cancer_dynamics Files

Alberto Santos and Andrea Izquierdo Python's project

Our project is based on the article:
Controlled Drug Delivery in Cancer Immunotherapy: Stability, Optimization and Monte Carlo Analysis
by Andrea Minelli, Francesco Topputo, and Franco Bernelli-Zazzera (http://epubs.siam.org/siap/resource/1/smjmap/v71/i6/p2229_s1)

Our aims are the followings:
        •Analyse the evolution of a tumor and the immune system through time
        •Develop a web interface to show and download the results

METHODS OF THE ANALYSIS

The involved cells are the following:
        •Helper CD4 T cells
        •Cytotoxic CD8 T cells
        •Dendritic cells
        •Tumor cells

We will also include the Interleukin 2 involved in the stimulation of the immune system.

To do so, we solved the following system of ordinary linear equations:

        dH/dt = a0 + b0 DH(1-H/f0) - c0 H
        dM/dt = b2 M (1 - M/f2) - d2 M C
        dC/dt = a1 + b1 I(M + D)C(1 - C/f1) - c1 C
        dD/dt = -d3 DC + u
        dI/dt = b4 DH - e4 IC - c4 I

       	helper CD4 T cells (H) 			cytotoxic CD8 T cells (C)	dendritic cells (D)		interleukin-2 (I)
	CD4 T birth rate (a0)			CD4 T proliferation rate (b0) 	CD4 T death rate (c0)		Carrying capacity of CD4 T (f0)
	CD8 T birth rate (a1)			CD8 T proliferation rate (b1) 	CD8 T death rate (c1)		Carrying capacity of CD8 T (f1)
	1/2 saturations const of tumor (b2)	Killing by CD8 T of tumor (d2) 	Carrying capacity of tumor (f2)	CD8 T killing of DC (d3)
	IL-2 production by CD4 T (b4)		IL-2 degradation rate (c4) 	IL-2 uptake by CD8 T (e4)

The fundamental time unit is one hour. We are taken the follwing interval of time: 0h to 20h with a time step of 5h
The user will be able to choose the constants of the system definded above

RESULTS OF THE ANALYSIS

The results are the images and video showing the dynamics of the tumor for the given constants.

The images are of two kinds:
       •Several graphs showing the dynamics of the cells of the system, one image for each time step
       •One graph showing the concentrations of each cells through time
The video is the sequence of images generated

The user will be able to download the full results as a packed file containing the images and the video

### REQUIREMENTS AND INSTALATION###

* Python 2.7
* Apache server (http://httpd.apache.org ) 
* Matplotlib – library used to create all the graph images (http://matplotlib.sourceforge.net/)
* Numpy – library used to solve the system of ordinary differential equations 
(http://numpy.scipy.org/)
* Tarfile – library used to compress the graphs 
(http://docs.python.org/library/tarfile.html) 
* mod_wsgi – apache http server that provide a WSGI compilant interface for hosting Python 2.3+ based web applications under apache 
(http://code.google.com/p/modwsgi) 

It is needed to have all the modules in the following location: /var/www/ 
and create a tmp directory (with writing permission). It will also be needed to give write permissions to the log directory.
The level of log can be changed. It is currently set to DEBUG.

After the installation you would be able to access the webside in your localhost, index.html will redirect you to the initial page.