def calc_observable(pb=0.0, kex=0.0, dw_n=0.0, ppm_to_rads_n_1=1.0,
ppm_to_rads_n_2=1.0):
"""Returns: float"""
dw_n_1 = dw_n * ppm_to_rads_n_1
dw_n_2 = dw_n * ppm_to_rads_n_2
shift_sq_1 = correct_chemical_shift(pb, kex, dw_n_1)[0] / ppm_to_rads_n_1
shift_sq_2 = correct_chemical_shift(pb, kex, dw_n_2)[0] / ppm_to_rads_n_2
return (shift_sq_1 - shift_sq_2) * 1e3
def calc_observable(pb=0.0, kex=0.0, dw_h=0.0, dw_n=0.0, ppm_to_rads_h=1.0,
ppm_to_rads_n=1.0):
""" Returns: float """
dw_h *= ppm_to_rads_h
dw_n *= ppm_to_rads_n
shift_sq = correct_chemical_shift(pb, kex, dw_n)[0]
shift_mq = 0.5 * (correct_chemical_shift(pb, kex, dw_n + dw_h)[0] +
correct_chemical_shift(pb, kex, dw_n - dw_h)[0])
return (shift_sq - shift_mq) / ppm_to_rads_n * 1e3
def calc_observable(pb=0.0,
kex=0.0,
dw_n=0.0,
ppm_to_rads_n_1=1.0,
ppm_to_rads_n_2=1.0):
"""Returns: float"""
dw_n_1 = dw_n * ppm_to_rads_n_1
dw_n_2 = dw_n * ppm_to_rads_n_2
shift_sq_1 = correct_chemical_shift(pb, kex, dw_n_1)[0] / ppm_to_rads_n_1
shift_sq_2 = correct_chemical_shift(pb, kex, dw_n_2)[0] / ppm_to_rads_n_2
return (shift_sq_1 - shift_sq_2) * 1e3
def _calc_observable(pb=0.0, kex=0.0, dw=0.0, r_cz=1.5, r_cxy=0.0, dr_cxy=0.0, cs=0.0):
"""
Calculate the intensity in presence of exchange after a CEST block assuming
initial intensity of 1.0.
Parameters
----------
pb : float
Fractional population of state B,
0.0 for 0%, 1.0 for 100%
kex : float
Exchange rate between state A and B in /s.
dw : float
Chemical shift difference between states A and B in rad/s.
r_cz : float
Longitudinal relaxation rate of state {a,b} in /s.
r_cxy : float
Transverse relaxation rate of state a in /s.
dr_cxy : float
Transverse relaxation rate difference between states a and b in /s.
cs : float
Resonance position in rad/s.
Returns
-------
out : float
Intensity after the CEST block
"""
if abs(b1_offset) >= 10000.0:
return 1.0 - pb
else:
dw *= ppm_to_rads
mag_eq = compute_cz_eq(pb)
exchange_induced_shift, _ = correct_chemical_shift(pb=pb, kex=kex, dw=dw,
r_ixy=r_cxy, dr_ixy=dr_cxy)
wg = (cs - carrier) * ppm_to_rads - exchange_induced_shift
liouvillians = base_liouvillians + compute_free_liouvillian(pb=pb, kex=kex, dw=dw,
r_cxy=r_cxy, dr_cxy=dr_cxy,
r_cz=r_cz, cs_offset=wg)
propagator = sc.zeros_like(liouvillians[0])
for liouvillian, weight in zip(liouvillians, weights):
propagator += weight * expm(liouvillian * time_t1)
propagator /= sum(weights)
magz_a, _ = get_cz(sc.dot(propagator, mag_eq))
return magz_a
def _calc_observable(pb=0.0, kex=0.0, dw=0.0, r_nz=1.5, r_nxy=0.0,
dr_nxy=0.0, cs=0.0):
"""
Calculate the intensity in presence of exchange after a CEST block assuming
initial intensity of 1.0.
Parameters
----------
pb : float
Fractional population of state B,
0.0 for 0%, 1.0 for 100%
kex : float
Exchange rate between state A and B in /s.
dw : float
Chemical shift difference between states A and B in rad/s.
r_nz : float
Longitudinal relaxation rate of state {a,b} in /s.
r_nxy : float
Transverse relaxation rate of state a in /s.
dr_nxy : float
Transverse relaxation rate difference between states a and b in /s.
cs : float
Resonance position in rad/s.
Returns
-------
out : float
Intensity after the CEST block
"""
if abs(b1_offset) >= 10000.0:
magz_a = 1.0 - pb
else:
dw *= ppm_to_rads
exchange_induced_shift, _ = correct_chemical_shift(
pb=pb,
kex=kex,
dw=dw,
r_ixy=r_nxy,
dr_ixy=dr_nxy
)
wg = (
(cs - carrier) * ppm_to_rads -
exchange_induced_shift -
w1_offset
)
magz_eq = sc.asarray([[1 - pb], [pb]])
magz_a = 0.0
for j, weight in multiplet:
liouvillian = compute_liouvillian(
pb=pb,
kex=kex,
dw=dw,
r_nxy=r_nxy,
dr_nxy=dr_nxy,
r_nz=r_nz,
cs_offset=(wg + j),
w1=w1
)
s, vr = eig(liouvillian)
vri = inv(vr)
sl1 = [2, 5]
sl2 = [i for i, w in enumerate(s.imag) if abs(w) < 1.0e-6]
sl3 = [2]
vri = vri[sc.ix_(sl2, sl1)].real
t = diag(exp(s[sl2].real * time_t1))
vr = vr[sc.ix_(sl3, sl2)].real
magz_a += (
weight *
dot(dot(dot(vr, t), vri), magz_eq)[0, 0]
)
return magz_a
def _calc_observable(pb=0.0,
kex=0.0,
dw_h=0.0,
dw_n=0.0,
r_nxy=5.0,
dr_nxy=None,
r_nz=1.5,
r_2hznz=None,
r_2hxynxy=0.0,
r_hxy=10.0,
r_hz=1.0,
etaxy=0.0,
etaz=0.0,
j_hn=JHN,
cs_n=0.0,
cs_h=0.0):
"""
Calculate the intensity in presence of exchange during a cpmg-type pulse train.
Keyword arguments:
I0 -- Initial intensity,
0.0 (default),
pb -- population of state B,
0.0 for 0% (default),
1.0 for 100%
kex -- exchange rate between state A and B in /s,
0.0 (default)
dw -- chemical shift difference between states A and B in /s,
0.0 /s (default)
r_Nxy -- transverse relaxation rate in /s,
5.0 (default)
dr_Nxy -- transverse relaxation rate difference in /s between states a and b,
0.0 (default)
r_Nz -- longitudinal relaxation rate in /s,
1.5 (default)
cs_offset -- chemical shift from the carrier in rad/s,
0.0 (default)
B1_offset -- frequency offset of the applied B1 field in Hz,
0.0 Hz (default)
B1_frq -- strength of the applied B1 field in Hz,
0.0 Hz (default)
B1_inh -- B1 field inhomogeneity in Hz,
0.0 Hz (default)
time_t1 -- time of the CW block,
0 ms (default)
Returns: float
"""
wg_h = (cs_h - carrier_h) * ppm_to_rads_h
wg_n = (cs_n - carrier) * ppm_to_rads
dw_h_rads = dw_h * ppm_to_rads_h
dw_n_rads = dw_n * ppm_to_rads
mag_eq = set_nz(pb)
if abs(b1_offset) > 9999.0:
mag = mag_eq
else:
exchange_induced_shift_n, _ = correct_chemical_shift(pb=pb,
kex=kex,
dw=dw_n_rads,
r_ixy=r_nxy,
dr_ixy=dr_nxy)
offset_n = wg_n - exchange_induced_shift_n - b1_offset * 2.0 * pi
liouvillian = compute_liouvillian_free_precession(
pb=pb,
kex=kex,
dw_h=dw_h_rads,
dw_n=dw_n_rads,
r_nxy=r_nxy,
dr_nxy=dr_nxy,
r_nz=r_nz,
r_2hznz=r_2hznz,
r_2hxynxy=r_2hxynxy,
r_hxy=r_hxy,
r_hz=r_hz,
etaxy=etaxy,
etaz=etaz,
cs_offset_h=wg_h,
cs_offset_n=offset_n,
j_hn=j_hn)
b1_frq_n_list = linspace(-2.0, 2.0, b1_inh_res) * b1_inh + b1_frq
b1_frq_n_scales = norm.pdf(b1_frq_n_list, b1_frq, b1_inh)
b1_frq_n_scales /= b1_frq_n_scales.sum()
mag = sum(
scale * make_pulse_nh(liouvillian=liouvillian,
w1_h=TWO_PI * b1_frq_h,
phase_h=0.0,
w1_n=TWO_PI * b1_frq_n,
phase_n=0.0,
pw=time_t1).dot(mag_eq)
for b1_frq_n, scale in zip(b1_frq_n_list, b1_frq_n_scales))
return get_nz(mag)[0]
def _calc_observable(pb=0.0, kex=0.0, dw_h=0.0, dw_n=0.0, r_nxy=5.0,
dr_nxy=None, r_nz=1.5, r_2hznz=None, r_2hxynxy=0.0,
r_hxy=10.0, r_hz=1.0, etaxy=0.0, etaz=0.0, j_hn=JHN,
cs_n=0.0, cs_h=0.0):
"""
Calculate the intensity in presence of exchange during a cpmg-type pulse train.
Keyword arguments:
I0 -- Initial intensity,
0.0 (default),
pb -- population of state B,
0.0 for 0% (default),
1.0 for 100%
kex -- exchange rate between state A and B in /s,
0.0 (default)
dw -- chemical shift difference between states A and B in /s,
0.0 /s (default)
r_Nxy -- transverse relaxation rate in /s,
5.0 (default)
dr_Nxy -- transverse relaxation rate difference in /s between states a and b,
0.0 (default)
r_Nz -- longitudinal relaxation rate in /s,
1.5 (default)
cs_offset -- chemical shift from the carrier in rad/s,
0.0 (default)
B1_offset -- frequency offset of the applied B1 field in Hz,
0.0 Hz (default)
B1_frq -- strength of the applied B1 field in Hz,
0.0 Hz (default)
B1_inh -- B1 field inhomogeneity in Hz,
0.0 Hz (default)
time_t1 -- time of the CW block,
0 ms (default)
Returns: float
"""
wg_h = (cs_h - carrier_h) * ppm_to_rads_h
wg_n = (cs_n - carrier) * ppm_to_rads
dw_h_rads = dw_h * ppm_to_rads_h
dw_n_rads = dw_n * ppm_to_rads
mag_eq = set_nz(pb)
if abs(b1_offset) > 9999.0:
mag = mag_eq
else:
exchange_induced_shift_n, _ = correct_chemical_shift(
pb=pb,
kex=kex,
dw=dw_n_rads,
r_ixy=r_nxy,
dr_ixy=dr_nxy
)
offset_n = wg_n - exchange_induced_shift_n - b1_offset * 2.0 * pi
liouvillian = compute_liouvillian_free_precession(
pb=pb,
kex=kex,
dw_h=dw_h_rads,
dw_n=dw_n_rads,
r_nxy=r_nxy,
dr_nxy=dr_nxy,
r_nz=r_nz,
r_2hznz=r_2hznz,
r_2hxynxy=r_2hxynxy,
r_hxy=r_hxy,
r_hz=r_hz,
etaxy=etaxy,
etaz=etaz,
cs_offset_h=wg_h,
cs_offset_n=offset_n,
j_hn=j_hn
)
b1_frq_n_list = linspace(-2.0, 2.0, b1_inh_res) * b1_inh + b1_frq
b1_frq_n_scales = norm.pdf(b1_frq_n_list, b1_frq, b1_inh)
b1_frq_n_scales /= b1_frq_n_scales.sum()
mag = sum(
scale *
make_pulse_nh(
liouvillian=liouvillian,
w1_h=TWO_PI * b1_frq_h,
phase_h=0.0,
w1_n=TWO_PI * b1_frq_n,
phase_n=0.0,
pw=time_t1
).dot(mag_eq)
for b1_frq_n, scale in zip(b1_frq_n_list, b1_frq_n_scales)
)
return get_nz(mag)[0]
def _calc_observable(pb=0.0,
kex=0.0,
dw=0.0,
r_cz=1.5,
r_cxy=0.0,
dr_cxy=0.0,
cs=0.0):
"""
Calculate the intensity in presence of exchange after a CEST block assuming
initial intensity of 1.0.
Parameters
----------
pb : float
Fractional population of state B,
0.0 for 0%, 1.0 for 100%
kex : float
Exchange rate between state A and B in /s.
dw : float
Chemical shift difference between states A and B in rad/s.
r_cz : float
Longitudinal relaxation rate of state {a,b} in /s.
r_cxy : float
Transverse relaxation rate of state a in /s.
dr_cxy : float
Transverse relaxation rate difference between states a and b in /s.
cs : float
Resonance position in rad/s.
Returns
-------
out : float
Intensity after the CEST block
"""
if abs(b1_offset) >= 10000.0:
return 1.0 - pb
else:
dw *= ppm_to_rads
mag_eq = compute_cz_eq(pb)
exchange_induced_shift, _ = correct_chemical_shift(pb=pb,
kex=kex,
dw=dw,
r_ixy=r_cxy,
dr_ixy=dr_cxy)
wg = (cs - carrier) * ppm_to_rads - exchange_induced_shift
liouvillians = base_liouvillians + compute_free_liouvillian(
pb=pb,
kex=kex,
dw=dw,
r_cxy=r_cxy,
dr_cxy=dr_cxy,
r_cz=r_cz,
cs_offset=wg)
propagator = sc.zeros_like(liouvillians[0])
for liouvillian, weight in zip(liouvillians, weights):
propagator += weight * expm(liouvillian * time_t1)
propagator /= sum(weights)
magz_a, _ = get_cz(sc.dot(propagator, mag_eq))
return magz_a
def _calc_observable(pb=0.0,
kex=0.0,
dw=0.0,
r_nz=1.5,
r_nxy=0.0,
dr_nxy=0.0,
cs=0.0):
"""
Calculate the intensity in presence of exchange after a CEST block assuming
initial intensity of 1.0.
Parameters
----------
pb : float
Fractional population of state B,
0.0 for 0%, 1.0 for 100%
kex : float
Exchange rate between state A and B in /s.
dw : float
Chemical shift difference between states A and B in rad/s.
r_nz : float
Longitudinal relaxation rate of state {a,b} in /s.
r_nxy : float
Transverse relaxation rate of state a in /s.
dr_nxy : float
Transverse relaxation rate difference between states a and b in /s.
cs : float
Resonance position in rad/s.
Returns
-------
out : float
Intensity after the CEST block
"""
if abs(b1_offset) >= 10000.0:
magz_a = 1.0 - pb
else:
dw *= ppm_to_rads
exchange_induced_shift, _ = correct_chemical_shift(pb=pb,
kex=kex,
dw=dw,
r_ixy=r_nxy,
dr_ixy=dr_nxy)
wg = ((cs - carrier) * ppm_to_rads - exchange_induced_shift -
w1_offset)
magz_eq = sc.asarray([[1 - pb], [pb]])
magz_a = 0.0
for j, weight in multiplet:
liouvillian = compute_liouvillian(pb=pb,
kex=kex,
dw=dw,
r_nxy=r_nxy,
dr_nxy=dr_nxy,
r_nz=r_nz,
cs_offset=(wg + j),
w1=w1)
s, vr = eig(liouvillian)
vri = inv(vr)
sl1 = [2, 5]
sl2 = [i for i, w in enumerate(s.imag) if abs(w) < 1.0e-6]
sl3 = [2]
vri = vri[sc.ix_(sl2, sl1)].real
t = diag(exp(s[sl2].real * time_t1))
vr = vr[sc.ix_(sl3, sl2)].real
magz_a += (weight * dot(dot(dot(vr, t), vri), magz_eq)[0, 0])
return magz_a
def _calc_observable(pb=0.0, kex=0.0, dw_h=0.0, dw_n=0.0, r_nxy=5.0,
dr_nxy=None, r_nz=1.5, r_2hznz=None, r_2hxynxy=0.0,
r_hxy=10.0, r_hz=1.0, etaxy=0.0, etaz=0.0, j_hn=JHN,
cs_n=0.0, cs_h=0.0):
"""
Calculate the intensity in presence of exchange during a cpmg-type pulse train.
Keyword arguments:
I0 -- Initial intensity,
0.0 (default),
pb -- population of state B,
0.0 for 0% (default),
1.0 for 100%
kex -- exchange rate between state A and B in /s,
0.0 (default)
dw -- chemical shift difference between states A and B in /s,
0.0 /s (default)
r_Nxy -- transverse relaxation rate in /s,
5.0 (default)
dr_Nxy -- transverse relaxation rate difference in /s between states a and b,
0.0 (default)
r_Nz -- longitudinal relaxation rate in /s,
1.5 (default)
cs_offset -- chemical shift from the carrier in rad/s,
0.0 (default)
B1_offset -- frequency offset of the applied B1 field in Hz,
0.0 Hz (default)
B1_frq -- strength of the applied B1 field in Hz,
time_t1 -- time of the CW block,
0 ms (default)
Returns: float
"""
wg_h = (cs_h - carrier_h) * ppm_to_rads_h
wg_n = (cs_n - carrier) * ppm_to_rads
dw_h_rads = dw_h * ppm_to_rads_h
dw_n_rads = dw_n * ppm_to_rads
if abs(b1_offset) > 9999.0:
magz_a = 1.0 - pb
else:
exchange_induced_shift_n, _ = correct_chemical_shift(
pb=pb,
kex=kex,
dw=dw_n_rads,
r_ixy=r_nxy,
dr_ixy=dr_nxy
)
offset_n = wg_n - exchange_induced_shift_n - b1_offset * TWO_PI
liouvillian = compute_liouvillian(
pb=pb,
kex=kex,
dw_h=dw_h_rads,
dw_n=dw_n_rads,
r_nxy=r_nxy,
dr_nxy=dr_nxy,
r_nz=r_nz,
r_2hznz=r_2hznz,
r_2hxynxy=r_2hxynxy,
r_hxy=r_hxy,
r_hz=r_hz,
etaxy=etaxy,
etaz=etaz,
cs_offset_h=wg_h,
cs_offset_n=offset_n,
j_hn=j_hn,
w1_h=TWO_PI * b1_frq_h,
w1_n=TWO_PI * b1_frq,
)
s, vr = eig(liouvillian)
vri = inv(vr)
sl1 = [5, 20]
sl2 = [i for i, w in enumerate(s.imag) if abs(w) < 1.0e-6]
sl3 = [5]
vri = vri[ix_(sl2, sl1)].real
t = diag(exp(s[sl2].real * time_t1))
vr = vr[ix_(sl3, sl2)].real
magz_eq = asarray([[1 - pb], [pb]])
magz_a = dot(dot(dot(vr, t), vri), magz_eq)[0, 0]
return magz_a