Diffusion derivatives

Preprocessed diffusion-weighted images

Multiple different versions of preprocessing can be stored for the same source data. To distinguish them from each other, the desc filename keyword can be used. Details of preprocessing performed for each variation of the processing should be included in the pipeline documentation.

<pipeline_name>/
sub-<participant_label>/
dwi/
<source_keywords>[_space-<space>][_desc-<label>]_dwi.nii[.gz]
<source_keywords>[_space-<space>][_desc-<label>]_dwi.bvals
<source_keywords>[_space-<space>][_desc-<label>]_dwi.bvecs
<source_keywords>[_space-<space>][_desc-<label>]_dwi.json


The JSON sidecar file is REQUIRED (due to the REQUIRED SkullStripped field - see Common Data Types), and MAY additionally be used to store information about what preprocessing options were used (for example whether denoising was performed, corrections applied for field inhomogeneity / gradient non-linearity / subject motion / eddy currents, etc.).

Key name Description
Denoising OPTIONAL. String. Denoising method
GibbsRingingCorrection OPTIONAL. Boolean. Removal of Gibbs ringing artifacts
MotionCorrection OPTIONAL. String. Motion correction; allowed values: none, volume, slice
EddyCurrentCorrection OPTIONAL. String. Eddy current distortion correction; reserved values: none, linear, quadratic, cubic
IntensityNormalizationMethod OPTIONAL. String. Method (if any) used for intensity normalization
FieldInhomogeneityEstimation OPTIONAL. String. Method (if any) used for estimation of the B0 inhomogeneity field; reserved values: multiecho, phaseencode, registration
FieldInhomogeneityCorrection OPTIONAL. String. Correction for geometric distortions arising from B0 magnetic field inhomogeneity; reserved values: none, static, dynamic
GradientNonLinearityGeometryCorrection OPTIONAL. Boolean. Correction for geometric distortions arising from non-linearity of gradients
GradientNonLinearityQSpaceCorrection OPTIONAL. Boolean. Correction for spatial inhomogeneity of diffusion sensitisation gradient strength
SliceDropoutDetection OPTIONAL. Boolean. Detection of signal dropout in acquired slices during pre-processing
SliceDropoutReplacement OPTIONAL. Boolean. Replacement of image data within slices containing signal dropout with predicted values
BiasFieldCorrectionMethod OPTIONAL. String. Method (if any) used for correction of B1 RF field inhomogeneity

Diffusion models

Diffusion MRI can be modeled using various paradigms to extract more informative representations of the diffusion process and the underlying biological structure. A wide range of such models are available, each of which has its own unique requirements with respect to:

• The input parameters required in order to define / constrain the model;

• The appropriate data representations utilised to store information parameterised by or from the model onto the filesystem;

• The requirements for encapsulation and complete representation of derived orientation information, which is a key strength of diffusion MRI but presents unique challenges for correct interpretation.

Parameter terminology

Throughout this document, the term "parameter" is used to refer to multiple distinct sources of information. The distinction between these uses is defined thus:

1. Input model parameter:

Value or non-numerical setting that influences the conformation of the diffusion model to the empirical diffusion-weighted data.

1. Intrinsic model parameter:

Value that is the direct result of fitting the diffusion model to the empirical diffusion-weighted data.

1. Extrinsic model parameter:

Value that can be calculated directly from previously estimated intrinsic model parameters, without necessitating reference to the empirical diffusion-weighted data.

For example, consider a diffusion tensor model fit: the number of iterations in the optimisation algorithm would be an input parameter; the six unique diffusion tensor coefficients would be the intrinsic parameters; the Fractional Anisotropy (FA) would be an extrinsic parameter (as it is calculated from the diffusion tensor coefficients rather than the image data).

File names

<pipeline_name>/
sub-<participant_label>/
dwi/
<source_keywords>[_space-<space>][_desc-<label>]_parameter-<intparam1>_<model>.nii[.gz]
<source_keywords>[_space-<space>][_desc-<label>]_parameter-<intparam2>_<model>.nii[.gz]
<source_keywords>[_space-<space>][_desc-<label>]_<model>.json

[<source_keywords>[_space-<space>][_desc-<label>]_parameter-<extparam1>_<model>.nii[.gz]]
[<source_keywords>[_space-<space>][_desc-<label>]_parameter-<extparam1>_<model>.json]
[<source_keywords>[_space-<space>][_desc-<label>]_parameter-<extparam2>_<model>.nii[.gz]]
[<source_keywords>[_space-<space>][_desc-<label>]_parameter-<extparam2>_<model>.json]

• Field "<model>" is a unique identifier corresponding to the particular diffusion model. If the particular diffusion model is one that is included in this specification, then the prescribed model label MUST be utilised; e.g. "dti" for the diffusion tensor model.

• Files "<source_keywords>[_space-<space>][_desc-<label>]_parameter-<intparam*>_<model>.nii[.gz]" provide data corresponding to the various intrinsic parameters of the model. In cases where intrinsic model parameters are all contained within a single image file, field "_parameter-" nevertheless MUST be included, with value "all"; e.g.:

<pipeline_name>/
sub-<participant_label>/
dwi/
<source_keywords>[_space-<space>][_desc-<label>]_parameter-all_<model>.nii[.gz]
<source_keywords>[_space-<space>][_desc-<label>]_<model>.json

• File "<source_keywords>[_space-<space>][_desc-<label>]_<model>.json" provides basic model information and input model parameters.

• OPTIONAL images "<source_keywords>[_space-<space>][_desc-<label>]_parameter-<extparam*>_<model>.nii[.gz]" may be defined, in order to provide additional extrinsic model parameters.

• OPTIONAL files "<source_keywords>[_space-<space>][_desc-<label>]_parameter-<extparam*>_<model>.json" may be defined to provide only information or parameters relevant to derivation of each relevant extrinsic model parameter image.

Data representations

There are multiple techniques by which data that relate to the anisotropic nature of either the diffusion process or underlying tissue may be arranged and/or encoded into NIfTI image data. A list of known techniques is enumerated below, accompanied by requisite information specific to the reading / writing of each representation.

For data that encode orientation information, there are fields that MUST be specified in the sidecar JSON file in order to ensure appropriate interpretation of that information; see orientation specification).

Any model parameter image (whether intrinsic or extrinsic) where a solitary numerical value is defined in each 3D image voxel is referred to here as a "scalar" image.

4D image with three volumes, intended to be interpreted as red, green and blue colour intensities for visualisation [Pajevic1999]. Image data MUST NOT contain negative values.

4D image where data across volumes within each voxel encode one or more discrete orientations using angles on the 2-sphere, optionally exploiting the distance from origin to encode the value of some parameter.

This may take one of two forms:

1. Value per direction

Each consecutive triplet of image volumes encodes a spherical coordinate, using ISO convention for both the order of parameters and reference frame for angles:

1. Distance from origin; value of embedded parameter MUST be indicated in "_parameter-*" filename field;

2. Inclination / polar angle, in radians, relative to the zenith direction being the positive direction of the third reference axis (see orientation specification);

3. Azimuth angle, in radians, orthogonal to the zenith direction, with value of 0.0 corresponding to the first reference axis (see orientation specification), increasing according to the right-hand rule about the zenith direction.

Number of image volumes is equal to (3xN), where N is the maximum number of discrete orientations in any voxel in the image.

2. Directions only

Each consecutive pair of image volumes encodes inclination / azimuth pairs, with order & convention identical to that above (equivalent to spherical coordinate with assumed unity distance from origin).

Number of image volumes is equal to (2xN), where N is the maximum number of discrete orientations in any voxel in the image.

4D image where data across volumes within each voxel encode one or more discrete orientations using triplets of axis dot products.

This representation may be used in one of two ways:

1. Value per direction

Each 3-vector, once explicitly normalized, provides a direction on the unit sphere; the norm of each 3-vector additionally encodes the magnitude of some model parameter, the nature of which MUST be indicated in the "_parameter-*" filename field.

2. Directions only

Each triplet of values encodes an orientation on the unit sphere (i.e. the 3-vector data are normalized); no quantitative value is associated with each triplet.

Number of image volumes is equal to (3xN), where N is the maximum number of discrete orientations in any voxel in the image.

4D image where data across volumes within each voxel represent a continuous function spanning the 2-sphere as coefficient values using a spherical harmonics basis.

Number of image volumes depends on the spherical harmonic basis employed, and the maximal spherical harmonic degree lmax (see spherical harmonics bases).

4D image where data across volumes within each voxel represent amplitudes of a discrete function spanning the 2-sphere.

Number of image volumes corresponds to the number of discrete directions on the unit sphere along which samples for the spherical function in each voxel are provided; these directions MUST themselves be provided in the associated sidecar JSON file (see orientation specification).

TODO

4D image containing, for every image voxel, data corresponding to some set of model parameters, the names and order of which are defined within the intrinsic model parameters section.

Intrinsic model parameters

The following models are codified within the specification, and the model label should be used as the final field in the filename for storage of any intrinsic or extrinsic parameters. If a new model is used, common sense should be used to derive a name following the BIDS standard, and should ideally be integrated in a future version of the specification.

Model label Full Name Data representation
bs Ball-and-Stick(s) model [Behrens2003],[Behrens2007],[Jbabdi2012] One spherical coordinates image with parameter name "sticks", providing both fibre volume fractions and orientations using polar angles;
Optional scalar images with parameter names {"bzero", "dmean", "dstd"} providing the model-estimated b=0 signal intensity, mean stick diffusivity, and standard deviation of stick diffusivities respectively
csa Constant Solid Angle [Aganj2010] Spherical harmonics image
csd Constrained Spherical Deconvolution [Tournier2007],[Descoteaux2009],[Jeurissen2014] Spherical harmonics image
If a multi-tissue decomposition is performed, provide one individual 4D image per tissue, with "_desc-<desc>" filename field being an abbreviation of the tissue estimated by that particular ODF
dki Diffusion Kurtosis Imaging [Jensen2005] Single parameter vectors image with parameter name "all" with 21 volumes in the order: Dxx, Dxy, Dxz, Dyy, Dyz, Dzz, Wxxxx, Wyyyy, Wzzzz, Wxxxy, Wxxxz, Wxyyy, Wyyyz, Wxzzz, Wyzzz, Wxxyy, Wxxzz, Wyyzz, Wxxyz, Wxyyz, Wxyzz (D is the diffusion tensor, W is the kurtosis tensor)
OR
6 diffusion tensor coefficients as parameter vectors image with parameter name "tensor";
15 kurtosis tensor coefficients as parameter vectors image with parameter name "kurtosis";
Optional: estimated b=0 intensity as scalar image with parameter name "bzero"
dsi Diffusion Spectrum Imaging [Wedeen2008],[Paquette2017] Probability distribution functions
dti Diffusion Tensor Imaging [Basser1994] Single parameter vectors image with parameter name "all" with 6 volumes in the order: Dxx, Dxy, Dxz, Dyy, Dyz, Dzz
OR
Tensor coefficients as parameter vectors image with parameter name "tensor";
Estimated b=0 intensity as scalar image with parameter name "bzero"
forecast Fiber ORientation Estimated using Continuous Axially Symmetric Tensors [Zuchelli2017] Spherical harmonics image
fwdti Free water DTI [Hoy2015] One parameter vectors image with parameter name "tensor", containing 6 volumes in the order: Dcxx, Dcxy, Dcxz, Dcyy, Dcyz, Dczz (Dc is the free-water-corrected diffusion tensor);
One scalar image with parameter name "fwf" corresponding to the estimated free water fraction
mapmri Mean Apparent Propagator MRI [Ozarslan2013]
noddi Neurite Orientation Dispersion and Density Imaging [Zhang2012],[Daducci2015] Three scalar images, with parameter names equal to {"icvf", "isovf", "od"} (ICVF is the “intracellular volume fraction” (also known as NDI); ISOVF is the "isotropic component volume fraction"; OD is the “orientation dispersion” (the variance of the Watson distribution; also known as ODI));
One 3-vectors image with parameter name "direction" to provide the estimated fibre orientation
qbi Q-Ball Imaging [Tuch2004], [Hess2006] Single amplitudes image
OR
Single spherical harmonics image
shore Simple Harmonic Oscillator-based Reconstruction and Estimation [Ozarslan2008]
wmti White Matter Tract Integrity [Fieremans2011] One parameter vectors image with parameter name "coeffs", with 33 volumes in the order: Dxx, Dxy, Dxz, Dyy, Dyz, Dzz, Wxxxx, Wyyyy, Wzzzz, Wxxxy, Wxxxz, Wxyyy, Wyyyz, Wxzzz, Wyzzz, Wxxyy, Wxxzz, Wyyzz, Wxxyz, Wxyyz, Wxyzz, Dhxx, Dhxy, Dhxz, Dhyy, Dhyz, Dhzz, Drxx, Drxy, Drxz, Dryy, Dryz, Drzz (D is the diffusion tensor and W is the kurtosis tensor);
One scalar image with parameter name "awf", representing the estimated axonal water fraction

The JSON sidecar for the intrinsic diffusion model parameters may contain the following key/value pairs irrespective of the particular model:

Key name Description
Gradients OPTIONAL. List of 3-vectors. Subset of gradients utilized to fit the model, as a list of three-elements lists. If not present, all gradients were used.
Shells OPTIONAL. List of floats. Shells that were utilized to fit the model, as a list of b-values. If the key is not present, it should be assumed that all shells were used during model fitting.
Mask OPTIONAL. String. Name of image that was used as a binary mask to specify those voxels for which the model was fit.
ModelDescription OPTIONAL. String. Extended information to describe the model.
ModelURL OPTIONAL. String. URL to the implementation of the specific model utilized.
Parameters OPTIONAL. Dictionary. Input model parameters that are constant across the image (see examples below).

Model bootstrapping

Results of model bootstrapping can be provided by concatenating multiple realisations of model intrinsic parameters along an additional image axis.

The corresponding sidecar JSON file may include dictionary field "BootstrapParameters", descibing those input parameters specific to the determination and export of multiple realisations of the model fit in each image voxel.

Input model parameters

Parameters that may / must be stored within the JSON sidecar "Parameters" field depends on the particular model used.

"Parameters" fields that may be applicable to multiple models:

Key name Description
FitMethod OPTIONAL. String. The optimisation procedure used to fit the intrinsic model parameters to the empirical diffusion-weighted signal. Options are: "ols" (Ordinary Least Squares); "wls" (Weighted Least Squares); "iwls" (Iterative Weighted Least Squares); "nlls" (Non-Linear Least Squares).
Iterations OPTIONAL. Integer. The number of iterations used for any form of model fitting procedure where the number of iterations is a fixed input parameter.
OutlierRejection OPTIONAL. Boolean. Value indicating whether or not rejection of outlier values was performed during fitting of the intrinsic model parameters.
Samples OPTIONAL. Integer. The number of realisations of a diffusion model from which statistical summaries (e.g. mean, standard deviation) of those parameters are provided.

Reserved keywords for models built into the specification are as follows:

• bs :

• ARDFudgeFactor: Float. Weight applied to Automatic Relevance Determination (ARD).

• Fibers: Integer. Number of discrete fibres to fit in each voxel.
• ModelBall: String. Model used to describe the "ball" component in the model.
• ModelSticks: String. Model used to describe the "stick" component in the model.

• csa :

• SphericalHarmonicOrder : value

• Smoothing : value
• Basis : value

• csd:

• NonNegativityConstraint: String. Options are: { soft, hard }. Specifies whether the ODF was estimated using regularisation ("soft") or prevention ("hard") of negative values.

• ResponseFunctionZSH: Two options:
• Vector of floating-point values, where values correspond to the response function coefficient for each consecutive even zonal spherical harmonic degree starting from zero (in this case field "Shells" should contain a single integer value);
• Matrix of floating-point values: 1 row per unique b-value as listed in "Shells"; 1 column per even zonal spherical harmonic degree starting from zero; if there are a different number of non-zero zonal spherical harmonic coefficients for different b-values, these must be padded with zeroes such that all rows contain the same number of columns.
• ResponseFunctionTensor: Vector of 4 floating-point values: three tensor eigenvalues, then reference b=0 intensity
• SphericalHarmonicBasis: String. Options are: { MRtrix3, Descoteaux }. Details are provided in the spherical harmonics bases section.
• SphericalHarmonicDegree: Integer. The maximal spherical harmonic order lmax; the number of volumes in the associated NIfTI image must correspond to this value as per the relationship described in spherical harmonics bases section.
• Tissue: String. A more verbose description for the tissue estimated via this specific ODF.

• dsi :

• GridSize : value

• RStart : value
• RStep : value
• REnd : value
• FilterWidth : value

• dti :

• RESTORESigma: Float

• forecast :

• Sphere : value

• DecAlg : value
• LambdaLb : value
• SphericalHarmonicsOrder : value

• mapmri :

• RadialOrder : value

• LaplacianRegularization : bool
• LaplacianWeighting : value
• PositivityConstraint : bool
• Tau : value
• ConstrainE0 : value
• PositiveConstraint : value
• PosGrid : value
• PosRadius : value
• AnisotropicScaling : bool
• EigenvalueThreshold : value
• PosGrid : value
• BvalThreshold : value
• DTIScaleEstimation : bool
• StaticDiffusivity : value

• noddi:

• DPar : value

• DIso : value
• Lambda1 : value
• Lambda2 : value

• shore :

• RadialOrder : value

• Zeta : value
• LambdaN : value
• LambdaL : value
• Tau : value
• ConstrainE0 : value
• PositiveConstraint : value
• PosGrid : value
• PosRadius : value

Extrinsic model parameters

<parameter> value Description Data representation Possible Model sources Unit or scale
ad Axial Diffusivity (also called parallel diffusivity) Scalar { dki, dti, forecast, fwdti, wmti } \mu m2.ms-1 1
ak Axial kurtosis Scalar { dki, wmti } Unitless
afdtotal Total Apparent Fibre Density (AFD) [Calamante2015] Scalar { csd } Unitless
cl Tensor linearity [Westin1997] Scalar { dki, dti, fwdti, wmti }
cp Tensor planarity [Westin1997] Scalar { dki, dti, fwdti, wmti }
cs Tensor sphericity [Westin1997] Scalar { dki, dti, fwdti, wmti }
evec Eigenvector(s) 3-vectors { dki, dti, fwdti, wmti } \mu m2.ms-1 1
fa Fractional Anisotropy [Basser1996] Scalar { dki, dti, forecast, fwdti, wmti } Proportion [0.0-1.0]
fsum Sum of partial volume fractions of stick components Scalar { bs } Volume fraction [0.0-1.0]
gfa Generalized Fractional Anisotropy [Tuch2004] Scalar { csa, csd, forecast, mapmri, shore } Proportion [0.0-1.0]
md Mean diffusivity (also called apparent diffusion coefficient, ADC) Scalar { dki, dti, forecast, fwdti, wmti } \mu m2.ms-1 1
mk Mean kurtosis Scalar { dki, wmti } Unitless
mode Mode of the tensor Scalar { dki, dti, fwdti, wmti }
msd Mean-Squared Displacement Scalar { mapmri, shore }
pdf Diffusion propagator 3-vectors
peak Direction(s) and amplitude(s) of ODF maximum (maxima) 3-vectors { csa, csd, forecast, shore } Same units as ODF
rd Radial Diffusivity (also called perpendicular diffusivity) Scalar { dki, dti, forecast, fwdti, wmti } \mu m2.ms-1 1
rk Radial kurtosis Scalar { dki, wmti } Unitless
rtap Return To Axis Probability Scalar { mapmri } Probability [0.0-1.0]
rtop Return To Origin Probability Scalar { shore } Probability [0.0-1.0]
rtpp Return To Plane Probability Scalar { mapmri } Probability [0.0-1.0]
tort Tortuosity of extra-cellular space Scalar { dki }

While not explicitly included in the table above, any scalar extrinsic parameter can theoretically be combined with a separate source of orientation information from the diffusion model in order to produce a directionally-encoded colour, spherical coordinates or 3-vectors image.

Orientation specification

Key name Relevant data representations Description
AntipodalSymmetry Spherical coordinates, 3-vectors, spherical harmonics, amplitudes, probability distribution functions, parameter vectors OPTIONAL. Boolean. Indicates whether orientation information should be interpreted as being antipodally symmetric. Assumed to be True if omitted.
Directions Amplitudes REQUIRED. List. Data are either spherical coordinates (directions only) or 3-vectors with unit norm. Defines the dense directional basis set on which samples of a spherical function within each voxel are provided.
FillValue Spherical coordinates, 3-vectors OPTIONAL. Float; allowed values: { 0.0, NaN }. Value stored in image when number of discrete orientations in a voxel is fewer than the maximal number for that image.
OrientationRepresentation All except scalar REQUIRED. String; allowed values: { dec, unitspherical, spherical, unit3vector, 3vector, sh, amp, pdf, param }. The data representation used to encode orientation information within the NIfTI image.
ReferenceAxes All except scalar REQUIRED. String; allowed values: { ijk, xyz }. Indicates whether the NIfTI image axes, or scanner-space axes, are used as reference axes for orientation information.
SphericalHarmonicBasis Spherical harmonics REQUIRED. String; allowed values: { MRtrix3, Descoteaux }. Basis by which to define the interpretation of image values across volumes as spherical harmonics coefficients.
SphericalHarmonicDegree Spherical harmonics REQUIRED. Integer. Maximal degree of the spherical harmonic basis employed.

If AntipodalSymmetry is True, then no constraints are imposed with respect to the domain on the 2-sphere in which orientations may be specified; for instance, 3-vectors { 0.57735, 0.57735, 0.57735 } and { -0.57735, -0.57735, -0.57735 } are both permissible and equivalent to one another.

Spherical Harmonics bases

• MRtrix3

• Antipodally symmetric: all basis functions with odd degree are assumed zero; AntipodalSymmetry MUST NOT be set to True.

• Functions assumed to be real: conjugate symmetry is assumed, i.e. Y(l,-m) = Y(l,m)*, where * denotes the complex conjugate.

• Mapping of image volumes to spherical harmonic basis function coefficients:

Volume Coefficient
0 l = 0, m = 0
1 l = 2, m = 2 (imaginary part)
2 l = 2, m = 1 (imaginary part)
3 l = 2, m = 0
4 l = 2, m = 1 (real part)
5 l = 2, m = 2 (real part)
6 l = 4, m = 4 (imaginary part)
7 l = 4, m = 3 (imaginary part)
... etc.
• Normalisation: TODO

• Relationship between maximal spherical harmonic degree lmax and number of image volumes N:

N = ((lmax+1) x (lmax+2)) / 2

lmax 0 2 4 6 8 ...
N 1 6 15 28 45 etc.
• Relationship between maximal degree of zonal spherical harmonic function (spherical harmonics function where all m != 0 terms are assumed to be zero; used for e.g. response function definition) and number of coefficients N:

N = 1 + (lmax / 2)

lmax 0 2 4 6 8 ...
N 1 2 3 4 5 etc.
• Descoteaux

TODO

Demonstrative examples

• A basic Diffusion Tensor fit:
my_diffusion_pipeline/
sub-01/
dwi/
sub-01_dti.nii.gz
sub-01_dti.json


Dimensions of NIfTI image "sub-01_dti.nii.gz": IxJxKx6 (parameter vectors)

Contents of JSON file:

{
"Model": "Diffusion Tensor",
"OrientationRepresentation": "param",
"ReferenceAxes": "xyz",
"Parameters": {
"FitMethod": "ols",
"OutlierRejection": False
}
}

• A multi-shell, multi-tissue Constrained Spherical Deconvolution fit:
my_diffusion_pipeline/
sub-01/
dwi/
sub-01_desc-wm_csd.nii.gz
sub-01_desc-wm_csd.json
sub-01_desc-gm_csd.nii.gz
sub-01_desc-gm_csd.json
sub-01_desc-csf_csd.nii.gz
sub-01_desc-csf_csd.json
sub-01_csd.json


Dimensions of NIfTI image "sub-01_desc-wm_csd.nii.gz": IxJxKx45 (spherical harmonics) Dimensions of NIfTI image "sub-01_desc-gm_csd.nii.gz": IxJxKx1 (spherical harmonics) Dimensions of NIfTI image "sub-01_desc-csf_csd.nii.gz": IxJxKx1 (spherical harmonics)

Contents of file "sub-01_csd.json" (common to all intrinsic model parameter images):

{
"Model": "Multi-Shell Multi-Tissue (MSMT) Constrained Spherical Deconvolution (CSD)",
"Shells": [ 0, 1000, 2000, 3000 ],
"Parameters": {
"SphericalHarmonicBasis": "MRtrix3",
"NonNegativityConstraint": "hard"
}
}


Contents of JSON file "sub-01_desc-wm_csd.json":

{
"OrientationRepresentation": "sh",
"ReferenceAxes": "xyz",
"ResponseFunctionZSH": [ [ 600.2 0.0 0.0 0.0 0.0 0.0 ],
[ 296.3 -115.2 24.7 -4.4 -0.5 1.8 ],
[ 199.8 -111.3 41.8 -10.2 2.1 -0.7 ],
[ 158.3 -98.7 48.4 -17.1 4.5 -1.4 ] ],
"SphericalHarmonicDegree": 8,
"Tissue": "White matter"
}


Contents of JSON file "sub-01_desc-gm_csd.json":

{
"OrientationRepresentation": "sh",
"ReferenceAxes": "xyz",
"ResponseFunctionZSH": [ [ 1041.0 ],
[ 436.6 ],
[ 224.9 ],
[ 128.8 ] ],
"SphericalHarmonicDegree": 0,
"Tissue": "Grey matter"
}

• A NODDI fit:
my_diffusion_pipeline/
sub-01/
dwi/
sub-01_parameter-icvf_noddi.nii.gz
sub-01_parameter-isovf_noddi.nii.gz
sub-01_parameter-od_noddi.nii.gz
sub-01_parameter-direction_noddi.nii.gz
sub-01_parameter-direction_noddi.json
sub-01_noddi.json


Dimensions of NIfTI image "sub-01_parameter-icvf_noddi.nii.gz": IxJxK (scalar) Dimensions of NIfTI image "sub-01_parameter-isovf_noddi.nii.gz": IxJxK (scalar) Dimensions of NIfTI image "sub-01_parameter-od_noddi.nii.gz": IxJxK (scalar) Dimensions of NIfTI image "sub-01_parameter-direction_noddi.nii.gz": IxJxKx3 (3-vectors)

Contents of file "sub-01_noddi.json" (common to all intrinsic model parameter images):

{
"Model": "Neurite Orientation Dispersion and Density Imaging (NODDI)",
"ModelURL": "https://www.nitrc.org/projects/noddi_toolbox"
}


Contents of JSON file "sub-01_parameter-direction_noddi.json":

{
"OrientationRepresentation": "3vector",
"ReferenceAxes": "???"
}

• An FSL bedpostx Ball-And-Sticks fit (including both mean parameters and bootstrap realisations):
my_diffusion_pipeline/
sub-01/
dwi/
sub-01_desc-mean_parameter-bzero_bs.nii.gz
sub-01_desc-mean_parameter-dmean_bs.nii.gz
sub-01_desc-mean_parameter-dstd_bs.nii.gz
sub-01_desc-mean_parameter-sticks_bs.nii.gz
sub-01_desc-mean_parameter-sticks_bs.json
sub-01_desc-merged_parameter-sticks_bs.nii.gz
sub-01_desc-merged_parameter-sticks_bs.json
sub-01_bs.json


Dimensions of NIfTI image "sub-01_desc-mean_parameter-bzero_bs.nii.gz": IxJxK (scalar) Dimensions of NIfTI image "sub-01_desc-mean_parameter-dmean_bs.nii.gz": IxJxK (scalar) Dimensions of NIfTI image "sub-01_desc-mean_parameter-dstd_bs.nii.gz": IxJxK (scalar) Dimensions of NIfTI image "sub-01_desc-mean_parameter-sticks_bs.nii.gz": IxJxKx9 (spherical coordinates, distance from origin encodes fibre volume fraction) Dimensions of NIfTI image "sub-01_desc-merged_parameter-sticks_bs.nii.gz": IxJxKx9x50 (spherical coordinates, distance from origin encodes fibre volume fraction; 50 bootstrap realisations)

Contents of JSON files "sub-01_desc-mean_parameter-sticks_bs.json" and "sub-01_desc-merged_parameter-sticks_bs.json" (contents of two files are identical):

{
"OrientationRepresentation": "spherical",
"ReferenceAxes": "ijk"
}


Contents of JSON file "sub-01_bs.json":

{
"Model": "Ball-And-Sticks model using FSL bedpostx",
"ModelURL": "https://fsl.fmrib.ox.ac.uk/fsl/fslwiki/FDT",
"Parameters": {
"ARDFudgeFactor": 1.0,
"Fibers": 3,
"Samples": 50
},
"BootstrapParameters": {
"Burnin": 1000,
"Jumps": 1250,
"SampleEvery": 25
}
}


1: For example, for free water in body temperature, the diffusivity in units of \mu m2.ms-1 should be approximately 3.0.

[Aganj2010]: Aganj et al. 2010

[Basser1994]: Basser et al. 1994

[Basser1996]: Basser et al. 1996

[Behrens2003] Behrens et al. 2003

[Behrens2007] Behrens et al. 2007

[Calamante2015]: Calamante et al. 2015

[Descoteaux2009]: Descoteaux et al. 2009

[Fieremans2011]: Fieremans et al. 2011

[Hess2006]: Hess et al. 2006

[Hoy2014]: Hoy et al. 2014

[Jbabdi2012] Jbabdi et al. 2012

[Jensen2005]: Jensen et al. 2005

[Jeurissen2014]: Jeurissen et al. 2014

[Ozarslan2008]: Ozarslan et al. 2008

[Ozarslan2013]: Ozarslan 2013

[Paquette2017]: Paquette et al 2017

[Pajevic1999]: Pajevic et al 1999

[Tournier2007]: Tournier et al. 2007

[Tuch2004]: Tuch 2004

[Wedeen2008]: Wedeen et al. 2008

[Westin1997]: Westin 1997

[Zhang2012]: Zhang et al. 2012

[Zuchelli2017]: Zuchelli et al. 2017