Data simulation forms a crucial component of any data-driven experiment which deals with model fitting as it is the ground-truth that we will be comparing against. In my project, I will be working with the following 2 tools for data simulation:
- UCL Camino Diffusion MRI Toolkit
- DIPY Simulations (… Obviously!)
This post will cover Camino 1st and I aim to get into DIPY in the next post!
The most confusing part about the Camino documentation is understanding what the ‘scheme’ file is really made up of, because it needs to be passed as a parameter to the ‘datasynth’ command which we will look at for data simulation.
Scheme files accompany DWI data and describe imaging parameters that are used in image processing. For most users, we require the gradient directions and b-value of each measurement in the sequence.
Once you have this information, you can use the CAMINO commands described below to generate scheme files.
- Comments are allowed, the line must start with ‘#’
- The first non-comment line must be a header stating “VERSION: <version>”. In our case:
- After removing comments and the header, measurements are described in order, one per line. The order must correspond to the order of the DWI data.
- Entries on each line are separated by spaces or tabs.
The BVECTOR is the most common scheme format. Each line consists of four values: the (x, y, z) components of the gradient direction followed by the b-value. For example:
# Standard 6 DTI gradient directions, [b] = s / mm^2 VERSION: BVECTOR 0.000000 0.000000 0.000000 0.0 0.707107 0.000000 0.707107 1.000E03 -0.707107 0.000000 0.707107 1.000E03 0.000000 0.707107 0.707107 1.000E03 0.000000 0.707107 -0.707107 1.000E03 0.707107 0.707107 0.000000 1.000E03 -0.707107 0.707107 0.000000 1.000E03
If the measurement is unweighted, its gradient direction should be zero. Otherwise, the gradient directions should be unit vectors, followed by a scalar b-value. The b-value can be in any units. Units are defined implicitly, in the above example we have used s / mm^2. The choice of units affects the scale of the output tensors, if we used this scheme file we would get tensors in units of mm^2 / s. We could change the units of b to s / m^2 by scaling the b-values by 1E6. Our reconstructed tensors would then be specified in units of m^2 / s.
Finding the information for the scheme file
The best way to find the information for your scheme file is to talk to the person who programmed your MRI sequence. There is software that can help you recover them from DICOM or other scanner-specific data formats. The dcm2nii program will attempt to recover b-values and vectors in FSL format.
Converting to Camino format
If you have a list of gradient directions, you can convert them to Camino format by hand or by using
pointset2scheme. If you have FSL style bval and bvec files, you can use
fsl2scheme. See the man pages for more information.
Simulating the Data
Finally! Now that we know what the scheme files are, lets look at how to simulate the voxels…
I will be making use of the 2 utilities which I feel are relevant to my project and will test the simulation functionalities using the 59.scheme file which is present on the Camino website tutorial.
1. Synthesis Using Analytic Models
This uses Camino to synthesize diffusion-weighted MRI data with the white matter analytic models.
The method is explained in detail in (Panagiotaki et al NeuroImage 2011, doi:10.1016/j.neuroimage.2011.09.081).
The following example synthesizes data using the three-compartment model “ZeppelinCylinderDot“, which has an intra-axonal compartment of single radius, a cylindrically symmetric tensor for the extra-axonal space and a stationary third compartment.
datasynth -synthmodel compartment 3 CYLINDERGPD 0.6 1.7E-9 0.0 0.0 4E-6 zeppelin 0.1 1.7E-9 0.0 0.0 2E-10 Dot -schemefile 59.scheme -voxels 1 -outputfile ZCD.Bfloat
2. Crossing cylinders using Monte Carlo Diffusion Simulator
This simulator allows the simulation of diffusion from simple to extremely complex diffusion environments, called “substrates“. We will be looking at the Crossing fibres substrates as of now.
A substrate is envisaged to sit inside a single voxel, with spins diffusing across it. The boundaries of the voxel are usually periodic so that the substrate defines an environment made up of an infinite, 3D array of whatever you specify. The measurement model in the simulation does not capture the trade-off between voxel size and SNR and hence simulation "voxels" can be quite a bit smaller than those in actual scans. This simulation is, and has always been, intended as a tool to simulate signals due to sub-voxel structure, rather than large spatially-extended structures. [- UCL Camino Docs]
A situation that is often of interest in diffusion MR research is where we have more than one principle fibre direction. The simulation is able to model crossing fibres with a specified crossing angle. This substrate contains two populations of fibres in interleaved planes. One population is parallel to the z-axis and another is rotated about the y-axis by a given angle with respect to the first.
Cylinders on this substrate are arranged in parallel in the xz-plane in parallel layers one cylinder thick. i.e. a plane of cylinders parallel to the z-axis, with a rotated with respect the first, then another parallel z-axis and so on. Cylinders are all of a constant radius.
An example command to use here is:
datasynth -walkers 100000 -tmax 1000 -voxels 1 -p 0.0 -schemefile 59.scheme -initial uniform -substrate crossing -crossangle 0.7854 -cylinderrad 1E-6 -cylindersep 2.1E-6 > crossingcyls45.bfloat
Here we’ve specified a
crossing substrate. The crossing angle is specified in radians (NOT degrees) using the
-crossangle: 0.7854. This is approximately pi/4, or 45 degrees. The crossing angle can take on any value, just make sure you use radians!
 Panagiotaki et al NeuroImage 2011, doi:10.1016/j.neuroimage.2011.09.081