cornucopia.qmri

This module contains transforms that implement physics-based forward models of MR image formation.

RandomSusceptibilityMixtureTransform

RandomSusceptibilityMixtureTransform(mu_tissue=Uniform(9, 10), sigma_tissue=0.01, mu_bone=Uniform(12, 13), sigma_bone=0.1, fwhm=2, label_air=0, label_bone=None, dtype=None, *, shared='channels', **kwargs)

Bases: NonFinalTransform

A RandomGaussianMixtureTransform tailored to susceptibility maps.

This transform returns a delta susceptibility map (with respect to air), in ppm.

Parameters:

Name	Type	Description	Default
mu_tissue	float or Sampler	Distribution of negative susceptibility offsets (in ppm) of soft tissues with respect to air. Will be negated (air susceptibility is larger than all tissues). If float: upper bound.	Uniform(9, 10)
sigma_tissue	float or Sampler	Standard deviation of susceptibility offsets, within class. If float: uper bound.	0.01
mu_bone	float or Sampler	Distribution of negative susceptibility offsets (in ppm) of hard tissues with respect to air. Will be negated (air susceptibility is larger than all tissues). If float: upper bound.	Uniform(12, 13)
sigma_bone		Standard deviation of susceptibility offsets, within class. If float: upper bound.	0.1
fwhm	Sampler or [list of] float	Sampling function for smoothing width. If float: upper bound.	2
label_air	[list of] int	Labels corresponding to air.	0
label_bone	[list of] int	Labels corresponding to bone and teeth.	None

SusceptibilityToFieldmapTransform

SusceptibilityToFieldmapTransform(axis=-1, field_strength=3, larmor=42576000.0, s0=0.4, s1=-9.5, voxel_size=1, mask_air=False, **kwargs)

Bases: FinalTransform

Convert a susceptibiity map (in ppm) into a field map (in Hz)

Parameters:

Name	Type	Description	Default
axis	int	Readout dimension	-1
field_strength	float	Strength of the main magnetic field, in Tesla. If None, return a fieldmap in ppm.	3
larmor	float	Larmor frequency (default: Larmor frequency of water)	42576000.0
s0	float	Susceptibility of air (ppm)	0.4
s1	float	Susceptibility of tissue minus susceptiblity of air (ppm) (only used if ds is a boolean mask)	-9.5
voxel_size	[list of] float	Voxel size	1
mask_air	bool	Mask air (where delta susceptibility == 0) from resulting fieldmap.	False

ShimTransform

ShimTransform(linear=None, quadratic=None, isocenter=None, **kwargs)

Bases: FinalTransform

Parameters:

Name	Type	Description	Default
linear	(3 or 1) tensor or list of float	Linear components (3D: [XY, XZ, YX], 2D: [XY])	None
quadratic	(2 or 1) tensor or list of float	Quadratic components (3D: [XXYY, XXZZ], 2D: [XXYY])	None
isocenter	(3 or 2) tensor or list of float	Coordinates of the isocenter, in voxels	None

Other Parameters:

Name	Type	Description
returns	[list or dict of] {'input', 'output', 'shim'}

OptimalShimTransform

OptimalShimTransform(max_order=2, lam_abs=1, lam_grad=10, mask=True, **kwargs)

Bases: NonFinalTransform

Compute a linear combination of spherical harmonics that flattens the input field map

Parameters:

Name	Type	Description	Default
max_order	int	Maximum order of spherical basis functions	2
lam_abs	float	Regularization factor for absolute values	1
lam_grad	float	Regularization factor for first order gradients	10
mask	bool	Mask zeros/NaNs from objective functions	True

Other Parameters:

Name	Type	Description
returns	[list or dict of] {'input', 'output', 'shim'}

RandomShimTransform

RandomShimTransform(coefficients=5, max_order=2, shared=False, **kwargs)

Bases: NonFinalTransform

Sample a random (imperfect) shim.

This function randomly samples the coefficients of a field encoded by spherical harmonics.

Parameters:

Name	Type	Description	Default
coefficients	int or Sampler	Sampler for spherical harmonics coefficients (or upper bound)	5
max_order	int or Sampler	Sampler for spherical harmonics order (or upper bound)	2

Other Parameters:

Name	Type	Description
returns	[list or dict of] {'input', 'output', 'shim'}
shared	(channels, tensors, channels + tensors, '')

HertzToPhaseTransform

HertzToPhaseTransform(te=0, **kwargs)

Bases: FinalTransform

Converts a ΔB0 field (in Hz) into a Phase shift field Δφ (in rad)

Parameters:

Name	Type	Description	Default
te	float	Echo time, in sec.	0

GradientEchoTransform

GradientEchoTransform(tr=0.025, te=0.007, alpha=20, pd=None, t1=None, t2=None, b1=1, mt=0, **kwargs)

Bases: FinalTransform

Spoiled Gradient Echo forward model

Parameters:

Name	Type	Description	Default
tr	float	Repetition time, in sec	0.025
te	float	Echo time, in sec	0.007
alpha	float	Nominal flip angle, in degree	20
pd	float	Proton density (PD). If None, the first input channel is PD.	None
t1	float	Longitudinal relaxation time (T1), in sec. If None, the second input channel is T1.	None
t2	float	Apparent transverse relaxation time (T2), in sec. If None, the third input channel is T2.	None
b1	float	Transmit efficiency (B1+). 1 means 100% efficiency. If None, the fourth input channel is B1+.	1
mt	float	Magnetization transfer saturation (MTsat). If None, the fifth input channel is MTsat.	0

xform

xform(x)

Parameters:

Name	Type	Description	Default
x	(K, *spatial)	Parameters that were not set during class instantiation (i.e., whose value was None), in the order: - pd: Proton density - t1: Longitudinal relaxation time (T1), in sec. - t2: Apparent transverse relaxation time (T2*), in sec. - b1: Transmit efficiency (B1+). `1` means 100% efficiency. - mt: Magnetization transfer saturation (MTsat).	required

RandomGMMGradientEchoTransform

RandomGMMGradientEchoTransform(tr=0.05, te=0.05, alpha=90, pd=1, t1=10, t2=100, mt=0.1, b1=RandomMulFieldTransform(vmax=1.5), sigma=0.2, fwhm=2, **kwargs)

Bases: NonFinalTransform

Generate a Spoiled Gradient Echo image from synthetic PD/T1/T2 maps.

Parameters:

Name	Type	Description	Default
tr	Sampler or float	Random sampler for repetition time, or upper bound	0.05
te	Sampler or float	Random sampler for echo time, or upper bound	0.05
alpha	Sampler or float	Random sampler for nominal flip angle, or upper bound	90
pd	Sampler or float	Random sampler for proton density, or upper bound	1
t1	Sampler or float	Random sampler for longitudinal relaxation, or upper bound	10
t2	Sampler or float	Random sampler for apparent transverse relaxation, or upper bound	100
mt	Sampler or float	Random sampler for magnetization transfer saturation, or upper bound	0.1
b1	Transform	A transformation that samples a smooth multiplicative field	RandomMulFieldTransform(vmax=1.5)
sigma	Sampler or float	Random sampler for intra-class standard deviation (in percent), or upper bound	0.2
fwhm	Sampler or float	Random sampler for intra-class smoothing (in voxels), or upper bound	2

GREParameters

GREParameters(param, **kwargs)

Bases: FinalTransform

Store parameter maps

Final

Final(prm, fwd, mask, **kwargs)

Bases: FinalTransform

Apply GRE forward model to parameters, then mask