Practical model fitting

Someone has given you text file with concentration-time curves measured in an artery and in tumor tissue. This notebook demonstrates how such data can be analyzed with the compartment models library.

First, we need to import some libraries:



In [1]:

    
import numpy as np

# plotting and graphics settings
import matplotlib.pyplot as plt
%pylab inline

try:
    import seaborn as sns # pretty graphics. not strictly necessary.
    sns.set_context("notebook")
    sns.set_style("whitegrid")

except:
    pass # with less pretty graphics









    



Populating the interactive namespace from numpy and matplotlib

We can then load the data from the text file and store each of the three columns as a vector:



In [2]:

    
time, curve, aif = np.loadtxt('tests/tumor.csv', delimiter=',', unpack=True, comments='#')

print time[0:5]
print curve[0:5]
print aif[0:5]









    



[ 0.         2.         4.0000001  6.0000001  8.0000001]
[ 0.03825918 -0.4702525  -1.93690696 -4.21724918 -2.56101234]
[ 0.01500034 -0.32475457 -0.35223727  0.47622458 -0.41048893]

This is not very enlightening. Of course, we can do better and plot the two curves.



In [3]:

    
f, (a1,a2)=plt.subplots(1,2)
a1.plot(time, aif, label='AIF')
a2.plot(time,curve, label='Tissue curve')









    Out[3]:





[<matplotlib.lines.Line2D at 0x7f455e002610>]

This looks like a pretty arterial input function (left) and a tissue curve (right).

Tracer-kinetic analysis

To further analyze this data, we need a library for model fitting. Here, we use https://github.com/michimichi/compartmentmodels. This particular library is currently under development, but in a usable status.



In [4]:

    
import compartmentmodels.compartmentmodels as CM

Experience tells that this curve needs to be fitted with a two-compartment exchange model:



In [5]:

    
twocx = CM.TwoCXModel(time, curve, aif, 
                      startdict={'Fp':20.0, 'vp': 5.5, 'PS':0.1, 've':9.1})
twocx.fit_model()









    Out[5]:





True

Let us examine the model fit:



In [6]:

    
f, a = plt.subplots(1,1)
a.plot(time, curve, label='Tissue curve')
a.plot(time, twocx.fit, label='Model fit')
plt.legend(loc=4)









    Out[6]:





<matplotlib.legend.Legend at 0x7f455ce8b590>

This fit produced the following parameters:



In [7]:

    
print twocx.phys_parameters









    



{'Fp': 50.426690251207553, 'PS': 7.7330909906693188, 'E': 0.13296286240329339, 've': 12.561175349066955, 'TP': 8.3937209264061128, 'vp': 8.13628288141906, 'Iterations': 46, 'TE': 97.460449108046149}

This concludes our quick demonstration of this library.