Updates to key concepts and artifacts

Notebooks/Artifacts.ipynb

@@ -58,7 +58,7 @@
     "\n",
     "| Artifact Name | Source | Appearance | What to do? | Frequency or Phase encoding |\n",
     "|---|---|---|---|---|\n",
-    "| Aliasing | Sequence - FOV too small | Signal folds across image | Increase FOV, swap PE/FE | Phase encoding |\n",
+    "| Aliasing | Sequence - FOV too small, or parallel imaging failed | Signal folds across image | Increase FOV, swap PE/FE, reacquire sensitivity maps (parallel imaging) | Phase encoding |\n",
     "| Gibbs Ringing/Truncation | Sequence - due to Fourier encoding of edges | Ripples/ringing at sharp edges | Filtering of data | N/A |\n",
     "| Boundary Artifacts/Partial Volume | Sequence and Sample - opposite $M_{XY}$ phases with a voxel due to inversion or chemical shift | Artificial dark lines at tissue boundaries  | fat suppresion, fat/water imaging | N/A |\n",
     "| Motion/Flow | Sample - signal modulated during spatial encoding | Copies or \"Ghosts\" of image regions that are changing due to motion or flow | Breath-hold, gating, triggering, flow compensation, swap PE/FE | Phase encoding |\n",
@@ -85,15 +85,15 @@
     "    \n",
     "where $\\Delta f$ is the frequency shift, $RBW$ is the receiver bandwidth, and $FOV_{FE}$ is the field of view in the frequency encoding direction.\n",
     "\n",
-    "During EPI, there is typically a much larger shift in the phase encoding direction that depends on the echo spacing, $t_{esp}$.  For simplicity, I convert the echo spacing into a \"phase encoding bandwidth\", $BW_{PE} = 1/t_{esp}$:\n",
+    "During EPI, there is typically a much larger shift in the phase encoding direction that depends on how much phase accumulates across k-space.  This depends on the echo spacing, $t_{esp}$, and well as how many k-space lines are covered in adjacent echoes, defined here as $N_{steps}$.  To characterize this, we can define a \"phase encoding bandwidth\", $BW_{PE} = N_{steps}/t_{esp}$, and the displacement will be\n",
     "\n",
-    "$$\\Delta_{PE} = \\frac{\\Delta f}{BW_{PE} N_{interleaves}} FOV_{PE}$$\n",
+    "$$\\Delta_{PE} = \\frac{\\Delta f}{BW_{PE}} FOV_{PE}$$\n",
     "\n",
-    "where $N_{interleaves}$ is the number of interleaves that can be used to reduce the displacement.\n",
+    "$N_{steps}$ will depend on whether there is any interleaving, and whether parallel imaging is used to skip lines.  For example, EPI without acceleration in a single-shot is $N_{steps} = 1$, 2 interleaves would have $N_{steps} = 2$, while single-shot with $R=2$ parallel imaging acceleration would have $N_{steps} = 2$, and 2 interleaves with $R=2$ parallel imaging would have $N_{steps} = 4$.\n",
     "\n",
     "Finally, there will also be a displacement of the slice selection, and this will be\n",
     "\n",
-    "$$\\Delta_{SS} = \\frac{\\Delta f}{BW_{rf}} \\Delta_z$$\n",
+    "$$\\Delta_{SS} = \\frac{\\Delta f}{BW_{rf}} \\Delta z$$\n",
     "\n",
     "where $BW_{rf}$ is the slice select pulse bandwidth."
    ]
@@ -106,7 +106,7 @@
     "\n",
     "Motion, including flow, can result in artifacts in MRI if it leads to inconsistency in the data.\n",
     "\n",
-    "Periodic motion such as breathing, heart beating, and pulsatile flow will lead to distinct ghosting artifacts in the phase encoding direction.  The location of ghosting artifacts in sequential phase encoding, will be at predictable intervals in the phase encoding direction:\n",
+    "Periodic motion such as breathing, heart beating, and pulsatile flow will lead to distinct ghosting artifacts in the phase encoding direction.  The location of ghosting artifacts in sequential phase encoding without parallel imaging will be at predictable intervals in the phase encoding direction:\n",
     "\n",
     "$$\\Delta_{PE} = \\frac{TR}{T_{motion}} FOV_{PE}$$\n",
     "\n",
@@ -115,6 +115,35 @@
     "Incoherent or more random motion such as irregular breathing, arrhytthmias, coughing, bulk motion will lead to more diffuse ghosting artifacts."
    ]
   },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Artifact Examples\n",
+    "\n",
+    "### Aliasing\n",
+    "\n",
+    "![Axial abdomen image with aliasing](images/artifacts/abdomen_aliasing.png)\n",
+    "\n",
+    "### Motion\n",
+    "\n",
+    "![Axial abdomen image with motion](images/artifacts/abdomen_motion.png)\n",
+    "\n",
+    "![Coronal brain image with motion](images/artifacts/brain_coronal_eyes_artifact.jpg)\n",
+    "\n",
+    "![Axial brain image with motion](images/artifacts/brain_motion_artifact.jpg)\n",
+    "\n",
+    "### Image Displacement/Distortion\n",
+    "\n",
+    "![Axial brian EPI with distortion](images/artifacts/epi_distortion_artifact_changes.jpg)\n",
+    "\n",
+    "![Axial brian EPI with fat displacement](images/artifacts/epi_fat_artifact.jpg)\n",
+    "\n",
+    "### T2*\n",
+    "\n",
+    "![Axial brain image with T2* artifact](images/artifacts/epi_T2star_artifact.png)"
+   ]
+  },
   {
    "cell_type": "markdown",
    "metadata": {},

Notebooks/Key MRI Concepts.md

@@ -10,17 +10,22 @@ Signals and Systems
 
 ## MR Spin Physics
 
-Resonance
+Resonance - nuclear spins in a magnetic field precess at a frequency proportional to the magnetic field strength
+
 $$f = \bar{\gamma} \|\vec{B}\|$$
 
-Polarization and Net Magnetization 
+Polarization - equilibrium magnetization
+
+$$M_0(\vec{r}) = \frac{N(\vec{r}) \bar{\gamma}^2 h^2 I_Z (I_Z +1) B_0}{3 k T}$$
+
+Net Magnetization at Equilibrium
+
 $$\vec{M}(\vec{r},0) = 
 \begin{bmatrix}
 0 \\
 0 \\
 M_0(\vec{r})
 \end{bmatrix}$$
-$$M_0(\vec{r}) = \frac{N(\vec{r}) \bar{\gamma}^2 h^2 I_Z (I_Z +1) B_0}{3 k T}$$
 
 Excitation
 * Apply magnetic field at resonant frequency to rotate net magnetization out of alignment with static magnetic field
@@ -34,7 +39,9 @@ $$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})
 ## MRI System
 
 1. Main magnet - $B_0$
-1. Radiofrequency (RF) coils, including a transmit RF coil - $B_1^+(\vec{r},t)$ - and a receive RF coil - $B_1^-(\vec{r},t)$
+1. Radiofrequency (RF) coils
+    * transmit RF coil - $B_1^+(\vec{r},t)$: provide homogeneous excitation
+    * receive RF coil - $B_1^-(\vec{r},t)$: detect signal with high sensitivity
 1. Magnetic field gradient coils - $\vec{G}(t)$
 
 ## MRI Experiment
@@ -49,18 +56,25 @@ Experiment described by a "Pulse Sequence"
 
 ## MR Contrasts
 
+Contrast weightings
+* T1-weighted - short TE, short TR
+* T2-weighted - long TE, long TR
+* Proton Density (PD)-weighted - short TE, long TR
+
 spoiled GRE contrast
 
 $$S \propto M_0 \sin(\theta) \exp(-TE/T_2) \frac{1- \exp(-TR/T_1)}{1- \cos(\theta) \exp(-TR/T_1)}$$
 
-Contrast weightings: T1w, T2w, PDw
+Ernst angle - flip angle for maximum SNR
 
-Magnetization Preparation:
+$$\theta_{optimal} = \cos^{-1}(\exp(-TR/T_1))$$
 
+Magnetization Preparation:
 Inversion Recovery
+
 $$S_{IR} \propto M_0  \exp(-TE/T_2) (1 - 2\exp(-TI/T_1) + \exp(-TR/T_1) )$$
 
-## In vivo spin physics
+## In Vivo Spin Physics
 
 Magnetic susceptibility effects 
 * magnetic susceptibility is inherent property of materials
@@ -71,21 +85,23 @@ Chemical Shift
 * chemcial environment of an atom creates variations in local magnetic field
 * in vivo consideration: "fat", assumed to have a -3.5 ppm chemcial shift from water protons
 
-## In vivo contrasts
+## In Vivo Contrasts
+
+Phase - chemical shift and off-resonance (e.g. magnetic susceptibility effects) create phase differences in MR signal
 
 T2*
 * intra-voxel dephasing due to magnetic field inhomogeneity
 * largely driven by magnetic susceptibility
 * eliminate with spin-echo
 * create susceptibility contrast
 
-fat
+Fat
 * fat/water imaging - separate fat and water images based on multiple echo times
 * fat suppression - spectrally-selective RF pulses and/or inversion recovery
 
 Contrast Agents
-* Gd-based contrast agents - most common, primarily shortens $T_1$
-* iron-basec contrast agents - less common, shortens $T_1$ but also can shorten $T_2$
+* Gadolinium (Gd)-based contrast agents - most common, primarily shortens $T_1$
+* Iron-based contrast agents - less common, shortens $T_1$ but also can shorten $T_2$
 
 
 ## RF Pulses
@@ -128,21 +144,25 @@ $$s(t) = \mathcal{F}\{m(\vec{r}) \} |_{\vec{k} = \vec{k}(t)} = M(\vec{k}(t))$$
 * effects of gradients can be refocused
 * supports 2D and 3D imaging
 
-## Image Characeristics
+## Image Characteristics
 
 $$SNR \propto f_{seq}\ \mathrm{Voxel\ Volume}\ \sqrt{T_{meas}}$$
 
 $$ FOV = \frac{1}{\Delta k}$$
 
 $$ \delta = \frac{1}{2 k_{max}}$$
 
+Scan Time
+
+$$ T_{scan} = \frac{ TR \cdot N_{PE,total} \cdot NEX}{ETL \cdot R}$$
+
 ## FT Imaging Sequence
 
-Typical acquisition uses frequency and phase encoding.
+Typical acquisition uses frequency and phase encoding
 
 See [Pulse Sequence](./Pulse%20Sequence.ipynb) for a typical 2D gradient-echo sequence
 
-Can convert between sequence parameters (e.g. timings, gradient amplitudes) and the FOV, resolution and scan time
+Can convert between sequence parameters (e.g. timings, gradient amplitudes) and the FOV, resolution and scan time, as well as predict relative SNR
 
 ## Fast Imaging Pulse Sequences
 
@@ -178,11 +198,11 @@ Simultaneous Multi-slice
 * Why does it work?  RF coil arrays with different elements provide spatial encoding
 * How does it work?  Excite multiple slices simultaneously
 
-Compressed Sensing and Deep Learning Reconstructions
+Compressed Sensing
 * Why does it work?  MRI data has typical patterns that can be predicted are represented by sparse coefficients
 * How does it work?  Skip k-space data with a pseudo-random pattern.  Define a sparsity domain
 
-Deep Learning Reconstructions
+Deep Learning Reconstruction
 * Why does it work?  MRI data has typical patterns that can be learned
 * How does it work?  Skip k-space data.  Train a neural network using a large MRI dataset.
 

Notebooks/MRI Contrast.ipynb

@@ -225,8 +225,9 @@
     "\n",
     "$$S \\propto M_0 \\sin(\\theta) \\frac{1- \\exp(-TR/T_1)}{1- \\cos(\\theta) \\exp(-TR/T_1)}$$\n",
     "\n",
-    "Illustrated in this second example below.  This shows that the magnetization can take many TRs to reach steady state.\n",
-    "\n"
+    "Illustrated in this second example below.  This shows that the magnetization can take many TRs to reach steady state.  These acquisitions are commonly done to maximize signal for a typical $T_1$ range.  This is done by choosing using the so-called \"Ernst angle\", which is the flip angle that maximizes the signal for a given $T_1$ and $TR$:\n",
+    "\n",
+    "$$\\theta_{optimal} = \\cos^{-1}(\\exp(-TR/T_1))$$"
    ]
   },
   {