Introduce new models

[Lestropie]

There will always be new diffusion models that could be introduced into the specification. The intention is for the framework of the specification to be sufficiently general and extensible to be possible to utilise directly for new models, though precedents such as filename suffix & model parameter dictionary can still be set by introducing that model into the specification.

This issue is intended to serve as a list of prospective models that could be introduced into the specification, and to link to relevant Issues / PRs as necessary. The Issue will additionally be used to stash content from models that have been removed from earlier drafts of the specification.

For each model, we ideally don't want to base the specification off of one specific software implementation; the proposal needs to be compatible with all softwares providing implementations of that model. So proposal for inclusion of any of these models will need to include a search and listing of all relevant softwares.

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• [] Constant Solid Angle (CSA) Manuscript

• [] Diffusion Kurtosis Imaging (DKI) Manuscript

• [] Diffusion Spectrum Imaging (DSI) Manuscript

• [] Fiber ORientation Estimated using Continuous Axially Symmetric Tensors (FORECAST) Manuscript

• [] Free water DTI (Unsure whether this should be a "separate model", or whether it should be an integral part of the DTI model, with some instances simply failing to estimate the free water component)

• [] Mean Apparent Propagator MRI Manuscript

• [] NODDI Manuscript

• [] Q-Ball Imaging (QBI) Original manuscript SH version

• [] SHORE

• [] White Matter Tract Integrity (WMTI) Manuscript

[Lestropie]

Old draft contents for models removed in #40

### Intrinsic model parameters | Model label | Full Name | [Data representation](#data-representations) | | ----------- | ----------------------------------------------------------------------------------------------------------------------------------------------- | --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | | `csa` | Constant Solid Angle \[[Aganj2010](#aganj2010)\] | [Spherical harmonics](#data-sh) image | | `dki` | Diffusion Kurtosis Imaging \[[Jensen2005](#jensen2005)\] | Single [parameter vectors](#data-param) image with parameter name "`all`" with 21 volumes in the order: *D_xx*, *D_xy*, *D_xz*, *D_yy*, *D_yz*, *D_zz*, *W_xxxx*, *W_yyyy*, *W_zzzz*, *W_xxxy*, *W_xxxz*, *W_xyyy*, *W_yyyz*, *W_xzzz*, *W_yzzz*, *W_xxyy*, *W_xxzz*, *W_yyzz*, *W_xxyz*, *W_xyyz*, *W_xyzz* (*D* is the diffusion tensor, *W* is the kurtosis tensor)
OR
6 diffusion tensor coefficients as [parameter vectors](#data-param) image with parameter name "`tensor`";
15 kurtosis tensor coefficients as [parameter vectors](#data-param) image with parameter name "`kurtosis`";
Optional: estimated *b*=0 intensity as scalar image with parameter name "`bzero`" | | `dsi` | Diffusion Spectrum Imaging \[[Wedeen2008](#wedeen2008)\],\[[Paquette2017](paquette2017)\] | [Probability distribution functions](#data-pdf) | | `forecast` | Fiber ORientation Estimated using Continuous Axially Symmetric Tensors \[[Zuchelli2017](#zuchelli2017)\] | [Spherical harmonics](#data-sh) image | | `fwdti` | Free water DTI \[[Hoy2015](#hoy2015)\] | One [parameter vectors](#data-param) image with parameter name "`tensor`", containing 6 volumes in the order: *Dc_xx*, *Dc_xy*, *Dc_xz*, *Dc_yy*, *Dc_yz*, *Dc_zz* (*Dc* is the free-water-corrected diffusion tensor);
One [scalar](#data-scalar) image with parameter name "`fwf`" corresponding to the estimated free water fraction | | `mapmri` | Mean Apparent Propagator MRI \[[Ozarslan2013](#ozarslan2013)\] | | | `noddi` | Neurite Orientation Dispersion and Density Imaging \[[Zhang2012](#zhang2012)\],\[[Daducci2015](#daducci2015)\] | Three [scalar](#data-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](#data-3vector) image with parameter name "`direction`" to provide the estimated fibre orientation | | `qbi` | Q-Ball Imaging \[[Tuch2004](#tuch2004)\], \[[Hess2006](#hess2006)\] | Single [amplitudes](#data-amp) image
OR
Single [spherical harmonics](#data-sh) image | | `shore` | Simple Harmonic Oscillator-based Re[construction and Estimation \[[Ozarslan2008](#ozarslan2008)\] | | | `wmti` | White Matter Tract Integrity \[[Fieremans2011](#fieremans2011)\] | One [parameter vectors](#data-param) image with parameter name "`coeffs`", with 33 volumes in the order: *D_xx*, *D_xy*, *D_xz*, *D_yy*, *D_yz*, *D_zz*, *W_xxxx*, *W_yyyy*, *W_zzzz*, *W_xxxy*, *W_xxxz*, *W_xyyy*, *W_yyyz*, *W_xzzz*, *W_yzzz*, *W_xxyy*, *W_xxzz*, *W_yyzz*, *W_xxyz*, *W_xyyz*, *W_xyzz*, *Dh_xx*, *Dh_xy*, *Dh_xz*, *Dh_yy*, *Dh_yz*, *Dh_zz*, *Dr_xx*, *Dr_xy*, *Dr_xz*, *Dr_yy*, *Dr_yz*, *Dr_zz* (*D* is the diffusion tensor and *W* is the kurtosis tensor);
One [scalar](#data-scalar) image with parameter name "`awf`", representing the estimated axonal water fraction | ### Input model parameters - `csa` : - `SphericalHarmonicOrder` : value - `Smoothing` : value - `Basis` : value - `dsi` : - `GridSize` : value - `RStart` : value - `RStep` : value - `REnd` : value - `FilterWidth` : value - `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 | `` value | Description | [Data representation](#data-representations) | Possible Model sources | Unit or scale | | ------------------- | ---------------------------------------------------------------------- | -------------------------------------------- | ----------------------------------------------- | -------------------------------------------------------------- | | `ak` | Axial kurtosis | [Scalar](#data-scalar) | { `dki`, `wmti` } | Unitless | | `mk` | Mean kurtosis | [Scalar](#data-scalar) | { `dki`, `wmti` } | Unitless | | `msd` | Mean-Squared Displacement | [Scalar](#data-scalar) | { `mapmri`, `shore` } | | | `pdf` | Diffusion propagator | [3-vectors](#data-3vector) | | | | `rk` | Radial kurtosis | [Scalar](#data-scalar) | { `dki`, `wmti` } | Unitless | | `rtap` | Return To Axis Probability | [Scalar](#data-scalar) | { `mapmri` } | Probability \[0.0-1.0\] | | `rtop` | Return To Origin Probability | [Scalar](#data-scalar) | { `shore` } | Probability \[0.0-1.0\] | | `rtpp` | Return To Plane Probability | [Scalar](#data-scalar) | { `mapmri` } | Probability \[0.0-1.0\] | | `tort` | Tortuosity of extra-cellular space | [Scalar](#data-scalar) | { `dki` } | | ## Demonstrative examples - A NODDI fit: ```Text 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`": *I*x*J*x*K* ([scalar](#data-scalar)) Dimensions of NIfTI image "`sub-01_parameter-isovf_noddi.nii.gz`": *I*x*J*x*K* ([scalar](#data-scalar)) Dimensions of NIfTI image "`sub-01_parameter-od_noddi.nii.gz`": *I*x*J*x*K* ([scalar](#data-scalar)) Dimensions of NIfTI image "`sub-01_parameter-direction_noddi.nii.gz`": *I*x*J*x*K*x3 ([3-vectors](#data-3vector)) Contents of file "`sub-01_noddi.json`" (common to all [intrinsic](#paramdef-intrinsic) model parameter images): ```JSON { "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`": ```JSON { "OrientationRepresentation": "3vector", "ReferenceAxes": "???" } ```