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<h1 class="title toc-ignore">Data quality metrics</h1>
<h4 class="date">Last updated: May 07, 2024</h4>
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<p><br></p>
<p>Listed below are the data quality metrics that Gannet computes during
data processing, signal fitting, and tissue segmentation.</p>
<div id="linewidth" class="section level2 hasAnchor">
<h2 class="hasAnchor">Linewidth<a href="#linewidth"
class="anchor-section" aria-label="Anchor link to header"></a></h2>
<p>Linewidth is calculated as the full-width half-maximum (FWHM) (in Hz)
of fitted model signals. When reporting linewidths of datasets, it is
recommended to use the FWHM of Cr or NAA from the OFF spectrum, or the
FWHM of the water reference (if a water reference is provided).</p>
</div>
<div id="signal-to-noise-ratio-snr" class="section level2 hasAnchor">
<h2 class="hasAnchor">Signal-to-noise ratio (SNR)<a
href="#signal-to-noise-ratio-snr" class="anchor-section"
aria-label="Anchor link to header"></a></h2>
<p>The SNR of fitted signals is calculated as the amplitude of the given
signal model divided by twice the standard deviation of the noise
signal. To estimate the noise signal, Gannet takes two independent
segments of the OFF or DIFF spectrum (as appropriate to the modeled
signal of interest) between 8–9 ppm and 9–10 ppm, and detrends them
using a second-order polynomial function. Detrending is performed to
remove baseline artifacts (often related to the residual water signal).
The standard deviation of each detrended noise segment is then
calculated. The smaller of the two standard deviations is then used as
the estimate of noise, which is then multiplied by 2.</p>
<p>Formulaically, this is defined as:</p>
<p><span class="math display">\[
SNR_{signal} = \frac{A_{signal}}{2\cdot\mathrm{std}(noise)}
\]</span></p>
<p>where:</p>
<table>
<colgroup>
<col width="16%" />
<col width="83%" />
</colgroup>
<thead>
<tr class="header">
<th align="left"><u>Parameter</u></th>
<th align="left"><u>Definition</u></th>
</tr>
</thead>
<tbody>
<tr class="odd">
<td align="left"><span class="math inline">\(A_{signal}\)</span></td>
<td align="left">Signal model amplitude</td>
</tr>
<tr class="even">
<td align="left"><span class="math inline">\(noise\)</span></td>
<td align="left">Detrended noise signal between either 8–9 or 9–10 ppm
(whichever produces a lower standard deviation) in the appropriate
spectrum (i.e., either the OFF or DIFF spectrum)</td>
</tr>
</tbody>
</table>
</div>
<div id="frequency-offsets-frequency-driftmotion"
class="section level2 hasAnchor">
<h2 class="hasAnchor">Frequency offsets (frequency drift/motion)<a
href="#frequency-offsets-frequency-driftmotion" class="anchor-section"
aria-label="Anchor link to header"></a></h2>
<p>To estimate the degree of frequency offsets that result from
scanner-related frequency drift<span class="citation"><sup><a
href="#ref-Hui2021a">1</a></sup></span> and participant motion<span
class="citation"><sup><a href="#ref-Evans2013">2</a></sup></span>,
Gannet calculates an average frequency offset<span
class="citation"><sup><a href="#ref-Mikkelsen2017">3</a></sup></span>
<span class="math inline">\(\overline{\Delta\delta_{0}}\)</span>. This
is calculated as the mean (over the course of the acquisition)
difference between the observed frequency of the residual water signal
in the pre-frequency-corrected subspectra and the nominal water
frequency <span class="math inline">\(\delta_{0}\)</span> at 4.68 ppm
(4.8 ppm for room-temperature phantoms), or the nominal Cr frequency at
3.02 ppm for HERMES acquisitions. It should be noted that using the mean
of offset differences does not fully characterize frequency offsets but
is a useful heuristic.</p>
<p>Formulaically, this is defined as:</p>
<p><span class="math display">\[
\overline{\Delta\delta_{0}} = \frac{1}{m}\sum{\widehat{\delta_{0,m}} -
\delta_{0}}
\]</span> where:</p>
<table>
<colgroup>
<col width="16%" />
<col width="83%" />
</colgroup>
<thead>
<tr class="header">
<th align="left"><u>Parameter</u></th>
<th align="left"><u>Definition</u></th>
</tr>
</thead>
<tbody>
<tr class="odd">
<td align="left"><span class="math inline">\(m\)</span></td>
<td align="left">Each individual subspectrum index number</td>
</tr>
<tr class="even">
<td align="left"><span
class="math inline">\(\widehat{\delta_{0,m}}\)</span></td>
<td align="left">Observed water or Cr frequency in each individual
subspectrum</td>
</tr>
<tr class="odd">
<td align="left"><span class="math inline">\(\delta_{0}\)</span></td>
<td align="left">Nominal water or Cr frequency</td>
</tr>
</tbody>
</table>
</div>
<div id="fit-error" class="section level2 hasAnchor">
<h2 class="hasAnchor">Fit error<a href="#fit-error"
class="anchor-section" aria-label="Anchor link to header"></a></h2>
<p>When fitting signal functions to metabolite peaks, Gannet will also
estimate the error of the fit. This is defined as the standard deviation
of the residuals of the signal model fit divided by the signal model
amplitude and multiplied by 100 to give a percentage.</p>
<p>For metabolite peak fits, this is:</p>
<p><span class="math display">\[
\epsilon_{metab} = 100\cdot\frac{\mathrm{std}(resid_{metab})}{A_{metab}}
\]</span></p>
<p>where:</p>
<table>
<thead>
<tr class="header">
<th align="left"><u>Parameter</u></th>
<th align="left"><u>Definition</u></th>
</tr>
</thead>
<tbody>
<tr class="odd">
<td align="left"><span class="math inline">\(resid_{metab}\)</span></td>
<td align="left">Signal model fit residuals</td>
</tr>
<tr class="even">
<td align="left"><span class="math inline">\(A_{metab}\)</span></td>
<td align="left">Signal model amplitude</td>
</tr>
</tbody>
</table>
<p>Similarly, for reference signal fits, this is:</p>
<p><span class="math display">\[
\epsilon_{ref} = 100\cdot\frac{\mathrm{std}(resid_{ref})}{A_{ref}}
\]</span></p>
<p>Since all metabolites are normalized to a reference signal (either Cr
or unsuppressed water) and reported as such, the fit error that really
should be considered (and reported) is the combined error of the
metabolite and reference signal model fits, which add up in
quadrature.</p>
<p>Formulaically, this is defined as:</p>
<p><span class="math display">\[
\epsilon_{metab,ref} = \sqrt{\epsilon_{metab}^2 + \epsilon_{ref}^2}
\]</span></p>
<div id="references" class="section level3 unnumbered hasAnchor">
<h3 class="unnumbered hasAnchor">References<a href="#references"
class="anchor-section" aria-label="Anchor link to header"></a></h3>
<div id="refs" class="references csl-bib-body">
<div id="ref-Hui2021a" class="csl-entry">
<div class="csl-left-margin">1. </div><div class="csl-right-inline">Hui
SCN, Mikkelsen M, Zöllner HJ, et al. <span class="nocase">Frequency
drift in MR spectroscopy at 3T</span>. <em>NeuroImage</em>.
2021;241(21):118430. doi:<a
href="https://doi.org/10.1016/j.neuroimage.2021.118430">10.1016/j.neuroimage.2021.118430</a></div>
</div>
<div id="ref-Evans2013" class="csl-entry">
<div class="csl-left-margin">2. </div><div
class="csl-right-inline">Evans CJ, Puts NAJ, Robson SE, et al. <span
class="nocase">Subtraction artifacts and frequency (Mis-)alignment in
J-difference GABA editing</span>. <em>Journal of Magnetic Resonance
Imaging</em>. 2013;38(4):970-975. doi:<a
href="https://doi.org/10.1002/jmri.23923">10.1002/jmri.23923</a></div>
</div>
<div id="ref-Mikkelsen2017" class="csl-entry">
<div class="csl-left-margin">3. </div><div
class="csl-right-inline">Mikkelsen M, Barker PB, Bhattacharyya PK, et
al. <span class="nocase">Big GABA: Edited MR spectroscopy at 24 research
sites</span>. <em>NeuroImage</em>. 2017;159:32-45. doi:<a
href="https://doi.org/10.1016/j.neuroimage.2017.07.021">10.1016/j.neuroimage.2017.07.021</a></div>
</div>
</div>
</div>
</div>
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</div>
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