Jadrian Miles: /* Mean Diffusivity */

2009-03-23T23:02:09Z

Mean Diffusivity

← Older revision		Revision as of 23:02, 23 March 2009
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	===== Mean Diffusivity =====		===== Mean Diffusivity =====
	Also known as "MD" and essentially equivalent to [[#Trace\|trace]], mean diffusivity is defined as:		Also known as "MD" and essentially equivalent to [[#Trace\|trace]], mean diffusivity is defined as:
	:<math>\mathbf{MD} \equiv Tr(D) / 3</math>		:<math>\mathbf{MD} \equiv \mathrm{Tr}(D) / 3</math>

	===== Linear Anisotropy =====		===== Linear Anisotropy =====

Jadrian Miles: New page: {{stub}} A diffusion tensor is a common model for representing the orientation distribution function of water diffusion within a voxel of a diffusion MRI dataset. A useful model for ...

2009-03-23T23:01:34Z

New page: {{stub}} A diffusion tensor is a common model for representing the orientation distribution function of water diffusion within a voxel of a diffusion MRI dataset. A useful model for ...

New page

{{stub}}

A diffusion tensor is a common model for representing the orientation distribution function of water diffusion within a voxel of a [[diffusion MRI]] dataset. A useful model for a diffusion tensor is a three-dimensional ellipsoid. The rate of water diffusion in a given direction is modeled as being proportional to the radius of the ellipsoid in that direction. Therefore, if one diffusion direction is strongly preferred over all others, the ellipsoid is cigar-shaped; if there are two directions with approximately equal high diffusion rates, it is shaped like an M&M; and if the diffusion is isotropic (no preferred direction), it is shaped like a sphere.

Mathematically, the tensor is represented by a 3x3 symmetric positive definite matrix. Such a matrix has six degrees of freedom.
:<math>
D = \left[\begin{array}{ c c c }
d_{xx} & d_{xy} & d_{xz} \\
d_{xy} & d_{yy} & d_{yz} \\
d_{xz} & d_{yz} & d_{zz}
\end{array} \right]
</math>
The eigenvalues and eigenvectors of this matrix are, respectively, <math>\lambda_1</math>, <math>\lambda_2</math>, <math>\lambda_3</math>, <math>e_1</math>, <math>e_2</math>, and <math>e_3</math>. Since the ordering of the eigenvalues and eigenvectors is arbitrary, by convention we define them such that <math>\lambda_1 > \lambda_2 > \lambda_3</math>.

=== Scalar Metrics ===
From the eigen decomposition, we may define a number of scalar values for the diffusion tensor that are hypothesized to have correlations with the structural properties of the white matter described by the tensor. Most of these can be computed from an [[MRIimage]] DTI with the program <code>mritensor</code>.

===== Fractional Anisotropy =====
Also known as "FA", fractional anisotropy is defined as:
:<math>\mathbf{FA} \equiv \sqrt{\frac{1}{2}} \frac{\sqrt{(\lambda_1 - \lambda_2)^2 + (\lambda_2 - \lambda_3)^2 + (\lambda_3 - \lambda_1)^2}}{\sqrt{\lambda_1^2 + \lambda_2^2 + \lambda_3^2}}</math>
For isotropic diffusion, <math>FA = 0</math>; for infinitely anisotropic diffusion, <math>FA = 1</math>. Decreases in FA are believed to correlate with demyelination.

===== Trace =====
Also known as "Tr(D)" and essentially equivalent to [[#Mean Diffusivity|mean diffusivity]], the trace of the diffusion tensor is defined as:
:<math>\mathbf{Tr(D)} \equiv d_{xx} + d_{yy} + d_{zz} = \lambda_1 + \lambda_2 + \lambda_3</math>

===== Mean Diffusivity =====
Also known as "MD" and essentially equivalent to [[#Trace|trace]], mean diffusivity is defined as:
:<math>\mathbf{MD} \equiv Tr(D) / 3</math>

===== Linear Anisotropy =====
Also known as "LA"

===== Planar Anisotropy =====
Also known as "PA"

===== Relative Anisotropy =====
Also known as "RA"

===== Tensor Magnitude =====
Also known as "Mag(D)", "<math>||D||</math>", and "mD"

===== Slant Tensor Magnitude =====
Also known as "magnitude of slant-D" and "msD"

===== Axial Diffusivity =====
Also known as "AD", axial diffusivity is defined as
:<math>\mathbf{AD} \equiv \lambda_1</math>
Decreases in AD are believed to correlate with axon breakage or dropout.

===== Radial Diffusivity =====
Also known as "RD", radial diffusivity is defined as
:<math>\mathbf{RD} \equiv (1/2) (\lambda_2 + \lambda_3)</math>
Increases in RD are believed to correlate with demyelination.

===== Isotropy =====
Also known as "I"

===== Lattice Index =====
Also known as "LI"

===== Prolation =====

[[Category:Diffusion MRI]]

Diffusion Tensor Properties - Revision history

Jadrian Miles: /* Mean Diffusivity */

Jadrian Miles: New page: {{stub}} A diffusion tensor is a common model for representing the orientation distribution function of water diffusion within a voxel of a diffusion MRI dataset. A useful model for ...