Display of tensor data by voxel
Tensor values where obtained by an algorithm which uses all available
gradient direction in order to reconstruct the symmetric second order
tensor which is a model for the water diffusivity in the brain.
Using more gradient directions for the computation of the tensor
increases the angular resolution of the tensor and counteracts noise
in the measurements. Nevertheless the degrees of freedom
in a symmetric tensor are reduced from 32 measurements to 6.
We obtain in this work more information by validating the tensor
representation obtained from a least-mean-squares fit against the
raw gradient directions. The model of the second order tensor may
not always sufficient to explain the local diffusion thus statistical
validation of the gradient directions against the tensor model will
indicate regions for which the model fits well against regions where
the model fit to the data is poor. Especially the regions where the
fit is poor are of interest because they may contain for example
crossing fiber bundles.
Visualization of the statistical fit is important to guide the
interpretation of the data.
Live demonstration
Compute the ADC from the raw data (webpage contains Quicktime movie)
Movies
one slice (webpage contains Quicktime movie)
Cylinders (mpg 35MB)
Ellipse (mpg 27MB)
Lines (mpg 28MB)
Images
Displaying tensor values by cylinders:
Displaying tensor values by ellipses:
Displaying tensor values by orthogonal lines:
Apparent diffusion coefficient in false color (301):
