MRI Notation and Terminology

The following is the standardized notation used in this book:

Notation	Definition	SI Units
\(\vec{r} = [x, y, z]^T\)	position in space	[m]
\(\vec{B}(\vec{r},t)\)	Magnetic field	[T]
\(\bar{\gamma}\)	gyromagnetic ratio	[Hz/T]
\(B_0\)	Main magnetic field	[T]
\(B_1^+(\vec{r},t)\)	RF transmit magnetic field	[T]
\(B_1^-(\vec{r},t)\)	RF receive magnetic field	[T]
\(\vec{G}(t) = [G_X(t), G_Y(t), G_Z(t)]^T \)	magnetic field gradients	[T/m]
\(\vec{M}(\vec{r},t)\)	Net Magnetization	[T]
\(M_{XY}(\vec{r}, t) = M_X(\vec{r}, t) + i M_Y(\vec{r}, t)\)	transverse magnetization	[T]
\(M_0(\vec{r})\)	Equilibrium magnetization	[T]
\(T_1(\vec{r}), T_2(\vec{r}), T_2^*(\vec{r})\)	relaxation rates	[s]

Definitions

Position in space

\[\begin{split}\vec{r} = \begin{bmatrix} x\\ y \\ z \end{bmatrix}\end{split}\]

Net magnetization

\[\begin{split}\vec{M} = \begin{bmatrix} M_X \\ M_Y \\ M_Z \end{bmatrix}\end{split}\]

It can vary over space, \(\vec{r} = [x,y,z]^T\) and time, \(t\):

\[\begin{split}\vec{M}(\vec{r},t) = \begin{bmatrix} M_X(\vec{r},t) \\ M_Y(\vec{r},t) \\ M_Z(\vec{r},t) \end{bmatrix}\end{split}\]

Shorthand for transverse magnetization using complex numbers

\[M_{XY}(\vec{r},t) = M_X(\vec{r},t) + i M_Y(\vec{r},t)\]

Magnetic field

\[\begin{split}\vec{B} = \begin{bmatrix} B_X \\ B_Y \\ B_Z \end{bmatrix}\end{split}\]

It can vary over space, \(\vec{r}\) and time, \(t\):

\[\begin{split}\vec{B}(\vec{r},t) = \begin{bmatrix} B_X(\vec{r},t) \\ B_Y(\vec{r},t) \\ B_Z(\vec{r},t) \end{bmatrix}\end{split}\]

Acronyms

MRI is full of jargon and acronyms, which can be intimidating and impede understanding. Luckily, there are a couple good resources to help you out:

Radiopaedia - general list: https://radiopaedia.org/articles/mri-pulse-sequence-abbreviations

MR-TIP - structured lists comparing acronyms across vendors

• https://mr-tip.com/serv1.php?type=cam

• https://mr-tip.com/serv1.php?type=cam&sub=1

Glossary

RF

Gradients

Spins

Excitation

Polarization

Voxel

Gradient Echo

Spin Echo