def test_banding_sim_2d(self):
'''Make sure banding looks the same coming from NMR params and ESM.'''
# To get periodic banding like we want to see, we need some serious
# field inhomogeneity.
dim = 256
min_df, max_df = 0, 500
x = np.linspace(min_df, max_df, dim)
y = np.zeros(dim)
field_map, _ = np.meshgrid(x, y)
# # Show the field map
# plt.imshow(field_map)
# plt.show()
# # Generate simulated banding image explicitly using NMR parameters
sig0 = ssfp(self.T1, self.T2, self.TR, self.alpha, field_map)
# plt.subplot(2,1,1)
# plt.imshow(np.abs(sig0))
# plt.subplot(2,1,2)
# plt.plot(np.abs(sig0[int(dim/2),:]))
# plt.show()
# Generate simulated banding image using elliptical signal model
M, a, b = elliptical_params(self.T1, self.T2, self.TR, self.alpha)
sig1 = ssfp_from_ellipse(M, a, b, self.TR, field_map)
self.assertTrue(np.allclose(sig0, sig1))
def test_center_of_mass(self):
'''Make sure we can find the center of mass of an ellipse.'''
M, a, b = elliptical_params(self.T1, self.T2, self.TR, self.alpha)
cm0 = get_center_of_mass(M, a, b)
cm1 = get_center_of_mass_nmr(self.T1, self.T2, self.TR, self.alpha)
self.assertTrue(np.allclose(cm0, cm1))
def test_center_of_mass(self):
from mr_utils.sim.ssfp import elliptical_params, get_center_of_mass, get_center_of_mass_nmr
M, a, b = elliptical_params(self.T1, self.T2, self.TR, self.alpha)
cm0 = get_center_of_mass(M, a, b)
cm1 = get_center_of_mass_nmr(self.T1, self.T2, self.TR, self.alpha)
self.assertTrue(np.allclose(cm0, cm1))
def test_ssfp_sim(self):
'''Generate signal from bSSFP signal eq and elliptical model.'''
# Do it the "normal" way
I0 = ssfp(self.T1, self.T2, self.TR, self.alpha, self.df)
# Now do it using the elliptical model
M, a, b = elliptical_params(self.T1, self.T2, self.TR, self.alpha)
I1 = ssfp_from_ellipse(M, a, b, self.TR, self.df)
self.assertTrue(np.allclose(I0, I1))
def test_ssfp_sim(self):
from mr_utils.sim.ssfp import ssfp, get_theta, elliptical_params, ssfp_from_ellipse
# Do it the "normal" way
I0 = ssfp(self.T1, self.T2, self.TR, self.alpha, self.df)
# Now do it using the elliptical model
M, a, b = elliptical_params(self.T1, self.T2, self.TR, self.alpha)
I1 = ssfp_from_ellipse(M, a, b, self.TR, self.df)
self.assertTrue(np.allclose(I0, I1))
def test_make_ellipse(self):
'''Make an ellipse given NMR params and elliptical params.'''
M, a, b = elliptical_params(self.T1, self.T2, self.TR, self.alpha)
xc, yc, A, B = get_cart_elliptical_params(M, a, b)
x, y = make_cart_ellipse(xc, yc, A, B)
res = np.zeros(x.shape)
for ii in range(x.size):
res[ii] = (x[ii] - xc)**2 / A**2 + (y[ii] - yc)**2 / B**2
# (x - xc)**2/A**2 + (y - yc)**2/B**2 == 1
# Make sure generated x,y satisfy equation for an ellipse
self.assertTrue(np.allclose(res, np.ones(res.shape)))