def test_one(save_png=False):
"""Perform the first test demonstrating a pi/2 pulse."""
# create output figure
fig = plt.figure(figsize=(7, 7))
ax1 = fig.add_subplot(221)
ax2 = fig.add_subplot(222, projection='3d')
ax3 = fig.add_subplot(223)
ax4 = fig.add_subplot(224, projection='3d')
# initialize pulse Bloch class
bloch = pulse(T1=0.001, T2=0.0005, t_sim=0.005)
# solve
bloch.solve(m_init=bloch.zunit)
# create lab-frame plots
bloch.plot_magnetization(ax1, version='lab')
bloch.plot_magnetization3d(ax2, version='lab')
# create rot-frame plots
bloch.plot_magnetization(ax3, version='rot')
bloch.plot_magnetization3d(ax4, version='rot')
# adjust axes position
low, bot, wid, hei = ax1.get_position().bounds
ax1.set_position([low, bot * 1.1, wid, hei - 0.05])
low, bot, wid, hei = ax3.get_position().bounds
ax3.set_position([low, bot * 1.1, wid, hei - 0.05])
# adjust titles
ax1.set_title(r'$^1$H | B0 = {:.1f}$\mu$T'.format(bloch.B0 * 1e6))
ax2.set_title(r'$\gamma>0$')
ax3.set_title(r'$^1$H | B1 ~ {:.2f}$\mu$T'.format(bloch.Pulse.factor *
bloch.B0 * 1e6))
ax4.set_title(r'$(\pi/2)_{+x}$ - pulse')
# adjust legends
ax1.legend(prop={"size": 8}, loc='lower left')
ax3.legend(prop={"size": 8}, loc='lower right')
# save figure
if save_png:
fig.savefig('example2a.png', dpi=300)
def test_four(save_png=False):
"""Perform the fourth test demonstrating different off-resonances.
here we basically re-plot Fig. 10.28 (p. 255) from
Levitt, 2008, "spin dynamics" 2nd ed
positive ratio means the pulse frequency is "higher" as absolute value
(i.e. instead of -2000 Hz it is -2100 Hz)
because of the negative Larmor frequency of H-protons the rotation axis
dips downwards for negative ratios
"""
# initialize pulse Bloch class
bloch = pulse(T1=0.001, T2=0.0005, t_sim=0.005)
# pulse axis
bloch.Pulse.axis = '+y'
# df/omega_nut ratio
ratio = np.arange(-4., 5., 1.)
# nutation frequency for a pi/2 pulse with 5 ms is 50 Hz
omega_nut = (np.pi / 2.0) / bloch.Pulse.t_pulse / 2.0 / np.pi # [Hz]
# create output figure
fig = plt.figure(figsize=(7, 7))
for i in np.arange(len(ratio)):
# frequency offsets [Hz]
freq_offset = ratio[i] * omega_nut
# update frequency offset parameter
bloch.Pulse.fmod.v_range[1] = freq_offset
# solve
bloch.solve(m_init=bloch.zunit)
# create rot-frame plot
ax1 = fig.add_subplot(331 + i, projection='3d')
bloch.plot_magnetization3d(ax1, version='rot')
ax1.set_title(r'$\Omega_0 / \omega_{{{}}}$ = {}'.format(
'nut', ratio[i]))
# save figure
if save_png:
fig.savefig('example2d.png', dpi=300)
def test_three(save_png=False):
"""Perform the third test demonstrating different pulse axes."""
# create output figure
fig = plt.figure(figsize=(7, 7))
ax1 = fig.add_subplot(221, projection='3d')
ax2 = fig.add_subplot(222, projection='3d')
ax3 = fig.add_subplot(223, projection='3d')
ax4 = fig.add_subplot(224, projection='3d')
# initialize pulse Bloch class
bloch = pulse(T1=0.001, T2=0.0005, t_sim=0.005)
# solve #1
bloch.solve(m_init=bloch.zunit)
# create rot-frame plot
bloch.plot_magnetization3d(ax1, version='rot')
# solve #2
bloch.Pulse.axis = '+y'
bloch.solve(m_init=bloch.zunit)
# create rot-frame plot
bloch.plot_magnetization3d(ax2, version='rot')
# solve #3
bloch.Pulse.axis = '-x'
bloch.solve(m_init=bloch.zunit)
# create rot-frame plot
bloch.plot_magnetization3d(ax3, version='rot')
# solve #4
bloch.Pulse.axis = '-y'
bloch.solve(m_init=bloch.zunit)
# create rot-frame plot
bloch.plot_magnetization3d(ax4, version='rot')
# adjust titles
ax1.set_title(r'$(\pi/2)_{+x}$ - pulse')
ax2.set_title(r'$(\pi/2)_{+y}$ - pulse')
ax3.set_title(r'$(\pi/2)_{-x}$ - pulse')
ax4.set_title(r'$(\pi/2)_{-y}$ - pulse')
# save figure
if save_png:
fig.savefig('example2c.png', dpi=300)
def test(save_png=False, save_data=False):
"""Perform the lookup table calculation."""
# LOOKUP TABLE SETTINGS
# global lookup table settings (change as you like):
# B1 excitation amplitude [T]
# in the Grunewald et al., 2016 paper, there are in total 5000 points which
# would increase the calculation time to more than 10h!
pulse_num = 1000
b_pulse = np.logspace(-8, -4, pulse_num)
# pulse length [s]
t_pulse = 0.08
# initialize pulse Bloch class
bloch = pulse(t_sim=t_pulse)
# set Larmor freq.
bloch.larmor_f = -2300
# pulse type
bloch.Pulse.pulse_type = 'AHP'
bloch.Pulse.axis = '+y'
# frequency modulation
bloch.Pulse.fmod.mod_type = 'lin'
bloch.Pulse.fmod.v_range[0] = -200
bloch.Pulse.fmod.v_range[1] = 0
# current modulation
bloch.Pulse.imod.mod_type = 'const'
bloch.Pulse.imod.qual_fac = 10
# create output dictionary
mag_final = np.zeros((pulse_num, 3))
# loop over all B1 values
for i_1 in reversed(np.arange(pulse_num)):
# because the B1 values are given in [T] they need to by divided by
# B0 because the pulse factor is given in units of [B0]
bloch.Pulse.factor = b_pulse[i_1] / bloch.B0
# solve
bloch.solve(m_init=bloch.zunit, use_numba=True)
# command line output
string = '{:d} / {:d}'.format(i_1 + 1, pulse_num)
print(string)
# save final magnetization orientation in rotating frame of reference
mag_final[i_1, :] = bloch.mrot[:, -1]
# create the output figure
fig = plt.figure(figsize=(7, 5))
ax1 = fig.add_subplot(121)
ax2 = fig.add_subplot(122)
# plot data
ax1.plot(mag_final[:, 0], b_pulse * 1e6)
ax2.plot(mag_final[:, 1], b_pulse * 1e6)
# adjust axes
ax1.set_yscale('log')
ax2.set_yscale('log')
ax1.set_xlim(-1, 1)
ax2.set_xlim(-1, 1)
ax1.set_ylim(b_pulse.min() * 1e6, b_pulse.max() * 1e6)
ax2.set_ylim(b_pulse.min() * 1e6, b_pulse.max() * 1e6)
ax1.set_xlabel(r'$M_x/M_0$')
ax2.set_xlabel(r'$M_y/M_0$')
ax1.set_ylabel(r'$B_1$ [$\mu T$]')
ax1.grid(color='lightgray')
ax2.grid(color='lightgray')
# save data
if save_data:
data = {'B1': b_pulse, 'M': mag_final}
np.save('example5_lookup-data', data, allow_pickle=True)
# save figure
if save_png:
fig.savefig('example5.png', dpi=300)