Diffusion Tensor Imaging

Compute DTI metrics from the eigenvalues of a diffusion tensor online

In this page you can compute any tensor metric from the eigenvalues of a diffusion tensor. Insert the values of the three eigenvalues in decreasing order, then click the HyperSpatioTensoral Button.

\[1 \ge \lambda_1 \ge \lambda_2 \ge \lambda_3 \ge 0\]

Lambda 1:

Lambda 2:

Lambda 3:

Metric Value
Mean Diffusivity
Fractional Anisotropy
Linearity
Planarity
Sphericity
Volume Ratio
Example of diffusion tensor in a crossing region.

Mean Diffusivity

  • Used in early stroke detection (it is sensitive to the presence of edema).
  • High MD in CSF (\(9.6 \cdot 10^{-3} mm^2/s\)).
  • Lower MD in GM and WM (between \(1.95\cdot 10^{-3} mm^2/s\) and \(2.2\cdot10^{-3} mm^2/s\)).
  • Water at 37° C has MD = \(9 \cdot 10^{-3} mm^2/s\) .
  • In ventricles or edema MD can be higher than in water due to water transportation.
\[MD = \bar{\lambda} = \frac{\lambda_1 + \lambda_2 + \lambda_3}{3}\]

Fractional Anisotropy

  • Measures how much of the observed diffusion is due to the anisotropy.
  • A ball has \(FA=0\).
  • It is the distance between the tensor`s ellipsoid shape and a spherical isotropic tensor.
  • Very often mistaken for a measure of WM integrity, but it is not.
\[FA = \sqrt{\frac{3}{2}}\sqrt{\frac{\left(\lambda_1 - \bar{\lambda}\right)^2 + \left(\lambda_2 - \bar{\lambda}\right)^2 + \left(\lambda_3 - \bar{\lambda}\right)^2 }{\lambda_1^2 + \lambda_2^2 + \lambda_3^2}}\]

Linearity

  • It measures how much the tensor is elongated along the main axis.
\[C_L = \frac{\lambda_1 - \lambda_2}{\lambda_1}\]

Planarity

  • It measures how much the tensor is close to a plane.
  • If \(C_P\) is high, the concept of principal fiber direction is not well defined.
\[C_P = \frac{\lambda_2 - \lambda_3}{\lambda_1}\]

Sphericity

  • It measures how much the tensor is close to being a sphere.
  • If \(C_S\) is high, the concept of principal fiber direction is not well defined.
  • Notice that \(C_L + C_P + C_S = 1\).
\[C_S = \frac{\lambda_3}{\lambda_1}\]

Volume Ratio

  • It is the ratio between the volume of the ellipsoid and that of a sphere with the same MD.
  • It tells you how much the tensor is far from being a sphere.
\[V_R = \frac{\lambda_1 \lambda_2 \lambda_3}{\bar{\lambda}^3}\]

References

  1. Curran, Kathleen M, Emsell, Louise, and Leemans, Alexander "Quantitative DTI measures". 2016.