# MultiTensor Simulation

In this example we show how someone can simulate the signal and the ODF of a single voxel using a MultiTensor.

import numpy as np
from dipy.sims.voxel import multi_tensor, multi_tensor_odf
from dipy.data import get_sphere


For the simulation we will need a GradientTable with the b-values and b-vectors Here we use the one we created in Gradients and Spheres.

from gradients_spheres import gtab


In mevals we save the eigenvalues of each tensor.

mevals = np.array([[0.0015, 0.0003, 0.0003],
[0.0015, 0.0003, 0.0003]])


In angles we save in polar coordinates ($$\theta, \phi$$) the principal axis of each tensor.

angles = [(0, 0), (60, 0)]


In fractions we save the percentage of the contribution of each tensor.

fractions = [50, 50]


The function multi_tensor will return the simulated signal and an array with the principal axes of the tensors in cartesian coordinates.

signal, sticks = multi_tensor(gtab, mevals, S0=100, angles=angles,
fractions=fractions, snr=None)


We can also add Rician noise with a specific SNR.

signal_noisy, sticks = multi_tensor(gtab, mevals, S0=100, angles=angles,
fractions=fractions, snr=20)

import matplotlib.pyplot as plt

plt.plot(signal, label='noiseless')

plt.plot(signal_noisy, label='with noise')
plt.legend()
#plt.show()
plt.savefig('simulated_signal.png')


Simulated MultiTensor signal

For the ODF simulation we will need a sphere. Because we are interested in a simulation of only a single voxel, we can use a sphere with very high resolution. We generate that by subdividing the triangles of one of DIPY’s cached spheres, which we can read in the following way.

sphere = get_sphere('repulsion724')
sphere = sphere.subdivide(2)

odf = multi_tensor_odf(sphere.vertices, mevals, angles, fractions)

from dipy.viz import window, actor

# Enables/disables interactive visualization
interactive = False

ren = window.Renderer()

odf_actor = actor.odf_slicer(odf[None, None, None, :], sphere=sphere, colormap='plasma')
odf_actor.RotateX(90)

print('Saving illustration as multi_tensor_simulation')
window.record(ren, out_path='multi_tensor_simulation.png', size=(300, 300))
if interactive:
window.show(ren)


Simulating a MultiTensor ODF.

Example source code

You can download the full source code of this example. This same script is also included in the dipy source distribution under the doc/examples/ directory.