Parallel Imaging
@@ -480,10 +480,10 @@ Learning Goals
For advanced image reconstruction methods, it is helpful to reformulate the reconstruction problem as a linear system and using standard mathematical notation describing linear systems as:
-\[ \mathbf{y} = \mathbf{Ex} + \mathbf{n} \]
-where \(\mathbf{y}\) is the acquired data, \(\mathbf{E}\) is the encoding matrix, \(\mathbf{x}\) is the spatial distribution of the transverse magnetization (e.g. image), and \(\mathbf{n}\) is noise. In this formulation, the image is vectorized. For example, 2D FT sampled data and the corresponding 2D image would be converted to:
+\[ y = \mathbf{E}x + n \]
+where \(y\) is the acquired data, \(\mathbf{E}\) is the encoding matrix, \(x\) is the spatial distribution of the transverse magnetization (e.g. image), and \(n\) is noise. In this formulation, the image is vectorized. For example, 2D FT sampled data and the corresponding 2D image would be converted to:
-\[\begin{split} \mathbf{y} = \left[
+\[\begin{split} y = \left[
\begin{array}{c}
s_1(t_1) \\
s_1(t_2) \\
@@ -496,7 +496,7 @@
General Formulation of MRI Reconstruction
and image reconstruction is performed by inverse discrete Fourier Transform, which for fully sampled 2D FT imaging is well defined by matrix inversion:
-\[ \mathbf{\hat{x}} = \mathbf{F^{H} y} \]
+\[ \hat{x} = \mathbf{F^{H}} y \]
Parallel Imaging
For parallel imaging (PI), we need to consider the coil sensitivity profiles, \(\mathbf{C}_q\) , for each RF coil into encoding matrix along with a Fourier Transform encoding matrix, \(\mathbf{F}\) , as well as a k-space sub-sampling operator, \(\mathbf{S}\) , for the measurements from each RF coil, \(\mathbf{y}_q\) :
-\[\mathbf{y}_q = \mathbf{E}_q \mathbf{x} + \mathbf{n}_q = \mathbf{S} \mathbf{F} \mathbf{C_q} \mathbf{x} + \mathbf{n}_q \]
+\[ y_q = \mathbf{E}_q x + n_q = \mathbf{S} \mathbf{F} \mathbf{C_q} x + n_q \]
The coil sensitivity profiles \(\mathbf{C}_q\) is a diagonal matrix with entries corresponding to the coil sensitivity profile at each location in \(\mathbf{x}\) .
The k-space sub-sampling operator \(\mathbf{S}\) , is a diagnoal matrix with entries of 1 or 0, describing whether an expect grid location was sampled. It is convenient to use when describing image reconstruction as filling in points in k-space.
-Here we can return to our original formulation by concatenating the coil dimension, for example as:
+Here we can return to our original formulation by creating augmented matrices, concatenating along the coil elements dimension for example as:
-\[\mathbf{y} = [\mathbf{y}_1 \ \mathbf{y}_2 \ldots \mathbf{y}_N]\]
+\[\mathbf{y} = [y_1 \ y_2 \ldots y_N]\]
\[\mathbf{E} = [\mathbf{E}_1 \ \mathbf{E}_2 \ldots \mathbf{E}_N]\]
-\[\mathbf{y} = [\mathbf{n}_1 \ \mathbf{n}_2 \ldots \mathbf{n}_N]\]
+\[\mathbf{n} = [n_1 \ n_2 \ldots n_N]\]
resulting in:
\[ \mathbf{y} = \mathbf{Ex} + \mathbf{n} \]
@@ -545,8 +545,8 @@ Image-space Methods Parallel Imaging
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+ MRI Questions — Principles of MRI
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+MRI Questions
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+Magnetic Fields and RF Coils
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+Contrast
+
+What flip angle gives the highest SNR for a spoiled gradient echo pulse sequence?
+
+What magnetic resonance property is used to perform fat/water (Dixon) imaging?
+
+Proton density
T1
T2
T2*
Chemical Shift
+What are the minimum measurements required to create separate fat and water images?
+
+What is “magnetization preparation” used for?
+
+(T/F) Multiple readouts can be used following a magnetization preparation pulse to improve efficiency
+
+
+Pulse Sequence
+In a typical pulse sequence, identify the gradients that serve the following functions:
+
+spoil transverse magnetization
refocus Mxy phase across the slice
move to the edge of k-space
+Which of the following statement is true for the slice select refocusing gradient?
+
+The slice select refocusing gradient must have the same gradient amplitude with the slice selective excitation pulse.
The slice select refocusing gradient must have the same gradient area with the slice selective excitation pulse.
The slice select refocusing gradient can overlap with the prewinder of the frequency encoding gradient.
The slice select refocusing gradient can overlap with the gradient echo.
+(T/F) For 2D FT imaging, gradient spoiling is usually applied in the slice select direction because the voxel size is larger thus more dephasing can happen within a voxel in that direction.
+(T/F) For a GRE or SE with no phase encoding gradient, the k-space position at TE equals 0 (i.e, \(\vec{k}(TE) = 0\) ).
+
+
+
+Spatial Encoding
+Which k-space line is acquired by the following magnetic field gradients?
+In 3DFT imaging, the gradient added to the slice encoding axis (compared to a 2DFT) is a …
+
+
+
+Image Reconstruction
+For a real-valued image \(m(x,y)\) , which of the following equation holds for its k-space data \(M(k_x,k_y)\) ?
+
+\(M(k_x,k_y) = M(-k_x,-k_y)\)
\(M(k_x,k_y) = -M(-k_x,-k_y)\)
\(\mathcal{Real}\{M(k_x,k_y)\} = \mathcal{Real}\{ M(-k_x,-k_y) \}\)
\(\mathcal{Imag}\{M(k_x,k_y) \} = \mathcal{Imag}\{M(-k_x,-k_y) \}\)
+(T/F) In MRI we only look at the magnitude images.
+(T/F) The center of k-space always contains the maximum signal.
+
+
+Image Characteristics (FOV and Resolution)
+The field of view is inversely proportional to…
+
+The field of view is directly proportional to…
+
+(T/F) An anti-aliasing filter can be applied in the phase encoding direction.
+The resolution in frequency encoding direction ( \(\delta_x\) ) is equal to …
+
+
+
+SNR
+SNR can be increased by …
+
+decreasing voxel size
increasing total time
increasing NEX
+
+
+Artifacts
+Chemical shift displacement artifact is characterized by …
+
+Susceptibility displacement artifact is characterized by …
+
+Truncation artifacts can be reduced by …
+
+improving resolution
filtering in k-space
increasing FOV
increasing NEX
+(T/F) Motion artifacts occur only along the phase-encoding direction.
+
+
+Fast Imaging Pulse Sequences
+What does it mean to use a multiple spin echo pulse sequence?
+
+multiple spin echoes are created following a single excitation pulse
multiple k-space lines acquired sequentially
multiple gradient-echo repetitions after a magnetization preparation pulse
fully refocused gradients and no spoiling in every TR
+What types of contrast can be created with a multiple spin echo pulse sequence?
+
+proton density weighted
T1 weighted
T2 weighted
T2* weighted
+What are the limitations of multiple spin echo pulse sequences?
+
+What does it mean to use echo planar imaging (EPI)?
+
+multiple spin echoes are created following a single excitation pulse
multiple k-space lines acquired sequentially
multiple gradient-echo repetitions after a magnetization preparation pulse
fully refocused gradients and no spoiling in every TR
+What are the advantages of EPI?
+
+Create additional T1, T2, and/or T2* contrast
Rapidly acquire k-space
Robust to motion
Repeated refocusing of intravoxel dephasing
+What are the artifacts associated with EPI?
+
+What does it mean to use balanced steady-state free-precession (bSSFP)?
+
+multiple spin echoes are created following a single excitation pulse
multiple k-space lines acquired sequentially
multiple gradient-echo repetitions after a magnetization preparation pulse
fully refocused gradients and no spoiling in every TR
+
+
+Accelerated Imaging Methods
+Match the acceleration methods
+
+Partial Fourier
Parallel Imaging
Compressed Sensing
Deep Learning
+with the following concept they rely on:
+
+conjugate symmetry in k-space
spatial encoding from receive coil arrays
a sparse representation of the image
training on prior images to learn expected patterns
+(T/R) Partial Fourier, parallel imaging, and compressed sensing or deep learning reconstructions can be used simultaneously.
+How is coil sensitivity information gathered for parallel imaging?
+
+It is stored in a database on the scanner
A separate scan to measure coil sensitivity maps
Using fully-sampled data from the center of k-space
Using fully-sampled data from outer k-space
+What is the “g-factor” in parallel imaging?
+
+How much faster scan can be performed
Describes noise amplification
Describes SNR loss
Describes magnetic field gradients
+Compared to the SNR a fully sampled acquistion (\(SNR_{full}\) ), the SNR Of a parallel imaging acquisition (\(SNR_{PI}\) ) with an acceleration factor, \(R\) , and \(g\) -factor is
+
+\(SNR_{PI} = SNR_{full}\)
\(SNR_{PI} = SNR_{full} / \sqrt{R}\)
\(SNR_{PI} = SNR_{full} / g(\vec{r}) \)
\(SNR_{PI} = SNR_{full} / (g(\vec{r}) \sqrt{R})\)
+(T/F) Parallel imaging undersampling can be performed in any direction, regardless of the RF coil configuration.
+Simultaneous multi-slice parallel imaging
+
+enables acceleration in the slice direction
requires no modifications to the pulse sequence
requires RF pulses that excite multiple slices
requires coil sensitivity information
+What type of k-space sampling is required for compressed sensing?
+
+full sampling
equally spaced undersampling
equally spaced undersampling with fully-sampled center of k-space
pseudo-random undersampling
+At least how many training datasets are typically required to develop deep learning MRI reconstruction methods?
+
+1
10-100
1000-10,000
100,000-1,000,000
+Generalization problems can arise in deep learning MRI reconstruction methods when applied to situations that area different from the training data in which of the following ways:
+
+Which type of architecture is commonly used for physics-based deep learning MRI reconstruction networks?
+
+Encoder-decoder
Unet
Unrolled
Recurrant
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SNR Dependencies
The MRI signal is an integral over a volume of the transverse magnetization. Therefore there is a linear dependency on the MRI signal and the volume of magnetization being examined. So we have
-\[SNR \propto \mathrm{Voxel\ Volume} = \delta x\ \delta y\ \delta z\]
-where \(\delta x, \delta y, \delta z\) are the voxel dimensions in x, y, and z.
+\[SNR \propto \mathrm{Voxel\ Volume} = \delta_x\ \delta_y\ \delta_z\]
+where \(\delta_x, \delta_y, \delta_z\) are the voxel dimensions in x, y, and z.
Data Acquisition Time
diff --git a/_sources/Accelerated Imaging Methods.ipynb b/_sources/Accelerated Imaging Methods.ipynb
index 9d8844b..26c528f 100644
--- a/_sources/Accelerated Imaging Methods.ipynb
+++ b/_sources/Accelerated Imaging Methods.ipynb
@@ -29,11 +29,11 @@
"\n",
"For advanced image reconstruction methods, it is helpful to reformulate the reconstruction problem as a linear system and using standard mathematical notation describing linear systems as:\n",
"\n",
- "$$ \\mathbf{y} = \\mathbf{Ex} + \\mathbf{n} $$\n",
+ "$$ y = \\mathbf{E}x + n $$\n",
"\n",
- "where $\\mathbf{y}$ is the acquired data, $\\mathbf{E}$ is the encoding matrix, $\\mathbf{x}$ is the spatial distribution of the transverse magnetization (e.g. image), and $\\mathbf{n}$ is noise. In this formulation, the image is vectorized. For example, 2D FT sampled data and the corresponding 2D image would be converted to:\n",
+ "where $y$ is the acquired data, $\\mathbf{E}$ is the encoding matrix, $x$ is the spatial distribution of the transverse magnetization (e.g. image), and $n$ is noise. In this formulation, the image is vectorized. For example, 2D FT sampled data and the corresponding 2D image would be converted to:\n",
"\n",
- "$$ \\mathbf{y} = \\left[ \n",
+ "$$ y = \\left[ \n",
" \\begin{array}{c}\n",
"s_1(t_1) \\\\\n",
"s_1(t_2) \\\\\n",
@@ -47,7 +47,7 @@
"\n",
"where $s_m(t_n)$ is the data from the $m$th TR at the $n$th sample.\n",
"\n",
- "$$ \\mathbf{x} = \\left[ \n",
+ "$$ x = \\left[ \n",
" \\begin{array}{c}\n",
"m(x_1,y_1) \\\\\n",
"m(x_2,y_1) \\\\\n",
@@ -67,11 +67,11 @@
"\n",
"In this case, the measurement is the discrete Fourier Transform of the image\n",
"\n",
- "$$ \\mathbf{y} = \\mathbf{Fx} + \\mathbf{n} $$\n",
+ "$$ y = \\mathbf{F}x + n $$\n",
"\n",
"and image reconstruction is performed by inverse discrete Fourier Transform, which for fully sampled 2D FT imaging is well defined by matrix inversion:\n",
"\n",
- "$$ \\mathbf{\\hat{x}} = \\mathbf{F^{H} y} $$"
+ "$$ \\hat{x} = \\mathbf{F^{H}} y $$"
]
},
{
@@ -82,18 +82,18 @@
"\n",
"For parallel imaging (PI), we need to consider the coil sensitivity profiles, $\\mathbf{C}_q$, for each RF coil into encoding matrix along with a Fourier Transform encoding matrix, $\\mathbf{F}$, as well as a k-space sub-sampling operator, $\\mathbf{S}$, for the measurements from each RF coil, $\\mathbf{y}_q$:\n",
"\n",
- "$$\\mathbf{y}_q = \\mathbf{E}_q \\mathbf{x} + \\mathbf{n}_q = \\mathbf{S} \\mathbf{F} \\mathbf{C_q} \\mathbf{x} + \\mathbf{n}_q $$\n",
+ "$$ y_q = \\mathbf{E}_q x + n_q = \\mathbf{S} \\mathbf{F} \\mathbf{C_q} x + n_q $$\n",
"\n",
"The coil sensitivity profiles $\\mathbf{C}_q$ is a diagonal matrix with entries corresponding to the coil sensitivity profile at each location in $\\mathbf{x}$.\n",
"\n",
"The k-space sub-sampling operator $\\mathbf{S}$, is a diagnoal matrix with entries of 1 or 0, describing whether an expect grid location was sampled. It is convenient to use when describing image reconstruction as filling in points in k-space.\n",
"\n",
- "Here we can return to our original formulation by concatenating the coil dimension, for example as:\n",
+ "Here we can return to our original formulation by creating augmented matrices, concatenating along the coil elements dimension for example as:\n",
"\n",
- "$$\\mathbf{y} = [\\mathbf{y}_1 \\ \\mathbf{y}_2 \\ldots \\mathbf{y}_N]$$ \n",
+ "$$\\mathbf{y} = [y_1 \\ y_2 \\ldots y_N]$$ \n",
"\n",
"$$\\mathbf{E} = [\\mathbf{E}_1 \\ \\mathbf{E}_2 \\ldots \\mathbf{E}_N]$$ \n",
- "$$\\mathbf{y} = [\\mathbf{n}_1 \\ \\mathbf{n}_2 \\ldots \\mathbf{n}_N]$$ \n",
+ "$$\\mathbf{n} = [n_1 \\ n_2 \\ldots n_N]$$ \n",
"\n",
"resulting in:\n",
"\n",
@@ -111,7 +111,7 @@
"\n",
"The k-space sampling patterns used for these methods typically use regular undersampling, meaning there is a consistent pattern of acquired and skipped k-space lines.\n",
"\n",
- "### K-space Methods\n",
+ "### Auto-calibrated K-space Methods\n",
"\n",
"K-space parallel imaging methods (e.g. GRAPPA) utilize a calibration kernel, computed from the data itself and captured in the matrix $\\mathbf{G}$. These can also be generally formulated as the following optimization problem\n",
"\n",
@@ -128,9 +128,9 @@
"There is an SNR penalty when using these methods that varies in severity depending on the conditioning of the undersampled reconstruction matrix. Typically, more RF coil elements in the direction of the undersampling leads to a more well-conditioned reconstruction and lower SNR penalty. Conversely, fewer RF coil elements in the direction of the undersampling leads to a more ill-conditioned reconstruction matrix and higher SNR penatly. Also, regions will little difference betweeen RF coils (typically in the center of the body), also tend to have larger SNR penalties.\n",
"\n",
"\n",
- "This is characterized by the \"g-factor\", where $g \\geq 1$ characterizes the SNR loss that is dependent on the coil loading and geometry, k-space sampling pattern, and parallel imaging reconstruction method. When appyling an acceleration factor of $R$, the total readout time reduces the SNR by $\\sqrt{R}$ as well, leading to the SNR relationship:\n",
+ "This is characterized by the \"g-factor\", where $g(\\vec{r}) \\geq 1$ characterizes a spatially-varying SNR loss that is dependent on the coil loading and geometry, k-space sampling pattern, and parallel imaging reconstruction method. When appyling an acceleration factor of $R$, the total readout time reduces the SNR by $\\sqrt{R}$ as well, leading to the SNR relationship:\n",
"\n",
- "$$SNR_{PI} = \\frac{SNR_{full}}{g\\sqrt{R}}$$\n",
+ "$$SNR_{PI} = \\frac{SNR_{full}}{g(\\vec{r})\\sqrt{R}}$$\n",
"\n",
"### Artifacts with Parallel Imaging\n",
"\n",
@@ -147,7 +147,7 @@
"\n",
"Compressed Sensing is formulated as the following optimization problem, specifically using the $\\ell_1$-norm ($\\|x\\|_1 = \\sum_{i=1}^n |x_i|$) that promotes sparsity in the solution:\n",
"\n",
- "$$\\hat{x}_{CS} = \\arg \\min_\\mathbf{x} \\frac{1}{2} \\| \\mathbf{y} - \\mathbf{Ex} \\|^2_2 + \\lambda_{CS} \\| \\mathbf{Wx} \\|_1 $$\n",
+ "$$\\mathbf{\\hat{x}}_{CS} = \\arg \\min_\\mathbf{x} \\frac{1}{2} \\| \\mathbf{y} - \\mathbf{Ex} \\|^2_2 + \\lambda_{CS} \\| \\mathbf{Wx} \\|_1 $$\n",
"\n",
"which includes a data consistency term where the data multiplied by the encoding matrix must match the reconstructed image, and a regularization term that enforces that the image is sparse using the $\\ell_1$ norm in some domain through the sparsifying transform, $\\mathbf{W}$. There is a regularization factor, $\\lambda_{CS}$, that must be chosen to balance the data consistency and sparsity terms.\n",
"\n",
@@ -203,9 +203,9 @@
"\n",
"The Model-based Deep Learning (MoDL) method uses the formulation where the regularizer is a CNN that estimates the noise and aliasing patterns\n",
"\n",
- "$$ \\mathcal{R}_{MoDL}(\\mathbf{x}) = \\lambda \\| \\mathcal{N}_\\mathbf{w}(\\mathbf{x}) \\|^2$$\n",
+ "$$ \\mathcal{R}_{MoDL}(\\mathbf{x}) = \\lambda \\| \\mathcal{N}_w(\\mathbf{x}) \\|^2$$\n",
"\n",
- "and the estimated depends on a set of learned parameters, $\\mathbf{w}$, in the neural network. It's structure is overall similar to VarNets, as both are unrolled architectures, but with slightly different formulations.\n",
+ "and the estimate depends on a set of learned parameters, $w$, in the neural network, $\\mathcal{N}_\\mathbf{w}(\\cdot)$. It's structure is overall similar to VarNets, as both are unrolled architectures, but with slightly different formulations.\n",
"\n",
"\n",
"### Deep Learning Requirements\n",
diff --git a/_sources/Questions.md b/_sources/Questions.md
new file mode 100644
index 0000000..3996a0d
--- /dev/null
+++ b/_sources/Questions.md
@@ -0,0 +1,250 @@
+# MRI Questions
+
+
+## MRI System
+
+
+
+## MR Physics
+
+
+
+## Magnetic Fields and RF Coils
+
+
+## Contrast
+
+1. What flip angle gives the highest SNR for a spoiled gradient echo pulse sequence?
+ - 45-degrees
+ - 90-degrees
+ - 180-degrees
+ - $\cos^{-1} ( \exp(-TR/T_1) )$
+
+
+
+1. What magnetic resonance property is used to perform fat/water (Dixon) imaging?
+ - Proton density
+ - T1
+ - T2
+ - T2*
+ - Chemical Shift
+
+1. What are the minimum measurements required to create separate fat and water images?
+ - In-phase TE
+ - Out-of-phase TE
+ - In-phase TE & Out-of-phase TE
+
+1. What is "magnetization preparation" used for?
+ - polarization
+ - data acquisition
+ - create additoinal contrast
+ - tissue suppression
+
+1. (T/F) Multiple readouts can be used following a magnetization preparation pulse to improve efficiency
+
+
+## Pulse Sequence
+
+In a typical pulse sequence, identify the gradients that serve the following functions:
+1. spoil transverse magnetization
+1. refocus Mxy phase across the slice
+1. move to the edge of k-space
+
+
+Which of the following statement is true for the slice select refocusing gradient?
+* The slice select refocusing gradient must have the same gradient amplitude with the slice selective excitation pulse.
+* The slice select refocusing gradient must have the same gradient area with the slice selective excitation pulse.
+* The slice select refocusing gradient can overlap with the prewinder of the frequency encoding gradient.
+* The slice select refocusing gradient can overlap with the gradient echo.
+
+(T/F) For 2D FT imaging, gradient spoiling is usually applied in the slice select direction because the voxel size is larger thus more dephasing can happen within a voxel in that direction.
+
+(T/F) For a GRE or SE with no phase encoding gradient, the k-space position at TE equals 0 (i.e, $\vec{k}(TE) = 0$).
+
+## RF Pulses
+
+
+## Spatial Encoding
+
+Which k-space line is acquired by the following magnetic field gradients?
+
+In 3DFT imaging, the gradient added to the slice encoding axis (compared to a 2DFT) is a ...
+* frequency encoding gradient
+* phase encoding gradient
+* either frequency or phase encoding gradient
+
+## Image Reconstruction
+
+For a real-valued image $m(x,y)$, which of the following equation holds for its k-space data $M(k_x,k_y)$?
+* $M(k_x,k_y) = M(-k_x,-k_y)$
+* $M(k_x,k_y) = -M(-k_x,-k_y)$
+* $\mathcal{Real}\{M(k_x,k_y)\} = \mathcal{Real}\{ M(-k_x,-k_y) \}$
+* $\mathcal{Imag}\{M(k_x,k_y) \} = \mathcal{Imag}\{M(-k_x,-k_y) \}$
+
+(T/F) In MRI we only look at the magnitude images.
+
+(T/F) The center of k-space always contains the maximum signal.
+
+## Image Characteristics (FOV and Resolution)
+
+The field of view is inversely proportional to...
+* receiver BW (RBW)
+* readout gradient strength (Gxr)
+* TR
+* TE
+
+The field of view is directly proportional to...
+* receiver BW (RBW)
+* readout gradient strength (Gxr)
+* TR
+* TE
+
+(T/F) An anti-aliasing filter can be applied in the phase encoding direction.
+
+The resolution in frequency encoding direction ( $\delta_x$ ) is equal to ...
+* $ \frac{1}{W_{kx}} $
+* $ \frac{1}{\frac{\gamma}{2\pi} G_{xr} t_{read}} $
+* $ \frac{FOV_x}{N_{FE}} $
+* None of the above
+
+
+## SNR
+
+SNR can be increased by ...
+* decreasing voxel size
+* increasing total time
+* increasing NEX
+
+
+## Artifacts
+
+Chemical shift displacement artifact is characterized by ...
+* signal stretch and pile-up
+* bright and dark bands
+* Gibbs ringing
+* ghosting
+
+Susceptibility displacement artifact is characterized by ...
+* signal stretch and pile-up
+* bright and dark bands
+* Gibbs ringing
+* ghosting
+
+Truncation artifacts can be reduced by ...
+* improving resolution
+* filtering in k-space
+* increasing FOV
+* increasing NEX
+
+(T/F) Motion artifacts occur only along the phase-encoding direction.
+
+## Fast Imaging Pulse Sequences
+
+What does it mean to use a multiple spin echo pulse sequence?
+- multiple spin echoes are created following a single excitation pulse
+- multiple k-space lines acquired sequentially
+- multiple gradient-echo repetitions after a magnetization preparation pulse
+- fully refocused gradients and no spoiling in every TR
+
+What types of contrast can be created with a multiple spin echo pulse sequence?
+* proton density weighted
+* T1 weighted
+* T2 weighted
+* T2* weighted
+
+What are the limitations of multiple spin echo pulse sequences?
+- Chemical shift and susceptibility displacement artifacts
+- T2 blurring artifacts
+- ghosting
+- SAR
+
+What does it mean to use echo planar imaging (EPI)?
+- multiple spin echoes are created following a single excitation pulse
+- multiple k-space lines acquired sequentially
+- multiple gradient-echo repetitions after a magnetization preparation pulse
+- fully refocused gradients and no spoiling in every TR
+
+What are the advantages of EPI?
+- Create additional T1, T2, and/or T2* contrast
+- Rapidly acquire k-space
+- Robust to motion
+- Repeated refocusing of intravoxel dephasing
+
+What are the artifacts associated with EPI?
+- Chemical shift displacement
+- Distortion due to magnetic susceptibility differences
+- T2* blurring
+- ghosting
+
+What does it mean to use balanced steady-state free-precession (bSSFP)?
+- multiple spin echoes are created following a single excitation pulse
+- multiple k-space lines acquired sequentially
+- multiple gradient-echo repetitions after a magnetization preparation pulse
+- fully refocused gradients and no spoiling in every TR
+
+## Accelerated Imaging Methods
+
+Match the acceleration methods
+* Partial Fourier
+* Parallel Imaging
+* Compressed Sensing
+* Deep Learning
+
+with the following concept they rely on:
+- conjugate symmetry in k-space
+- spatial encoding from receive coil arrays
+- a sparse representation of the image
+- training on prior images to learn expected patterns
+
+(T/R) Partial Fourier, parallel imaging, and compressed sensing or deep learning reconstructions can be used simultaneously.
+
+How is coil sensitivity information gathered for parallel imaging?
+- It is stored in a database on the scanner
+- A separate scan to measure coil sensitivity maps
+- Using fully-sampled data from the center of k-space
+- Using fully-sampled data from outer k-space
+
+What is the "g-factor" in parallel imaging?
+- How much faster scan can be performed
+- Describes noise amplification
+- Describes SNR loss
+- Describes magnetic field gradients
+
+
+Compared to the SNR a fully sampled acquistion ($SNR_{full}$), the SNR Of a parallel imaging acquisition ($SNR_{PI}$) with an acceleration factor, $R$, and $g$-factor is
+- $SNR_{PI} = SNR_{full}$
+- $SNR_{PI} = SNR_{full} / \sqrt{R}$
+- $SNR_{PI} = SNR_{full} / g(\vec{r}) $
+- $SNR_{PI} = SNR_{full} / (g(\vec{r}) \sqrt{R})$
+
+(T/F) Parallel imaging undersampling can be performed in any direction, regardless of the RF coil configuration.
+
+Simultaneous multi-slice parallel imaging
+- enables acceleration in the slice direction
+- requires no modifications to the pulse sequence
+- requires RF pulses that excite multiple slices
+- requires coil sensitivity information
+
+What type of k-space sampling is required for compressed sensing?
+- full sampling
+- equally spaced undersampling
+- equally spaced undersampling with fully-sampled center of k-space
+- pseudo-random undersampling
+
+At least how many training datasets are typically required to develop deep learning MRI reconstruction methods?
+- 1
+- 10-100
+- 1000-10,000
+- 100,000-1,000,000
+
+Generalization problems can arise in deep learning MRI reconstruction methods when applied to situations that area different from the training data in which of the following ways:
+- different anatomy
+- different contrasts
+- different sampling patterns
+- different B0
+
+Which type of architecture is commonly used for physics-based deep learning MRI reconstruction networks?
+- Encoder-decoder
+- Unet
+- Unrolled
+- Recurrant
\ No newline at end of file
diff --git a/_sources/Signal to Noise Ratio.ipynb b/_sources/Signal to Noise Ratio.ipynb
index 2446c31..c77ad80 100644
--- a/_sources/Signal to Noise Ratio.ipynb
+++ b/_sources/Signal to Noise Ratio.ipynb
@@ -29,9 +29,9 @@
"\n",
"The MRI signal is an integral over a volume of the transverse magnetization. Therefore there is a linear dependency on the MRI signal and the volume of magnetization being examined. So we have\n",
"\n",
- "$$SNR \\propto \\mathrm{Voxel\\ Volume} = \\delta x\\ \\delta y\\ \\delta z$$\n",
+ "$$SNR \\propto \\mathrm{Voxel\\ Volume} = \\delta_x\\ \\delta_y\\ \\delta_z$$\n",
"\n",
- "where $\\delta x, \\delta y, \\delta z$ are the voxel dimensions in x, y, and z.\n",
+ "where $\\delta_x, \\delta_y, \\delta_z$ are the voxel dimensions in x, y, and z.\n",
"\n",
"### Data Acquisition Time\n",
"\n",
diff --git a/objects.inv b/objects.inv
index 147d807..86dd3db 100644
Binary files a/objects.inv and b/objects.inv differ
diff --git a/searchindex.js b/searchindex.js
index cb2be18..a56a385 100644
--- a/searchindex.js
+++ b/searchindex.js
@@ -1 +1 @@
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