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<h1 class="title toc-ignore">Quantification & tissue correction</h1>
<h4 class="date">Last updated: October 14, 2024</h4>
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<p><br></p>
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<p><i class="fa fa-info-circle" style="color: white"></i> The formulas
below apply to releases 3.1+ and may not be applicable to older
releases.</p>
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<p>Gannet quantifies metabolite levels in different ways at various
points in the pipeline depending on what reference signals are present
and if structural image data are available. It is important to
understand what the underlying quantification formulas are for the
interpretation and reporting of results.</p>
<p><u>A note on units of concentration</u></p>
<p>There is a perennial issue surrounding how quantified in vivo MRS
measurements should be expressed; that is, in what biochemical units (if
any) they should be reported. In vivo MRS measurements can be, and have
been, reported in molar, molal, and institutional units or as simple
ratios. However, this makes interpreting and comparing such values,
especially across published studies, highly challenging. While Gannet
does apply a number of signal scaling factors to water-referenced
metabolite measurements (that are required when reporting absolute
concentrations), it is our philosophy that these measurements should be
considered pseudo-absolute because accounting for all empirical signal
scaling factors is impractical (even impossible) to permit truly
absolute quantification. Thus, we denote our water-referenced metabolite
measurements in institutional units (i.u.).</p>
<div id="gannetfit" class="section level2 hasAnchor">
<h2 class="hasAnchor">GannetFit<a href="#gannetfit"
class="anchor-section" aria-label="Anchor link to header"></a></h2>
<p><code>MRS_struct.out.vox1.(metab).ConcCr</code>,
<code>MRS_struct.out.vox1.(metab).ConcCho</code>, and
<code>MRS_struct.out.vox1.(metab).ConcNAA</code> are simple signal
integral ratios of the metabolite of interest and the metabolite
reference signals Cr, Cho, and NAA, respectively:</p>
<p><span class="math display">\[C = \frac{I_{M}}{I_{ref}}\]</span></p>
<p>If a water reference is provided,
<code>MRS_struct.out.vox1.(metab).ConcIU</code> is also calculated. It
is defined as the signal integral ratio of the metabolite of interest
and water reference scaled by a number of global signal scaling
factors:</p>
<p><span class="math display">\[
C_{corr} =
\frac{I_{M}}{I_{W}}\cdot
\frac{H_{W}}{H_{M}}\cdot
\frac{MM}{\kappa}\cdot
C_{W}\cdot
W_{vis}\cdot
\frac{\exp\left(-\frac{TE_{W}}{T_{2W}}\right)\left[1-\exp\left(-\frac{TR_{W}}{T_{1W}}\right)\right]}
{\exp\left(-\frac{TE_{M}}{T_{2M}}\right)\left[1-\exp\left(-\frac{TR_{M}}{T_{1M}}\right)\right]}
\]</span></p>
<p>where:</p>
<table>
<colgroup>
<col width="11%" />
<col width="50%" />
<col width="38%" />
</colgroup>
<thead>
<tr class="header">
<th align="left"><u>Parameter</u></th>
<th align="left"><u>Description</u></th>
<th align="left"><u>Default value</u></th>
</tr>
</thead>
<tbody>
<tr class="odd">
<td align="left"><span class="math inline">\(C_{corr}\)</span></td>
<td align="left">Estimated metabolite concentration in i.u.</td>
<td align="left"></td>
</tr>
<tr class="even">
<td align="left"><span class="math inline">\(I_{M}\)</span></td>
<td align="left">Metabolite signal integral</td>
<td align="left"></td>
</tr>
<tr class="odd">
<td align="left"><span class="math inline">\(I_{W}\)</span></td>
<td align="left">Water signal integral</td>
<td align="left"></td>
</tr>
<tr class="even">
<td align="left"><span class="math inline">\(H_{M}\)</span></td>
<td align="left">Number of <sup>1</sup>H protons that give rise to the
metabolite signal</td>
<td align="left">Metabolite dependent; see <code>GannetFit.m</code> for
default values</td>
</tr>
<tr class="odd">
<td align="left"><span class="math inline">\(H_{W}\)</span></td>
<td align="left">Number of <sup>1</sup>H protons that give rise to the
water signal</td>
<td align="left">2</td>
</tr>
<tr class="even">
<td align="left"><span class="math inline">\(MM\)</span></td>
<td align="left">Correction factor for the contribution of the co-edited
macromolecule signal in the metabolite signal</td>
<td align="left">0.45 for GABA editing and 1 for all other edited
metabolites</td>
</tr>
<tr class="odd">
<td align="left"><span class="math inline">\(\kappa\)</span></td>
<td align="left">Editing efficiency</td>
<td align="left">Acquisition dependent; 0.5 for GABA editing</td>
</tr>
<tr class="even">
<td align="left"><span class="math inline">\(C_{W}\)</span></td>
<td align="left">Molal concentration of pure water</td>
<td align="left">55.51 mol/kg</td>
</tr>
<tr class="odd">
<td align="left"><span class="math inline">\(W_{vis}\)</span></td>
<td align="left">Approximate relative MR visibility of water in brain
tissue</td>
<td align="left">0.65<span class="citation"><sup><a
href="#ref-Ernst1993">1</a></sup></span></td>
</tr>
<tr class="even">
<td align="left"><span class="math inline">\(TE_{W}\)</span></td>
<td align="left">Echo time of the water reference acquisition</td>
<td align="left">Acquisition dependent</td>
</tr>
<tr class="odd">
<td align="left"><span class="math inline">\(TR_{W}\)</span></td>
<td align="left">Repetition time of the water reference acquisition</td>
<td align="left">Acquisition dependent</td>
</tr>
<tr class="even">
<td align="left"><span class="math inline">\(TE_{M}\)</span></td>
<td align="left">Echo time of the metabolite acquisition</td>
<td align="left">Acquisition dependent</td>
</tr>
<tr class="odd">
<td align="left"><span class="math inline">\(TR_{M}\)</span></td>
<td align="left">Repetition time of the metabolite acquisition</td>
<td align="left">Acquisition dependent</td>
</tr>
<tr class="even">
<td align="left"><span class="math inline">\(T_{2W}\)</span></td>
<td align="left">Average transverse relaxation time of water in GM and
WM</td>
<td align="left">1.100 s<span class="citation"><sup><a
href="#ref-Wansapura1999">2</a></sup></span></td>
</tr>
<tr class="odd">
<td align="left"><span class="math inline">\(T_{1W}\)</span></td>
<td align="left">Average longitudinal relaxation time of water in GM and
WM</td>
<td align="left">0.095 s<span class="citation"><sup><a
href="#ref-Wansapura1999">2</a></sup></span></td>
</tr>
<tr class="even">
<td align="left"><span class="math inline">\(T_{2M}\)</span></td>
<td align="left">Transverse relaxation time of metabolite</td>
<td align="left">Metabolite dependent; see <code>GannetFit.m</code> for
default values</td>
</tr>
<tr class="odd">
<td align="left"><span class="math inline">\(T_{1M}\)</span></td>
<td align="left">Longitudinal relaxation time of metabolite</td>
<td align="left">Metabolite dependent; see <code>GannetFit.m</code> for
default values</td>
</tr>
</tbody>
</table>
</div>
<div id="gannetsegment" class="section level2 hasAnchor">
<h2 class="hasAnchor">GannetSegment<a href="#gannetsegment"
class="anchor-section" aria-label="Anchor link to header"></a></h2>
<p>When segmenting structural images to obtain voxel volume fractions of
GM, WM, and CSF, and if a water reference is available, a CSF-only
correction is applied to the <code>ConcIU</code> measurement.</p>
<p><code>MRS_struct.out.vox1.(metab).ConcIU_CSFcorr</code>:</p>
<p><span class="math display">\[
C_{CSFcorr} =
\frac{I_{M}}{I_{W}}\cdot
\frac{H_{W}}{H_{M}}\cdot
\frac{MM}{\kappa}\cdot
C_{W}\cdot
W_{vis}\cdot
\frac{\exp\left(-\frac{TE_{W}}{T_{2W}}\right)\left[1-\exp\left(-\frac{TR_{W}}{T_{1W}}\right)\right]}
{\exp\left(-\frac{TE_{M}}{T_{2M}}\right)\left[1-\exp\left(-\frac{TR_{M}}{T_{1M}}\right)\right]}\cdot
\frac{1}{1-f_{CSF}}
\]</span></p>
<p>where <span class="math inline">\(C_{CSFcorr}\)</span> is the
estimated metabolite concentration in i.u. corrected for CSF and <span
class="math inline">\(f_{CSF}\)</span> is the voxel volume fraction of
CSF.</p>
</div>
<div id="gannetquantify" class="section level2 hasAnchor">
<h2 class="hasAnchor">GannetQuantify<a href="#gannetquantify"
class="anchor-section" aria-label="Anchor link to header"></a></h2>
<p><code>GannetQuantify.m</code> goes a step further and corrects for
partial volume effects that attenuate the observed water and metabolite
signals. There are two approaches that are employed. The first is termed
the Gasparovic et al.<span class="citation"><sup><a
href="#ref-Gasparovic2006">3</a></sup></span> method and the second is
termed the Harris et al.<span class="citation"><sup><a
href="#ref-Harris2015">4</a></sup></span> method. Although similar, the
difference between these approaches is that the Harris et al. method
additionally accounts for intrinsic differences in metabolite
concentrations in GM and WM.</p>
<div id="the-gasparovic-et-al.-method" class="section level3 hasAnchor">
<h3 class="hasAnchor"><u>The Gasparovic et al. method</u><a
href="#the-gasparovic-et-al.-method" class="anchor-section"
aria-label="Anchor link to header"></a></h3>
<p><code>MRS_struct.out.vox1.(metab).ConcIU_TissCorr</code>:</p>
<p><span class="math display">\[
C_{TissCorr} =
\frac{I_{M}}{I_{W}}\cdot
\frac{H_{W}}{H_{M}}\cdot
\frac{MM}{\kappa}\cdot
C_{W}\cdot
\frac{\sum_{i}^{GM,WM,CSF}f_{i}\beta_{i}\exp\left(-\frac{TE_{W}}{T_{2W,i}}\right)\left[1-\exp\left(-\frac{TR_{W}}{T_{1W,i}}\right)\right]}
{(1-f_{CSF})\exp\left(-\frac{TE_{M}}{T_{2M}}\right)\left[1-\exp\left(-\frac{TR_{M}}{T_{1M}}\right)\right]}
\]</span></p>
<p>where:</p>
<table>
<colgroup>
<col width="11%" />
<col width="50%" />
<col width="38%" />
</colgroup>
<thead>
<tr class="header">
<th align="left"><u>Parameter</u></th>
<th align="left"><u>Description</u></th>
<th align="left"><u>Default value</u></th>
</tr>
</thead>
<tbody>
<tr class="odd">
<td align="left"><span class="math inline">\(C_{TissCorr}\)</span></td>
<td align="left">Estimated metabolite concentration in i.u. corrected
for partial volume effects of water</td>
<td align="left"></td>
</tr>
<tr class="even">
<td align="left"><span class="math inline">\(f_{i}\)</span></td>
<td align="left">Voxel volume fraction of GM, WM, or CSF</td>
<td align="left"></td>
</tr>
<tr class="odd">
<td align="left"><span class="math inline">\(\beta_i\)</span></td>
<td align="left">Relative MR visibility of water in GM, WM, or CSF</td>
<td align="left">0.78, 0.65, and 0.97<span class="citation"><sup><a
href="#ref-Ernst1993">1</a></sup></span></td>
</tr>
<tr class="even">
<td align="left"><span class="math inline">\(T_{2W,i}\)</span></td>
<td align="left">Transverse relaxation time of water in GM, WM, or
CSF</td>
<td align="left">0.110, 0.0792, and 0.503 s<span
class="citation"><sup><a href="#ref-Wansapura1999">2</a>,<a
href="#ref-Piechnik2009">5</a></sup></span></td>
</tr>
<tr class="odd">
<td align="left"><span class="math inline">\(T_{1W,i}\)</span></td>
<td align="left">Longitudinal relaxation time of water in GM, WM, or
CSF</td>
<td align="left">1.331, 0.832, and 3.817 s<span class="citation"><sup><a
href="#ref-Wansapura1999">2</a>,<a
href="#ref-Lu2005">6</a></sup></span></td>
</tr>
</tbody>
</table>
</div>
<div id="the-harris-et-al.-method" class="section level3 hasAnchor">
<h3 class="hasAnchor"><u>The Harris et al. method</u><a
href="#the-harris-et-al.-method" class="anchor-section"
aria-label="Anchor link to header"></a></h3>
<p><code>MRS_struct.out.vox1.(metab).ConcIU_AlphaTissCorr</code>:</p>
<p><span class="math display">\[
C_{AlphaCorr} =
\frac{I_{M}}{I_{W}}\cdot
\frac{H_{W}}{H_{M}}\cdot
\frac{MM}{\kappa}\cdot
\frac{\sum_{i}^{GM,WM,CSF}f_{i}C_{W,i}\exp\left(-\frac{TE_{W}}{T_{2W,i}}\right)\left[1-\exp\left(-\frac{TR_{W}}{T_{1W,i}}\right)\right]}
{\exp\left(-\frac{TE_{M}}{T_{2M}}\right)\left[1-\exp\left(-\frac{TR_{M}}{T_{1M}}\right)\right]}\cdot
\frac{1}{f_{GM}+\alpha{f_{WM}}}
\]</span></p>
<p>where:</p>
<table>
<colgroup>
<col width="11%" />
<col width="50%" />
<col width="38%" />
</colgroup>
<thead>
<tr class="header">
<th align="left"><u>Parameter</u></th>
<th align="left"><u>Description</u></th>
<th align="left"><u>Default value</u></th>
</tr>
</thead>
<tbody>
<tr class="odd">
<td align="left"><span class="math inline">\(C_{AlphaCorr}\)</span></td>
<td align="left">Estimated metabolite concentration in i.u. corrected
for partial volume effects of water and metabolite</td>
<td align="left"></td>
</tr>
<tr class="even">
<td align="left"><span class="math inline">\(C_{W,i}\)</span></td>
<td align="left">Molal concentration of water in GM, WM, or CSF</td>
<td align="left">43.30, 36.08, and 53.84 mol/kg<span
class="citation"><sup><a href="#ref-Ernst1993">1</a>,<a
href="#ref-Gasparovic2006">3</a></sup></span></td>
</tr>
<tr class="odd">
<td align="left"><span class="math inline">\(\alpha\)</span></td>
<td align="left">Ratio of intrinsic WM:GM metabolite concentrations</td>
<td align="left">Metabolite dependent; see <code>GannetQuantify.m</code>
for default values</td>
</tr>
</tbody>
</table>
<p>A modification of the Harris et al. method is also calculated where
<code>ConcIU_AlphaTissCorr</code> is further scaled by the average voxel
GM and WM composition of all datasets in a group.</p>
<p><code>MRS_struct.out.vox1.(metab).ConcIU_AlphaTissCorr_GrpNorm</code>:</p>
<p><span class="math display">\[
C_{AlphaCorrNorm} =
\frac{I_{M}}{I_{W}}\cdot
\frac{H_{W}}{H_{M}}\cdot
\frac{MM}{\kappa}\cdot
\frac{\sum_{i}^{GM,WM,CSF}f_{i}C_{W,i}\exp\left(-\frac{TE_{W}}{T_{2W,i}}\right)\left[1-\exp\left(-\frac{TR_{W}}{T_{1W,i}}\right)\right]}
{\exp\left(-\frac{TE_{M}}{T_{2M}}\right)\left[1-\exp\left(-\frac{TR_{M}}{T_{1M}}\right)\right]}\cdot
\frac{\mu_{GM}+\alpha{\mu_{WM}}}{(f_{GM}+\alpha{f_{WM}})(\mu_{GM}+{\mu_{WM}})}
\]</span></p>
<p>where:</p>
<table>
<colgroup>
<col width="18%" />
<col width="81%" />
</colgroup>
<thead>
<tr class="header">
<th align="left"><u>Parameter</u></th>
<th align="left"><u>Description</u></th>
</tr>
</thead>
<tbody>
<tr class="odd">
<td align="left"><span
class="math inline">\(C_{AlphaCorrNorm}\)</span></td>
<td align="left">Estimated metabolite concentration in i.u. corrected
for partial volume effects of water and metabolite and adjusted to the
average voxel GM and WM composition across a group</td>
</tr>
<tr class="even">
<td align="left"><span class="math inline">\({\mu_{GM}}\)</span></td>
<td align="left">Group-averaged voxel volume fraction of GM</td>
</tr>
<tr class="odd">
<td align="left"><span class="math inline">\({\mu_{WM}}\)</span></td>
<td align="left">Group-averaged voxel volume fraction of WM</td>
</tr>
</tbody>
</table>
<p><br></p>
</div>
<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-Ernst1993" class="csl-entry">
<div class="csl-left-margin">1. </div><div
class="csl-right-inline">Ernst T, Kreis R, Ross BD. <span
class="nocase">Absolute quantitation of water and metabolites in the
human brain. I. Compartments and water</span>. <em>Journal of Magnetic
Resonance, Series B</em>. 1993;102(1):1-8. doi:<a
href="https://doi.org/10.1006/jmrb.1993.1055">10.1006/jmrb.1993.1055</a></div>
</div>
<div id="ref-Wansapura1999" class="csl-entry">
<div class="csl-left-margin">2. </div><div
class="csl-right-inline">Wansapura JP, Holland SK, Dunn RS, Ball WS.
<span class="nocase">NMR relaxation times in the human brain at 3.0
Tesla</span>. <em>Journal of Magnetic Resonance Imaging</em>.
1999;9(4):531-538. doi:<a
href="https://doi.org/10.1002/(SICI)1522-2586(199904)9:4<531::AID-JMRI4>3.0.CO;2-L">10.1002/(SICI)1522-2586(199904)9:4<531::AID-JMRI4>3.0.CO;2-L</a></div>
</div>
<div id="ref-Gasparovic2006" class="csl-entry">
<div class="csl-left-margin">3. </div><div
class="csl-right-inline">Gasparovic C, Song T, Devier D, et al. <span
class="nocase">Use of tissue water as a concentration reference for
proton spectroscopic imaging</span>. <em>Magnetic Resonance in
Medicine</em>. 2006;55(6):1219-1226. doi:<a
href="https://doi.org/10.1002/mrm.20901">10.1002/mrm.20901</a></div>
</div>
<div id="ref-Harris2015" class="csl-entry">
<div class="csl-left-margin">4. </div><div
class="csl-right-inline">Harris AD, Puts NAJ, Edden RAE. <span
class="nocase">Tissue correction for GABA-edited MRS: Considerations of
voxel composition, tissue segmentation, and tissue relaxations</span>.
<em>Journal of Magnetic Resonance Imaging</em>. 2015;42(5):1431-1440.
doi:<a
href="https://doi.org/10.1002/jmri.24903">10.1002/jmri.24903</a></div>
</div>
<div id="ref-Piechnik2009" class="csl-entry">
<div class="csl-left-margin">5. </div><div
class="csl-right-inline">Piechnik SK, Evans J, Bary LH, Wise RG, Jezzard
P. <span class="nocase">Functional changes in CSF volume estimated using
measurement of water T2 relaxation</span>. <em>Magnetic Resonance in
Medicine</em>. 2009;61(3):579-586. doi:<a
href="https://doi.org/10.1002/mrm.21897">10.1002/mrm.21897</a></div>
</div>
<div id="ref-Lu2005" class="csl-entry">
<div class="csl-left-margin">6. </div><div class="csl-right-inline">Lu
H, Nagae-Poetscher LM, Golay X, Lin D, Pomper M, Zijl PCM van. <span
class="nocase">Routine clinical brain MRI sequences for use at 3.0
Tesla</span>. <em>Journal of Magnetic Resonance Imaging</em>.
2005;22(1):13-22. doi:<a
href="https://doi.org/10.1002/jmri.20356">10.1002/jmri.20356</a></div>
</div>
</div>
</div>
</div>
<div id="rmd-source-code">---
title: "Quantification & tissue correction"
date: "Last updated: `r format(Sys.time(), '%B %d, %Y')`"
bibliography: bibliography.bib
csl: american-medical-association.csl
link-citations: yes
output:
  html_document:
    toc: TRUE
    toc_depth: 2
    toc_float:
      collapsed: FALSE
---

```{r setup, include = FALSE}
knitr::opts_chunk$set(echo = TRUE)
```

```{r, child = "js/back-to-top.js"}
```

```{css, echo = FALSE}
.info {
  margin-bottom: 20px;
}

table {
  margin: auto;
}

table thead th {
  border-bottom: 1px solid #ddd;
}

th, td {
  padding: 5px;
}

tfoot, tr:nth-child(even) {
  background: #eee;
}
```

<br>

::: info
<i class="fa fa-info-circle" style="color: white"></i>&nbsp; The formulas below apply to releases 3.1+ and may not be applicable to older releases.
:::

Gannet quantifies metabolite levels in different ways at various points in the pipeline depending on what reference signals are present and if structural image data are available. It is important to understand what the underlying quantification formulas are for the interpretation and reporting of results.

<u>A note on units of concentration</u>

There is a perennial issue surrounding how quantified in vivo MRS measurements should be expressed; that is, in what biochemical units (if any) they should be reported. In vivo MRS measurements can be, and have been, reported in molar, molal, and institutional units or as simple ratios. However, this makes interpreting and comparing such values, especially across published studies, highly challenging. While Gannet does apply a number of signal scaling factors to water-referenced metabolite measurements (that are required when reporting absolute concentrations), it is our philosophy that these measurements should be considered pseudo-absolute because accounting for all empirical signal scaling factors is impractical (even impossible) to permit truly absolute quantification. Thus, we denote our water-referenced metabolite measurements in institutional units (i.u.).

## GannetFit

`MRS_struct.out.vox1.(metab).ConcCr`, `MRS_struct.out.vox1.(metab).ConcCho`, and `MRS_struct.out.vox1.(metab).ConcNAA` are simple signal integral ratios of the metabolite of interest and the metabolite reference signals Cr, Cho, and NAA, respectively:

$$C = \frac{I_{M}}{I_{ref}}$$

If a water reference is provided, `MRS_struct.out.vox1.(metab).ConcIU` is also calculated. It is defined as the signal integral ratio of the metabolite of interest and water reference scaled by a number of global signal scaling factors:

$$
C_{corr} =
\frac{I_{M}}{I_{W}}\cdot
\frac{H_{W}}{H_{M}}\cdot
\frac{MM}{\kappa}\cdot
C_{W}\cdot
W_{vis}\cdot
\frac{\exp\left(-\frac{TE_{W}}{T_{2W}}\right)\left[1-\exp\left(-\frac{TR_{W}}{T_{1W}}\right)\right]}
{\exp\left(-\frac{TE_{M}}{T_{2M}}\right)\left[1-\exp\left(-\frac{TR_{M}}{T_{1M}}\right)\right]}
$$

where:

| <u>Parameter</u> | <u>Description</u> | <u>Default value</u> |
| :- | :-------- | :------ |
| $C_{corr}$ | Estimated metabolite concentration in i.u. | |
| $I_{M}$ | Metabolite signal integral | |
| $I_{W}$ | Water signal integral | |
| $H_{M}$ | Number of ^1^H protons that give rise to the metabolite signal | Metabolite dependent; see `GannetFit.m` for default values |
| $H_{W}$ | Number of ^1^H protons that give rise to the water signal | 2 |
| $MM$ | Correction factor for the contribution of the co-edited macromolecule signal in the metabolite signal | 0.45 for GABA editing and 1 for all other edited metabolites |
| $\kappa$ | Editing efficiency | Acquisition dependent; 0.5 for GABA editing |
| $C_{W}$ | Molal concentration of pure water | 55.51 mol/kg |
| $W_{vis}$ | Approximate relative MR visibility of water in brain tissue | 0.65 [@Ernst1993] |
| $TE_{W}$ | Echo time of the water reference acquisition | Acquisition dependent |
| $TR_{W}$ | Repetition time of the water reference acquisition | Acquisition dependent |
| $TE_{M}$ | Echo time of the metabolite acquisition | Acquisition dependent |
| $TR_{M}$ | Repetition time of the metabolite acquisition | Acquisition dependent |
| $T_{2W}$ | Average transverse relaxation time of water in GM and WM | 1.100 s [@Wansapura1999] |
| $T_{1W}$ | Average longitudinal relaxation time of water in GM and WM | 0.095 s [@Wansapura1999] |
| $T_{2M}$ | Transverse relaxation time of metabolite | Metabolite dependent; see `GannetFit.m` for default values |
| $T_{1M}$ | Longitudinal relaxation time of metabolite | Metabolite dependent; see `GannetFit.m` for default values |

## GannetSegment

When segmenting structural images to obtain voxel volume fractions of GM, WM, and CSF, and if a water reference is available, a CSF-only correction is applied to the `ConcIU` measurement.

`MRS_struct.out.vox1.(metab).ConcIU_CSFcorr`:

$$
C_{CSFcorr} =
\frac{I_{M}}{I_{W}}\cdot
\frac{H_{W}}{H_{M}}\cdot
\frac{MM}{\kappa}\cdot
C_{W}\cdot
W_{vis}\cdot
\frac{\exp\left(-\frac{TE_{W}}{T_{2W}}\right)\left[1-\exp\left(-\frac{TR_{W}}{T_{1W}}\right)\right]}
{\exp\left(-\frac{TE_{M}}{T_{2M}}\right)\left[1-\exp\left(-\frac{TR_{M}}{T_{1M}}\right)\right]}\cdot
\frac{1}{1-f_{CSF}}
$$

where $C_{CSFcorr}$ is the estimated metabolite concentration in i.u. corrected for CSF and $f_{CSF}$ is the voxel volume fraction of CSF.

## GannetQuantify

`GannetQuantify.m` goes a step further and corrects for partial volume effects that attenuate the observed water and metabolite signals. There are two approaches that are employed. The first is termed the Gasparovic et al. [@Gasparovic2006] method and the second is termed the Harris et al. [@Harris2015] method. Although similar, the difference between these approaches is that the Harris et al. method additionally accounts for intrinsic differences in metabolite concentrations in GM and WM. 

### <u>The Gasparovic et al. method</u>

`MRS_struct.out.vox1.(metab).ConcIU_TissCorr`:

$$
C_{TissCorr} =
\frac{I_{M}}{I_{W}}\cdot
\frac{H_{W}}{H_{M}}\cdot
\frac{MM}{\kappa}\cdot
C_{W}\cdot
\frac{\sum_{i}^{GM,WM,CSF}f_{i}\beta_{i}\exp\left(-\frac{TE_{W}}{T_{2W,i}}\right)\left[1-\exp\left(-\frac{TR_{W}}{T_{1W,i}}\right)\right]}
{(1-f_{CSF})\exp\left(-\frac{TE_{M}}{T_{2M}}\right)\left[1-\exp\left(-\frac{TR_{M}}{T_{1M}}\right)\right]}
$$

where:

| <u>Parameter</u> | <u>Description</u> | <u>Default value</u> |
| :- | :-------- | :------ |
| $C_{TissCorr}$ | Estimated metabolite concentration in i.u. corrected for partial volume effects of water | |
| $f_{i}$ | Voxel volume fraction of GM, WM, or CSF | |
| $\beta_i$ | Relative MR visibility of water in GM, WM, or CSF | 0.78, 0.65, and 0.97 [@Ernst1993] |
| $T_{2W,i}$ | Transverse relaxation time of water in GM, WM, or CSF | 0.110, 0.0792, and 0.503 s [@Wansapura1999; @Piechnik2009] |
| $T_{1W,i}$ | Longitudinal relaxation time of water in GM, WM, or CSF | 1.331, 0.832, and 3.817 s [@Wansapura1999; @Lu2005] |

### <u>The Harris et al. method</u>

`MRS_struct.out.vox1.(metab).ConcIU_AlphaTissCorr`:

$$
C_{AlphaCorr} =
\frac{I_{M}}{I_{W}}\cdot
\frac{H_{W}}{H_{M}}\cdot
\frac{MM}{\kappa}\cdot
\frac{\sum_{i}^{GM,WM,CSF}f_{i}C_{W,i}\exp\left(-\frac{TE_{W}}{T_{2W,i}}\right)\left[1-\exp\left(-\frac{TR_{W}}{T_{1W,i}}\right)\right]}
{\exp\left(-\frac{TE_{M}}{T_{2M}}\right)\left[1-\exp\left(-\frac{TR_{M}}{T_{1M}}\right)\right]}\cdot
\frac{1}{f_{GM}+\alpha{f_{WM}}}
$$

where:

| <u>Parameter</u> | <u>Description</u> | <u>Default value</u> |
| :- | :-------- | :------ |
| $C_{AlphaCorr}$ | Estimated metabolite concentration in i.u. corrected for partial volume effects of water and metabolite | |
| $C_{W,i}$ | Molal concentration of water in GM, WM, or CSF | 43.30, 36.08, and 53.84 mol/kg [@Ernst1993; @Gasparovic2006] |
| $\alpha$ | Ratio of intrinsic WM:GM metabolite concentrations | Metabolite dependent; see `GannetQuantify.m` for default values |

A modification of the Harris et al. method is also calculated where `ConcIU_AlphaTissCorr` is further scaled by the average voxel GM and WM composition of all datasets in a group.

`MRS_struct.out.vox1.(metab).ConcIU_AlphaTissCorr_GrpNorm`:

$$
C_{AlphaCorrNorm} =
\frac{I_{M}}{I_{W}}\cdot
\frac{H_{W}}{H_{M}}\cdot
\frac{MM}{\kappa}\cdot
\frac{\sum_{i}^{GM,WM,CSF}f_{i}C_{W,i}\exp\left(-\frac{TE_{W}}{T_{2W,i}}\right)\left[1-\exp\left(-\frac{TR_{W}}{T_{1W,i}}\right)\right]}
{\exp\left(-\frac{TE_{M}}{T_{2M}}\right)\left[1-\exp\left(-\frac{TR_{M}}{T_{1M}}\right)\right]}\cdot
\frac{\mu_{GM}+\alpha{\mu_{WM}}}{(f_{GM}+\alpha{f_{WM}})(\mu_{GM}+{\mu_{WM}})}
$$

where:

| <u>Parameter</u> | <u>Description</u> |
| :- | :-------- |
| $C_{AlphaCorrNorm}$ | Estimated metabolite concentration in i.u. corrected for partial volume effects of water and metabolite and adjusted to the average voxel GM and WM composition across a group |
| ${\mu_{GM}}$ | Group-averaged voxel volume fraction of GM |
| ${\mu_{WM}}$ | Group-averaged voxel volume fraction of WM |

<br>

### References


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