signal_models
¶
Module: signal_models.capped_cylinder_models
¶
-
class
dmipy.signal_models.capped_cylinder_models.
CC3CappedCylinderCallaghanApproximation
(mu=None, diameter=None, length=None, diffusion_intra=1.7e-09, number_of_roots_cylinder=20, number_of_functions_cylinder=50, number_of_roots_plane=40)¶ The Callaghan model [R50] - a cylinder with finite radius - for intra-axonal diffusion. The perpendicular diffusion is modelled after Callaghan’s solution for the disk. The parallel diffusion of the capped cylinder is modelled using the same Callaghan approximation but between two parallel planes with a certain distance or ‘length’ between them.
Parameters: mu : array, shape(2),
angles [theta, phi] representing main orientation on the sphere. theta is inclination of polar angle of main angle mu [0, pi]. phi is polar angle of main angle mu [-pi, pi].
diameter : float,
cylinder (axon) diameter in meters.
length : float,
cylinder length in meters.
diffusion_intra : float,
The diffusion constant of the water particles inside the cylinder. The default value is the approximate diffusivity of water inside axons as 1.7e-9 m^2/s.
number_of_roots_cylinder : integer,
number of roots for the cylinder Callaghan approximation.
number_of_functions_cylinder : integer,
number of functions for the cylinder Callaghan approximation.
number_of_roots_plane : integer,
number of roots for the plane Callaghan approximation.
References
[R50] (1, 2) Callaghan, Paul T. “Pulsed-gradient spin-echo NMR for planar, cylindrical, and spherical pores under conditions of wall relaxation.” Journal of magnetic resonance, Series A 113.1 (1995): 53-59. Attributes
Methods
Module: signal_models.cylinder_models
¶
-
class
dmipy.signal_models.cylinder_models.
C1Stick
(mu=None, lambda_par=None)¶ The Stick model [R51] - a cylinder with zero radius - typically used for intra-axonal diffusion.
Parameters: mu : array, shape(2),
angles [theta, phi] representing main orientation on the sphere. theta is inclination of polar angle of main angle mu [0, pi]. phi is polar angle of main angle mu [-pi, pi].
lambda_par : float,
parallel diffusivity in m^2/s.
References
[R51] (1, 2) Behrens et al. “Characterization and propagation of uncertainty in
diffusion-weighted MR imaging”Magnetic Resonance in Medicine (2003)
Attributes
Methods
-
rotational_harmonics_representation
(acquisition_scheme, **kwargs)¶ The rotational harmonics of the model, such that Y_lm = Yl0. Axis aligned with z-axis to be used as kernel for spherical convolution. Returns an array with rotational harmonics for each shell.
Parameters: acquisition_scheme : DmipyAcquisitionScheme instance,
An acquisition scheme that has been instantiated using dMipy.
kwargs: keyword arguments to the model parameter values, :
Is internally given as **parameter_dictionary.
Returns: rh_array : array, shape(Nshells, N_rh_coef),
Rotational harmonics coefficients for each shell.
-
spherical_mean
(acquisition_scheme, **kwargs)¶ Estimates spherical mean for every shell in acquisition scheme for Stick model.
Parameters: acquisition_scheme : DmipyAcquisitionScheme instance,
An acquisition scheme that has been instantiated using dMipy.
kwargs: keyword arguments to the model parameter values, :
Is internally given as **parameter_dictionary.
Returns: E_mean : array of size (Nshells)
spherical mean of the Stick model for every acquisition shell.
-
-
class
dmipy.signal_models.cylinder_models.
C2CylinderSodermanApproximation
(mu=None, lambda_par=None, diameter=None)¶ The Soderman model [R52] - a cylinder with finite radius - typically used for intra-axonal diffusion. Assumes that the pulse length is infinitely short and the diffusion time is infinitely long, and is therefore only dependent on the q-value.
Parameters: mu : array, shape(2),
angles [theta, phi] representing main orientation on the sphere. theta is inclination of polar angle of main angle mu [0, pi]. phi is polar angle of main angle mu [-pi, pi].
lambda_par : float,
parallel diffusivity in m^2/s.
diameter : float,
cylinder diameter in meters.
Returns: E : array, shape (N,)
signal attenuation
References
Attributes
Methods
-
perpendicular_attenuation
(q, diameter)¶ Returns the cylinder’s perpendicular signal attenuation.
-
rotational_harmonics_representation
(acquisition_scheme, **kwargs)¶ The rotational harmonics of the model, such that Y_lm = Yl0. Axis aligned with z-axis to be used as kernel for spherical convolution. Returns an array with rotational harmonics for each shell.
Parameters: acquisition_scheme : DmipyAcquisitionScheme instance,
An acquisition scheme that has been instantiated using dMipy.
kwargs: keyword arguments to the model parameter values, :
Is internally given as **parameter_dictionary.
Returns: rh_array : array, shape(Nshells, N_rh_coef),
Rotational harmonics coefficients for each shell.
-
spherical_mean
(acquisition_scheme, **kwargs)¶ Estimates spherical mean for every shell in acquisition scheme.
Parameters: acquisition_scheme : DmipyAcquisitionScheme instance,
An acquisition scheme that has been instantiated using dMipy.
kwargs: keyword arguments to the model parameter values, :
Is internally given as **parameter_dictionary.
Returns: E_mean : float,
spherical mean of the model for every acquisition shell.
-
-
class
dmipy.signal_models.cylinder_models.
C3CylinderCallaghanApproximation
(mu=None, lambda_par=None, diameter=None, diffusion_perpendicular=1.7e-09, number_of_roots=20, number_of_functions=50)¶ The Callaghan model [R53] - a cylinder with finite radius - typically used for intra-axonal diffusion. The perpendicular diffusion is modelled after Callaghan’s solution for the disk. Is dependent on both q-value and diffusion time.
Parameters: mu : array, shape(2),
angles [theta, phi] representing main orientation on the sphere. theta is inclination of polar angle of main angle mu [0, pi]. phi is polar angle of main angle mu [-pi, pi].
lambda_par : float,
parallel diffusivity in m^2/s.
diameter : float,
cylinder (axon) diameter in meters.
diffusion_perpendicular : float,
the intra-cylindrical, perpenicular diffusivity. By default it is set to a typical value for intra-axonal diffusion as 1.7e-9 m^2/s.
number_of_roots : integer,
number of roots to use for the Callaghan cylinder model.
number_of_function : integer,
number of functions to use for the Callaghan cylinder model.
References
[R53] (1, 2) Callaghan, Paul T. “Pulsed-gradient spin-echo NMR for planar, cylindrical, and spherical pores under conditions of wall relaxation.” Journal of magnetic resonance, Series A 113.1 (1995): 53-59. Attributes
Methods
-
perpendicular_attenuation
(q, tau, diameter)¶ Implements the finite time Callaghan model for cylinders
-
rotational_harmonics_representation
(acquisition_scheme, **kwargs)¶ The rotational harmonics of the model, such that Y_lm = Yl0. Axis aligned with z-axis to be used as kernel for spherical convolution. Returns an array with rotational harmonics for each shell.
Parameters: acquisition_scheme : DmipyAcquisitionScheme instance,
An acquisition scheme that has been instantiated using dMipy.
kwargs: keyword arguments to the model parameter values, :
Is internally given as **parameter_dictionary.
Returns: rh_array : array, shape(Nshells, N_rh_coef),
Rotational harmonics coefficients for each shell.
-
spherical_mean
(acquisition_scheme, **kwargs)¶ Estimates spherical mean for every shell in acquisition scheme.
Parameters: acquisition_scheme : DmipyAcquisitionScheme instance,
An acquisition scheme that has been instantiated using dMipy.
kwargs: keyword arguments to the model parameter values, :
Is internally given as **parameter_dictionary.
Returns: E_mean : float,
spherical mean of the model for every acquisition shell.
-
-
class
dmipy.signal_models.cylinder_models.
C4CylinderGaussianPhaseApproximation
(mu=None, lambda_par=None, diameter=None, diffusion_perpendicular=1.7e-09)¶ The Gaussian phase model [R54] - a cylinder with finite radius - typically used for intra-axonal diffusion. The perpendicular diffusion is modelled after Van Gelderen’s solution for the disk. It is dependent on gradient strength, pulse separation and pulse length.
Parameters: mu : array, shape(2),
angles [theta, phi] representing main orientation on the sphere. theta is inclination of polar angle of main angle mu [0, pi]. phi is polar angle of main angle mu [-pi, pi].
lambda_par : float,
parallel diffusivity in 10^9 m^2/s.
diameter : float,
cylinder (axon) diameter in meters.
References
[R54] (1, 2) Van Gelderen et al. “Evaluation of Restricted Diffusion in Cylinders. Phosphocreatine in Rabbit Leg Muscle” Journal of Magnetic Resonance Series B (1994) Attributes
Methods
-
perpendicular_attenuation
(gradient_strength, delta, Delta, diameter)¶ Calculates the cylinder’s perpendicular signal attenuation.
-
rotational_harmonics_representation
(acquisition_scheme, **kwargs)¶ The rotational harmonics of the model, such that Y_lm = Yl0. Axis aligned with z-axis to be used as kernel for spherical convolution. Returns an array with rotational harmonics for each shell.
Parameters: acquisition_scheme : DmipyAcquisitionScheme instance,
An acquisition scheme that has been instantiated using dMipy.
kwargs: keyword arguments to the model parameter values, :
Is internally given as **parameter_dictionary.
Returns: rh_array : array, shape(Nshells, N_rh_coef),
Rotational harmonics coefficients for each shell.
-
spherical_mean
(acquisition_scheme, **kwargs)¶ Estimates spherical mean for every shell in acquisition scheme.
Parameters: acquisition_scheme : DmipyAcquisitionScheme instance,
An acquisition scheme that has been instantiated using dMipy.
kwargs: keyword arguments to the model parameter values, :
Is internally given as **parameter_dictionary.
Returns: E_mean : float,
spherical mean of the model for every acquisition shell.
-
Module: signal_models.gaussian_models
¶
Document Module
-
class
dmipy.signal_models.gaussian_models.
G1Ball
(lambda_iso=None)¶ The Ball model [R55] - an isotropic Tensor with one diffusivity.
Parameters: lambda_iso : float,
isotropic diffusivity in m^2/s.
References
[R55] (1, 2) Behrens et al. “Characterization and propagation of uncertainty in
diffusion-weighted MR imaging”Magnetic Resonance in Medicine (2003)
Attributes
Methods
-
rotational_harmonics_representation
(acquisition_scheme, **kwargs)¶ The rotational harmonics of the model, such that Y_lm = Yl0. Axis aligned with z-axis to be used as kernel for spherical convolution. Returns an array with rotational harmonics for each shell.
Parameters: acquisition_scheme : DmipyAcquisitionScheme instance,
An acquisition scheme that has been instantiated using dMipy.
kwargs: keyword arguments to the model parameter values, :
Is internally given as **parameter_dictionary.
Returns: rh_array : array, shape(Nshells, N_rh_coef),
Rotational harmonics coefficients for each shell.
-
spherical_mean
(acquisition_scheme, **kwargs)¶ Estimates spherical mean for every shell in acquisition scheme
Parameters: acquisition_scheme : DmipyAcquisitionScheme instance,
An acquisition scheme that has been instantiated using dMipy.
kwargs: keyword arguments to the model parameter values, :
Is internally given as **parameter_dictionary.
Returns: E_mean : float,
spherical mean of the model for every acquisition shell.
-
-
class
dmipy.signal_models.gaussian_models.
G2Zeppelin
(mu=None, lambda_par=None, lambda_perp=None)¶ The Zeppelin model [R56] - an axially symmetric Tensor - typically used for extra-axonal diffusion.
Parameters: mu : array, shape(2),
angles [theta, phi] representing main orientation on the sphere. theta is inclination of polar angle of main angle mu [0, pi]. phi is polar angle of main angle mu [-pi, pi].
lambda_par : float,
parallel diffusivity in m^2/s.
lambda_perp : float,
perpendicular diffusivity in m^2/s.
Returns: E_zeppelin : float or array, shape(N),
signal attenuation.
References
[R56] (1, 2) Panagiotaki et al. “Compartment models of the diffusion MR signal in brain white
matter: a taxonomy and comparison”. NeuroImage (2012)Attributes
Methods
-
rotational_harmonics_representation
(acquisition_scheme, **kwargs)¶ The rotational harmonics of the model, such that Y_lm = Yl0. Axis aligned with z-axis to be used as kernel for spherical convolution. Returns an array with rotational harmonics for each shell.
Parameters: acquisition_scheme : DmipyAcquisitionScheme instance,
An acquisition scheme that has been instantiated using dMipy.
kwargs: keyword arguments to the model parameter values, :
Is internally given as **parameter_dictionary.
Returns: rh_array : array, shape(Nshells, N_rh_coef),
Rotational harmonics coefficients for each shell.
-
spherical_mean
(acquisition_scheme, **kwargs)¶ Estimates spherical mean for every shell in acquisition scheme for Zeppelin model.
Parameters: acquisition_scheme : DmipyAcquisitionScheme instance,
An acquisition scheme that has been instantiated using dMipy.
kwargs: keyword arguments to the model parameter values, :
Is internally given as **parameter_dictionary.
Returns: E_mean : float,
spherical mean of the Zeppelin model for every acquisition shell.
-
-
class
dmipy.signal_models.gaussian_models.
G3RestrictedZeppelin
(mu=None, lambda_par=None, lambda_inf=None, A=None)¶ The restricted Zeppelin model [R57] - an axially symmetric Tensor - for extra-axonal diffusion.
Parameters: mu : array, shape(2),
angles [theta, phi] representing main orientation on the sphere. theta is inclination of polar angle of main angle mu [0, pi]. phi is polar angle of main angle mu [-pi, pi].
lambda_par : float,
parallel diffusivity in 10^9 m^2/s.
lambda_inf : float,
bulk diffusivity constant 10^9 m^2/s.
A: float, :
characteristic coefficient in 10^6 m^2
Returns: E_zeppelin : float or array, shape(N),
signal attenuation.
References
[R57] (1, 2) Burcaw, L.M., Fieremans, E., Novikov, D.S., 2015. Mesoscopic structure of neuronal tracts from time-dependent diffusion. NeuroImage 114, 18. Attributes
Methods
-
rotational_harmonics_representation
(acquisition_scheme, **kwargs)¶ The rotational harmonics of the model, such that Y_lm = Yl0. Axis aligned with z-axis to be used as kernel for spherical convolution. Returns an array with rotational harmonics for each shell.
Parameters: acquisition_scheme : DmipyAcquisitionScheme instance,
An acquisition scheme that has been instantiated using dMipy.
kwargs: keyword arguments to the model parameter values, :
Is internally given as **parameter_dictionary.
Returns: rh_array : array, shape(Nshells, N_rh_coef),
Rotational harmonics coefficients for each shell.
-
spherical_mean
(acquisition_scheme, **kwargs)¶ Estimates spherical mean for every shell in acquisition scheme for Restricted Zeppelin model.
Parameters: acquisition_scheme : DmipyAcquisitionScheme instance,
An acquisition scheme that has been instantiated using dMipy.
kwargs: keyword arguments to the model parameter values, :
Is internally given as **parameter_dictionary.
Returns: E_mean : float,
spherical mean of the Restricted Zeppelin model for every acquisition shell.
-
Module: signal_models.plane_models
¶
-
class
dmipy.signal_models.plane_models.
P3PlaneCallaghanApproximation
(diameter=None, diffusion_constant=1.7e-09, number_of_roots=40)¶ The Callaghan model [1]_ of diffusion between two parallel infinite plates.
Parameters: diameter : float
Distance between the two plates in meters.
diffusion_constant : float,
The diffusion constant of the water particles between the two planes. The default value is the approximate diffusivity of water inside axons as 1.7e-9 m^2/s.
number_of_roots : integer,
The number of roots for the Callaghan approximation.
References
- [1] Callaghan, “Pulsed-Gradient Spin-Echo NMR for Planar, Cylindrical,
- and Spherical Pores under Conditions of Wall Relaxation”, JMR 1995
Attributes
Methods
-
plane_attenuation
(q, tau, diameter)¶ Implements the finite time Callaghan model for planes.
Module: signal_models.sphere_models
¶
-
class
dmipy.signal_models.sphere_models.
S1Dot
¶ The Dot model [R58] - an non-diffusing compartment. It has no parameters and returns 1 no matter the input.
References
[R58] (1, 2) Panagiotaki et al. “Compartment models of the diffusion MR signal in brain white
matter: a taxonomy and comparison”. NeuroImage (2012)Attributes
Methods
-
rotational_harmonics_representation
(acquisition_scheme, **kwargs)¶ The rotational harmonics of the model, such that Y_lm = Yl0. Axis aligned with z-axis to be used as kernel for spherical convolution. Returns an array with rotational harmonics for each shell.
Parameters: acquisition_scheme : DmipyAcquisitionScheme instance,
An acquisition scheme that has been instantiated using dMipy.
kwargs: keyword arguments to the model parameter values, :
Is internally given as **parameter_dictionary.
Returns: rh_array : array, shape(Nshells, N_rh_coef),
Rotational harmonics coefficients for each shell.
-
spherical_mean
(acquisition_scheme, **kwargs)¶ Estimates spherical mean for every shell in acquisition scheme.
Parameters: acquisition_scheme : DmipyAcquisitionScheme instance,
An acquisition scheme that has been instantiated using dMipy.
kwargs: keyword arguments to the model parameter values, :
Is internally given as **parameter_dictionary.
Returns: E_mean : float,
spherical mean of the model for every acquisition shell.
-
-
class
dmipy.signal_models.sphere_models.
S2SphereSodermanApproximation
(diameter=None)¶ The Stejskal Tanner signal approximation of a sphere model. It assumes that pulse length is infinitessimally small and diffusion time large enough so that the diffusion is completely restricted. Only depends on q-value.
Parameters: diameter : float,
sphere diameter in meters.
References
[R59] Balinov, Balin, et al. “The NMR self-diffusion method applied to restricted diffusion. Simulation of echo attenuation from molecules in spheres and between planes.” Journal of Magnetic Resonance, Series A 104.1 (1993): 17-25. Attributes
Methods
-
rotational_harmonics_representation
(acquisition_scheme, **kwargs)¶ The rotational harmonics of the model, such that Y_lm = Yl0. Axis aligned with z-axis to be used as kernel for spherical convolution. Returns an array with rotational harmonics for each shell.
Parameters: acquisition_scheme : DmipyAcquisitionScheme instance,
An acquisition scheme that has been instantiated using dMipy.
kwargs: keyword arguments to the model parameter values, :
Is internally given as **parameter_dictionary.
Returns: rh_array : array, shape(Nshells, N_rh_coef),
Rotational harmonics coefficients for each shell.
-
sphere_attenuation
(q, diameter)¶ The signal attenuation for the sphere model.
-
spherical_mean
(acquisition_scheme, **kwargs)¶ Estimates spherical mean for every shell in acquisition scheme.
Parameters: acquisition_scheme : DmipyAcquisitionScheme instance,
An acquisition scheme that has been instantiated using dMipy.
kwargs: keyword arguments to the model parameter values, :
Is internally given as **parameter_dictionary.
Returns: E_mean : float,
spherical mean of the model for every acquisition shell.
-
CC2CappedCylinderStejskalTannerApproximation
¶
-
class
dmipy.signal_models.capped_cylinder_models.
CC2CappedCylinderStejskalTannerApproximation
(mu=None, diameter=None, length=None)¶ Bases:
dmipy.core.modeling_framework.ModelProperties
The Stejskal-Tanner model for intra-cylindrical diffusion inside a capped cylinder with finite radius and length. The perpendicular diffusion is modelled after Soderman’s solution for the disk [R60]. The parallel diffusion between planes has been implemented according to Balinov [R61].
Parameters: mu : array, shape(2),
angles [theta, phi] representing main orientation on the sphere. theta is inclination of polar angle of main angle mu [0, pi]. phi is polar angle of main angle mu [-pi, pi].
diameter : float,
capped cylinder (axon) diameter in meters.
length : float,
capped cylinder length in meters.
References
[R60] (1, 2) Soderman, Olle, and Bengt Jonsson. “Restricted diffusion in cylindrical geometry.” Journal of Magnetic Resonance, Series A 117.1 (1995): 94-97. [R61] (1, 2) Balinov, Balin, et al. “The NMR self-diffusion method applied to restricted diffusion. Simulation of echo attenuation from molecules in spheres and between planes.” Journal of Magnetic Resonance, Series A 104.1 (1993): 17-25. Attributes
Methods
-
__init__
(mu=None, diameter=None, length=None)¶
-
CC3CappedCylinderCallaghanApproximation
¶
-
class
dmipy.signal_models.capped_cylinder_models.
CC3CappedCylinderCallaghanApproximation
(mu=None, diameter=None, length=None, diffusion_intra=1.7e-09, number_of_roots_cylinder=20, number_of_functions_cylinder=50, number_of_roots_plane=40) Bases:
dmipy.core.modeling_framework.ModelProperties
The Callaghan model [R62] - a cylinder with finite radius - for intra-axonal diffusion. The perpendicular diffusion is modelled after Callaghan’s solution for the disk. The parallel diffusion of the capped cylinder is modelled using the same Callaghan approximation but between two parallel planes with a certain distance or ‘length’ between them.
Parameters: mu : array, shape(2),
angles [theta, phi] representing main orientation on the sphere. theta is inclination of polar angle of main angle mu [0, pi]. phi is polar angle of main angle mu [-pi, pi].
diameter : float,
cylinder (axon) diameter in meters.
length : float,
cylinder length in meters.
diffusion_intra : float,
The diffusion constant of the water particles inside the cylinder. The default value is the approximate diffusivity of water inside axons as 1.7e-9 m^2/s.
number_of_roots_cylinder : integer,
number of roots for the cylinder Callaghan approximation.
number_of_functions_cylinder : integer,
number of functions for the cylinder Callaghan approximation.
number_of_roots_plane : integer,
number of roots for the plane Callaghan approximation.
References
[R62] (1, 2) Callaghan, Paul T. “Pulsed-gradient spin-echo NMR for planar, cylindrical, and spherical pores under conditions of wall relaxation.” Journal of magnetic resonance, Series A 113.1 (1995): 53-59. Attributes
Methods
-
__init__
(mu=None, diameter=None, length=None, diffusion_intra=1.7e-09, number_of_roots_cylinder=20, number_of_functions_cylinder=50, number_of_roots_plane=40)¶
-
ModelProperties
¶
-
class
dmipy.signal_models.capped_cylinder_models.
ModelProperties
¶ Contains various properties for CompartmentModels.
Attributes
-
parameter_cardinality
¶ Returns the cardinality of model parameters
-
parameter_names
¶ Returns the names of model parameters.
-
parameter_ranges
¶ Returns the optimization ranges of the model parameters. These ranges are given in O(1) scale so optimization algorithms don’t suffer from large scale differences in optimization parameters.
-
parameter_scales
¶ Returns the optimization scales for the model parameters. The scales scale the parameter_ranges to their actual size inside optimization algorithms.
-
parameter_types
¶ Returns the optimization scales for the model parameters. The scales scale the parameter_ranges to their actual size inside optimization algorithms.
-
C1Stick
¶
-
class
dmipy.signal_models.cylinder_models.
C1Stick
(mu=None, lambda_par=None) Bases:
dmipy.core.modeling_framework.ModelProperties
The Stick model [R63] - a cylinder with zero radius - typically used for intra-axonal diffusion.
Parameters: mu : array, shape(2),
angles [theta, phi] representing main orientation on the sphere. theta is inclination of polar angle of main angle mu [0, pi]. phi is polar angle of main angle mu [-pi, pi].
lambda_par : float,
parallel diffusivity in m^2/s.
References
[R63] (1, 2) Behrens et al. “Characterization and propagation of uncertainty in
diffusion-weighted MR imaging”Magnetic Resonance in Medicine (2003)
Attributes
Methods
-
__init__
(mu=None, lambda_par=None)¶
-
rotational_harmonics_representation
(acquisition_scheme, **kwargs) The rotational harmonics of the model, such that Y_lm = Yl0. Axis aligned with z-axis to be used as kernel for spherical convolution. Returns an array with rotational harmonics for each shell.
Parameters: acquisition_scheme : DmipyAcquisitionScheme instance,
An acquisition scheme that has been instantiated using dMipy.
kwargs: keyword arguments to the model parameter values, :
Is internally given as **parameter_dictionary.
Returns: rh_array : array, shape(Nshells, N_rh_coef),
Rotational harmonics coefficients for each shell.
-
spherical_mean
(acquisition_scheme, **kwargs) Estimates spherical mean for every shell in acquisition scheme for Stick model.
Parameters: acquisition_scheme : DmipyAcquisitionScheme instance,
An acquisition scheme that has been instantiated using dMipy.
kwargs: keyword arguments to the model parameter values, :
Is internally given as **parameter_dictionary.
Returns: E_mean : array of size (Nshells)
spherical mean of the Stick model for every acquisition shell.
-
C2CylinderSodermanApproximation
¶
-
class
dmipy.signal_models.cylinder_models.
C2CylinderSodermanApproximation
(mu=None, lambda_par=None, diameter=None) Bases:
dmipy.core.modeling_framework.ModelProperties
The Soderman model [R64] - a cylinder with finite radius - typically used for intra-axonal diffusion. Assumes that the pulse length is infinitely short and the diffusion time is infinitely long, and is therefore only dependent on the q-value.
Parameters: mu : array, shape(2),
angles [theta, phi] representing main orientation on the sphere. theta is inclination of polar angle of main angle mu [0, pi]. phi is polar angle of main angle mu [-pi, pi].
lambda_par : float,
parallel diffusivity in m^2/s.
diameter : float,
cylinder diameter in meters.
Returns: E : array, shape (N,)
signal attenuation
References
Attributes
Methods
-
__init__
(mu=None, lambda_par=None, diameter=None)¶
-
perpendicular_attenuation
(q, diameter) Returns the cylinder’s perpendicular signal attenuation.
-
rotational_harmonics_representation
(acquisition_scheme, **kwargs) The rotational harmonics of the model, such that Y_lm = Yl0. Axis aligned with z-axis to be used as kernel for spherical convolution. Returns an array with rotational harmonics for each shell.
Parameters: acquisition_scheme : DmipyAcquisitionScheme instance,
An acquisition scheme that has been instantiated using dMipy.
kwargs: keyword arguments to the model parameter values, :
Is internally given as **parameter_dictionary.
Returns: rh_array : array, shape(Nshells, N_rh_coef),
Rotational harmonics coefficients for each shell.
-
spherical_mean
(acquisition_scheme, **kwargs) Estimates spherical mean for every shell in acquisition scheme.
Parameters: acquisition_scheme : DmipyAcquisitionScheme instance,
An acquisition scheme that has been instantiated using dMipy.
kwargs: keyword arguments to the model parameter values, :
Is internally given as **parameter_dictionary.
Returns: E_mean : float,
spherical mean of the model for every acquisition shell.
-
C3CylinderCallaghanApproximation
¶
-
class
dmipy.signal_models.cylinder_models.
C3CylinderCallaghanApproximation
(mu=None, lambda_par=None, diameter=None, diffusion_perpendicular=1.7e-09, number_of_roots=20, number_of_functions=50) Bases:
dmipy.core.modeling_framework.ModelProperties
The Callaghan model [R65] - a cylinder with finite radius - typically used for intra-axonal diffusion. The perpendicular diffusion is modelled after Callaghan’s solution for the disk. Is dependent on both q-value and diffusion time.
Parameters: mu : array, shape(2),
angles [theta, phi] representing main orientation on the sphere. theta is inclination of polar angle of main angle mu [0, pi]. phi is polar angle of main angle mu [-pi, pi].
lambda_par : float,
parallel diffusivity in m^2/s.
diameter : float,
cylinder (axon) diameter in meters.
diffusion_perpendicular : float,
the intra-cylindrical, perpenicular diffusivity. By default it is set to a typical value for intra-axonal diffusion as 1.7e-9 m^2/s.
number_of_roots : integer,
number of roots to use for the Callaghan cylinder model.
number_of_function : integer,
number of functions to use for the Callaghan cylinder model.
References
[R65] (1, 2) Callaghan, Paul T. “Pulsed-gradient spin-echo NMR for planar, cylindrical, and spherical pores under conditions of wall relaxation.” Journal of magnetic resonance, Series A 113.1 (1995): 53-59. Attributes
Methods
-
__init__
(mu=None, lambda_par=None, diameter=None, diffusion_perpendicular=1.7e-09, number_of_roots=20, number_of_functions=50)¶
-
perpendicular_attenuation
(q, tau, diameter) Implements the finite time Callaghan model for cylinders
-
rotational_harmonics_representation
(acquisition_scheme, **kwargs) The rotational harmonics of the model, such that Y_lm = Yl0. Axis aligned with z-axis to be used as kernel for spherical convolution. Returns an array with rotational harmonics for each shell.
Parameters: acquisition_scheme : DmipyAcquisitionScheme instance,
An acquisition scheme that has been instantiated using dMipy.
kwargs: keyword arguments to the model parameter values, :
Is internally given as **parameter_dictionary.
Returns: rh_array : array, shape(Nshells, N_rh_coef),
Rotational harmonics coefficients for each shell.
-
spherical_mean
(acquisition_scheme, **kwargs) Estimates spherical mean for every shell in acquisition scheme.
Parameters: acquisition_scheme : DmipyAcquisitionScheme instance,
An acquisition scheme that has been instantiated using dMipy.
kwargs: keyword arguments to the model parameter values, :
Is internally given as **parameter_dictionary.
Returns: E_mean : float,
spherical mean of the model for every acquisition shell.
-
C4CylinderGaussianPhaseApproximation
¶
-
class
dmipy.signal_models.cylinder_models.
C4CylinderGaussianPhaseApproximation
(mu=None, lambda_par=None, diameter=None, diffusion_perpendicular=1.7e-09) Bases:
dmipy.core.modeling_framework.ModelProperties
The Gaussian phase model [R66] - a cylinder with finite radius - typically used for intra-axonal diffusion. The perpendicular diffusion is modelled after Van Gelderen’s solution for the disk. It is dependent on gradient strength, pulse separation and pulse length.
Parameters: mu : array, shape(2),
angles [theta, phi] representing main orientation on the sphere. theta is inclination of polar angle of main angle mu [0, pi]. phi is polar angle of main angle mu [-pi, pi].
lambda_par : float,
parallel diffusivity in 10^9 m^2/s.
diameter : float,
cylinder (axon) diameter in meters.
References
[R66] (1, 2) Van Gelderen et al. “Evaluation of Restricted Diffusion in Cylinders. Phosphocreatine in Rabbit Leg Muscle” Journal of Magnetic Resonance Series B (1994) Attributes
Methods
-
__init__
(mu=None, lambda_par=None, diameter=None, diffusion_perpendicular=1.7e-09)¶
-
perpendicular_attenuation
(gradient_strength, delta, Delta, diameter) Calculates the cylinder’s perpendicular signal attenuation.
-
rotational_harmonics_representation
(acquisition_scheme, **kwargs) The rotational harmonics of the model, such that Y_lm = Yl0. Axis aligned with z-axis to be used as kernel for spherical convolution. Returns an array with rotational harmonics for each shell.
Parameters: acquisition_scheme : DmipyAcquisitionScheme instance,
An acquisition scheme that has been instantiated using dMipy.
kwargs: keyword arguments to the model parameter values, :
Is internally given as **parameter_dictionary.
Returns: rh_array : array, shape(Nshells, N_rh_coef),
Rotational harmonics coefficients for each shell.
-
spherical_mean
(acquisition_scheme, **kwargs) Estimates spherical mean for every shell in acquisition scheme.
Parameters: acquisition_scheme : DmipyAcquisitionScheme instance,
An acquisition scheme that has been instantiated using dMipy.
kwargs: keyword arguments to the model parameter values, :
Is internally given as **parameter_dictionary.
Returns: E_mean : float,
spherical mean of the model for every acquisition shell.
-
ModelProperties
¶
-
class
dmipy.signal_models.cylinder_models.
ModelProperties
¶ Contains various properties for CompartmentModels.
Attributes
-
parameter_cardinality
¶ Returns the cardinality of model parameters
-
parameter_names
¶ Returns the names of model parameters.
-
parameter_ranges
¶ Returns the optimization ranges of the model parameters. These ranges are given in O(1) scale so optimization algorithms don’t suffer from large scale differences in optimization parameters.
-
parameter_scales
¶ Returns the optimization scales for the model parameters. The scales scale the parameter_ranges to their actual size inside optimization algorithms.
-
parameter_types
¶ Returns the optimization scales for the model parameters. The scales scale the parameter_ranges to their actual size inside optimization algorithms.
-
optional_package¶
-
dmipy.signal_models.cylinder_models.
optional_package
(name, trip_msg=None)¶ Return package-like thing and module setup for package name
Parameters: name : str
package name
trip_msg : None or str
message to give when someone tries to use the return package, but we could not import it, and have returned a TripWire object instead. Default message if None.
Returns: pkg_like : module or
TripWire
instanceIf we can import the package, return it. Otherwise return an object raising an error when accessed
have_pkg : bool
True if import for package was successful, false otherwise
module_setup : function
callable usually set as
setup_module
in calling namespace, to allow skipping tests.
G1Ball
¶
-
class
dmipy.signal_models.gaussian_models.
G1Ball
(lambda_iso=None) Bases:
dmipy.core.modeling_framework.ModelProperties
The Ball model [R67] - an isotropic Tensor with one diffusivity.
Parameters: lambda_iso : float,
isotropic diffusivity in m^2/s.
References
[R67] (1, 2) Behrens et al. “Characterization and propagation of uncertainty in
diffusion-weighted MR imaging”Magnetic Resonance in Medicine (2003)
Attributes
Methods
-
__init__
(lambda_iso=None)¶
-
rotational_harmonics_representation
(acquisition_scheme, **kwargs) The rotational harmonics of the model, such that Y_lm = Yl0. Axis aligned with z-axis to be used as kernel for spherical convolution. Returns an array with rotational harmonics for each shell.
Parameters: acquisition_scheme : DmipyAcquisitionScheme instance,
An acquisition scheme that has been instantiated using dMipy.
kwargs: keyword arguments to the model parameter values, :
Is internally given as **parameter_dictionary.
Returns: rh_array : array, shape(Nshells, N_rh_coef),
Rotational harmonics coefficients for each shell.
-
spherical_mean
(acquisition_scheme, **kwargs) Estimates spherical mean for every shell in acquisition scheme
Parameters: acquisition_scheme : DmipyAcquisitionScheme instance,
An acquisition scheme that has been instantiated using dMipy.
kwargs: keyword arguments to the model parameter values, :
Is internally given as **parameter_dictionary.
Returns: E_mean : float,
spherical mean of the model for every acquisition shell.
-
G2Zeppelin
¶
-
class
dmipy.signal_models.gaussian_models.
G2Zeppelin
(mu=None, lambda_par=None, lambda_perp=None) Bases:
dmipy.core.modeling_framework.ModelProperties
The Zeppelin model [R68] - an axially symmetric Tensor - typically used for extra-axonal diffusion.
Parameters: mu : array, shape(2),
angles [theta, phi] representing main orientation on the sphere. theta is inclination of polar angle of main angle mu [0, pi]. phi is polar angle of main angle mu [-pi, pi].
lambda_par : float,
parallel diffusivity in m^2/s.
lambda_perp : float,
perpendicular diffusivity in m^2/s.
Returns: E_zeppelin : float or array, shape(N),
signal attenuation.
References
[R68] (1, 2) Panagiotaki et al. “Compartment models of the diffusion MR signal in brain white
matter: a taxonomy and comparison”. NeuroImage (2012)Attributes
Methods
-
__init__
(mu=None, lambda_par=None, lambda_perp=None)¶
-
rotational_harmonics_representation
(acquisition_scheme, **kwargs) The rotational harmonics of the model, such that Y_lm = Yl0. Axis aligned with z-axis to be used as kernel for spherical convolution. Returns an array with rotational harmonics for each shell.
Parameters: acquisition_scheme : DmipyAcquisitionScheme instance,
An acquisition scheme that has been instantiated using dMipy.
kwargs: keyword arguments to the model parameter values, :
Is internally given as **parameter_dictionary.
Returns: rh_array : array, shape(Nshells, N_rh_coef),
Rotational harmonics coefficients for each shell.
-
spherical_mean
(acquisition_scheme, **kwargs) Estimates spherical mean for every shell in acquisition scheme for Zeppelin model.
Parameters: acquisition_scheme : DmipyAcquisitionScheme instance,
An acquisition scheme that has been instantiated using dMipy.
kwargs: keyword arguments to the model parameter values, :
Is internally given as **parameter_dictionary.
Returns: E_mean : float,
spherical mean of the Zeppelin model for every acquisition shell.
-
G3RestrictedZeppelin
¶
-
class
dmipy.signal_models.gaussian_models.
G3RestrictedZeppelin
(mu=None, lambda_par=None, lambda_inf=None, A=None) Bases:
dmipy.core.modeling_framework.ModelProperties
The restricted Zeppelin model [R69] - an axially symmetric Tensor - for extra-axonal diffusion.
Parameters: mu : array, shape(2),
angles [theta, phi] representing main orientation on the sphere. theta is inclination of polar angle of main angle mu [0, pi]. phi is polar angle of main angle mu [-pi, pi].
lambda_par : float,
parallel diffusivity in 10^9 m^2/s.
lambda_inf : float,
bulk diffusivity constant 10^9 m^2/s.
A: float, :
characteristic coefficient in 10^6 m^2
Returns: E_zeppelin : float or array, shape(N),
signal attenuation.
References
[R69] (1, 2) Burcaw, L.M., Fieremans, E., Novikov, D.S., 2015. Mesoscopic structure of neuronal tracts from time-dependent diffusion. NeuroImage 114, 18. Attributes
Methods
-
__init__
(mu=None, lambda_par=None, lambda_inf=None, A=None)¶
-
rotational_harmonics_representation
(acquisition_scheme, **kwargs) The rotational harmonics of the model, such that Y_lm = Yl0. Axis aligned with z-axis to be used as kernel for spherical convolution. Returns an array with rotational harmonics for each shell.
Parameters: acquisition_scheme : DmipyAcquisitionScheme instance,
An acquisition scheme that has been instantiated using dMipy.
kwargs: keyword arguments to the model parameter values, :
Is internally given as **parameter_dictionary.
Returns: rh_array : array, shape(Nshells, N_rh_coef),
Rotational harmonics coefficients for each shell.
-
spherical_mean
(acquisition_scheme, **kwargs) Estimates spherical mean for every shell in acquisition scheme for Restricted Zeppelin model.
Parameters: acquisition_scheme : DmipyAcquisitionScheme instance,
An acquisition scheme that has been instantiated using dMipy.
kwargs: keyword arguments to the model parameter values, :
Is internally given as **parameter_dictionary.
Returns: E_mean : float,
spherical mean of the Restricted Zeppelin model for every acquisition shell.
-
ModelProperties
¶
-
class
dmipy.signal_models.gaussian_models.
ModelProperties
¶ Contains various properties for CompartmentModels.
Attributes
-
parameter_cardinality
¶ Returns the cardinality of model parameters
-
parameter_names
¶ Returns the names of model parameters.
-
parameter_ranges
¶ Returns the optimization ranges of the model parameters. These ranges are given in O(1) scale so optimization algorithms don’t suffer from large scale differences in optimization parameters.
-
parameter_scales
¶ Returns the optimization scales for the model parameters. The scales scale the parameter_ranges to their actual size inside optimization algorithms.
-
parameter_types
¶ Returns the optimization scales for the model parameters. The scales scale the parameter_ranges to their actual size inside optimization algorithms.
-
optional_package¶
-
dmipy.signal_models.gaussian_models.
optional_package
(name, trip_msg=None)¶ Return package-like thing and module setup for package name
Parameters: name : str
package name
trip_msg : None or str
message to give when someone tries to use the return package, but we could not import it, and have returned a TripWire object instead. Default message if None.
Returns: pkg_like : module or
TripWire
instanceIf we can import the package, return it. Otherwise return an object raising an error when accessed
have_pkg : bool
True if import for package was successful, false otherwise
module_setup : function
callable usually set as
setup_module
in calling namespace, to allow skipping tests.
ModelProperties
¶
-
class
dmipy.signal_models.plane_models.
ModelProperties
¶ Contains various properties for CompartmentModels.
Attributes
-
parameter_cardinality
¶ Returns the cardinality of model parameters
-
parameter_names
¶ Returns the names of model parameters.
-
parameter_ranges
¶ Returns the optimization ranges of the model parameters. These ranges are given in O(1) scale so optimization algorithms don’t suffer from large scale differences in optimization parameters.
-
parameter_scales
¶ Returns the optimization scales for the model parameters. The scales scale the parameter_ranges to their actual size inside optimization algorithms.
-
parameter_types
¶ Returns the optimization scales for the model parameters. The scales scale the parameter_ranges to their actual size inside optimization algorithms.
-
P2PlaneStejskalTannerApproximation
¶
-
class
dmipy.signal_models.plane_models.
P2PlaneStejskalTannerApproximation
(diameter=None)¶ Bases:
dmipy.core.modeling_framework.ModelProperties
Stejskal-Tanner approximation of diffusion between two infinitely large parallel planes. Assumes short-gradient pulse (SGP) approximation (pulse length towards zero) and the long diffusion time limit (pulse separation towards infinity). We follow the notation of Balinov [R70].
References
[R70] (1, 2) Balinov, Balin, et al. “The NMR self-diffusion method applied to restricted diffusion. Simulation of echo attenuation from molecules in spheres and between planes.” Journal of Magnetic Resonance, Series A 104.1 (1993): 17-25. Attributes
Methods
-
__init__
(diameter=None)¶
-
plane_attenuation
(q, diameter)¶ Equation 6 in Balinov et al. (1993).
-
P3PlaneCallaghanApproximation
¶
-
class
dmipy.signal_models.plane_models.
P3PlaneCallaghanApproximation
(diameter=None, diffusion_constant=1.7e-09, number_of_roots=40) Bases:
dmipy.core.modeling_framework.ModelProperties
The Callaghan model [1]_ of diffusion between two parallel infinite plates.
Parameters: diameter : float
Distance between the two plates in meters.
diffusion_constant : float,
The diffusion constant of the water particles between the two planes. The default value is the approximate diffusivity of water inside axons as 1.7e-9 m^2/s.
number_of_roots : integer,
The number of roots for the Callaghan approximation.
References
- [1] Callaghan, “Pulsed-Gradient Spin-Echo NMR for Planar, Cylindrical,
- and Spherical Pores under Conditions of Wall Relaxation”, JMR 1995
Attributes
Methods
-
__init__
(diameter=None, diffusion_constant=1.7e-09, number_of_roots=40)¶
-
plane_attenuation
(q, tau, diameter) Implements the finite time Callaghan model for planes.
ModelProperties
¶
-
class
dmipy.signal_models.sphere_models.
ModelProperties
¶ Contains various properties for CompartmentModels.
Attributes
-
parameter_cardinality
¶ Returns the cardinality of model parameters
-
parameter_names
¶ Returns the names of model parameters.
-
parameter_ranges
¶ Returns the optimization ranges of the model parameters. These ranges are given in O(1) scale so optimization algorithms don’t suffer from large scale differences in optimization parameters.
-
parameter_scales
¶ Returns the optimization scales for the model parameters. The scales scale the parameter_ranges to their actual size inside optimization algorithms.
-
parameter_types
¶ Returns the optimization scales for the model parameters. The scales scale the parameter_ranges to their actual size inside optimization algorithms.
-
S1Dot
¶
-
class
dmipy.signal_models.sphere_models.
S1Dot
Bases:
dmipy.core.modeling_framework.ModelProperties
The Dot model [R71] - an non-diffusing compartment. It has no parameters and returns 1 no matter the input.
References
[R71] (1, 2) Panagiotaki et al. “Compartment models of the diffusion MR signal in brain white
matter: a taxonomy and comparison”. NeuroImage (2012)Attributes
Methods
-
rotational_harmonics_representation
(acquisition_scheme, **kwargs) The rotational harmonics of the model, such that Y_lm = Yl0. Axis aligned with z-axis to be used as kernel for spherical convolution. Returns an array with rotational harmonics for each shell.
Parameters: acquisition_scheme : DmipyAcquisitionScheme instance,
An acquisition scheme that has been instantiated using dMipy.
kwargs: keyword arguments to the model parameter values, :
Is internally given as **parameter_dictionary.
Returns: rh_array : array, shape(Nshells, N_rh_coef),
Rotational harmonics coefficients for each shell.
-
spherical_mean
(acquisition_scheme, **kwargs) Estimates spherical mean for every shell in acquisition scheme.
Parameters: acquisition_scheme : DmipyAcquisitionScheme instance,
An acquisition scheme that has been instantiated using dMipy.
kwargs: keyword arguments to the model parameter values, :
Is internally given as **parameter_dictionary.
Returns: E_mean : float,
spherical mean of the model for every acquisition shell.
-
S2SphereSodermanApproximation
¶
-
class
dmipy.signal_models.sphere_models.
S2SphereSodermanApproximation
(diameter=None) Bases:
dmipy.core.modeling_framework.ModelProperties
The Stejskal Tanner signal approximation of a sphere model. It assumes that pulse length is infinitessimally small and diffusion time large enough so that the diffusion is completely restricted. Only depends on q-value.
Parameters: diameter : float,
sphere diameter in meters.
References
[R72] Balinov, Balin, et al. “The NMR self-diffusion method applied to restricted diffusion. Simulation of echo attenuation from molecules in spheres and between planes.” Journal of Magnetic Resonance, Series A 104.1 (1993): 17-25. Attributes
Methods
-
__init__
(diameter=None)¶
-
rotational_harmonics_representation
(acquisition_scheme, **kwargs) The rotational harmonics of the model, such that Y_lm = Yl0. Axis aligned with z-axis to be used as kernel for spherical convolution. Returns an array with rotational harmonics for each shell.
Parameters: acquisition_scheme : DmipyAcquisitionScheme instance,
An acquisition scheme that has been instantiated using dMipy.
kwargs: keyword arguments to the model parameter values, :
Is internally given as **parameter_dictionary.
Returns: rh_array : array, shape(Nshells, N_rh_coef),
Rotational harmonics coefficients for each shell.
-
sphere_attenuation
(q, diameter) The signal attenuation for the sphere model.
-
spherical_mean
(acquisition_scheme, **kwargs) Estimates spherical mean for every shell in acquisition scheme.
Parameters: acquisition_scheme : DmipyAcquisitionScheme instance,
An acquisition scheme that has been instantiated using dMipy.
kwargs: keyword arguments to the model parameter values, :
Is internally given as **parameter_dictionary.
Returns: E_mean : float,
spherical mean of the model for every acquisition shell.
-
S4SphereGaussianPhaseApproximation
¶
-
class
dmipy.signal_models.sphere_models.
S4SphereGaussianPhaseApproximation
(diameter=None, diffusion_constant=1.7e-09)¶ Bases:
dmipy.core.modeling_framework.ModelProperties
The gaussian phase approximation for diffusion inside a sphere according to [R73]. It is dependent on gradient strength, pulse separation and pulse length.
References
[R73] (1, 2) Balinov, Balin, et al. “The NMR self-diffusion method applied to restricted diffusion. Simulation of echo attenuation from molecules in spheres and between planes.” Journal of Magnetic Resonance, Series A 104.1 (1993): 17-25. Attributes
Methods
-
__init__
(diameter=None, diffusion_constant=1.7e-09)¶
-
SPHERE_TRASCENDENTAL_ROOTS
= array([ 2.08157598, 5.94036999, 9.20584014, 12.40444502, 15.57923641, 18.74264558, 21.89969648, 25.05282528, 28.203361 , 31.35209173, 34.49951492, 37.64596032, 40.79165523, 43.93676147, 47.08139741, 50.22565165, 53.3695918 , 56.51327045, 59.656729 , 62.80000055, 65.9431119 , 69.08608495, 72.22893775, 75.3716854 , 78.51434055, 81.6569138 , 84.7994144 , 87.94185005, 91.0842275 , 94.22655255, 97.36883035, 100.5110653 , 103.6532613 , 106.7954217 , 109.9375497 , 113.079648 , 116.2217188 , 119.3637645 , 122.505787 , 125.647788 , 128.789769 , 131.9317315 , 135.0736768 , 138.2156061 , 141.3575204 , 144.4994207 , 147.641308 , 150.7831829 , 153.9250463 , 157.0668989 , 160.2087413 , 163.3505741 , 166.4923978 , 169.6342129 , 172.77602 , 175.9178194 , 179.0596116 , 182.2013968 , 185.3431756 , 188.4849481 , 191.6267147 , 194.7684757 , 197.9102314 , 201.051982 , 204.1937277 , 207.3354688 , 210.4772054 , 213.6189378 , 216.7606662 , 219.9023907 , 223.0441114 , 226.1858287 , 229.3275425 , 232.469253 , 235.6109603 , 238.7526647 , 241.8943662 , 245.0360648 , 248.1777608 , 251.3194542 , 254.4611451 , 257.6028336 , 260.7445198 , 263.8862038 , 267.0278856 , 270.1695654 , 273.3112431 , 276.4529189 , 279.5945929 , 282.736265 , 285.8779354 , 289.0196041 , 292.1612712 , 295.3029367 , 298.4446006 , 301.5862631 , 304.7279241 , 307.8695837 , 311.011242 , 314.152899 ])¶
-
rotational_harmonics_representation
(acquisition_scheme, **kwargs)¶ The rotational harmonics of the model, such that Y_lm = Yl0. Axis aligned with z-axis to be used as kernel for spherical convolution. Returns an array with rotational harmonics for each shell.
Parameters: acquisition_scheme : DmipyAcquisitionScheme instance,
An acquisition scheme that has been instantiated using dMipy.
kwargs: keyword arguments to the model parameter values, :
Is internally given as **parameter_dictionary.
Returns: rh_array : array, shape(Nshells, N_rh_coef),
Rotational harmonics coefficients for each shell.
-
sphere_attenuation
(gradient_strength, delta, Delta, diameter)¶ Calculates the sphere signal attenuation.
-
spherical_mean
(acquisition_scheme, **kwargs)¶ Estimates spherical mean for every shell in acquisition scheme.
Parameters: acquisition_scheme : DmipyAcquisitionScheme instance,
An acquisition scheme that has been instantiated using dMipy.
kwargs: keyword arguments to the model parameter values, :
Is internally given as **parameter_dictionary.
Returns: E_mean : float,
spherical mean of the model for every acquisition shell.
-