+
+
+
+Key MRI Concepts and Equations#
+SEE ALSO MRI Math Concepts
+ +Spin Physics#
+Larmor Frequency
+M0
+Polarization
+
+\[M_{XY}(\vec{r},t) = M_{XY}(\vec{r},0) e^{-t/T_2(\vec{r})}\]
+
+\[M_Z(\vec{r},t) = M_Z(\vec{r},0)e^{-t/T_1} + M_0(\vec{r})(1- e^{-t/T_1(\vec{r})})\]
+Contrast#
+T2/T2*
+T1
+spoiled GRE contrast
+
+\[S \propto M_0 \sin(\theta) \exp(-TE/T_2) \frac{1- \exp(-TR/T_1)}{1- \cos(\theta) \exp(-TR/T_1)}\]
+Inversion Recovery +$\(S_{IR} \propto M_0 \exp(-TE/T_2) (1 - 2\exp(-TI/T_1) + \exp(-TR/T_1) )\)$
+RF Pulses#
+flip angle
+SAR
+TBW = BW_RF T_{RF}
+Slice thickness
+slice shifting
+Spatial Encoding#
+k-space
+
+\[\vec{k}(t) = \frac{\gamma}{2\pi} \int_0^t \vec{G}(\tau) d\tau\]
+
+\[M_{XY}(\vec{r}, t) = M_{XY}(\vec{r}, 0) e^{ -i 2 \pi \vec{k}(t) \cdot \vec{r} }\]
+
+\[\begin{split}\begin{align}
+s(t) & = \int_\mathrm{Volume} M_{XY}(\vec{r},t) \ d\vec{r} \\
+ & = \int_{\textrm{Volume}} M_{XY}(\vec{r},0) \exp(-i2\pi \vec{k}(t) \cdot \vec{r}) \ d\vec{r}
+ \end{align}\end{split}\]
+
+\[s(t) = \int m(\vec{r})\ e^{-i 2 \pi \vec{k}(t) \cdot \vec{r}} \ d\vec{r}\]
+
+\[s(t) = \mathcal{F}\{m(\vec{r}) \} |_{\vec{k} = \vec{k}(t)}$ = M(\vec{k}(t))\]
+Image Characeristics#
+SNR
+FOV/resolution - in general, in Cartesian sequence
+MRI Signal Equation#
+Fast Imaging#
+Scan times
+effective TE
+