time_step = 0.01
pulse_length = 500
mode = 'free'
Gx = np.ones(pulse_length)
Gy = np.ones(pulse_length)
readout = np.zeros(pulse_length, dtype=bool)
for i in range(len(readout)):
if not i % 2:
readout[i] = True
pulse = Pulse(mode=mode, Gx=Gx, Gy=Gy, readout=readout, time_step=time_step)
# Initialize simulation
num_ems = 1
main_field = 10.0
pulse_sequence = [pulse]
sim = Sim(num_ems, main_field, pulse_sequence)
# Run simulation and collect MR signal
mr_signals = sim.run_sim()
mr_signal = mr_signals[0]
# Plot MR signal (FID of one em)
t_readout = []
for step_no in range(pulse_length):
if readout[step_no]:
t_readout.append(time_step * step_no)
plt.plot(t_readout, mr_signal.real, '-o')
plt.xlabel('Time (s)')
plt.ylabel('MR signal (a.u.)')
plt.title('FID of a single em')
plt.savefig('fid_one_em.pdf')
if run_simulation: # Runs simulation with and without refocus
pulse_sequences = [[pulse_tip], [pulse_tip, pulse_refocus]]
num_sims = len(pulse_sequences)
m = np.empty([num_sims, num_ems], dtype=complex)
for sim_no, pulse_sequence in zip(range(num_sims), pulse_sequences):
# Initialize simulation
# Long relaxation times
def T1_map(position):
return 100.0
def T2_map(position):
return 100.0
sim = Sim(em_magnetizations, em_positions, em_velocities,
em_gyromagnetic_ratio, em_shielding_constants,
em_equilibrium_magnetization, T1_map, T2_map, main_field,
pulse_sequence)
# Run simulation
ems, mrsignals = sim.run_sim()
# Extract tranverse magnetization as a function of position
m[sim_no, :] = np.empty(num_ems, dtype=complex)
for em_no in range(num_ems):
em = ems[em_no]
m[sim_no, em_no] = em.mu[0] + em.mu[1] * 1j
# Plot and calculate theoretical values
phase_theory = np.angle(m[0, :]) - em_gyromagnetic_ratio * (
main_field - Gz_tip_amp * z_positions) * pulse_refocus_length * delta_t
phase_theory = np.mod(phase_theory, 2 * np.pi)
# Create pulse sequence
pulse_sequence = generate_DWI_sequence(main_field,Gz_amplitude,slice_width,gyromagnetic_ratio,fe_sample_radius,pe_sample_radius,kx_max,ky_max,kmove_time,kread_time,repetition_time,pulse_delta_t,read_all,diffusion_gradients,diffusion_gradient_time,diffusion_time)
if run_sim:
# Run simulation
def T1_map(position): return T1_max
def T2_map(position): return T2_max
def D_map(position):
if position[0]>0:
return np.array([5e-6,5e-6,0.0])
else:
return np.array([0.0,0.0,0.0])
print('beginning sim with ' + str(num_ems) + ' ems')
sim = Sim(em_magnetizations,em_positions,em_gyromagnetic_ratio,em_shielding_constants,em_equilibrium_magnetization,em_delta_t,T1_map,T2_map,main_field,pulse_sequence,D_map)
ems,mrs = sim.run_sim()
num_pe_samples = int(2*pe_sample_radius+1)
num_fe_samples = int(2*fe_sample_radius+1)
S = np.empty([num_pe_samples,num_fe_samples],dtype=complex)
for line_no in range(num_pe_samples):
S[line_no,:] = mrs[line_no]
img,x,y = reconstruct_from_2DFT(S,kx_max,ky_max)
np.savetxt('em-positions_'+fig_params+'.csv',em_positions,delimiter=',')
np.savetxt('img_'+fig_params+'.csv',img,delimiter=',')
np.savetxt('x_'+fig_params+'.csv',x,delimiter=',')
np.savetxt('y_'+fig_params+'.csv',y,delimiter=',')
if plot_sim_results:
em_positions_0 = 1e-2*np.array([[0.5,0.5,0.0],
[0.5,0.0,0.0],