The b-value b or diffusion weighting is a function of the strength, duration and temporal spacing and timing parameters of the specific paradigm. This function is derived from the Bloch-Torrey equations. In the case of the classical Stejskal-Tanner pulsed gradient spin-echo (PGSE) sequence, at the time of readout b=\gamma^{2}G^{2}\delta^{2}\left(\Delta-\frac{\delta}{3}\right) where \gamma is the gyromagnetic radio, \delta denotes the pulse width, G is the gradient amplitude and \Delta the centre to centre spacing. \gamma is a constant, but we can change the other three parameters and in that way control the b-value.
Q-space is the space of one or more 3D spin displacement wave vectors \mathbf{q} as shown in equation ref{eq:fourier}. The vector \mathbf{q} parametrises the space of diffusion gradients. It is related to the applied magnetic gradient \mathbf{g} by the formula \mathbf{q}=(2\pi)^{-1}\gamma\delta\mathbf{g}. Every single vector \mathbf{q} has the same orientation as the direction of diffusion gradient \mathbf{g} and length proportional to the strength g of the gradient field. Every single point in q-space corresponds to a possible 3D volume of the MR signal for a specific gradient direction and strength. Therefore if, for example, we have programmed the scanner to apply 60 gradient directions then our data should have 60 diffusion volumes with each volume obtained for a specific gradient. A Diffusion Weighted Image (DWI) is the volume acquired from only one direction gradient.
Diffusion Weighted Imaging (DWI) is MRI imaging designed to be sensitive to diffusion. A diffusion weighted image is a volume of voxel data gathered by applying only one gradient direction using a diffusion sequence. We expect that the signal in any voxel should be low if there is greater mobility of water molecules along the specified gradient direction and it should be high if there is less movement in that direction. Yes, it is counterintuitive but correct! However greater mobility gives greater opportunity for the proton spins to be dephased producing a smaller RF signal.
Diffusion MRI (dMRI or dwMRI) are prefered terms if you want to speak about diffusion weighted MRI in general. DTI (diffusion tensor imaging) is just one of the many ways you can reconstruct the voxel from your measured signal. There are plenty of others for example DSI, GQI, QBI etc.
Registration can be tricky. But this is what usually works for us for normal healthy adult subjects. We register the FA (fractional anisotropy) images to the FMRIB_FA_1mm template which is in MNI space using flirt and fnirth from FSL. Then we can apply the warping displacements in any other scalar volumes that we have to register that scalar volume into the MNI space. We need the corresponding inverse displacements to map a tractography into MNI space.
Image coordinates have positive integer values and represent the centres (i, j, k) of the voxels. There is an affine transform (stored in the nifti file) that takes the image coordinates and transforms them to millimeter (mm) in real world space. World coordinates have floating point precision and your dataset have 3 real dimensions e.g. (x, y, z).
Tractography is only an approximation or simulation - if you prefer - of the real tracts (brain neural fiber pathways or brain nerves). Therefore we prefer to call these simulated tracts as tracks (trajectories or curves represented as sequences of points joined by line segments) so that others will be clear that they are not the real tracts (fibers) but only an estimate or suggestion. We hope that in the future tractography could reach a point that what you see on your screen is a very faithful representation of what is actually in the white matter of the brain. However the field is not yet at this level of detail.
We wanted to create at the outset a tractographic method which will help us and you to get closer to datasets in a very efficient way. Therefore, we created first the EuDX (Euler Delta Crossings) algorithm which is a tracking method which can work both with model or model-free input and resolve also crossing fibers with a high order of crossings. Also it is very fast to calculate (~2 minutes for 1 million tracks ). We hope that at a later stage we will be able to incorporate and test more methods e.g. probabilistic, global and graph-theoretic.
You need to resample your raw data to an isotropic size. Have a look at the module dipy.align.noniso2iso. (We think it is a mistake to acquire nonisotropic data because the directional resolution of the data will depend on the orientation of the gradient with respect to the voxels, being lower when aligned with a longer voxel dimension.)
If for example you have 2 \times 2 \times 4 \textrm{mm}^3 voxels, the last dimension will be averaged over the double distance and less detail will be captured compared to the other two dimensions. Furthermore, with very nonisotropic voxels the uncertainty on orientation estimates will depend on the position of the subject in the scanner.
python is free, batteries included, very well designed, painless to read and easy to use. There is nothing else like it. Give it a go. Once with python always with python.
True, some times python can be slow if you are using for example multiple nested for loops. In that case we use cython which takes execution up to C speed.
The best ever designed numerical library numpy.
ipython
We use fosvtk(fvtk) which depends in turn on python-vtk:
from dipy.viz import fvtk
There is already interaction in the fvtk module but we have started a new project only for visualization which we plan to integrate in dipy in the near future for more information have a look at http://fos.me
Nifti (.nii), Dicom (Siemens(read-only)), Trackvis (.trk), Dipy (.dpy), Numpy (.npy, ,npz), text and any other formats supported by nibabel and pydicom.
You can also read/save in Matlab version v4 (Level 1.0), v6 and v7 to 7.2 using scipy.io.loadmat. For higher versions >= 7.3 you can use pytables or any other python to hdf5 library e.g. h5py .
For object serialization you can used dipy.io.pickles function load_pickle, save_pickle.
dpy is an hdf5 file format which we use in dipy to store tractography and other information. This allows us to store huge tractographies and load different parts of the datasets directly from the disk as if it were in memory.
Any text editor would do the job but we prefer the following Aptana, Emacs, Vim and Eclipse (with PyDev).
Use Chris Roden’s dcm2nii to transform them to nifti files. http://www.cabiatl.com/mricro/mricron/dcm2nii.html Or you can make your own reader using pydicom http://code.google.com/p/pydicom/ and then use nibabel to store the data as niftis.
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