$','$z$'])

show('The derivative $f_x(a,b)\\approx'+str(n(fx(a,b),digits=3))+'$.')
show(p+point((a,f(a,b)), color='black', size=150,zorder=5))
show('The derivative $f_y(a,b)\\approx'+str(n(fy(a,b),digits=3))+'$.')
show(q+point((b,f(a,b)), color='black', size=100,zorder=5))