Imaging con tensore di diffusione: differenze tra le versioni

Versione delle 11:23, 25 ott 2010

Versione delle 11:27, 25 ott 2010

Riga 9:

Si tratta di associare ad ogni punto dello spazio un tensore, aumentando il numero dei parametri associati ad ogni posizione. Per acquisire immagini sensibili agli effetti di diffusione occorre introdurre nella sequenza di acquisizione dei gradienti di campo magnetico ad hoc.

[[Categoria:Imaging biomedico]]

==Bloch–Torrey equation==

In 1956, H.C. Torrey mathematically showed how the [[Bloch equations]] for magnetization would change with the addition of diffusion.<ref>{{cite journal |doi=10.1103/PhysRev.104.563 |bibcode=1956PhRv..104..563T |title=Bloch Equations with Diffusion Terms |year=1956 |last1=Torrey |first1=H. C. |journal=Physical Review |volume=104 |pages=563}}</ref> Torrey modified Bloch's original description of transverse magnetization to include diffusion terms and the application of a spatially varying gradient. The Bloch-Torrey equation neglecting relaxation is:

:<math> \frac{dM_+}{dt}=-j \gamma \vec r \cdot \vec G M_+ + \vec \nabla^T \cdot \vec {\vec D} \cdot \vec \nabla M_+ </math>

For the simplest case where the diffusion is isotropic the diffusion tensor is

:<math>\vec {\vec D} = D \cdot \vec {\vec I} = D \cdot \begin{bmatrix}

1 & 0 & 0 \\

0 & 1 & 0 \\

0 & 0 & 1 \end{bmatrix},</math>

which means that the Bloch&ndash;Torrey equation will have the solution

:<math>M_+(\vec r,t)=M_0e^{-\frac{1}{3}D\gamma ^2G^2t^3}e^{-j\gamma \vec r \cdot \int_0^tdt' \vec G(t')}.</math>

This demonstrates a cubic dependence of transverse magnetization on time. Anisotropic diffusion will have a similar solution method, but with a more complex diffusion tensor.

==Voci correlate==

* [[3D Slicer]]

* [[FSL]]

* [[SPM]]

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