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6 Magnetization Transfer Imaging/2 Magnetization Transfer Ratio/01-Introduction.md

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+---
+title: Introduction
+subtitle: Magnetization Transfer Ratio
+date: 2024-07-25
+authors:
+  - name: Mathieu Boudreau
+    affiliations:
+      - NeuroPoly Lab, Polytechnique Montreal, Quebec, Canada
+numbering:
+  heading_2: false
+  figure:
+    template: Fig. %s
+---
+
+Conventional MRI techniques, such as those used for clinical diagnosis, can only directly measure hydrogen bonded to water molecules. Thus, a non-negligible proportion of body mass is not visible with clinical MRIs, such as non-hydrogen atoms (different resonance frequencies) and hydrogen atoms bonded to large molecules which restricts the motion of the atoms (rapid signal decay, T2 ~ μs). The latter, called macromolecules, play an important role in the physiology of the body; for example, myelin in the white matter of the brain plays an important role in signal transmission, and is composed largely of macromolecules (lipids and proteins). Although the images acquired by clinical MRI machines can only be generated from signal from mobile hydrogen, these do interact with nearby molecules and atoms via the electromagnetic fields they mutually generate, and in the 70s and 80s a cross-relaxation mechanism was discovered that sensitizes mobile protons to nearby targeted semi-solid molecules, such as myelin (H. T. Edzes and Samulski 1977; Hommo T. Edzes and Samulski 1978; Wolff and Balaban 1989). With proper experimental design, a higher density of nearby macromolecules in the tissue results in a lower MRI signal. This class of MRI techniques is known as magnetization transfer (MT) imaging.
+In the preceding chapter, we delved into the quantitative aspects of magnetization transfer (qMT) imaging, exploring the Bloch-McConnell model, signal modeling, and fitting techniques using qMRLab. Now, we shift our focus to the more accessible and widely used application of MT: magnetization transfer ratio (MTR). Although less quantitative than qMT, MTR is easier to set up and implement, making it popular choices in the MRI community interested in quantifying myelin loss.
+In the simplest and most used MT imaging method, only two images are acquired (one with MT preparation, and one without), and a normalized difference between the two images is calculated. This quantity is known as the magnetization transfer ratio (MTR), and has been used extensively to infer information on myelin diseases and disorders, such as multiple sclerosis. The proportional relationship between MTR and myelin density has been established using post-mortem immunohistological studies in humans (Schmierer et al. 2004, 2007) and animals (Merkler et al. 2005; Zaaraoui et al. 2008). MTR has also already been used in clinical drug trials for MS (Maguire et al. 2013; Brown et al. 2016). Its widespread use is due to the fact that most scanners are equipped with the necessary software so that it can be added to an imaging protocol with the click of a button, and it is also a very quick measurement with a short acquisition time.
+
+Table 1  MTR values in human brain vs vendor vs field strength
+
+As summarized in the previous chapter, MR physicists have also developed other MT-related techniques that aim to extract quantitative physical information of tissues, using the mathematical models that describe the MT process. This sub-field is called quantitative MT, and the tissue properties that are typically measured are: the pool-size ratio F (density of the macromolecular content’s (restricted pool) equilibrium magnetization divided by the the same value for the liquid content (free pool)), the exchange rate R, the longitudinal relaxation of the free pool T1f, and the transverse relaxation of both the free and restricted pools (T2f and T2r). In contrast to MTR, quantitative MT techniques are not as widely used because of the long image acquisition times required that impedes clinical use. qMT also requires additional calibration measurements (B0, B1+, and T1), which can be challenging to measure accurately and thus contribute to additional propagation of errors to the measured qMT parameters (Boudreau, Stikov, and Pike 2018; Boudreau and Pike 2018). Despite these challenges, a lot of research focuses on developing and using qMT techniques in smaller studies, because the measured qMT parameters are desensitized to effects that can bias MTR measurements (eg T1, B1+). Another semi-quantitative MT technique that was recently developed is the MT saturation (MTsat) technique, which will be the focus of the third chapter in the Magnetization Transfer section of this book. 

6 Magnetization Transfer Imaging/2 Magnetization Transfer Ratio/02-MTR in theory.md

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+---
+title: MTR in theory
+subtitle: Magnetization Transfer Ratio
+date: 2024-07-25
+authors:
+  - name: Mathieu Boudreau
+    affiliations:
+      - NeuroPoly Lab, Polytechnique Montreal, Quebec, Canada
+numbering:
+  heading_2: false
+  figure:
+    template: Fig. %s
+---
+The full mathematical description of the magnetization transfer two-pool exchange model was explained in Chapter 6.1 that focuses on qMT. Although it’s these same equations that explain the signal differences between the two images acquired used to calculate MTR, in this section we’ll present a more conceptual explanation of the MT exchange process.
+
+In its most basic form, MT is modeled as an exchange process between two “pools” of protons, those from “mobile” protons (eg, hydrogen in liquid water) named the “free” pool (those that are directly measured with conventional MRI), and those from “restricted” protons (i.e. macromolecules) named the “restricted” pool (these cannot be measured directly with conventional MRI). Macromolecular hydrogen cannot be measured directly because the restricted movement creates a more static local electromagnetic environment that doesn’t average out, and this results in a transverse relaxation T2r (signal decay) that is too short to provide measurable signal (T2r ~ μs << feasible TE). Another consequence of this short signal decay time is a broadening of the absorption lineshape in the frequency domain (eg. the range of “resonant” frequencies of that pool of protons). This is a known property of the Fourier Transform, and the phenomenon is isomorphic to the quantum mechanics uncertainty principle; as Δx⋅Δp ≥ constant in quantum mechanics means that if Δx increases Δp will decrease, we observe a similar relationship approximated to T2⋅FWHM of the frequencies = constant such that if T2 decreases, the FWHM of the frequencies will increase. If T2 is very very short (such as the case for macromolecules), the range of resonant frequencies will be very wide. MT leverages this property by selectively exciting restricted protons far from the mobile proton resonance frequency (applying a pulse off-resonance), but where the energy will be absorbed by some of the protons in the restricted pool. This is the initial preparation of the MT experiment that triggers the conditions needed for cross-relaxation between the unobservable molecules (restricted pool) and observable protons (free pool).
+
+Conventionally, the two-pool exchange model is explained conceptually as a process of magnetization exchange, which is also how it’s described mathematically using the Bloch-McConnel equations. However, this conceptual model can be challenging to understand, particularly for people with physics backgrounds, because unlike energy and momentum, the total magnetization in a voxel is not a conserved physical property. This can be seen simply by observing the evolution of the total magnetization vector after an excitation pulse; the total magnetization vector is (mostly) conserved during the RF pulse, but then decays quickly to near 0 due to T2 relaxation, and takes a long time to grow back to M0 from T1 relaxation. The vector is not constant. So, if magnetization is not a conserved property, how do we know if and how much of it is being exchanged?
+
+As explained in more detail in Appendix A, an MT experiment involves the conservation and transfer of energy between spin populations. The off-resonance RF pulse introduces extra energy into the restricted pool of protons, and the relaxation back to thermal equilibrium occurs through spin-lattice relaxation, where the "lattice" includes nearby free-pool protons. This energy exchange results in a reduction of net magnetization in the free pool and a corresponding decrease in observable MR signal. This process underlies the contrast observed in MT imaging, which reflects differences in tissue microstructure and composition.
+
+Now that we have a better grasp of the magnetization exchange process, we can see how this applies for MTR. In MTR, we acquire one image with MT saturation (low signal where there is high macromolecular density), and one image without MT saturation (higher relative signal where there are macromolecules). The MTR signal is then simply calculated as a normalized difference in percentage, that is:
+
+```{math}
+:label: mtrEq1
+:enumerator:6.1
+\begin{equation}
+\text{MTR} \left( \text{%} \right) = \frac{S_{0}-S_{MT}}{S_{0}}\cdot 100
+\end{equation}
+```
+
+What does this calculated MTR value mean? MTR is the reduction in the steady-state signal resulting from an MT-sensitizing pulse and the ensuing MT exchange that occurs. The higher the density of macromolecular content there is, the more reduction in MT-weighted signal will occur, resulting in a higher MTR value. Typically, MTR values in healthy white matter are higher than in grey matter, and MTR values where there is myelin loss are smaller relative to healthy tissue.

6 Magnetization Transfer Imaging/2 Magnetization Transfer Ratio/03-MTR in practice.md

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+---
+title: MTR in practice
+subtitle: Magnetization Transfer Ratio
+date: 2024-07-25
+authors:
+  - name: Mathieu Boudreau
+    affiliations:
+      - NeuroPoly Lab, Polytechnique Montreal, Quebec, Canada
+numbering:
+  heading_2: false
+  figure:
+    template: Fig. %s
+---
+
+Typically, MTR imaging protocols are implemented on the scanner by adding a relatively long (~5-10 ms) high amplitude off-resonance (~2kHz) preparation RF pulse prior to each TR of an existing imaging sequence. In the early days of MT, the MT pulse was a very long pulse (~10 seconds) prior to one imaging readout of saturation-recovery sequences, but this results in impractically long acquisition times and is very SAR prohibitive. Alternative approaches were explored (eg. 1-2-1 pulses), however now most MT-weighted sequences are done using steady-state sequences (eg SPGR) with a shorter preparation pulse (~10 milliseconds). Figure 1 illustrated this using a spoiled-gradient recalled echo (SPGR) sequence, with a Gaussian-shaped MT preparation pulse prior to the excitation pulse.
+
+```{figure} img/sequence.png
+:label: mtrFig1
+:enumerator: 6.1  
+Simplified pulse sequence diagram of an MTR imaging sequence. An off-resonance and high powered MT-preparation pulse is followed by a spoiler gradient to destroy any transverse magnetization prior the application of the imaging sequence, in this case a spoiled gradient recalled echo (SPGR).
+```
+
+Each MRI vendor optimizes their MT-weighted protocol parameters (eg MT shape, duration, frequency, and amplitude), and few of these details are typically shared with the end-user. Table 2 shares protocol parameters used by different MRI manufacturers as reported by two publications.
+
+Table 2. Literature MTR protocol parameters
+
+
+:::{table} Area Comparisons (written in fancy HTML)
+:label: tbl:areas-html
+
+<table>
+   <tr>
+      <th rowspan="2">Projection</th>
+      <th colspan="3" align="center">Area in square miles</th>
+   </tr>
+   <tr>
+      <th align="right">Large Horizontal Area</th>
+      <th align="right" style="background: -webkit-linear-gradient(20deg, #09009f, #E743D9); -webkit-background-clip: text; -webkit-text-fill-color: transparent;">Large Vertical Area</th>
+      <th align="right">Smaller Square Area
+      <th>
+   </tr>
+   <tr>
+      <td>Albers Equal Area</td>
+      <td align="right">7,498.7</td>
+      <td align="right">10,847.3</td>
+      <td align="right">35.8</td>
+   </tr>
+   <tr>
+      <td>Web Mercator</td>
+      <td align="right">13,410.0</td>
+      <td align="right">18,271.4</td>
+      <td align="right">63.0</td>
+   </tr>
+   <tr>
+      <td>Difference</td>
+      <td align="right" style="background-color: red;color: white">5,911.3</td>
+      <td align="right">7,424.1</td>
+      <td align="right">27.2</td>
+   </tr>
+   <tr>
+      <td>
+         <bold>Percent Difference</bold>
+      </td>
+      <td align="right" style="background-color: green;color: white">44%</td>
+      <td align="right">41%</td>
+      <td align="right">43%</td>
+   </tr>
+</table>
+:::
+
+Brown 2013
+Krakuzu 2022
+
+
+Siemens
+Philips
+GE
+Siemens
+FA
+15
+15
+6
+6
+TR
+30
+47
+32
+32
+TE
+11
+8
+4
+4
+offset
+1500
+1100
+1200
+1200
+MT shape
+Gaussian
+Sinc-Gaussian
+Fermi
+Gaussian
+MT duration
+7.68
+15
+8
+10
+MT angle
+500
+620
+540
+540
+