def test_modify_gradient(self):
g1 = make_trapezoid(channel='x',
amplitude=5000,
duration=1e-3,
rise_time=1e-4)
g1_area = g1.area
g1_flat = g1.flat_area
g2 = make_extended_trapezoid(channel='z',
amplitudes=[4000, 5000, 5000, 6000],
times=[0, 1e-3, 6e-3, 7e-3])
# Use a random scale
sc = np.random.rand()
# Modify a trapezoidal gradient
modify_gradient(g1, scale=sc, channel='z')
np.testing.assert_equal(g1.amplitude, 5000 * sc)
np.testing.assert_equal(g1.channel, 'z')
np.testing.assert_equal(g1.area, g1_area * sc)
np.testing.assert_equal(g1.flat_area, g1_flat * sc)
# Modify an arbitrary gradient
modify_gradient(g2, scale=0, channel='y')
np.testing.assert_equal(g2.channel, 'y')
np.testing.assert_equal(np.sum(g2.waveform), 0)
np.testing.assert_equal(g2.first, 0)
np.testing.assert_equal(g2.last, 0)
def test_make_scaled_extended_trapezoid(self):
sc = np.random.rand() + 0.5
g0 = make_extended_trapezoid(channel='x',
system=Opts(),
times=[0, 1e-3, 6e-3, 7e-3],
amplitudes=[4e3, 5e3, 5e3, 6e3])
g1 = make_scaled_extended_trapezoid(
channel='x',
system=Opts(),
scale=1,
times=np.array([0, 1e-3, 6e-3, 7e-3]),
amplitudes=np.array([4e3, 5e3, 5e3, 6e3]))
g2 = make_scaled_extended_trapezoid(
channel='x',
system=Opts(),
scale=sc,
times=np.array([0, 1e-3, 6e-3, 7e-3]),
amplitudes=np.array([4e3, 5e3, 5e3, 6e3]))
g3 = make_scaled_extended_trapezoid(
channel='x',
system=Opts(),
scale=0,
times=np.array([0, 1e-3, 6e-3, 7e-3]),
amplitudes=np.array([4e3, 5e3, 5e3, 6e3]))
np.testing.assert_equal(g0.channel, g1.channel)
np.testing.assert_array_equal(g0.waveform, g1.waveform)
np.testing.assert_equal(g0.type, g1.type)
np.testing.assert_array_equal(g0.t, g1.t)
np.testing.assert_array_almost_equal(g0.waveform * sc, g2.waveform)
np.testing.assert_equal(g3.type, 'trap')
np.testing.assert_equal(g3.amplitude, 0)
np.testing.assert_equal(g3.area, 0)
GR_acq = make_trapezoid(channel='x', system=system, flat_area=k_width, flat_time=readout_time, rise_time=dG)
adc = make_adc(num_samples=Nx, duration=GR_acq.flat_time - 40e-6, delay=20e-6)
GR_spr = make_trapezoid(channel='x', system=system, area=GR_acq.area * fspR, duration=t_sp, rise_time=dG)
GR_spex = make_trapezoid(channel='x', system=system, area=GR_acq.area * (1 + fspR), duration=t_sp_ex, rise_time=dG)
AGR_spr = GR_spr.area
AGR_preph = GR_acq.area / 2 + AGR_spr
GR_preph = make_trapezoid(channel='x', system=system, area=AGR_preph, duration=t_sp_ex, rise_time=dG)
n_ex = 1
PE_order = np.arange(-Ny_pre, Ny + 1).T
phase_areas = PE_order * delta_k
GS1_times = [0, GS_ex.rise_time]
GS1_amp = [0, GS_ex.amplitude]
GS1 = make_extended_trapezoid(channel='z', times=GS1_times, amplitudes=GS1_amp)
GS2_times = [0, GS_ex.flat_time]
GS2_amp = [GS_ex.amplitude, GS_ex.amplitude]
GS2 = make_extended_trapezoid(channel='z', times=GS2_times, amplitudes=GS2_amp)
GS3_times = [0, GS_spex.rise_time, GS_spex.rise_time + GS_spex.flat_time,
GS_spex.rise_time + GS_spex.flat_time + GS_spex.fall_time]
GS3_amp = [GS_ex.amplitude, GS_spex.amplitude, GS_spex.amplitude, GS_ref.amplitude]
GS3 = make_extended_trapezoid(channel='z', times=GS3_times, amplitudes=GS3_amp)
GS4_times = [0, GS_ref.flat_time]
GS4_amp = [GS_ref.amplitude, GS_ref.amplitude]
GS4 = make_extended_trapezoid(channel='z', times=GS4_times, amplitudes=GS4_amp)
GS5_times = [0, GS_spr.rise_time, GS_spr.rise_time + GS_spr.flat_time,
def split_gradient_at(grad: np.ndarray, time_point: float, system: Opts = Opts()):
"""
Split gradient waveform `grad` into two at time point `time_point`.
Parameters
----------
grad : numpy.ndarray
Gradient waveform to be split into two gradient waveforms.
time_point : float, optional
Time point at which `grad` will be split into two gradient waveforms.
system : Opts, optional
System limits. Default is a system limits object initialised to default values.
Returns
-------
grad1, grad2 : numpy.ndarray
Gradient waveforms after splitting.
"""
grad_raster_time = system.grad_raster_time
time_index = round(time_point / grad_raster_time)
time_point = time_index * grad_raster_time
time_index += 1
if grad.type == 'trap':
ch = grad.channel
grad.delay = round(grad.delay / grad_raster_time) * grad_raster_time
grad.rise_time = round(grad.rise_time / grad_raster_time) * grad_raster_time
grad.flat_time = round(grad.flat_time / grad_raster_time) * grad_raster_time
grad.fall_time = round(grad.fall_time / grad_raster_time) * grad_raster_time
if grad.flat_time == 0:
times = [0, grad.rise_time, grad.rise_time + grad.fall_time]
amplitudes = [0, grad.amplitude, 0]
else:
times = [0, grad.rise_time, grad.rise_time + grad.flat_time,
grad.rise_time + grad.flat_time + grad.fall_time]
amplitudes = [0, grad.amplitude, grad.amplitude, 0]
if time_point < grad.delay:
times = np.insert(grad.delay + times, 0, 0)
amplitudes = [0, amplitudes]
grad.delay = 0
amplitudes = np.array(amplitudes)
times = np.array(times)
amp_tp = np.interp(x=time_point, xp=times, fp=amplitudes)
times1 = np.append(times[np.where(times < time_point)], time_point)
amplitudes1 = np.append(amplitudes[np.where(times < time_point)], amp_tp)
times2 = np.insert(times[times > time_point], 0, time_point) - time_point
amplitudes2 = np.insert(amplitudes[times > time_point], 0, amp_tp)
grad1 = make_extended_trapezoid(channel=ch, system=system, times=times1, amplitudes=amplitudes1,
skip_check=True)
grad1.delay = grad.delay
grad2 = make_extended_trapezoid(channel=ch, system=system, times=times2, amplitudes=amplitudes2,
skip_check=True)
grad2.delay = time_point
return grad1, grad2
elif grad.type == 'grad':
if time_index == 1 or time_index >= len(grad.t):
return grad
else:
grad1 = grad
grad2 = grad
grad1.last = grad.waveform[time_index]
grad2.first = grad.waveform[time_index]
grad2.delay = grad.delay + grad.t[time_index]
grad1.t = grad.t[:time_index]
grad1.waveform = grad.waveform[:time_index]
grad2.t = grad.t[time_index:]
grad2.waveform = grad.waveform[time_index:]
return grad1, grad2
else:
raise ValueError('Splitting of unsupported event.')
system=system,
area=agr_preph,
duration=t_spex,
rise_time=dG)
n_ex = math.floor(Ny / n_echo)
pe_steps = np.arange(1, n_echo * n_ex + 1) - 0.5 * n_echo * n_ex - 1
if divmod(n_echo, 2)[1] == 0:
pe_steps = np.roll(pe_steps, -round(n_ex / 2))
pe_order = pe_steps.reshape((n_ex, n_echo), order='F').T
phase_areas = pe_order * delta_k
# Split gradients and recombine into blocks
gs1_times = [0, gs_ex.rise_time]
gs1_amp = [0, gs_ex.amplitude]
gs1 = make_extended_trapezoid(channel='z', times=gs1_times, amplitudes=gs1_amp)
gs2_times = [0, gs_ex.flat_time]
gs2_amp = [gs_ex.amplitude, gs_ex.amplitude]
gs2 = make_extended_trapezoid(channel='z', times=gs2_times, amplitudes=gs2_amp)
gs3_times = [
0, gs_spex.rise_time, gs_spex.rise_time + gs_spex.flat_time,
gs_spex.rise_time + gs_spex.flat_time + gs_spex.fall_time
]
gs3_amp = [
gs_ex.amplitude, gs_spex.amplitude, gs_spex.amplitude, gs_ref.amplitude
]
gs3 = make_extended_trapezoid(channel='z', times=gs3_times, amplitudes=gs3_amp)
gs4_times = [0, gs_ref.flat_time]
def make_extended_trapezoid_area(channel: str, Gs: float, Ge: float, A: float,
system: Opts) -> Tuple[SimpleNamespace, np.array, np.array]:
"""
Makes shortest possible extended trapezoid with a given area.
Parameters
----------
channel : str
Orientation of extended trapezoidal gradient event. Must be one of 'x', 'y' or 'z'.
Gs : float
Starting non-zero gradient value.
Ge : float
Ending non-zero gradient value.
A : float
Area of extended trapezoid.
system: Opts
System limits.
Returns
-------
grad : SimpleNamespace
Extended trapezoid event.
times : numpy.ndarray
amplitude : numpy.ndarray
Raises
------
ValueError
"""
SR = system.max_slew * 0.99
Tp = 0
obj1 = lambda x: (A - __testGA(x, 0, SR, system.grad_raster_time, Gs, Ge)) ** 2
res = minimize(fun=obj1, x0=0, method='Nelder-Mead')
Gp, obj1val = *res.x, res.fun
if obj1val > 1e-3 or abs(Gp) > system.max_grad: # Search did not converge
Gp = system.max_grad * np.sign(Gp)
obj2 = lambda x: (A - __testGA(Gp, x, SR, system.grad_raster_time, Gs, Ge)) ** 2
res2 = minimize(fun=obj2, x0=0, method='Nelder-Mead')
T, obj2val = *res2.x, res2.fun
assert obj2val < 1e-2
Tp = math.ceil(T / system.grad_raster_time) * system.grad_raster_time
# Fix the ramps
Tru = math.ceil(abs(Gp - Gs) / SR / system.grad_raster_time) * system.grad_raster_time
Trd = math.ceil(abs(Gp - Ge) / SR / system.grad_raster_time) * system.grad_raster_time
obj3 = lambda x: (A - __testGA1(x, Tru, Tp, Trd, Gs, Ge)) ** 2
res = minimize(fun=obj3, x0=Gp, method='Nelder-Mead')
Gp, obj3val = *res.x, res.fun
assert obj3val < 1e-3
if Tp > 0:
times = np.cumsum([0, Tru, Tp, Trd])
amplitudes = [Gs, Gp, Gp, Ge]
else:
Tru = math.ceil(abs(Gp - Gs) / SR / system.grad_raster_time) * system.grad_raster_time
Trd = math.ceil(abs(Gp - Ge) / SR / system.grad_raster_time) * system.grad_raster_time
if Trd > 0:
if Tru > 0:
times = np.cumsum([0, Tru, Trd])
amplitudes = np.array([Gs, Gp, Ge])
else:
times = np.cumsum([0, Trd])
amplitudes = np.array([Gs, Ge])
else:
times = np.cumsum([0, Tru])
amplitudes = np.array([Gs, Ge])
grad = make_extended_trapezoid(channel=channel, system=system, times=times, amplitudes=amplitudes)
return grad, times, amplitudes
def split_gradient(grad: SimpleNamespace,
system: Opts = Opts()) -> Tuple[SimpleNamespace, SimpleNamespace, SimpleNamespace]:
"""
Split gradient waveform `grad` into two gradient waveforms at the center.
Parameters
----------
grad : array_like
Gradient waveform to be split into two gradient waveforms.
system : Opts, optional, default=Opts()
System limits.
Returns
-------
grad1, grad2 : numpy.ndarray
Split gradient waveforms.
Raises
------
ValueError
If arbitrary gradients are passed.
If non-gradient event is passed.
"""
grad_raster_time = system.grad_raster_time
total_length = calc_duration(grad)
if grad.type == 'trap':
ch = grad.channel
grad.delay = round(grad.delay / grad_raster_time) * grad_raster_time
grad.rise_time = round(grad.rise_time / grad_raster_time) * grad_raster_time
grad.flat_time = round(grad.flat_time / grad_raster_time) * grad_raster_time
grad.fall_time = round(grad.fall_time / grad_raster_time) * grad_raster_time
times = [0, grad.rise_time]
amplitudes = [0, grad.amplitude]
ramp_up = make_extended_trapezoid(channel=ch, system=system, times=times, amplitudes=amplitudes,
skip_check=True)
ramp_up.delay = grad.delay
times = [0, grad.fall_time]
amplitudes = [grad.amplitude, 0]
ramp_down = make_extended_trapezoid(channel=ch, system=system, times=times, amplitudes=amplitudes,
skip_check=True)
ramp_down.delay = total_length - grad.fall_time
ramp_down.t = ramp_down.t * grad_raster_time
flat_top = SimpleNamespace()
flat_top.type = 'grad'
flat_top.channel = ch
flat_top.delay = grad.delay + grad.rise_time
flat_top.t = np.arange(step=grad_raster_time,
stop=ramp_down.delay - grad_raster_time - grad.delay - grad.rise_time)
flat_top.waveform = grad.amplitude * np.ones(len(flat_top.t))
flat_top.first = grad.amplitude
flat_top.last = grad.amplitude
return ramp_up, flat_top, ramp_down
elif grad.type == 'grad':
raise ValueError('Splitting of arbitrary gradients is not implemented yet.')
else:
raise ValueError('Splitting of unsupported event.')
def bssfp_readout(seq, system, fov=200e-3, Nstartup=11, Ny=128):
"""
Creates a Balanced steady-state free precession (bSSFP) sequence and adds
to seq object
Parameters
----------
seq: object
Sequence object
system : Opts
System limits.
fov : float, optional
Field-of-view [m]. Default is 0.2 m.
Nstartup : float, optional
Number of start-up RF pulses. Default is 11
Ny : float, optional
Number of phase encoding lines. Default is 128.
Returns
-------
seq : SimpleNamespace
Seq object with bSSFP readout
TR : float
Repetition time
Ny : float
Final number of phase encoding lines.
"""
# Sequence Parameters
enc = 'xyz'
Nx = 128
thk = 6e-3
fa = 35 # [deg]
Nramp = Nstartup
# ADC duration (controls TR/TE)
adc_dur = 2560 / 2 # [us]
rf_dur = 490 # [us]
rf_apo = 0.5
rf_bwt = 1.5
#############################################################################
# Create slice selection pulse and gradient
rf, g_ss, __ = make_sinc_pulse(
flip_angle=fa * pi / 180,
system=system,
duration=rf_dur * 1e-6,
slice_thickness=thk,
apodization=rf_apo,
time_bw_product=rf_bwt
) # for next pyPulseq version add:, return_gz=True)
g_ss.channel = enc[2]
# Slice refocusing
g_ss_reph = make_trapezoid(channel=enc[2],
system=system,
area=-g_ss.area / 2,
duration=0.00017 * 2)
#############################################################################
rf.delay = calc_duration(g_ss) - calc_duration(rf) + rf.delay
#############################################################################
# Readout gradient and ADC
delta_k = 1 / fov
kWidth = Nx * delta_k
# Readout and ADC
g_ro = make_trapezoid(channel=enc[0],
system=system,
flat_area=kWidth,
flat_time=(adc_dur) * 1e-6)
adc = make_adc(num_samples=Nx,
duration=g_ro.flat_time,
delay=g_ro.rise_time)
# Readout rewinder
g_ro_pre = make_trapezoid(channel=enc[0],
system=system,
area=-g_ro.area / 2)
phaseAreas_tmp = np.arange(0, Ny, 1).tolist()
phaseAreas = np.dot(np.subtract(phaseAreas_tmp, Ny / 2), delta_k)
gs8_times = [
0, g_ro.fall_time, g_ro.fall_time + g_ro_pre.rise_time,
g_ro.fall_time + g_ro_pre.rise_time + g_ro_pre.flat_time,
g_ro.fall_time + g_ro_pre.rise_time + g_ro_pre.flat_time +
g_ro_pre.fall_time
]
gs8_amp = [g_ro.amplitude, 0, g_ro_pre.amplitude, g_ro_pre.amplitude, 0]
gx_2 = make_extended_trapezoid(channel=enc[0],
times=gs8_times,
amplitudes=gs8_amp)
# Calculate phase encoding gradient duration
pe_dur = calc_duration(gx_2)
gx_allExt_times = [
0, g_ro_pre.rise_time, g_ro_pre.rise_time + g_ro_pre.flat_time,
g_ro_pre.rise_time + g_ro_pre.flat_time + g_ro_pre.fall_time,
g_ro_pre.rise_time + g_ro_pre.flat_time + g_ro_pre.fall_time +
g_ro.rise_time, g_ro_pre.rise_time + g_ro_pre.flat_time +
g_ro_pre.fall_time + g_ro.rise_time + g_ro.flat_time + 1e-5,
g_ro_pre.rise_time + g_ro_pre.flat_time + g_ro_pre.fall_time +
g_ro.rise_time + g_ro.flat_time + 1e-5 + g_ro.fall_time,
g_ro_pre.rise_time + g_ro_pre.flat_time + g_ro_pre.fall_time +
g_ro.rise_time + g_ro.flat_time + 1e-5 + g_ro.fall_time +
g_ro_pre.rise_time, g_ro_pre.rise_time + g_ro_pre.flat_time +
g_ro_pre.fall_time + g_ro.rise_time + g_ro.flat_time + 1e-5 +
g_ro.fall_time + g_ro_pre.rise_time + g_ro_pre.flat_time,
g_ro_pre.rise_time + g_ro_pre.flat_time + g_ro_pre.fall_time +
g_ro.rise_time + g_ro.flat_time + 1e-5 + g_ro.fall_time +
g_ro_pre.rise_time + g_ro_pre.flat_time + g_ro_pre.fall_time
]
gx_allExt_amp = [
0, g_ro_pre.amplitude, g_ro_pre.amplitude, 0, g_ro.amplitude,
g_ro.amplitude, 0, g_ro_pre.amplitude, g_ro_pre.amplitude, 0
]
gx_all = make_extended_trapezoid(channel=enc[0],
times=gx_allExt_times,
amplitudes=gx_allExt_amp)
#############################################################################
gzrep_times = [
0, g_ss_reph.rise_time, g_ss_reph.rise_time + g_ss_reph.flat_time,
g_ss_reph.rise_time + g_ss_reph.flat_time + g_ss_reph.fall_time,
g_ss_reph.rise_time + g_ss_reph.flat_time + g_ss_reph.fall_time +
calc_duration(g_ro) + 2 * calc_duration(g_ro_pre) -
2 * calc_duration(g_ss_reph) + 1e-5, g_ss_reph.rise_time +
g_ss_reph.flat_time + g_ss_reph.fall_time + calc_duration(g_ro) +
2 * calc_duration(g_ro_pre) - 2 * calc_duration(g_ss_reph) + 1e-5 +
g_ss_reph.rise_time, g_ss_reph.rise_time + g_ss_reph.flat_time +
g_ss_reph.fall_time + calc_duration(g_ro) +
2 * calc_duration(g_ro_pre) - 2 * calc_duration(g_ss_reph) + 1e-5 +
g_ss_reph.rise_time + g_ss_reph.flat_time, g_ss_reph.rise_time +
g_ss_reph.flat_time + g_ss_reph.fall_time + calc_duration(g_ro) +
2 * calc_duration(g_ro_pre) - 2 * calc_duration(g_ss_reph) + 1e-5 +
g_ss_reph.rise_time + g_ss_reph.flat_time + g_ss_reph.fall_time
]
gzrep_amp = [
0, g_ss_reph.amplitude, g_ss_reph.amplitude, 0, 0, g_ss_reph.amplitude,
g_ss_reph.amplitude, 0
]
gzrep_all = make_extended_trapezoid(channel=enc[2],
times=gzrep_times,
amplitudes=gzrep_amp)
adc.delay = g_ro_pre.rise_time + g_ro_pre.flat_time + g_ro_pre.fall_time + g_ro.rise_time + 0.5e-5
# finish timing calculation
TR = calc_duration(g_ss) + calc_duration(gx_all)
TE = TR / 2
ni_acqu_pattern = np.arange(1, Ny + 1, 1)
Ny_aq = len(ni_acqu_pattern)
print('Acquisition window is: %3.2f ms' % (TR * Ny_aq * 1e3))
rf05 = rf
rf_waveform = rf.signal
############################################################################
# Start-up RF pulses
# (ramp-up of Nramp)
for nRamp in np.arange(1, Nramp + 1, 1):
if np.mod(nRamp, 2):
rf.phase_offset = 0
adc.phase_offset = 0
else:
rf.phase_offset = -pi
adc.phase_offset = -pi
rf05.signal = np.divide(nRamp, Nramp) * rf_waveform
gyPre_2 = make_trapezoid('y',
area=phaseAreas[0],
duration=pe_dur,
system=system)
gyPre_1 = make_trapezoid('y',
area=-phaseAreas[0],
duration=pe_dur,
system=system)
gyPre_times = [
0, gyPre_2.rise_time, gyPre_2.rise_time + gyPre_2.flat_time,
gyPre_2.rise_time + gyPre_2.flat_time + gyPre_2.fall_time,
gyPre_2.rise_time + gyPre_2.flat_time + gyPre_2.fall_time +
g_ro.flat_time + 1e-5, gyPre_2.rise_time + gyPre_2.flat_time +
gyPre_2.fall_time + g_ro.flat_time + 1e-5 + gyPre_1.rise_time,
gyPre_2.rise_time + gyPre_2.flat_time + gyPre_2.fall_time +
g_ro.flat_time + 1e-5 + gyPre_1.rise_time + gyPre_1.flat_time,
gyPre_2.rise_time + gyPre_2.flat_time + gyPre_2.fall_time +
g_ro.flat_time + 1e-5 + gyPre_1.rise_time + gyPre_1.flat_time +
gyPre_1.fall_time
]
gyPre_amp = [
0, gyPre_2.amplitude, gyPre_2.amplitude, 0, 0, gyPre_1.amplitude,
gyPre_1.amplitude, 0
]
gyPre_all = make_extended_trapezoid(channel=enc[1],
times=gyPre_times,
amplitudes=gyPre_amp)
if nRamp == 1:
seq.add_block(rf05, g_ss)
seq.add_block(gx_all, gyPre_all, gzrep_all)
else:
seq.add_block(rf05, g_ss)
seq.add_block(gx_all, gyPre_all, gzrep_all)
############################################################################
############################################################################
# Actual Readout iterate number of phase encoding steps Ny
for i in np.arange(1, Ny + 1, 1):
# *******************************
# Phase cycling
if np.mod(i + Nramp, 2):
rf.phase_offset = 0
adc.phase_offset = 0
else:
rf.phase_offset = -pi
adc.phase_offset = -pi
# *******************************
# ***************************************************************************************
# Create phase encoding gradients
if np.mod(Nramp, 2):
gyPre_2 = make_trapezoid('y',
area=phaseAreas[i - 1],
duration=pe_dur,
system=system)
if i > 1:
gyPre_1 = make_trapezoid(
'y',
area=-phaseAreas[np.mod(i + Ny - 2, Ny)],
duration=pe_dur,
system=system)
else:
gyPre_1 = make_trapezoid(
'y',
area=-phaseAreas[np.mod(i + Ny - 1, Ny)],
duration=pe_dur,
system=system)
else:
gyPre_2 = make_trapezoid('y',
area=phaseAreas[i],
duration=pe_dur,
system=system)
if i > 1:
gyPre_1 = make_trapezoid(
'y',
area=-phaseAreas[np.mod(i + Ny - 2, Ny)],
duration=pe_dur,
system=system)
else:
gyPre_1 = make_trapezoid('y',
area=phaseAreas[np.mod(
i + Ny - 2, Ny)],
duration=pe_dur,
system=system)
gyPre_times = [
0, gyPre_2.rise_time, gyPre_2.rise_time + gyPre_2.flat_time,
gyPre_2.rise_time + gyPre_2.flat_time + gyPre_2.fall_time,
gyPre_2.rise_time + gyPre_2.flat_time + gyPre_2.fall_time +
g_ro.flat_time + 1e-5, gyPre_2.rise_time + gyPre_2.flat_time +
gyPre_2.fall_time + g_ro.flat_time + 1e-5 + gyPre_2.rise_time,
gyPre_2.rise_time + gyPre_2.flat_time + gyPre_2.fall_time +
g_ro.flat_time + 1e-5 + gyPre_2.rise_time + gyPre_2.flat_time,
gyPre_2.rise_time + gyPre_2.flat_time + gyPre_2.fall_time +
g_ro.flat_time + 1e-5 + gyPre_2.rise_time + gyPre_2.flat_time +
gyPre_2.fall_time
]
gyPre_amp = [
0, gyPre_2.amplitude, gyPre_2.amplitude, 0, 0, -gyPre_2.amplitude,
-gyPre_2.amplitude, 0
]
# Verify if phase encoding gradient amplitude is not zero
try:
gyPre_all = make_extended_trapezoid(channel=enc[1],
times=gyPre_times,
amplitudes=gyPre_amp)
flag_zerogy = 0
except:
gyPre_times = [
0, pe_dur, pe_dur + g_ro.flat_time + 1e-5,
pe_dur + g_ro.flat_time + 1e-5 + pe_dur
]
gyPre_amp = [0, gyPre_2.amplitude, 0, 0]
flag_zerogy = 1
# ***************************************************************************************
# add RF and Slice selecitve gradient
seq.add_block(rf, g_ss)
# add Phase and frequency encoding gradients and ADC
if flag_zerogy == 1:
seq.add_block(gx_all, gzrep_all, adc)
else:
seq.add_block(gx_all, gyPre_all, gzrep_all, adc)
return seq, TR, Ny
def write_tse(n=256,
fov=250e-3,
thk=5e-3,
fa_exc=90,
fa_ref=180,
te=50e-3,
tr=2000e-3,
slice_locations=[0],
turbo_factor=4,
enc='xyz'):
"""
2D TSE sequence with interleaved slices and user-defined turbo factor
Inputs
------
n : integer
Matrix size (isotropic)
fov : float
Field-of-View in [meters]
thk : float
Slice thickness in [meters]
fa_exc : float
Initial excitation flip angle in [degrees]
fa_ref : float
All following flip angles for spin echo refocusing in [degrees]
te : float
Echo Time in [seconds]
tr : float
Repetition Time in [seconds]
slice_locations : array_like
Array of slice locations from isocenter in [meters]
turbo_factor : integer
Number of echoes per TR
enc : str
Spatial encoding directions; 1st - readout; 2nd - phase encoding; 3rd - slice select
Use str with any permutation of x, y, and z to obtain orthogonal slices
e.g. The default 'xyz' means axial(z) slice with readout in x and phase encoding in y
Returns
-------
seq : pypulseq.Sequence.sequence Sequence object
Output sequence object. Can be saved with seq.write('file_name.seq')
pe_order : numpy.ndarray
(turbo_factor) x (number_of_excitations) matrix of phase encoding order
This is required for phase sorting before ifft2 reconstruction.
"""
# Set system limits
ramp_time = 250e-6 # Ramp up/down time for all gradients where this is specified
system = Opts(
max_grad=32,
grad_unit='mT/m',
max_slew=130,
slew_unit='T/m/s',
rf_ringdown_time=100e-6, # changed from 30e-6
rf_dead_time=100e-6,
adc_dead_time=20e-6)
# Initialize sequence
seq = Sequence(system)
# Spatial encoding directions
ch_ro = enc[0]
ch_pe = enc[1]
ch_ss = enc[2]
# Derived parameters
Nf, Np = (n, n)
delta_k = 1 / fov
k_width = Nf * delta_k
# Number of echoes per excitation (i.e. turbo factor)
n_echo = turbo_factor
# Readout duration
readout_time = 6.4e-3 + 2 * system.adc_dead_time
# Excitation pulse duration
t_ex = 2.5e-3
t_exwd = t_ex + system.rf_ringdown_time + system.rf_dead_time
# Refocusing pulse duration
t_ref = 2e-3
t_refwd = t_ref + system.rf_ringdown_time + system.rf_dead_time
# Time gaps for spoilers
t_sp = 0.5 * (te - readout_time - t_refwd
) # time gap between pi-pulse and readout
t_spex = 0.5 * (te - t_exwd - t_refwd
) # time gap between pi/2-pulse and pi-pulse
# Spoiling factors
fsp_r = 1 # in readout direction per refocusing
fsp_s = 0.5 # in slice direction per refocusing
# 3. Calculate sequence components
## Slice-selective RF pulses & gradient
#* RF pulses with zero frequency shift are created. The frequency is then changed before adding the pulses to sequence blocks for each slice.
# 90 deg pulse (+y')
rf_ex_phase = np.pi / 2
flip_ex = fa_exc * np.pi / 180
rf_ex, g_ss, _ = make_sinc_pulse(flip_angle=flip_ex,
system=system,
duration=t_ex,
slice_thickness=thk,
apodization=0.5,
time_bw_product=4,
phase_offset=rf_ex_phase,
return_gz=True)
gs_ex = make_trapezoid(channel=ch_ss,
system=system,
amplitude=g_ss.amplitude,
flat_time=t_exwd,
rise_time=ramp_time)
# 180 deg pulse (+x')
rf_ref_phase = 0
flip_ref = fa_ref * np.pi / 180
rf_ref, gz, _ = make_sinc_pulse(flip_angle=flip_ref,
system=system,
duration=t_ref,
slice_thickness=thk,
apodization=0.5,
time_bw_product=4,
phase_offset=rf_ref_phase,
use='refocusing',
return_gz=True)
gs_ref = make_trapezoid(channel=ch_ss,
system=system,
amplitude=gs_ex.amplitude,
flat_time=t_refwd,
rise_time=ramp_time)
rf_ex, g_ss, _ = make_sinc_pulse(flip_angle=flip_ex,
system=system,
duration=t_ex,
slice_thickness=thk,
apodization=0.5,
time_bw_product=4,
phase_offset=rf_ex_phase,
return_gz=True)
## Make gradients and ADC
# gs_spex : slice direction spoiler between initial excitation and 1st 180 pulse
# gs_spr : slice direction spoiler between 180 pulses
# gr_spr : readout direction spoiler; area is (fsp_r) x (full readout area)
# SS spoiling
ags_ex = gs_ex.area / 2
gs_spr = make_trapezoid(channel=ch_ss,
system=system,
area=ags_ex * (1 + fsp_s),
duration=t_sp,
rise_time=ramp_time)
gs_spex = make_trapezoid(channel=ch_ss,
system=system,
area=ags_ex * fsp_s,
duration=t_spex,
rise_time=ramp_time)
# Readout gradient and ADC
gr_acq = make_trapezoid(channel=ch_ro,
system=system,
flat_area=k_width,
flat_time=readout_time,
rise_time=ramp_time)
# No need for risetime delay since it is set at beginning of flattime; delay is ADC deadtime
adc = make_adc(num_samples=Nf,
duration=gr_acq.flat_time - 40e-6,
delay=20e-6)
# RO spoiling
gr_spr = make_trapezoid(channel=ch_ro,
system=system,
area=gr_acq.area * fsp_r,
duration=t_sp,
rise_time=ramp_time)
# Following is not used anywhere
# gr_spex = make_trapezoid(channel=ch_ro, system=system, area=gr_acq.area * (1 + fsp_r), duration=t_spex, rise_time=ramp_time)
# Prephasing gradient in RO direction
agr_preph = gr_acq.area / 2 + gr_spr.area
gr_preph = make_trapezoid(channel=ch_ro,
system=system,
area=agr_preph,
duration=t_spex,
rise_time=ramp_time)
# Phase encoding areas
# Need to export the pe_order for reconsturuction
# Number of readouts/echoes to be produced per TR
n_ex = math.floor(Np / n_echo)
pe_steps = np.arange(1, n_echo * n_ex + 1) - 0.5 * n_echo * n_ex - 1
if divmod(n_echo, 2)[1] == 0: # If there is an even number of echoes
pe_steps = np.roll(pe_steps, -round(n_ex / 2))
pe_order = pe_steps.reshape((n_ex, n_echo), order='F').T
savemat('pe_info.mat', {'order': pe_order, 'dims': ['n_echo', 'n_ex']})
phase_areas = pe_order * delta_k
# Split gradients and recombine into blocks
# gs1 : ramp up of gs_ex
gs1_times = [0, gs_ex.rise_time]
gs1_amp = [0, gs_ex.amplitude]
gs1 = make_extended_trapezoid(channel=ch_ss,
times=gs1_times,
amplitudes=gs1_amp)
# gs2 : flat part of gs_ex
gs2_times = [0, gs_ex.flat_time]
gs2_amp = [gs_ex.amplitude, gs_ex.amplitude]
gs2 = make_extended_trapezoid(channel=ch_ss,
times=gs2_times,
amplitudes=gs2_amp)
# gs3 : Bridged slice pre-spoiler
gs3_times = [
0, gs_spex.rise_time, gs_spex.rise_time + gs_spex.flat_time,
gs_spex.rise_time + gs_spex.flat_time + gs_spex.fall_time
]
gs3_amp = [
gs_ex.amplitude, gs_spex.amplitude, gs_spex.amplitude, gs_ref.amplitude
]
gs3 = make_extended_trapezoid(channel=ch_ss,
times=gs3_times,
amplitudes=gs3_amp)
# gs4 : Flat slice selector for pi-pulse
gs4_times = [0, gs_ref.flat_time]
gs4_amp = [gs_ref.amplitude, gs_ref.amplitude]
gs4 = make_extended_trapezoid(channel=ch_ss,
times=gs4_times,
amplitudes=gs4_amp)
# gs5 : Bridged slice post-spoiler
gs5_times = [
0, gs_spr.rise_time, gs_spr.rise_time + gs_spr.flat_time,
gs_spr.rise_time + gs_spr.flat_time + gs_spr.fall_time
]
gs5_amp = [gs_ref.amplitude, gs_spr.amplitude, gs_spr.amplitude, 0]
gs5 = make_extended_trapezoid(channel=ch_ss,
times=gs5_times,
amplitudes=gs5_amp)
# gs7 : The gs3 for next pi-pulse
gs7_times = [
0, gs_spr.rise_time, gs_spr.rise_time + gs_spr.flat_time,
gs_spr.rise_time + gs_spr.flat_time + gs_spr.fall_time
]
gs7_amp = [0, gs_spr.amplitude, gs_spr.amplitude, gs_ref.amplitude]
gs7 = make_extended_trapezoid(channel=ch_ss,
times=gs7_times,
amplitudes=gs7_amp)
# gr3 : pre-readout gradient
gr3 = gr_preph
# gr5 : Readout post-spoiler
gr5_times = [
0, gr_spr.rise_time, gr_spr.rise_time + gr_spr.flat_time,
gr_spr.rise_time + gr_spr.flat_time + gr_spr.fall_time
]
gr5_amp = [0, gr_spr.amplitude, gr_spr.amplitude, gr_acq.amplitude]
gr5 = make_extended_trapezoid(channel=ch_ro,
times=gr5_times,
amplitudes=gr5_amp)
# gr6 : Flat readout gradient
gr6_times = [0, readout_time]
gr6_amp = [gr_acq.amplitude, gr_acq.amplitude]
gr6 = make_extended_trapezoid(channel=ch_ro,
times=gr6_times,
amplitudes=gr6_amp)
# gr7 : the gr3 for next repeat
gr7_times = [
0, gr_spr.rise_time, gr_spr.rise_time + gr_spr.flat_time,
gr_spr.rise_time + gr_spr.flat_time + gr_spr.fall_time
]
gr7_amp = [gr_acq.amplitude, gr_spr.amplitude, gr_spr.amplitude, 0]
gr7 = make_extended_trapezoid(channel=ch_ro,
times=gr7_times,
amplitudes=gr7_amp)
# Timing (delay) calculations
# delay_TR : delay at the end of each TSE pulse train (i.e. each TR)
t_ex = gs1.t[-1] + gs2.t[-1] + gs3.t[-1]
t_ref = gs4.t[-1] + gs5.t[-1] + gs7.t[-1] + readout_time
t_end = gs4.t[-1] + gs5.t[-1]
TE_train = t_ex + n_echo * t_ref + t_end
TR_fill = (tr - n_slices * TE_train) / n_slices
TR_fill = system.grad_raster_time * round(
TR_fill / system.grad_raster_time)
if TR_fill < 0:
TR_fill = 1e-3
print(
f'TR too short, adapted to include all slices to: {1000 * n_slices * (TE_train + TR_fill)} ms'
)
else:
print(f'TR fill: {1000 * TR_fill} ms')
delay_TR = make_delay(TR_fill)
# Add building blocks to sequence
for k_ex in range(n_ex + 1): # For each TR
for s in range(n_slices): # For each slice (multislice)
if slice_locations is None:
rf_ex.freq_offset = gs_ex.amplitude * thk * (
s - (n_slices - 1) / 2)
rf_ref.freq_offset = gs_ref.amplitude * thk * (
s - (n_slices - 1) / 2)
rf_ex.phase_offset = rf_ex_phase - 2 * np.pi * rf_ex.freq_offset * calc_rf_center(
rf_ex)[0]
rf_ref.phase_offset = rf_ref_phase - 2 * np.pi * rf_ref.freq_offset * calc_rf_center(
rf_ref)[0]
else:
rf_ex.freq_offset = gs_ex.amplitude * slice_locations[s]
rf_ref.freq_offset = gs_ref.amplitude * slice_locations[s]
rf_ex.phase_offset = rf_ex_phase - 2 * np.pi * rf_ex.freq_offset * calc_rf_center(
rf_ex)[0]
rf_ref.phase_offset = rf_ref_phase - 2 * np.pi * rf_ref.freq_offset * calc_rf_center(
rf_ref)[0]
seq.add_block(gs1)
seq.add_block(gs2, rf_ex) # make sure gs2 has channel ch_ss
seq.add_block(gs3, gr3)
for k_echo in range(n_echo): # For each echo
if k_ex > 0:
phase_area = phase_areas[k_echo, k_ex - 1]
else:
# First TR is skipped so zero phase encoding is needed
phase_area = 0.0 # 0.0 and not 0 because -phase_area should successfully result in negative zero
gp_pre = make_trapezoid(channel=ch_pe,
system=system,
area=phase_area,
duration=t_sp,
rise_time=ramp_time)
# print('gp_pre info: ', gp_pre)
gp_rew = make_trapezoid(channel=ch_pe,
system=system,
area=-phase_area,
duration=t_sp,
rise_time=ramp_time)
seq.add_block(gs4, rf_ref)
seq.add_block(gs5, gr5, gp_pre)
# Skipping first TR
if k_ex > 0:
seq.add_block(gr6, adc)
else:
seq.add_block(gr6)
seq.add_block(gs7, gr7, gp_rew)
seq.add_block(gs4)
seq.add_block(gs5)
seq.add_block(delay_TR)
# Check timing to make sure sequence runs on scanner
seq.check_timing()
return seq, pe_order
def write_irse_interleaved_split_gradient(n=256,
fov=250e-3,
thk=5e-3,
fa=90,
te=12e-3,
tr=2000e-3,
ti=150e-3,
slice_locations=[0],
enc='xyz'):
"""
2D IRSE sequence with overlapping gradient ramps and interleaved slices
Inputs
------
n : integer
Matrix size (isotropic)
fov : float
Field-of-View in [meters]
thk : float
Slice thickness in [meters]
fa : float
Flip angle in [degrees]
te : float
Echo Time in [seconds]
tr : float
Repetition Time in [seconds]
ti : float
Inversion Time in [seconds]
slice_locations : array_like
Array of slice locations from isocenter in [meters]
enc : str
Spatial encoding directions; 1st - readout; 2nd - phase encoding; 3rd - slice select
Use str with any permutation of x, y, and z to obtain orthogonal slices
e.g. The default 'xyz' means axial(z) slice with readout in x and phase encoding in y
Returns
-------
seq : pypulseq.Sequence.sequence Sequence object
Output sequence object. Can be saved with seq.write('file_name.seq')
sl_order : numpy.ndarray
Randomly generated slice order. Useful for reconstruction.
"""
# =========
# SYSTEM LIMITS
# =========
# Set the hardware limits and initialize sequence object
dG = 250e-6 # Fixed ramp time for all gradients
system = Opts(max_grad=32,
grad_unit='mT/m',
max_slew=130,
slew_unit='T/m/s',
rf_ringdown_time=100e-6,
rf_dead_time=100e-6,
adc_dead_time=10e-6)
seq = Sequence(system)
# =========
# TIME CALCULATIONS
# =========
readout_time = 6.4e-3 + 2 * system.adc_dead_time
t_ex = 2.5e-3
t_exwd = t_ex + system.rf_ringdown_time + system.rf_dead_time
t_ref = 2e-3
t_refwd = t_ref + system.rf_ringdown_time + system.rf_dead_time
t_sp = 0.5 * (te - readout_time - t_refwd)
t_spex = 0.5 * (te - t_exwd - t_refwd)
fsp_r = 1
fsp_s = 0.5
# =========
# ENCODING DIRECTIONS
# ==========
ch_ro = enc[0]
ch_pe = enc[1]
ch_ss = enc[2]
# =========
# RF AND GRADIENT SHAPES - BASED ON RESOLUTION REQUIREMENTS : kmax and Npe
# =========
# RF Phases
rf_ex_phase = np.pi / 2
rf_ref_phase = 0
# Excitation phase (90 deg)
flip_ex = 90 * np.pi / 180
rf_ex, gz, _ = make_sinc_pulse(flip_angle=flip_ex,
system=system,
duration=t_ex,
slice_thickness=thk,
apodization=0.5,
time_bw_product=4,
phase_offset=rf_ex_phase,
return_gz=True)
gs_ex = make_trapezoid(channel=ch_ss,
system=system,
amplitude=gz.amplitude,
flat_time=t_exwd,
rise_time=dG)
# Refocusing (same gradient & RF is used for initial inversion)
flip_ref = fa * np.pi / 180
rf_ref, gz, _ = make_sinc_pulse(flip_angle=flip_ref,
system=system,
duration=t_ref,
slice_thickness=thk,
apodization=0.5,
time_bw_product=4,
phase_offset=rf_ref_phase,
use='refocusing',
return_gz=True)
gs_ref = make_trapezoid(channel=ch_ss,
system=system,
amplitude=gs_ex.amplitude,
flat_time=t_refwd,
rise_time=dG)
ags_ex = gs_ex.area / 2
gs_spr = make_trapezoid(channel=ch_ss,
system=system,
area=ags_ex * (1 + fsp_s),
duration=t_sp,
rise_time=dG)
gs_spex = make_trapezoid(channel=ch_ss,
system=system,
area=ags_ex * fsp_s,
duration=t_spex,
rise_time=dG)
delta_k = 1 / fov
k_width = n * delta_k
gr_acq = make_trapezoid(channel=ch_ro,
system=system,
flat_area=k_width,
flat_time=readout_time,
rise_time=dG)
adc = make_adc(num_samples=n,
duration=gr_acq.flat_time - 40e-6,
delay=20e-6)
gr_spr = make_trapezoid(channel=ch_ro,
system=system,
area=gr_acq.area * fsp_r,
duration=t_sp,
rise_time=dG)
gr_spex = make_trapezoid(channel=ch_ro,
system=system,
area=gr_acq.area * (1 + fsp_r),
duration=t_spex,
rise_time=dG)
agr_spr = gr_spr.area
agr_preph = gr_acq.area / 2 + agr_spr
gr_preph = make_trapezoid(channel=ch_ro,
system=system,
area=agr_preph,
duration=t_spex,
rise_time=dG)
phase_areas = (np.arange(n) - n / 2) * delta_k
# Split gradients and recombine into blocks
gs1_times = [0, gs_ex.rise_time]
gs1_amp = [0, gs_ex.amplitude]
gs1 = make_extended_trapezoid(channel=ch_ss,
times=gs1_times,
amplitudes=gs1_amp)
gs2_times = [0, gs_ex.flat_time]
gs2_amp = [gs_ex.amplitude, gs_ex.amplitude]
gs2 = make_extended_trapezoid(channel=ch_ss,
times=gs2_times,
amplitudes=gs2_amp)
gs3_times = [
0, gs_spex.rise_time, gs_spex.rise_time + gs_spex.flat_time,
gs_spex.rise_time + gs_spex.flat_time + gs_spex.fall_time
]
gs3_amp = [
gs_ex.amplitude, gs_spex.amplitude, gs_spex.amplitude, gs_ref.amplitude
]
gs3 = make_extended_trapezoid(channel=ch_ss,
times=gs3_times,
amplitudes=gs3_amp)
gs4_times = [0, gs_ref.flat_time]
gs4_amp = [gs_ref.amplitude, gs_ref.amplitude]
gs4 = make_extended_trapezoid(channel=ch_ss,
times=gs4_times,
amplitudes=gs4_amp)
gs5_times = [
0, gs_spr.rise_time, gs_spr.rise_time + gs_spr.flat_time,
gs_spr.rise_time + gs_spr.flat_time + gs_spr.fall_time
]
gs5_amp = [gs_ref.amplitude, gs_spr.amplitude, gs_spr.amplitude, 0]
gs5 = make_extended_trapezoid(channel=ch_ss,
times=gs5_times,
amplitudes=gs5_amp)
gs7_times = [
0, gs_spr.rise_time, gs_spr.rise_time + gs_spr.flat_time,
gs_spr.rise_time + gs_spr.flat_time + gs_spr.fall_time
]
gs7_amp = [0, gs_spr.amplitude, gs_spr.amplitude, gs_ref.amplitude]
gs7 = make_extended_trapezoid(channel=ch_ss,
times=gs7_times,
amplitudes=gs7_amp)
gr3 = gr_preph
gr5_times = [
0, gr_spr.rise_time, gr_spr.rise_time + gr_spr.flat_time,
gr_spr.rise_time + gr_spr.flat_time + gr_spr.fall_time
]
gr5_amp = [0, gr_spr.amplitude, gr_spr.amplitude, gr_acq.amplitude]
gr5 = make_extended_trapezoid(channel=ch_ro,
times=gr5_times,
amplitudes=gr5_amp)
gr6_times = [0, readout_time]
gr6_amp = [gr_acq.amplitude, gr_acq.amplitude]
gr6 = make_extended_trapezoid(channel=ch_ro,
times=gr6_times,
amplitudes=gr6_amp)
gr7_times = [
0, gr_spr.rise_time, gr_spr.rise_time + gr_spr.flat_time,
gr_spr.rise_time + gr_spr.flat_time + gr_spr.fall_time
]
gr7_amp = [gr_acq.amplitude, gr_spr.amplitude, gr_spr.amplitude, 0]
gr7 = make_extended_trapezoid(channel=ch_ro,
times=gr7_times,
amplitudes=gr7_amp)
t_ex = gs1.t[-1] + gs2.t[-1] + gs3.t[-1]
t_ref = gs4.t[-1] + gs5.t[-1] + gs7.t[-1] + readout_time
t_end = gs4.t[-1] + gs5.t[-1]
# Calculate maximum number of slices that can fit in one TR
# Without spoilers on each side
TE_prime = 0.5 * calc_duration(gs_ref) + ti + te + 0.5 * readout_time + np.max(
[calc_duration(gs7), calc_duration(gr7)]) + \
calc_duration(gs4) + calc_duration(gs5)
ns_per_TR = np.floor(tr / TE_prime)
print('Number of slices that can be accommodated = ' + str(ns_per_TR))
# Lengthen TR to accommodate slices if needed, and display message
n_slices = len(slice_locations)
if (ns_per_TR < n_slices):
print(
f'TR too short, adapted to include all slices to: {n_slices * TE_prime + 50e-6} s'
)
TR = round(n_slices * TE_prime + 50e-6, ndigits=5)
print('New TR = ' + str(TR))
ns_per_TR = np.floor(TR / TE_prime)
if (n_slices < ns_per_TR):
ns_per_TR = n_slices
# randperm so that adjacent slices do not get excited one after the other
sl_order = np.random.permutation(n_slices)
print('Number of slices acquired per TR = ' + str(ns_per_TR))
# Delays
TI_fill = ti - (0.5 * calc_duration(gs_ref) + calc_duration(gs1) +
0.5 * calc_duration(gs2))
delay_TI = make_delay(TI_fill)
TR_fill = tr - ns_per_TR * TE_prime
delay_TR = make_delay(TR_fill)
for k_ex in range(n):
phase_area = phase_areas[k_ex]
gp_pre = make_trapezoid(channel=ch_pe,
system=system,
area=phase_area,
duration=t_sp,
rise_time=dG)
gp_rew = make_trapezoid(channel=ch_pe,
system=system,
area=-phase_area,
duration=t_sp,
rise_time=dG)
s_in_TR = 0
for s in range(len(sl_order)):
# rf_ex.freq_offset = gs_ex.amplitude * slice_thickness * (sl_order[s] - (n_slices - 1) / 2)
# rf_ref.freq_offset = gs_ref.amplitude * slice_thickness * (sl_order[s] - (n_slices - 1) / 2)
rf_ex.freq_offset = gs_ex.amplitude * slice_locations[sl_order[s]]
rf_ref.freq_offset = gs_ref.amplitude * slice_locations[
sl_order[s]]
rf_ex.phase_offset = rf_ex_phase - 2 * np.pi * rf_ex.freq_offset * calc_rf_center(
rf_ex)[0]
rf_ref.phase_offset = rf_ref_phase - 2 * np.pi * rf_ref.freq_offset * calc_rf_center(
rf_ref)[0]
# Inversion using refocusing pulse
seq.add_block(gs_ref, rf_ref)
seq.add_block(delay_TI)
# SE portion
seq.add_block(gs1)
seq.add_block(gs2, rf_ex)
seq.add_block(gs3, gr3)
seq.add_block(gs4, rf_ref)
seq.add_block(gs5, gr5, gp_pre)
seq.add_block(gr6, adc)
seq.add_block(gs7, gr7, gp_rew)
seq.add_block(gs4)
seq.add_block(gs5)
s_in_TR += 1
if (s_in_TR == ns_per_TR):
seq.add_block(delay_TR)
s_in_TR = 0
# Check timing to make sure sequence runs on scanner
seq.check_timing()
return seq, sl_order
def split_gradient_at(
grad: SimpleNamespace, time_point: float, system: Opts = Opts()
) -> Union[SimpleNamespace, Tuple[SimpleNamespace, SimpleNamespace]]:
"""
Split gradient waveform `grad` into two at time point `time_point`.
Parameters
----------
grad : SimpleNamespace
Gradient event to be split into two gradient events.
time_point : float
Time point at which `grad` will be split into two gradient waveforms.
system : Opts, optional, default=Opts()
System limits.
Returns
-------
grad1, grad2 : SimpleNamespace
Gradient waveforms after splitting.
Raises
------
ValueError
If non-gradient event is passed.
"""
grad_raster_time = system.grad_raster_time
time_index = round(time_point / grad_raster_time)
time_point = round(time_index * grad_raster_time,
6) # Work around floating-point arithmetic limitation
time_index += 1
if grad.type == 'trap':
ch = grad.channel
grad.delay = round(grad.delay / grad_raster_time) * grad_raster_time
grad.rise_time = round(
grad.rise_time / grad_raster_time) * grad_raster_time
grad.flat_time = round(
grad.flat_time / grad_raster_time) * grad_raster_time
grad.fall_time = round(
grad.fall_time / grad_raster_time) * grad_raster_time
if grad.flat_time == 0:
times = [0, grad.rise_time, grad.rise_time + grad.fall_time]
amplitudes = [0, grad.amplitude, 0]
else:
times = [
0, grad.rise_time, grad.rise_time + grad.flat_time,
grad.rise_time + grad.flat_time + grad.fall_time
]
amplitudes = [0, grad.amplitude, grad.amplitude, 0]
if time_point < grad.delay:
times = np.insert(grad.delay + times, 0, 0)
amplitudes = [0, amplitudes]
grad.delay = 0
amplitudes = np.array(amplitudes)
times = np.array(times).round(
6) # Work around floating-point arithmetic limitation
amp_tp = np.interp(x=time_point, xp=times, fp=amplitudes)
times1 = np.append(times[np.where(times < time_point)], time_point)
amplitudes1 = np.append(amplitudes[np.where(times < time_point)],
amp_tp)
times2 = np.insert(times[times > time_point], 0,
time_point) - time_point
amplitudes2 = np.insert(amplitudes[times > time_point], 0, amp_tp)
grad1 = make_extended_trapezoid(channel=ch,
system=system,
times=times1,
amplitudes=amplitudes1,
skip_check=True)
grad1.delay = grad.delay
grad2 = make_extended_trapezoid(channel=ch,
system=system,
times=times2,
amplitudes=amplitudes2,
skip_check=True)
grad2.delay = time_point
return grad1, grad2
elif grad.type == 'grad':
if time_index == 1 or time_index >= len(grad.t):
return grad
else:
grad1 = grad
grad2 = grad
grad1.last = 0.5 * (grad.waveform[time_index - 1] +
grad.waveform[time_index])
grad2.first = grad1.last
grad2.delay = grad.delay + grad.t[time_index]
grad1.t = grad.t[:time_index]
grad1.waveform = grad.waveform[:time_index]
grad2.t = grad.t[time_index:] - time_point
grad2.waveform = grad.waveform[time_index:]
return grad1, grad2
else:
raise ValueError('Splitting of unsupported event.')