An adaption of the Bortfeld bragg curve fit in python with scipy and numpy, strongly influenced by the original author.

You can install pybragg using pip install <optional: '--user'> git+https://github.com/flome/pybragg.git.

Please note that z needs to be passed in cm.

If you have a data set (z, D) with two arrays, z being the depth in mm in a phantom and Dbeing the deposited dose at that depth, you can fit the curve using the bortfeld fit with

from pybragg import fitBP
bortfeld_fit_params = fitBP(z, D)

The fit returns characteristic values like D100 (max. Dose) or the proton beam range R80D (distal side of the beam, 80% maximum dose).

The bortfeld fit result (parameters: bortfeld_fit_params['bortfeld_fit_p'], covariance matrix: bortfeld_fit_params['bortfeld_fit_cov']) can be plotted using the fit results:

from pybragg import bortfeld
z = np.linspace(0, 20, 500) # depth in cm
curve = bortfeld(z, *bortfeld_fit_params['bortfeld_fit_p'])
plt.plot(z, curve)

You can use the bortfeld equation for your own fit routine or to generate bragg peaks:

import numpy
from pybragg import bortfeld

z = np.linspace(0, 20, 500) # depth in cm
D = bortfeld(z, D100=600, R0=130, sigma=1.3)

import matplotlib.pyplot as plt

plt.plot(z, D, label='bortfeld function')
plt.xlabel('$z$ in mm')
plt.ylabel('$D$ in a.u.')
plt.legend(loc='best')
plt.tight_layout()

plt.show()