MathCancer Blog

ParaView for PhysiCell – Part 1

In this tutorial, we discuss the topic of visualizing data that is generated by PhysiCell. Specifically, we discuss the visualization of cells. In a later post, we’ll discuss options for visualizing the microenvironment. For 2-D models, PhysiCell generates Scalable Vector Graphics (SVG) files that depict cells’ positions, sizes (volumes), and colors (virtual pathology). Obviously, visualizing cells from 3-D models is more challenging. (Note: SVG files are also generated for 3-D models; however, they capture only the cells that intersect the Z=0 plane). Until now, we have only discussed a couple of applications for visualizing 3-D data from PhysiCell: MATLAB (or Octave) and POV-Ray. In this post, we describe ParaView: an open source, data analysis and visualization application from Kitware. ParaView can be used to visualize a wide variety of scientific data, as depicted on their gallery page.

Preliminary steps

Before we get started, just a reminder – if you have any problems or questions, please join our mailing list (physicell-users@googlegroups.com) to get help. In preparation for using the customized PhysiCell data reader in ParaView, you will need to have a specific Python module, scipy, installed. Python will be a useful language for other PhysiCell data analysis and visualization tasks too, so having it installed on your computer will come in handy later, beyond using ParaView. The confusion of installing/using Python (and the scipy module) for ParaView is due to multiple factors:

• you may or may not have Administrator permission on your computer,
• there are different versions of Python, including the major version confusion – 2 vs. 3,
• there are different distributions of Python, and
• ParaView comes with its own built-in Python (version 2), but it isn’t easily extensible.

Before we get operating system specific, we just want to point out that it is possible to have multiple versions and/or distributions of Python on your computer. Unfortunately, there is no guarantee that you can mix modules of one with another. This is especially true for one popular Python distribution, Anaconda, and any other distribution.

We now provide some detailed instructions for the primary operating systems. In the sections that follow, we assume you have Admin permission on your computer. If you do not and you need to install Python + scipy as a standard user, see Appendix A at the end.

Windows

Windows does not come with Python, by default. Therefore, you will need to download/install it from python.org – get the latest 2.x version – currently https://www.python.org/downloads/release/python-2714/.

During the installation process, you will be asked if you want to install for all users or just yourself. That is up to you.

You’ll have the option of changing the default installation directory. We recommend keeping the default: C:\Python27.

Finally, you will have the choice of having this python executable be your default. That is up to you. If you have another Python distribution installed that you want to keep as your default, then you should leave this choice unchecked, i.e. leave the “X”. But if you do want to use this one as your default, select “Add python.exe to Path”:

After completing the Python 2.7 installation, open a Command Prompt shell and run (or if you selected to use this python.exe as your default in the above step, you can just use ‘python’ instead of specifying the full path):

c:\python27\python.exe -m pip install scipy

This will download and install the scipy module which is what our PhysiCell data reader uses. You can verify that it got installed by running python and trying to import it:

c:\>python27\python.exe
Python 2.7.14 (v2.7.14:84471935ed, Sep 16 2017, 20:25:58) [MSC v.1500 64 bit (AMD64)] on win32
Type "help", "copyright", "credits" or "license" for more information.
>>> import scipy
>>> quit()

OSX and Linux

Both OSX and Linux come with a system-level version of Python pre-installed (/usr/bin/python). Regardless of whether you have installed additional versions of Python, you will want to make sure the pre-installed version has the scipy module. OSX should already have it. However, Linux will not and you will need to install it via:

/usr/bin/python -m pip install scipy

You can test if scipy is accessible by simply trying to import it:

/usr/bin/python
...
>>> import scipy
>>> quit()

Installing ParaView

After you have successfully installed Python + scipy, download and install the (binary) ParaView application for your particular platform. The current, stable version is 5.4.1.

Windows

Assuming you have Admin permission, download/install ParaView-5.4.1-Qt5-OpenGL2-Windows-64bit.exe. If you do not have Admin permission, see Appendix A.

OSX or Linux

On OSX, assuming you have Admin permissions, download/install ParaView-5.4.1-Qt5-OpenGL2-MPI-OSX10.8-64bit.dmg. If you do not have Admin permission, see Appendix A.

On Linux, download ParaView-5.4.1-Qt5-OpenGL2-MPI-Linux-64bit.tar.gz and uncompress it into an appropriate directory. For example, if you want to make ParaView available to everyone, you may want to uncompress it into /usr/local. If you only want to make it available for your personal use, see Appendix A.

Running ParaView

Before starting the ParaView application, you can set an environment variable, PHYSICELL_DATA, to be the full path to the directory where the PhysiCell data can be found. This will make it easier for the custom data reader (a Python script) in the ParaView pipeline to find the data. For example, in the next section we provide a link to some sample PhysiCell data. If you simply uncompress that zip archive into your Downloads directory, then (on Linux/OSX bash) you could:

$ export PHYSICELL_DATA=/path-to-your-home-dir/Downloads

(this Windows tutorial, while aimed at editing your PATH, will also help you find the environment variables setting).

If you choose not to set the PHYSICELL_DATA environment variable, the custom data reader will look in your user Downloads directory. Alternatively, you can simply edit the ParaView custom data reader Python script to point to your data directory (and then you would probably want to File -> Save State).

NOTE: if you are using OSX and want to use the PHYSICELL_DATA environment variable, you should start the ParaView application from the Terminal, e.g. $ /Applications/ParaView-5.4.1.app/Contents/MacOS/paraview &

Finally, go ahead and start the ParaView application. You should see a blank GUI (Figure 1). Don’t be frightened by the complexity of the GUI – yes, there are several widgets, but we will walk you down a minimal path to help you visualize PhysiCell cell data. Of course you have access to all of ParaView’s documentation – the Getting Started, Guide, and Tutorial under the Help menu are a good place to start. In addition to the downloadable (.pdf) documentation, there is also in-depth information online: https://www.paraview.org/Wiki/ParaView

Figure 1. The ParaView application

Note: the 3-D axis in the lower-left corner of the RenderView does not represent the origin. It is just a reference axis to provide 3-D orientation.

Before you get started with examples, you should open ParaView’s Settings (Preferences), select the General tab, and make sure “Auto Apply” is checked. This will avoid the need to manually “Apply” changes you make to an object’s properties.

Cancer immunity 3D example

We will use sample output data from the cancer_immune_3D project – one of the sample projects bundled with PhysiCell. You can refer to the PhysiCell Quickstart guide if you want to actually compile and run that project. But to simplify this tutorial, we provide sample data (a single time step) from that project, at:
https://sourceforge.net/projects/physicell/files/Tutorials/MultiCellDS/3D_PhysiCell_matlab_sample.zip/download

After you extract the files from this .zip, the file of interest for this tutorial is called output00003696_cells_physicell.mat. (And remember, as discussed above, to set the PHYSICELL_DATA environment variable to point to the directory where you extracted the files).

Additionally, for this tutorial, you’ll need some predefined ParaView state files (*.pvsm). A state file is just what it sounds like – it saves the entire state of a ParaView session so that you can easily re-use it. For this tutorial, we have provided the following state files to help you get started:

• physicell_glyphs.pvsm – render cells as simple vertex glyphs
• physicell_z0slice.pvsm – render the intersection of spherical glyphs with the Z=0 plane
• physicell_3clip_planes_ospray.pvsm – OSPRay renderer with 3 clipping planes
• physicell_cells_animate.pvsm – demonstrate how to do animation

Download them here: physicell_paraview_states.zip

Figure 2 is the SVG image from the sample data. It depicts the (3-D) cells that intersect the Z=0 plane.

Figure 2. snapshot00003696.svg generated by PhysiCell

Reading PhysiCell (cell) data

One way that ParaView offers extensibility is via Python scripts. To make it easier to read data generated by PhysiCell, we provide users with a “Programmable Source” that will read and process data in a file. In the ParaView screen-captured figures below, the Programmable Source (“PhysiCellReader_cells”) will be the very first module in the pipeline.

For this exercise, you can File->LoadState and select the physicell_glyphs.pvsm file that you downloaded above. Assuming you previously copied the output00003696_cells_physicell.mat sample data file into one of the default directories as described above, it should display the results in Figure 3. (Otherwise, you will likely see an error message appear, in which case see Appendix B). These are the simplest (and fastest) glyphs to represent PhysiCell cells. They are known as 2-D Vertex glyphs, although the 2-D is misleading since they are rendered in 3-space. At this point, you can interact – rotate, zoom, pan, with the visualization (rf. Sect. 4.4.2 in the ParaViewGuide-5.4.0 for an explanation of the controls, but basically: left-mouse button hold while moving cursor to rotate; Ctl-left-mouse for zoom; Ctl-Shift-left-mouse to pan).

For this particular ParaView state file, we use the following code to assign colors to cells (Note: the PhysiCell code in /custom_modules creates the SVG file using colors based on cells’ neighbor information. This information is not saved in the .mat output files, therefore we cannot faithfully reproduce SVG cell colors here):

   # The following lines assign an integer to represent
   # a color, defined in a Color Map.
   sval = 0   # immune cells are yellow?
   if val[5,idx] == 1:  # [5]=cell_type
     sval = 1   # lime green
   if (val[6,idx] == 6) or (val[6,idx] == 7):
     sval = 0
   if val[7,idx] == 100:  # [7]=current_phase
     sval = 3   # apoptotic: red
   if val[7,idx] > 100 and val[7,idx] < 104:
     sval = 2   # necrotic: brownish

Figure 3. Glyphs as vertices

Figure 4. Glyphs as spheres

The next exercise is a simple extension of the previous. We want to add a slice to our pipeline that will intersect the cells (spherical glyphs). Assuming the slice is the Z=0 plane, this will approximate the SVG in Figure 2. So, select Edit->ResetSession to start from scratch, then File->LoadState and select the physicell_z0slice.pvsm file. Note that the “Glyph1” node in the pipeline is invisible (its “eyeball” is toggled off). If you make it visible (select the eyeball), you will essentially reproduce Figure 4. But for this exercise, we want Glyph1 to be invisible and Slice1 visible. If you select Slice1 (its green box) in the pipeline, you can select its Properties tab (at the top) to see all its properties. Of particular interest is the “Show Plane” checkbox at the top.

If this is checked on, you can interactively translate the plane along its normal, as well as select and rotate the normal itself. Try it! You can also “hardcode” the slice plane parameters in its properties panel.

Figure 5. Z=0 slice through the spherical glyphs (approximate SVG slice)

Our final exercise with the sample dataset is to visualize cells using a higher quality renderer in ParaView known as OSPRay. So, as before, Edit->ResetSession to start from scratch, then File->LoadState and select the physicell_3clip_planes_ospray.pvsm file. This will create a pipeline that has 3 clipping planes aligned such that an octant of our spheroidal cell cluster is clipped away, letting us peer into its core (Figure 6). As with the previous slice plane, you can interactively reposition one or more of the clipping planes here.

Note: One (temporary) downside of using the OSPRay renderer is that cells (spheres) cannot be arbitrarily scaled in size. This will be fixed in a future release of ParaView. For now, we get around that by shrinking the distance of each cell from the origin. Obviously this is not a perfect solution, but for cells that are sort of clustered around the origin, it offers a decent approximation. We mention this 1) to disclose the inaccuracy, and 2) in case you look at the data ranges in the “Information” view/tab and notice they are not reflecting the domain of your simulation.

Figure 6. OSPRay-rendered cells, showing 1 of 3 interactive clipping planes

Animation in Time

At some point, you’ll want to see the dynamics of your simulation. This is where ParaView’s animation functionality comes in handy. It provides an easy way to let you render all (or a subset) of your PhysiCell output files, control the animation, and also save images (as .png files).

For this exercise, you will obviously want to have generated multiple output files from a PhysiCell project. Once you have those, e.g. from the cancer_immune_3D project, you can File->LoadState and select the physicell_cells_animate.pvsm file. This will show the following pipeline:

If you select the PhysiCellReader_cells (green box; leave its “eye” icon deselected) and click on the Properties tab, you will have access to the Script(RequestInformation) (you may need to click the “gear” icon next to the Properties tab Search bar to “Toggle advanced properties” to see this script):

In there, you will see the lines:

timeSteps = range(1,20,1)   # (start, stop+1, step)
#timeSteps = range(100,801,50)   # (start, stop+1 [, step])

You’ll want to edit the first line, specifying your desired start, stop, and (optionally) step values for your files’ numeric suffixes. We happened to use the second timeSteps line (currently commented out with the ‘#’) for data from our simulation, which resulted in 15 time steps (0-14) for the time values: 100,150,200,…800. Pressing the Play (center) button of the animation icons would animate those frames:

When you like what you see, you can select File->SaveAnimation to save the images. After you provide some minimal information for those images, e.g., resolution and filename prefix, press “OK” and you will see a horizontal progress bar being updated below the render window. After the animation images are generated, you can use your favorite image processing and movie generation tools to post-process them. In Figure 7, we used ImageMagick’s montage command to arrange the 15 images from a cancer_immune_3D simulation. And for generating a movie file, take a look at mplayer/mencoder as one open source option.

Figure 7. Images from cancer_immune_3D

Further Help

For questions specific to PhysiCell, have a look at our User Guide and join our mailing list to ask questions. For ParaView, have a look at their User Guide and join the ParaView mailing list to ask questions.

Thanks!

In closing, we would like to thank Kitware for their terrific open source software and the ParaView community (especially David DeMarle and Utkarsh Ayachit) for being so helpful answering questions and providing insight. We were honored that some of our early results got headlined on Kitware’s home page!

Appendix A: Installing without Admin permission

If you do not have Admin permission on your computer, we provide instructions for installing Python + scipy and ParaView using alternative approaches.

Windows

To install Python on Windows, without Admin permission, run the msiexec command on the .msi Python installer that you downloaded, specifying a (non-system) directory in which it should be installed via the targetdir keyword. After that completes, Python will be installed; however, the python command will not be in your PATH, i.e., it will not be globally accessible.

C:\Users\sue\Downloads>msiexec /a python-2.7.14.amd64.msi /qb targetdir=c:\py27

C:\Users\sue\Downloads>python
'python' is not recognized as an internal or external command,
operable program or batch file.

C:\Users\sue\Downloads>cd c:\py27

c:\py27>.\python.exe
Python 2.7.14 (v2.7.14:84471935ed, Sep 16 2017, 20:25:58) [MSC v.1500 64 bit (AMD64)] on win32
Type "help", "copyright", "credits" or "license" for more information.
>>>

Finally, download ParaView-5.4.1-Qt5-OpenGL2-Windows-64bit.zip and extract its contents into a permissible directory, e.g. under your home folder: C:\Users\sue\ParaView-5.4.1-Qt5-OpenGL2-Windows-64bit\

Then, in ParaView, using the Tools menu, open the Python Shell, and see if you can import scipy via:

>>> sys.path.insert(0,'c:\py27\Lib\site-packages')
>>> import scipy

Before proceeding with the tutorial using the PhysiCell state files, you will want to open ParaView’s Settings and check (toggle on) the “Auto Apply” property in the General settings tab.

OSX

OSX comes with a system Python pre-installed. And, at least with fairly recent versions of OSX, it comes with the scipy module also. You can test to see if that is the case on your system:

/usr/bin/python
>>> import scipy

To install ParaView, download a .pkg, not a .dmg, e.g. ParaView-5.4.1-Qt5-OpenGL2-MPI-OSX10.8-64bit.pkg. Then expand that .pkg contents into a permissible directory and untar its “Payload” which contains the actual paraview executable that you can open/run:

cd ~/Downloads
pkgutil --expand ParaView-5.4.1-Qt5-OpenGL2-MPI-OSX10.8-64bit.pkg ~/paraview
cd ~/paraview
tar -xvf Payload
open Contents/MacOS/paraview

Linux

Like OSX, Linux also comes with a system Python pre-installed. However, it does not come with the scipy module. To install the scipy Python module, run:

/usr/bin/python -m pip install scipy --user

To install and run ParaView, download the .tar.gz file, e.g. ParaView-5.4.1-Qt5-OpenGL2-MPI-Linux-64bit.tar.gz and uncompress it into a permissible directory. For example, from your home directory (after downloading):

mv ~/Downloads/ParaView-5.4.1-Qt5-OpenGL2-MPI-Linux-64bit.tar.gz .
tar -xvzf ParaView-5.4.1-Qt5-OpenGL2-MPI-Linux-64bit.tar.gz
cd ParaView-5.4.1-Qt5-OpenGL2-MPI-Linux-64bit/bin
./paraview

Appendix B: Editing the PhysiCellReader_cells Python Script

In case you encounter an error reading your .mat file(s) containing cell data, you will probably need to manually edit the directory path to the file. This is illustrated below in a 4-step process: 1) select the Pipeline Browser tab, 2) select the PhysiCellReader_cells object, 3) select its Properties, then 4) edit the relevant information in the (Python) script. (The script frame is scrollable).

!unzip 3D_PhysiCell_matlab_sample.zip

MCDS = read_MultiCellDS_xml( 'output00003696.xml'); 

k = find( MCDS.mesh.Z_coordinates == 0 ); 

contourf( MCDS.mesh.X(:,:,k), MCDS.mesh.Y(:,:,k), ...
     MCDS.continuum_variables(1).data(:,:,k) , 20 ) ;

axis image
colorbar 
xlabel( sprintf( 'x (%s)' , MCDS.metadata.spatial_units) ); 
ylabel( sprintf( 'y (%s)' , MCDS.metadata.spatial_units) ); 

title( sprintf('%s (%s) at t = %3.2f %s, z = %3.2f %s', MCDS.continuum_variables(1).name , ...
     MCDS.continuum_variables(1).units , ...
     MCDS.metadata.current_time , ...
     MCDS.metadata.time_units, ... 
     MCDS.mesh.Z_coordinates(k), ...
     MCDS.metadata.spatial_units ) ); 

print( '-dpng' , 'output_o2.png' );

plot3( MCDS.discrete_cells.state.position(:,1) , MCDS.discrete_cells.state.position(:,2), ...
	MCDS.discrete_cells.state.position(:,3) , 'bo' ); 

axis( 1000*[-1 1 -1 1 -1 1] )
axis square 

% make it easier to work with the cell positions; 
P = MCDS.discrete_cells.state.position;

% find type 1 cells
ind1 = find( MCDS.discrete_cells.metadata.type == 1 ); 
% better still, eliminate those out of the simulation domain 
ind1 = find( MCDS.discrete_cells.metadata.type == 1 & ...
    abs(P(:,1))' < 1000 & abs(P(:,2))' < 1000 & abs(P(:,3))' < 1000 );

% find type 0 cells
ind0 = find( MCDS.discrete_cells.metadata.type == 0 & ...
    abs(P(:,1))' < 1000 & abs(P(:,2))' < 1000 & abs(P(:,3))' < 1000 ); 

%now plot them
P = MCDS.discrete_cells.state.position;
plot3( P(ind0,1), P(ind0,2), P(ind0,3), 'bo' )
hold on
plot3( P(ind1,1), P(ind1,2), P(ind1,3), 'ro' )
hold off
axis( 1000*[-1 1 -1 1 -1 1] )
axis square

clf
simple_plot( MCDS,  MCDS, MCDS.discrete_cells.dead_cells , 'r' )

clf
simple_cutaway_plot( MCDS, MCDS, MCDS.discrete_cells.dead_cells , 'r' )

clf
composite_cutaway_plot( MCDS )

constants = set_MCDS_constants

% find the type 0 necrotic cells
ind0_necrotic = find( MCDS.discrete_cells.metadata.type == 0 & ...
    (MCDS.discrete_cells.phenotype.cycle.current_phase == constants.necrotic_swelling | ...
    MCDS.discrete_cells.phenotype.cycle.current_phase == constants.necrotic_lysed | ...
    MCDS.discrete_cells.phenotype.cycle.current_phase == constants.necrotic) ); 

% find the live type 0 cells
ind0_live = find( MCDS.discrete_cells.metadata.type == 0 & ...
    (MCDS.discrete_cells.phenotype.cycle.current_phase ~= constants.necrotic_swelling & ...
    MCDS.discrete_cells.phenotype.cycle.current_phase ~= constants.necrotic_lysed & ...
    MCDS.discrete_cells.phenotype.cycle.current_phase ~= constants.necrotic & ...
    MCDS.discrete_cells.phenotype.cycle.current_phase ~= constants.apoptotic) ); 

clf
% plot live tumor cells red, in cutaway view
simple_cutaway_plot( MCDS, ind0_live , 'r' ); 
hold on 
% plot dead tumor cells black, in cutaway view 
simple_cutaway_plot( MCDS, ind0_necrotic , 'k' ) 
% plot all immune cells, but without cutaway (to show how they infiltrate)
simple_plot( MCDS, ind1, 'g' ) 
hold off

// the program name, version, and project website:
BioFVM_metadata.program.program_name = "BioFVM MultiCellDS Test";
BioFVM_metadata.program.program_version = "1.0";
BioFVM_metadata.program.program_URL = "http://BioFVM.MathCancer.org";
 
// who created the program (if known)
BioFVM_metadata.program.creator.surname = "Macklin";
BioFVM_metadata.program.creator.given_names = "Paul";
BioFVM_metadata.program.creator.email = "Paul.Macklin@usc.edu";
BioFVM_metadata.program.creator.URL = "http://BioFVM.MathCancer.org";
BioFVM_metadata.program.creator.organization = "University of Southern California";
BioFVM_metadata.program.creator.department = "Center for Applied Molecular Medicine";
BioFVM_metadata.program.creator.ORCID = "0000-0002-9925-0151";
 
// (generally peer-reviewed) citation information for the program
BioFVM_metadata.program.citation.DOI = "10.1093/bioinformatics/btv730";
BioFVM_metadata.program.citation.PMID = "26656933";
BioFVM_metadata.program.citation.PMCID = "PMC1234567";
BioFVM_metadata.program.citation.text = "A. Ghaffarizadeh, S.H. Friedman, and P. Macklin, 
    BioFVM: an efficient parallelized diffusive transport solver for 3-D biological 
    simulations, Bioinformatics, 2015. DOI: 10.1093/bioinformatics/btv730.";
BioFVM_metadata.program.citation.notes = "notes here";
BioFVM_metadata.program.citation.URL = "http://dx.doi.org/10.1093/bioinformatics/btv730";
 
// user information: who ran the program
BioFVM_metadata.program.user.surname = "Kirk";
BioFVM_metadata.program.user.given_names = "James T.";
BioFVM_metadata.program.user.email = "Jimmy.Kirk@starfleet.mil";
BioFVM_metadata.program.user.organization = "Starfleet";
BioFVM_metadata.program.user.department = "U.S.S. Enterprise (NCC 1701)";
BioFVM_metadata.program.user.ORCID = "0000-0000-0000-0000";
 
// And finally, data citation information (the publication where this simulation snapshot appeared)
BioFVM_metadata.data_citation.DOI = "10.1093/bioinformatics/btv730";
BioFVM_metadata.data_citation.PMID = "12345678";
BioFVM_metadata.data_citation.PMCID = "PMC1234567";
BioFVM_metadata.data_citation.text = "A. Ghaffarizadeh, S.H. Friedman, and P. Macklin, BioFVM: 
    an efficient parallelized diffusive transport solver for 3-D biological simulations, Bioinformatics, 
    2015. DOI: 10.1093/bioinformatics/btv730.";
BioFVM_metadata.data_citation.notes = "notes here";
BioFVM_metadata.data_citation.URL = "http://dx.doi.org/10.1093/bioinformatics/btv730";

BioFVM_metadata.sync_to_microenvironment( M ); 

BioFVM_metadata.display_information( std::cout ); 

set_save_biofvm_mesh_as_matlab( false );

set_save_biofvm_data_as_matlab( false ); 

set_save_biofvm_cell_data( false );

set_save_biofvm_cell_data_as_custom_matlab( false )

save_BioFVM_to_MultiCellDS_xml_pugi( "sample" , M , current_simulation_time );

double current_simulation_time = 10.347; 
char filename_base [1024]; 
sprintf( &filename_base , "sample_%f", current_simulation_time ); 
save_BioFVM_to_MultiCellDS_xml_pugi( filename_base , M,
   current_simulation_time ); 

PROGRAM_NAME := MCDS_test

all: $(BioFVM_OBJECTS) $(pugixml_OBJECTS) MultiCellDS_test.cpp

$(COMPILE_COMMAND) -o $(PROGRAM_NAME) $(BioFVM_OBJECTS) $(pugixml_OBJECTS) MultiCellDS_test.cpp

make
./MCDS_test

make
MCDS_test

MCDS = read_MultiCellDS_xml( 'sample.xml' );

mid_index = round( length(MCDS.mesh.Z_coordinates)/2 ); 

contourf( MCDS.mesh.X(:,:,mid_index), ...
	MCDS.mesh.Y(:,:,mid_index), ... 
	MCDS.continuum_variables(2).data(:,:,mid_index) , 20 ) ; 
axis image
colorbar 
xlabel( sprintf( 'x (%s)' , MCDS.metadata.spatial_units) ); 
ylabel( sprintf( 'y (%s)' , MCDS.metadata.spatial_units) ); 
title( sprintf('%s (%s) at t = %f %s, z = %f %s', MCDS.continuum_variables(2).name , ...
	MCDS.continuum_variables(2).units , ...
	MCDS.metadata.current_time , ...
	MCDS.metadata.time_units, ... 
	MCDS.mesh.Z_coordinates(mid_index), ...
	MCDS.metadata.spatial_units ) ); 

contourf( MCDS.mesh.X_coordinates , MCDS.mesh.Y_coordinates, ... 
	MCDS.continuum_variables(2).data(:,:,mid_index) , 20 ) ; 
axis image
colorbar 
xlabel( sprintf( 'x (%s)' , MCDS.metadata.spatial_units) ); 
ylabel( sprintf( 'y (%s)' , MCDS.metadata.spatial_units) ); 
title( sprintf('%s (%s) at t = %f %s, z = %f %s', ...
	MCDS.continuum_variables(2).name , ...
	MCDS.continuum_variables(2).units , ...
	MCDS.metadata.current_time , ...
	MCDS.metadata.time_units, ... 
	MCDS.mesh.Z_coordinates(mid_index), ...
	MCDS.metadata.spatial_units ) );  

surf( MCDS.mesh.X_coordinates , MCDS.mesh.Y_coordinates, ... 
	MCDS.continuum_variables(1).data(:,:,mid_index) ) ; 
colorbar 
axis tight
xlabel( sprintf( 'x (%s)' , MCDS.metadata.spatial_units) ); 
ylabel( sprintf( 'y (%s)' , MCDS.metadata.spatial_units) ); 
zlabel( sprintf( '%s (%s)', MCDS.continuum_variables(1).name, ...
	MCDS.continuum_variables(1).units ) ); 
title( sprintf('%s (%s) at t = %f %s, z = %f %s', MCDS.continuum_variables(1).name , ...
	MCDS.continuum_variables(1).units , ...
	MCDS.metadata.current_time , ...
	MCDS.metadata.time_units, ...
	MCDS.mesh.Z_coordinates(mid_index), ...
	MCDS.metadata.spatial_units ) );

clf
contourslice( MCDS.mesh.X , MCDS.mesh.Y, MCDS.mesh.Z , ...
	MCDS.continuum_variables(2).data , [],[], ...
	MCDS.mesh.Z_coordinates(1:15:length(MCDS.mesh.Z_coordinates)),20);
view([-45 10]);
axis tight; 
xlabel( sprintf( 'x (%s)' , MCDS.metadata.spatial_units) ); 
ylabel( sprintf( 'y (%s)' , MCDS.metadata.spatial_units) ); 
zlabel( sprintf( 'z (%s)' , MCDS.metadata.spatial_units) ); 
title( sprintf('%s (%s) at t = %f %s', ...
	MCDS.continuum_variables(2).name , ...
	MCDS.continuum_variables(2).units , ...
	MCDS.metadata.current_time, ... 
	MCDS.metadata.time_units ) ); 

clf
patch( isosurface( MCDS.mesh.X , MCDS.mesh.Y, MCDS.mesh.Z, ...
	MCDS.continuum_variables(1).data, 1000 ), 'edgecolor', ...
	'none', 'facecolor', 'r' , 'facealpha' , 1 ); 
hold on
patch( isosurface( MCDS.mesh.X , MCDS.mesh.Y, MCDS.mesh.Z, ...
MCDS.continuum_variables(1).data, 5000 ), 'edgecolor', ...
	'none', 'facecolor', 'b' , 'facealpha' , 0.7 ); 
patch( isosurface( MCDS.mesh.X , MCDS.mesh.Y, MCDS.mesh.Z, ...
	MCDS.continuum_variables(1).data, 10000 ), 'edgecolor', ...
	'none', 'facecolor', 'g' , 'facealpha' , 0.5 ); 
hold off
% shading interp 
camlight
view(3)
axis image 
axis tightcamlight lighting gouraud
xlabel( sprintf( 'x (%s)' , MCDS.metadata.spatial_units) ); 
ylabel( sprintf( 'y (%s)' , MCDS.metadata.spatial_units) ); 
zlabel( sprintf( 'z (%s)' , MCDS.metadata.spatial_units) );
title( sprintf('%s (%s) at t = %f %s', ... 
	MCDS.continuum_variables(1).name , ...
	MCDS.continuum_variables(1).units , ...
	MCDS.metadata.current_time, ... 
	MCDS.metadata.time_units ) );

plot3( MCDS.discrete_cells.state.position(:,1) , ...
	MCDS.discrete_cells.state.position(:,2) , ...
	MCDS.discrete_cells.state.position(:,3) , 'bo' );
view(3)
axis tight
xlabel( sprintf( 'x (%s)' , MCDS.metadata.spatial_units) ); 
ylabel( sprintf( 'y (%s)' , MCDS.metadata.spatial_units) ); 
zlabel( sprintf( 'z (%s)' , MCDS.metadata.spatial_units) );
title( sprintf('Cells at t = %f %s', MCDS.metadata.current_time, ...
	MCDS.metadata.time_units ) );

scatter3( MCDS.discrete_cells.state.position(:,1), ...
	MCDS.discrete_cells.state.position(:,2), ...
	MCDS.discrete_cells.state.position(:,3) , 'bo' );
view(3)
axis tight
xlabel( sprintf( 'x (%s)' , MCDS.metadata.spatial_units) ); 
ylabel( sprintf( 'y (%s)' , MCDS.metadata.spatial_units) ); 
zlabel( sprintf( 'z (%s)' , MCDS.metadata.spatial_units) ); 
title( sprintf('Cells at t = %f %s', MCDS.metadata.current_time, ...
	MCDS.metadata.time_units ) );