deploy: f5fbcc4

Artifacts.html

@@ -413,6 +413,7 @@ <h2> Contents </h2>
             <nav aria-label="Page">
                 <ul class="visible nav section-nav flex-column">
 <li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#learning-goals">Learning Goals</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#introduction">Introduction</a></li>
 <li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#artifact-comparison">Artifact Comparison</a></li>
 <li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#simulations-of-artifacts">Simulations of Artifacts</a></li>
 </ul>
@@ -450,6 +451,11 @@ <h2>Learning Goals<a class="headerlink" href="#learning-goals" title="Permalink
 <li><p>Identify artifacts and how to mitigate them</p></li>
 </ol>
 </section>
+<section id="introduction">
+<h2>Introduction<a class="headerlink" href="#introduction" title="Permalink to this heading">#</a></h2>
+<p>Many of the artifacts that occur in MRI can be understood and analyzed using the k-space perspective.  In particular, they can be understood as the k-space data being modified by some function.  This is described mathematically in
+<span class="xref myst">MRI Signal Equation and K-psace - K-space Data Weighting</span></p>
+</section>
 <section id="artifact-comparison">
 <h2>Artifact Comparison<a class="headerlink" href="#artifact-comparison" title="Permalink to this heading">#</a></h2>
 <table class="table">
@@ -755,6 +761,7 @@ <h2>Simulations of Artifacts<a class="headerlink" href="#simulations-of-artifact
   <nav class="bd-toc-nav page-toc">
     <ul class="visible nav section-nav flex-column">
 <li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#learning-goals">Learning Goals</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#introduction">Introduction</a></li>
 <li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#artifact-comparison">Artifact Comparison</a></li>
 <li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#simulations-of-artifacts">Simulations of Artifacts</a></li>
 </ul>

Fast Imaging Pulse Sequences.html

@@ -415,6 +415,12 @@ <h2> Contents </h2>
 <li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#learning-goals">Learning Goals</a></li>
 <li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#echo-planar-imaging-epi">Echo-planar Imaging (EPI)</a></li>
 <li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#fast-turbo-spin-echo-fse-tse">Fast/Turbo Spin-echo (FSE/TSE)</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#fast-gradient-echo-sequences">Fast gradient-echo sequences</a><ul class="nav section-nav flex-column">
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#spoiler-or-crusher-gradients">Spoiler or Crusher gradients</a></li>
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#rf-spoiling">RF spoiling</a></li>
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#types-of-fast-gradient-echo-sequences">Types of fast gradient-echo sequences</a></li>
+</ul>
+</li>
 </ul>
             </nav>
         </div>
@@ -442,18 +448,21 @@ <h2>Learning Goals<a class="headerlink" href="#learning-goals" title="Permalink
 <ul class="simple">
 <li><p>Describe how EPI works</p></li>
 <li><p>Describe how FSE/TSE sequences work</p></li>
+<li><p>Describe how fast gradient-echo sequences work</p></li>
 </ul>
 </li>
 <li><p>Manipulate MRI sequence parameters to improve performance</p>
 <ul class="simple">
 <li><p>Understand how and when to accelerate with EPI</p></li>
 <li><p>Understand how and when to accelerate with FSE/TSE</p></li>
+<li><p>Understand how contrast changes in fast gradient-echo sequences</p></li>
 </ul>
 </li>
 <li><p>Identify artifacts and how to mitigate them</p>
 <ul class="simple">
 <li><p>Identify EPI artifacts including distortion and T2*</p></li>
 <li><p>Identify FSE/TSE artifacts include T2 blurring</p></li>
+<li><p>Identify fast gradient-echo artifacts such as banding in bSSFP</p></li>
 </ul>
 </li>
 </ol>
@@ -466,6 +475,47 @@ <h2>Echo-planar Imaging (EPI)<a class="headerlink" href="#echo-planar-imaging-ep
 <h2>Fast/Turbo Spin-echo (FSE/TSE)<a class="headerlink" href="#fast-turbo-spin-echo-fse-tse" title="Permalink to this heading">#</a></h2>
 <p>These pulse sequences use multiple spin-echo refocusing pulses after a single exictation pulse.  This enables multiple k-space lines to be acquired during the multiple spin-echoes that are formed.  This technique was originally called Rapid Acquisition with Relaxation Enhancement (RARE), and is known on various MRI scanners as fast spin-echo (FSE, GE Healthcare), turbo spin-echo (TSE, Siemens Healthineers), or turbo field-echo (TFE, Philips Healthcare).</p>
 </section>
+<section id="fast-gradient-echo-sequences">
+<h2>Fast gradient-echo sequences<a class="headerlink" href="#fast-gradient-echo-sequences" title="Permalink to this heading">#</a></h2>
+<p>The basic gradient-echo sequence is typically a spoiled gradient-echo sequence.  The sequence is called spoiled because the transverse magnetization is spoiled by a spoiler gradient before the next RF pulse.</p>
+<section id="spoiler-or-crusher-gradients">
+<h3>Spoiler or Crusher gradients<a class="headerlink" href="#spoiler-or-crusher-gradients" title="Permalink to this heading">#</a></h3>
+<p>A large, unbalanced gradient will create dephasing of the transverse magnetization across the imaging voxels.  This effectively eliminates the signal.  However, the net magnetization is not truly eliminated, and this can be refocused by gradients.</p>
+</section>
+<section id="rf-spoiling">
+<h3>RF spoiling<a class="headerlink" href="#rf-spoiling" title="Permalink to this heading">#</a></h3>
+<p>The RF axis of rotation is changed every TR.  This reduces the chances of magnetization from previous TRs to become coherently excited.  Specific RF spoiling schemes, such as quadratic phase incrementation, is required for this to be effective.</p>
+</section>
+<section id="types-of-fast-gradient-echo-sequences">
+<h3>Types of fast gradient-echo sequences<a class="headerlink" href="#types-of-fast-gradient-echo-sequences" title="Permalink to this heading">#</a></h3>
+<p>Spoiled gradient-echo (SPGR)/fast low-angle shot (FLASH)</p>
+<ul class="simple">
+<li><p>Aims to full spoil transverse magnetization every TR</p></li>
+<li><p>Both gradient and RF spoiling are used</p></li>
+<li><p>Pure T1 weighted contrast</p></li>
+</ul>
+<p>Gradient-recalled acquisition in the steady state (GRASS)/fast imaging with steady-state precession (FISP)</p>
+<ul class="simple">
+<li><p>Allows for residual transverse magnetization to be used in the next TR</p></li>
+<li><p>Refouces frequency and phase encoding gradients</p></li>
+<li><p>RF spoiling used</p></li>
+<li><p>Increases T2* contrast</p></li>
+</ul>
+<p>Steady-state free precession (SSFP)/time-reversed fast imaging with steady-state precession (PSIF)</p>
+<ul class="simple">
+<li><p>Use gradients to refocus signals from previous TRs</p></li>
+<li><p>Gradient spoiling but refocused in later TRs</p></li>
+<li><p>Creates T2/T1 contrast</p></li>
+</ul>
+<p>Balanced SSFP/TrueFISP</p>
+<ul class="simple">
+<li><p>Balanced gradients every TR</p></li>
+<li><p>No spoiling, all magnetization preserved each TR</p></li>
+<li><p>Creates T2/T1 contrast</p></li>
+<li><p>High SNR efficiency</p></li>
+</ul>
+</section>
+</section>
 </section>
 
     <script type="text/x-thebe-config">
@@ -534,6 +584,12 @@ <h2>Fast/Turbo Spin-echo (FSE/TSE)<a class="headerlink" href="#fast-turbo-spin-e
 <li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#learning-goals">Learning Goals</a></li>
 <li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#echo-planar-imaging-epi">Echo-planar Imaging (EPI)</a></li>
 <li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#fast-turbo-spin-echo-fse-tse">Fast/Turbo Spin-echo (FSE/TSE)</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#fast-gradient-echo-sequences">Fast gradient-echo sequences</a><ul class="nav section-nav flex-column">
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#spoiler-or-crusher-gradients">Spoiler or Crusher gradients</a></li>
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#rf-spoiling">RF spoiling</a></li>
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#types-of-fast-gradient-echo-sequences">Types of fast gradient-echo sequences</a></li>
+</ul>
+</li>
 </ul>
   </nav></div>
 

Gradient and Spin Echoes.html

@@ -487,8 +487,8 @@ <h2>Gradient Echo Pulse Sequence (GE or GRE)<a class="headerlink" href="#gradien
 <h2>Off-resonance<a class="headerlink" href="#off-resonance" title="Permalink to this heading">#</a></h2>
 <p>Ideally, the magnetic field is uniform in the absense of any applied gradients.  However, in practice there are unavoidable variations in the magnetic field that lead to changes in resonance frequency.  These magnetic field variations are referred to as “off-resonance”, and can be represented as</p>
 <div class="math notranslate nohighlight">
-\[\Delta f_r(\vec{r})\]</div>
-<p>This typically includes imperfections in the main <span class="math notranslate nohighlight">\(B_0\)</span> magnetic as well as subject-specific changes in the magnetic field that are largely due to magnetic susceptibility effects.</p>
+\[\Delta f_r(\vec{r}) = \bar \gamma $\Delta B_0(\vec{r})$ \]</div>
+<p>These are due imperfections in the main <span class="math notranslate nohighlight">\(B_0\)</span> magnet as well as subject-specific changes in the magnetic field that are largely due to magnetic susceptibility effects.</p>
 </section>
 <section id="effects-of-off-resonance-and-t2">
 <h2>Effects of Off-resonance and T2*<a class="headerlink" href="#effects-of-off-resonance-and-t2" title="Permalink to this heading">#</a></h2>

MRI Contrast.html

@@ -686,6 +686,13 @@ <h3>90-degree flip angles<a class="headerlink" href="#degree-flip-angles" title=
 <div class="math notranslate nohighlight">
 \[S \propto M_0 (1- \exp(-TR/T_1) )\]</div>
 <p>Illustrated in the first example below.  This shows that the magnetization reaches steady state in the 2nd TR.</p>
+</section>
+<section id="id3">
+<h3>&lt; 90-degree flip angles<a class="headerlink" href="#id3" title="Permalink to this heading">#</a></h3>
+<p>For T1-weighting, it is generally more efficient in terms of signal acqruied per time to use &lt; 90-degree flip angles every TR, in which case</p>
+<div class="math notranslate nohighlight">
+\[S \propto M_0 \sin(\theta) \frac{1- \exp(-TR/T_1)}{1- \cos(\theta) \exp(-TR/T_1)}\]</div>
+<p>Illustrated in this second example below.  This shows that the magnetization can take many TRs to reach steady state.</p>
 <div class="cell docutils container">
 <div class="cell_input docutils container">
 <div class="highlight-octave notranslate"><div class="highlight"><pre><span></span><span class="c">% Signal evolution between TRs with 90-degree pulses</span>
@@ -774,13 +781,6 @@ <h3>90-degree flip angles<a class="headerlink" href="#degree-flip-angles" title=
 <img alt="_images/eda58af1383601bd31799acf1da6673f51aedf43bb9071f27aa042e63808fbbb.png" src="_images/eda58af1383601bd31799acf1da6673f51aedf43bb9071f27aa042e63808fbbb.png" />
 </div>
 </div>
-</section>
-<section id="id3">
-<h3>&lt; 90-degree flip angles<a class="headerlink" href="#id3" title="Permalink to this heading">#</a></h3>
-<p>For T1-weighting, it is generally more efficient in terms of signal acqruied per time to use &lt; 90-degree flip angles every TR, in which case</p>
-<div class="math notranslate nohighlight">
-\[S \propto M_0 \sin(\theta) \frac{1- \exp(-TR/T_1)}{1- \cos(\theta) \exp(-TR/T_1)}\]</div>
-<p>Illustrated in this second example below.  This shows that the magnetization can take many TRs to reach steady state.</p>
 <div class="cell docutils container">
 <div class="cell_input docutils container">
 <div class="highlight-octave notranslate"><div class="highlight"><pre><span></span><span class="c">% Signal evolution between TRs with &lt;90-degree pulses</span>
@@ -1144,6 +1144,9 @@ <h2>Simple Contrast Phantom<a class="headerlink" href="#simple-contrast-phantom"
 <div class="highlight-Octave notranslate"><div class="highlight"><pre><span></span><span class="n">signal_gre</span> <span class="p">=</span> <span class="n">MRsignal_spoiled_gradient_echo</span><span class="p">(</span><span class="n">flip</span><span class="p">,</span> <span class="n">TE</span><span class="p">,</span> <span class="n">TR</span><span class="p">,</span> <span class="n">M0</span><span class="p">,</span> <span class="n">T1</span><span class="p">,</span> <span class="n">T2</span><span class="p">)</span>
 </pre></div>
 </div>
+<section id="challenge-yourself">
+<h3>Challenge Yourself!<a class="headerlink" href="#challenge-yourself" title="Permalink to this heading">#</a></h3>
+<p>Based on the images and TE/TR parameters below, can you estimate T1 and T2 relaxation times of the 3 objects?</p>
 <div class="cell docutils container">
 <div class="cell_input docutils container">
 <div class="highlight-octave notranslate"><div class="highlight"><pre><span></span><span class="c">% contrast_phantom</span>
@@ -1201,9 +1204,6 @@ <h2>Simple Contrast Phantom<a class="headerlink" href="#simple-contrast-phantom"
 <img alt="_images/03b97f10f51c0541981866f210657bdf0512e1458495d474287dff422cf2540f.png" src="_images/03b97f10f51c0541981866f210657bdf0512e1458495d474287dff422cf2540f.png" />
 </div>
 </div>
-<section id="challenge-yourself">
-<h3>Challenge Yourself!<a class="headerlink" href="#challenge-yourself" title="Permalink to this heading">#</a></h3>
-<p>Based on the images and TE/TR parameters above, can you estimate T1 and T2 relaxation times of the 3 objects?</p>
 </section>
 </section>
 </section>

MRI Signal Equation.html

@@ -578,8 +578,8 @@ <h2>Relaxation during signal acquisition<a class="headerlink" href="#relaxation-
 </div>
 </div>
 <div class="cell_output docutils container">
-<img alt="_images/92ac396d1094116faca36e071635f22ff14da490df79aa5b1e645af612d2ec53.png" src="_images/92ac396d1094116faca36e071635f22ff14da490df79aa5b1e645af612d2ec53.png" />
 <img alt="_images/04e32389def1da9556efd712d119655989abaa4ab970ce8cc166a8125b4a22c0.png" src="_images/04e32389def1da9556efd712d119655989abaa4ab970ce8cc166a8125b4a22c0.png" />
+<img alt="_images/92ac396d1094116faca36e071635f22ff14da490df79aa5b1e645af612d2ec53.png" src="_images/92ac396d1094116faca36e071635f22ff14da490df79aa5b1e645af612d2ec53.png" />
 </div>
 </div>
 <p>Thus the reconstructed image will corrupted by a convolution (denoted by <span class="math notranslate nohighlight">\(*\)</span>) based on the k-space amplitude weighting</p>
@@ -625,8 +625,8 @@ <h2>Relaxation during signal acquisition<a class="headerlink" href="#relaxation-
 </div>
 </div>
 <div class="cell_output docutils container">
-<img alt="_images/2ac77f1e3c485944eb84049be4e604109e3623a5e7fef06e080c1bd6acd6f1e0.png" src="_images/2ac77f1e3c485944eb84049be4e604109e3623a5e7fef06e080c1bd6acd6f1e0.png" />
 <img alt="_images/c2bc6f3fee2a679d68cb3956f1dd71771107c64c4330c26801b306718311c22e.png" src="_images/c2bc6f3fee2a679d68cb3956f1dd71771107c64c4330c26801b306718311c22e.png" />
+<img alt="_images/2ac77f1e3c485944eb84049be4e604109e3623a5e7fef06e080c1bd6acd6f1e0.png" src="_images/2ac77f1e3c485944eb84049be4e604109e3623a5e7fef06e080c1bd6acd6f1e0.png" />
 </div>
 </div>
 <p>In the above plots, the height of the main peak in the center represents the expected SNR, including losses due to blurring, while the signal amplitude outside of the main peak represents blurring that will occur.   These show that the blurring and signal loss from <span class="math notranslate nohighlight">\(T_2^*\)</span> gets worse as the relaxation time is shorter, the blurring it is much worse for EPI (in phase encoding direction) versus Cartesian trajectories.</p>
@@ -636,8 +636,8 @@ <h2>Off-resonance and Chemical Shift<a class="headerlink" href="#off-resonance-a
 <p>Off-resonance and chemical shift lead to changes in the precession frequency of the magnetization.  We can add this onto the idealized signal equation.</p>
 <p>Here we separately define:</p>
 <ul class="simple">
-<li><p><span class="math notranslate nohighlight">\(\Delta f_r(\vec{r})\)</span> magnetic field inhomogeneity (macroscopic), including main field imperfections, and magnetic susceptibility effects</p></li>
-<li><p><span class="math notranslate nohighlight">\(\Delta f_{cs}\)</span> frequency changes due to chemical shift, so depends on the chemical species being examined (could sum or index signal over this dimension)</p></li>
+<li><p><span class="math notranslate nohighlight">\(\Delta f_r(\vec{r}) = \bar \gamma \)</span>\Delta B_0(\vec{r})$$ - magnetic field inhomogeneities, including main field imperfections, and magnetic susceptibility effects</p></li>
+<li><p><span class="math notranslate nohighlight">\(\Delta f_{cs}\)</span> - frequency changes due to chemical shift, so depends on the chemical species being examined (could sum or index signal over this dimension)</p></li>
 </ul>
 <!-- $$s(t) = \int m(\vec{r})\ e^{-i 2 \pi \Delta f_{cs} t} e^{-i 2 \pi \Delta f_r(\vec{r}) t} e^{-i 2 \pi \vec{k}(t) \cdot \vec{r}} \  d\vec{r}$$ -->
 <p>For simplicity, combine all off-resonance and/or chemical shift into a single frequnecy shift term, <span class="math notranslate nohighlight">\(\Delta f(\vec{r}) = \Delta f_{cs} + \Delta f_r(\vec{r})\)</span> as</p>
@@ -697,8 +697,8 @@ <h2>Off-resonance and Chemical Shift<a class="headerlink" href="#off-resonance-a
 </div>
 </div>
 <div class="cell_output docutils container">
-<img alt="_images/8f6a3cbbd80b72ee00d3a30c540d68b3fd29709b58d9cb727045d05a021c1418.png" src="_images/8f6a3cbbd80b72ee00d3a30c540d68b3fd29709b58d9cb727045d05a021c1418.png" />
 <img alt="_images/7116ed83d8359b6883a12abf711538b5c0ffc32e612333da3dc4050edb5f88f6.png" src="_images/7116ed83d8359b6883a12abf711538b5c0ffc32e612333da3dc4050edb5f88f6.png" />
+<img alt="_images/8f6a3cbbd80b72ee00d3a30c540d68b3fd29709b58d9cb727045d05a021c1418.png" src="_images/8f6a3cbbd80b72ee00d3a30c540d68b3fd29709b58d9cb727045d05a021c1418.png" />
 </div>
 </div>
 <p>For frequency shift, the main peak of the convolution kernels is shifted frfom the origin.  This will result in a shift in the reconstructed image.  The shift is much larger for EPI and is in the phase encoding instead of the frequency encoding direction.  (The residual side lobes are due to sinc interpolation effects, similar to Gibbs ringing.)</p>
@@ -722,7 +722,7 @@ <h2>K-space Data Weighting<a class="headerlink" href="#k-space-data-weighting" t
 \[\hat{M}(\vec{k}) = M(\vec{k}) W(\vec{k}) \]</div>
 <div class="math notranslate nohighlight">
 \[\hat{m}(\vec{r}) = m(\vec{r}) * \mathcal{F}^{-1} \{ W(\vec{k}) \} = m(\vec{r}) * w(\vec{r})\]</div>
-<p>Where <span class="math notranslate nohighlight">\(w(\vec{r})\)</span> is the inverse Fourier Transform of the weighting function.Thus the effects can be boiled down to a convolution operation in the resulting reconstructed image.</p>
+<p>Where <span class="math notranslate nohighlight">\(w(\vec{r})\)</span> is the inverse Fourier Transform of the weighting function.  This is also known as a point spread function (PSF) or impulse response function.  Thus the effects can be boiled down to a convolution operation in the resulting reconstructed image.</p>
 <p>When the frequency shift and relaxation rates vary across space, it is helpful to decompose the image into components, <span class="math notranslate nohighlight">\(m_i\)</span> that experience the same weighting (e.g. same frequency shift, or same <span class="math notranslate nohighlight">\(T_2^*\)</span>) <span class="math notranslate nohighlight">\(W_i\)</span>.</p>
 <div class="math notranslate nohighlight">
 \[ m(\vec{r}) = \sum_i m_i(\vec{r}) \]</div>