def test_RTOP_to_diameter_soderman(samples=1000):
"""This tests if the RTAP of the sphere relates correctly to the diameter
of the sphere."""
diameter = 10e-6
delta = np.tile(1e-10, samples) # delta towards zero
Delta = np.tile(1e10, samples) # Delta towards infinity
qvals_perp = np.linspace(0, 10e6, samples)
n_perp = np.tile(np.r_[1., 0., 0.], (samples, 1))
scheme = acquisition_scheme_from_qvalues(
qvals_perp, n_perp, delta, Delta)
soderman = sphere_models.S2SphereStejskalTannerApproximation(
diameter=diameter)
E_soderman = soderman(scheme)
rtop_soderman = 4 * np.pi * np.trapz(
E_soderman * qvals_perp ** 2, x=qvals_perp
)
sphere_volume = 1. / rtop_soderman
diameter_soderman = 2 * (sphere_volume / ((4. / 3.) * np.pi)) ** (1. / 3.)
assert_almost_equal(diameter_soderman, diameter, 7)
def test_soderman_equivalent_to_callaghan_with_one_root_and_function(
samples=100):
mu = [0, 0]
lambda_par = .1
diameter = 10e-5
diffusion_perpendicular = 1.7e-09
delta = np.tile(1e-3, samples) # delta towards zero
Delta = np.tile(.15e-2, samples) # Delta towards infinity
qvals_perp = np.linspace(0, 1e5, samples)
n_perp = np.tile(np.r_[1., 0., 0.], (samples, 1))
scheme = acquisition_scheme_from_qvalues(qvals_perp, n_perp, delta, Delta)
soderman = cylinder_models.C2CylinderSodermanApproximation(
mu=mu, lambda_par=lambda_par, diameter=diameter)
callaghan = cylinder_models.C3CylinderCallaghanApproximation(
number_of_roots=1,
number_of_functions=1,
mu=mu,
lambda_par=lambda_par,
diameter=diameter,
diffusion_perpendicular=diffusion_perpendicular)
E_soderman = soderman(scheme)
E_callaghan = callaghan(scheme)
assert_array_almost_equal(E_soderman, E_callaghan)
def test_RTAP_to_diameter_soderman(samples=1000):
"""This tests if the RTAP of the cylinder relates correctly to the diameter
of the cylinder."""
mu = [0, 0]
lambda_par = 1.7
diameter = 10e-6
delta = np.tile(1e-10, samples) # delta towards zero
Delta = np.tile(1e10, samples) # Delta towards infinity
qvals_perp = np.linspace(0, 10e6, samples)
n_perp = np.tile(np.r_[1., 0., 0.], (samples, 1))
scheme = acquisition_scheme_from_qvalues(
qvals_perp, n_perp, delta, Delta)
soderman = cylinder_models.C2CylinderStejskalTannerApproximation(
mu=mu, lambda_par=lambda_par, diameter=diameter)
E_soderman = soderman(scheme)
rtap_soderman = 2 * np.pi * np.trapz(
E_soderman * qvals_perp, x=qvals_perp
)
diameter_soderman = 2 / np.sqrt(np.pi * rtap_soderman)
assert_almost_equal(diameter_soderman, diameter, 7)
def test_callaghan_profile_narrow_pulse_not_restricted(samples=100):
# in short diffusion times the model should approach a Gaussian
# profile as np.exp(-b * lambda_perp)
mu = [0, 0]
lambda_par = .1e-9
diameter = 10e-5
diffusion_perpendicular = 1.7e-09
delta = np.tile(1e-3, samples) # delta towards zero
Delta = np.tile(.15e-2, samples) # Delta towards infinity
qvals_perp = np.linspace(0, 3e5, samples)
n_perp = np.tile(np.r_[1., 0., 0.], (samples, 1))
scheme = acquisition_scheme_from_qvalues(qvals_perp, n_perp, delta, Delta)
# needed to increase the number of roots and functions to approximate
# the gaussian function.
callaghan = cylinder_models.C3CylinderCallaghanApproximation(
number_of_roots=20,
number_of_functions=50,
mu=mu,
lambda_par=lambda_par,
diameter=diameter,
diffusion_perpendicular=diffusion_perpendicular)
E_callaghan = callaghan(scheme)
E_free_diffusion = np.exp(-scheme.bvalues * diffusion_perpendicular)
assert_equal(np.max(np.abs(E_callaghan - E_free_diffusion)) < 0.01, True)
def test_equivalent_scheme_bvals_and_bvecs(Nsamples=10):
bvalues = np.tile(1, Nsamples)
bvecs = np.tile(np.r_[1., 0., 0.], (Nsamples, 1))
delta = np.ones(Nsamples)
Delta = np.ones(Nsamples)
scheme_from_bvals = acquisition_scheme_from_bvalues(
bvalues, bvecs, delta, Delta)
qvalues = scheme_from_bvals.qvalues
scheme_from_qvals = acquisition_scheme_from_qvalues(
qvalues, bvecs, delta, Delta)
bvalues_from_qvalues = scheme_from_qvals.bvalues
assert_array_equal(bvalues, bvalues_from_qvalues)
def test_RTPP_to_length_callaghan(samples=1000):
length = 10e-6
delta = 1e-10 # delta towards zero
Delta = 1e10 # Delta towards infinity
qvals_perp = np.linspace(0, 10e6, samples)
n_perp = np.tile(np.r_[1., 0., 0.], (samples, 1))
scheme = acquisition_scheme_from_qvalues(qvals_perp, n_perp, delta, Delta)
plane = plane_models.P3PlaneCallaghanApproximation(diameter=length)
E_callaghan = plane(scheme)
rtpp_callaghan = 2 * np.trapz(E_callaghan, x=qvals_perp)
length_callaghan = 1 / rtpp_callaghan
assert_almost_equal(length_callaghan, length, 7)
def test_sphere_gaussian_phase_profile_narrow_pulse_not_restricted(
samples=100):
# the Gaussian Phase model approaches the following equation
# when delta << tau according to Eq. (13) in VanGelderen et al:
# np.exp(-2 * (gamma * G * delta * lambda_perp) ** 2)
diameter = 1e-4
diffusion_perpendicular = 1.7e-09
delta = np.tile(1e-3, samples) # delta towards zero
Delta = np.tile(1e-3, samples) # Delta towards infinity
qvals_perp = np.linspace(0, 3e5, samples)
n_perp = np.tile(np.r_[1., 0., 0.], (samples, 1))
scheme = acquisition_scheme_from_qvalues(qvals_perp, n_perp, delta, Delta)
vangelderen = (sphere_models.S4SphereGaussianPhaseApproximation(
diameter=diameter))
E_vangelderen = vangelderen(scheme)
E_free_diffusion = np.exp(-scheme.bvalues * diffusion_perpendicular)
assert_equal(np.max(np.abs(E_vangelderen - E_free_diffusion)) < 0.01, True)
def test_callaghan_plane_profile_narrow_pulse_not_restricted(samples=100):
# in short diffusion times the model should approach a Gaussian
# profile as np.exp(-b * lambda_perp)
length = 10e-5
diffusion_perpendicular = 1.7e-09
delta = 1e-4 # delta towards zero
Delta = 2e-4 # Delta also small
qvals_perp = np.linspace(0, 3.0001e5, samples)
n_perp = np.tile(np.r_[1., 0., 0.], (samples, 1))
scheme = acquisition_scheme_from_qvalues(qvals_perp, n_perp, delta, Delta)
# needed to increase the number of roots and functions to approximate
# the gaussian function.
callaghan = plane_models.P3PlaneCallaghanApproximation(diameter=length,
number_of_roots=50)
E_callaghan = callaghan(scheme)
E_free_diffusion = np.exp(-scheme.bvalues * diffusion_perpendicular)
assert_equal(np.max(np.abs(E_callaghan - E_free_diffusion)) < 0.01, True)
def test_RTAP_to_diameter_callaghan(samples=10000):
mu = [0, 0]
lambda_par = 1.7
diameter = 10e-6
delta = np.tile(1e-10, samples) # delta towards zero
Delta = np.tile(1e10, samples) # Delta towards infinity
qvals_perp = np.linspace(0, 10e6, samples)
n_perp = np.tile(np.r_[1., 0., 0.], (samples, 1))
scheme = acquisition_scheme_from_qvalues(qvals_perp, n_perp, delta, Delta)
callaghan = cylinder_models.C3CylinderCallaghanApproximation(
mu=mu, lambda_par=lambda_par, diameter=diameter)
E_callaghan = callaghan(scheme)
rtap_callaghan = 2 * np.pi * np.trapz(E_callaghan * qvals_perp,
x=qvals_perp)
diameter_callaghan = 2 / np.sqrt(np.pi * rtap_callaghan)
assert_almost_equal(diameter_callaghan, diameter, 7)
def test_RTPP_to_diameter_soderman(samples=1000):
"""This tests if the RTPP of the plane relates correctly to the diameter
of the plane."""
diameter = 10e-6
delta = np.tile(1e-10, samples) # delta towards zero
Delta = np.tile(1e10, samples) # Delta towards infinity
qvals_perp = np.linspace(0, 10e6, samples)
n_perp = np.tile(np.r_[1., 0., 0.], (samples, 1))
scheme = acquisition_scheme_from_qvalues(
qvals_perp, n_perp, delta, Delta)
soderman = plane_models.P2PlaneStejskalTannerApproximation(
diameter=diameter)
E_soderman = soderman(scheme)
rtpp_soderman = 2 * np.trapz(
E_soderman, x=qvals_perp
)
diameter_soderman = 1 / rtpp_soderman
assert_almost_equal(diameter_soderman, diameter, 7)
