def test_maxGrad(self):
maxGrad = 50
gtrap = trapwave2(area=1,
mxg=maxGrad,
mxs=system['max_slew'],
rasterTime=system['grad_raster_time'])
self.assertLess(gtrap.max(), maxGrad)
def test_maxSlew(self):
maxSlew = 150
gtrap = trapwave2(area=1,
mxg=system['max_grad'],
mxs=maxSlew,
rasterTime=system['grad_raster_time'])
slew = np.diff(gtrap) / system['grad_raster_time'] * 1e-3
self.assertLess(slew.max(), maxSlew)
def test_area(self):
area_in = 10
gtrap = trapwave2(area=area_in,
mxg=system['max_grad'],
mxs=system['max_slew'],
rasterTime=system['grad_raster_time'])
base1 = gtrap.shape[1]
base2 = len(np.where(gtrap == gtrap.max())[1])
height = gtrap.max()
area_out = (base1 + base2
) * system['grad_raster_time'] / 2 * height # Hz/m*sec
self.assertEqual(area_in, round(area_out))
def make_balanced(g, max_grad, max_slew, system):
'''
Adds a trapezoid at end of the gradient waveform to make the total area zero.
Parameters
----------
g : numpy.ndarray
Gradient waveform in Hz/m
system : dict
System limits and specifications
Returns
-------
gbal : numpy.ndarray
Balanced gradient in Hz/m
'''
if len(g.shape) == 1:
g = g.reshape(g.shape[0], 1)
elif g.shape[1] > 1 and g.shape[0] == 1:
g = g.reshape(-1, 1)
elif g.shape[0] > 1 and g.shape[1] > 1:
raise ValueError('Only one dimensional waveforms are allowed')
if all([v == 0 for v in g]): #g.all() == 0:
raise ValueError('The gradient has to have nonzero elements')
if 'gamma' not in system or 'grad_raster_time' not in system:
raise ValueError('Gamma and gradient raster time have to be specified')
max_slew_Hzms = max_slew * system['gamma'] # Hz/m/s
# dt seconds
dt = system['grad_raster_time']
# ramp to zero
dg = -np.sign(g[-1]) * max_slew_Hzms * 0.995 * dt # Hz/sample
ramp = np.arange(g[-1], 0 + dg, dg)
g = np.concatenate((g, ramp[:-1].reshape(len(ramp) - 1, 1)))
# change of units
g = g * 1e3 / system['gamma'] # mT/m
# add balancing trapezoid
area = np.sum(g) * dt # mT * s / m
gblip = trapwave2(np.abs(area), max_grad * 0.995, max_slew * 0.995,
dt) * 1e-3 * system['gamma'] # Hz/m
g = g * 1e-3 * system['gamma'] # Hz/m
gbal = np.concatenate((g, -np.sign(area) * gblip.T))
return gbal
def make_crusher(ncycles, opslthick, gzarea, max_grad, max_slew, sys_lims):
'''
Creates a crusher gradient within the system limits given the number of phase cycles across a thickness
Parameters
----------
ncycles : int
Number of cycles of phase across slice/slab
opslthick : float
Slice/slab thickness in meters
gzarea : int
Half-area of slice-select gradient in mT/m*sec. Default: 0.
max_grad : int
Max gradient in mT/m
max_slew : float
Max slew rate in T/m/s
sys_lims : dict
System limits
Returns
-------
gcrush : numpy.ndarray
Crusher gradient waveform in Hz/m
'''
if ncycles <= 0:
raise ValueError(
'Number of phase cycles cannot be equal or smaller than 0.')
if opslthick == 0:
raise ValueError('Thickness cannot be 0')
if 'gamma' not in sys_lims:
raise ValueError('Please specify gamma in the system limits')
gamma = sys_lims['gamma'] # Hz/T
area = ncycles / (gamma * opslthick) * 1e3 # mT/m*s
dt = sys_lims['grad_raster_time'] # seconds
gcrush = trapwave2(area - gzarea, max_grad, max_slew,
dt) * 1e-3 * gamma # Hz/m
gcrush = makeSystemlength(gcrush.reshape(-1, 1),
sys_lims['grad_raster_time'])
gcrush[np.where(gcrush == -0.)] = 0
return gcrush
def test_rasterTime_val(self):
with self.assertRaises(ValueError):
trapwave2(area=1,
mxg=system['max_grad'],
mxs=system['max_slew'],
rasterTime=0)
def test_area_val(self):
with self.assertRaises(ValueError):
trapwave2(area=0,
mxg=system['max_grad'],
mxs=system['max_slew'],
rasterTime=system['grad_raster_time'])
def make_slr_rf(flip_angle: float, slice_thickness: float,
time_bw_product: float, duration: float, ncycles: int,
system: dict):
'''
Creates a slice-selective SLR pulse with gradient crusher (or balancing blip) before it.
Parameters
----------
flip_angle : float
Flip angle in degrees.
slice_thickness : float
Slab thickness in millimeters (mm) of accompanying slice select trapezoidal event. The slice thickness determines the area of the
slice select event.
time_bw_product : float
Time-bandwidth product of SLR pulse
duration : float
Duration in seconds (s).
ncycles : int
number of cycles of phase (spoiler) (0 = balanced)
system : dict
System limits. Default is a system limits object initialised to default values.
Returns
-------
rf : SimpleNamespace
Radio-frequency slr pulse event.
gz : SimpleNamespace, optional
Accompanying slice select trapezoidal gradient event. Returned only if `slice_thickness` is not zero.
'''
if flip_angle < 0 or flip_angle > 360:
raise ValueError('Flip angle in degrees has to be within [0, 360]')
if slice_thickness <= 0:
raise ValueError('Slice thickness has to be larger than 0')
if time_bw_product < 1.5:
raise ValueError('Time bandwidth product has to be at least 1.5')
if duration <= 0:
raise ValueError('Pulse duration cannot be 0 or negative')
# TODO: Remove commented lines
# TODO: Remove frequency offset from input
pulse_type = 'ex' # Only supported type by now
# make RF waveform
dt = system['rf_raster_time'] # s
res = round(duration / dt) # Number of (10us) samples in RF waveform
duration = res * dt
nrf = 200 # number of samples for SLR design
rf = JP_dzrf(nrf, time_bw_product, pulse_type)
rf = np.real(rf)
rf = resample_poly(rf, res, nrf)
flip = pi / 2
rf = flip * rf / np.sum(rf, axis=0)
rf = rf / dt / 2 / pi # Hz
rf = np.concatenate((rf.reshape(len(rf), 1), np.zeros((len(rf) % 2, 1))),
axis=0) # Make duration even
npix = len(rf)
iref, _ = np.where(rf == np.max(rf)) # Center of RF pulse
# make slice-select gradient waveform
bw = time_bw_product / duration # Hz
gplateau = bw / (system['gamma'] * slice_thickness) * 1e3 # mT / m
if gplateau > system['max_grad']:
raise ValueError('Gradient exceeds the maximum gradient')
# slice-select trapezoid
gss = gplateau * np.ones((1, npix))
s = system['max_slew'] * 1e3 * dt * 0.999 # mT/m
gss_ramp = np.arange(s, gplateau, s)
if np.all(gss_ramp == 0):
gss_ramp = np.asarray([[0]])
if gplateau - gss_ramp[-1] > 0:
gss_ramp = np.concatenate(
(gss_ramp.reshape(1, len(gss_ramp)),
((gplateau + gss_ramp[-1]) / 2).reshape(1, 1)),
axis=1)
gss_trap = np.concatenate((gss_ramp, gss, np.fliplr(gss_ramp)), axis=1)
iref = iref[0] + gss_ramp.shape[1]
# slice-select rephaser trapezoid
arearep = np.sum(gss_trap[:, iref:]) * dt # mT / m * s
gzrep = -trapwave2(arearep, system['max_grad'], system['max_slew'], dt)
# slice-select prephaser trapezoid
areaprep = np.sum(gss_trap[:, :iref]) * dt # mT / m * s
gzprep = -trapwave2(areaprep, system['max_grad'], system['max_slew'], dt)
#irep = (np.concatenate((gzprep, gss_trap), axis=1)).shape[1]
#iref = iref + gzprep.shape[1]
gex = np.concatenate(
(gzprep, gss_trap, gzrep), axis=1) * 1e-3 * system['gamma'] # Hz/m
#idep = gzprep.shape[1]
# make gss and rf the same length
rf = np.vstack((0 * gzprep.reshape(-1, 1), np.zeros(
(gss_ramp.shape[1], 1)), rf,
np.zeros((gss_ramp.shape[1] + gzrep.shape[1], 1))))
# rf = np.concatenate((0 * gzprep, np.zeros((1, gss_ramp.shape[1])), rf.T, np.zeros((1, gss_ramp.shape[1] + gzrep.shape[1]))), axis=1)
# ensure that duration is on a 40 us (4 sample) boundary
rf = makeSystemlength(rf, system['grad_raster_time'])
gex = makeSystemlength(gex, system['grad_raster_time'])
# make sure waveforms start and end at zero
rf = np.vstack((0, rf, 0))
# rf = np.concatenate((np.asarray([[0]]), rf, np.asarray([[0]])), axis=1)
gex = np.vstack((0, gex.reshape(-1, 1), 0))
# gex = np.concatenate((np.asarray([[0]]), gex, np.asarray([[0]])), axis=1)
rf = rf / 90 * flip_angle
# slice offset frequency
# gfreq = system['gamma']*gplateau*freq_offset
#remove -0 values
# rf[np.where(rf == -0.)] = 0
# gex[np.where(gex == -0.)] = 0
return rf, gex
sys_acq['max_slew'] / sqrt(2), sys_gen)
gy_ro_wav = make_balanced(g_ro_wav.imag, sys_acq['max_grad'],
sys_acq['max_slew'] / sqrt(2), sys_gen)
n = max(len(gx_ro_wav), len(gy_ro_wav))
gx_ro_wav = np.concatenate((gx_ro_wav, np.zeros((n - len(gx_ro_wav), 1))))
gy_ro_wav = np.concatenate((gy_ro_wav, np.zeros((n - len(gy_ro_wav), 1))))
# make it spiral in
gx_ro_wav = np.flipud(gx_ro_wav)
gy_ro_wav = np.flipud(gy_ro_wav)
# add partition (kz) enconding trapezoids
gzamp = (1 / sys_gen['grad_raster_time']) / (system.gamma *
acq_params['fovz']) * 1e3 # mT/m
zarea = gzamp * acq_params['nz'] * sys_gen['grad_raster_time'] # mT/m*s
gpe = -trapwave2(zarea / 2, sys_acq['max_grad'], sys_acq['max_slew'],
sys_gen['grad_raster_time']) * 1e-3 * system.gamma # Hz/m
gx_ro_wav_orig = makeSystemlength(
np.vstack((0 * gpe.reshape(-1, 1), np.zeros(
(2, 1)), gx_ro_wav, 0 * gpe.reshape(-1, 1))),
sys_gen['grad_raster_time']) #gx_ro_wav.T
gy_ro_wav_orig = makeSystemlength(
np.vstack((0 * gpe.reshape(-1, 1), np.zeros(
(2, 1)), gy_ro_wav, 0 * gpe.reshape(-1, 1))),
sys_gen['grad_raster_time']) #gy_ro_wav.T
gz_ro_wav_orig = makeSystemlength(
np.vstack((gpe.reshape(-1, 1), np.zeros(
(2, 1)), 0 * gx_ro_wav, -gpe.reshape(-1, 1))),
sys_gen['grad_raster_time'])
gx_ro_wav_orig = grad_interpolate(gx_ro_wav_orig)
gy_ro_wav_orig = grad_interpolate(gy_ro_wav_orig)