Add B0 chap citations

5 B0 Mapping/1 B0 Inhomogeneities/1-Introduction.md

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-The main magnetic field, also called the _B_{sub}`0` field, plays a crucial role in MRI. It dictates the precessional frequency of the spins and sets-up the bulk magnetization, which plays an important role in the image signal-to-noise ratio. Moreover, the radio frequency coils, tuned to the _B_{sub}`0` field, are responsible for flipping the spins in the transverse plane and for acquiring the signal. However, imaging reconstruction techniques assume a perfectly homogeneous _B_{sub}`0` field to reconstruct the signal from k-space data. An inhomogeneous _B_{sub}`0` field can lead to image artifacts such as signal loss, distortions [@Jezzard1995-qd], poor fat saturation [2] and many other image artifacts. In extreme cases, it can completely hinder the ability to create an image. _B_{sub}`0` inhomogeneities are also problematic for MR spectroscopy (MRS), because they widen the spectral linewidth.
+The main magnetic field, also called the _B_{sub}`0` field, plays a crucial role in MRI. It dictates the precessional frequency of the spins and sets-up the bulk magnetization, which plays an important role in the image signal-to-noise ratio. Moreover, the radio frequency coils, tuned to the _B_{sub}`0` field, are responsible for flipping the spins in the transverse plane and for acquiring the signal. However, imaging reconstruction techniques assume a perfectly homogeneous _B_{sub}`0` field to reconstruct the signal from k-space data. An inhomogeneous _B_{sub}`0` field can lead to image artifacts such as signal loss, distortions [@Jezzard1995-qd], poor fat saturation [@Anzai1992-j] and many other image artifacts. In extreme cases, it can completely hinder the ability to create an image. _B_{sub}`0` inhomogeneities are also problematic for MR spectroscopy (MRS), because they widen the spectral linewidth.
 
 When a subject is introduced in the scanner, the static _B_{sub}`0` field can be rendered more homogeneous through a technique called active shimming. Active shimming sends the appropriate amount of current through specific gradient and shim coils, in order to generate a magnetic field that will compensate for the existing (inhomogeneous) magnetic field. This procedure requires precise and accurate mapping of the _B_{sub}`0` field. _B_{sub}`0` maps show the difference between the current field and the expected field, and are typically displayed in units of magnetic field strength (Tesla [T]), precessional frequency (Hertz [Hz]) or in parts per million (ppm). [](#b0Eq1) can be used to convert from the different units. 
 

5 B0 Mapping/1 B0 Inhomogeneities/2-Sources/01-Hardware.md

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-Although scanner manufacturers try to make magnets that are as homogeneous as possible, they are far from perfect. The manufacturing process requires many kilometers of superconducting wire to be wound to create the main magnet and can lead to inhomogeneities due to manufacturing tolerances. Moreover, large metal objects near the scanner can interact with the field created by the scanner and impact the resulting field within the scanner. This is a more important problem with higher field strength. During the installation process, the empty bore is homogenized in a process called passive shimming. During this process, small ferromagnetic pieces are introduced in the scanner at optimized locations to produce a field that counteracts the inhomogeneities. Hardware inhomogeneities are relatively small (less than 1 ppm [3]).
+Although scanner manufacturers try to make magnets that are as homogeneous as possible, they are far from perfect. The manufacturing process requires many kilometers of superconducting wire to be wound to create the main magnet and can lead to inhomogeneities due to manufacturing tolerances. Moreover, large metal objects near the scanner can interact with the field created by the scanner and impact the resulting field within the scanner. This is a more important problem with higher field strength. During the installation process, the empty bore is homogenized in a process called passive shimming. During this process, small ferromagnetic pieces are introduced in the scanner at optimized locations to produce a field that counteracts the inhomogeneities. Hardware inhomogeneities are relatively small (less than 1 ppm [@Webb2016-xp]).
 
-Specialized equipment such as field probes [4] (e.g.: Skope Magnetic Resonance Technologies, LLC) can be used to evaluate the _B_{sub}`0` field of the scanner while it is being installed. This equipment can also be used after installation because it is more precise than _B_{sub}`0` field maps and offers better field temporal resolution, allowing the ability to observe [eddy currents](https://en.wikipedia.org/wiki/Eddy_current) created from gradient switching.
+Specialized equipment such as field probes [@Dietrich2016-iy] (e.g.: Skope Magnetic Resonance Technologies, LLC) can be used to evaluate the _B_{sub}`0` field of the scanner while it is being installed. This equipment can also be used after installation because it is more precise than _B_{sub}`0` field maps and offers better field temporal resolution, allowing the ability to observe [eddy currents](https://en.wikipedia.org/wiki/Eddy_current) created from gradient switching.
 
-During an imaging session, heating of the different components and of the main magnet can lead to temperature-dependent changes in the _B_{sub}`0` field. These can be observed by a frequency drift in the field. As an example, a ~0.4Hz/min has been observed in MRS at 3T but depends on multiple factors [5]. Modern scanners usually have systems in place to evaluate and correct for this drift [6].
+During an imaging session, heating of the different components and of the main magnet can lead to temperature-dependent changes in the _B_{sub}`0` field. These can be observed by a frequency drift in the field. As an example, a ~0.4Hz/min has been observed in MRS at 3T but depends on multiple factors [@noauthor_2021-cr]. Modern scanners usually have systems in place to evaluate and correct for this drift [@El-Sharkawy2006-hl].

5 B0 Mapping/1 B0 Inhomogeneities/2-Sources/02-Magnetic susceptibility.md

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-Materials have a property called magnetic susceptibility () that reflects their ability to become magnetized in response to an external magnetic field [7]. The change in magnetic field Bz (the subscript “z” is shown to make it explicit that we are referring to the component parallel to the _B_{sub}`0` field) is proportional to the magnetic susceptibility value, the magnetic field strength, and can be affected by the geometry and location of the tissues. It can be modeled as a convolution of the difference in magnetic susceptibility  with the component parallel to the magnetic field induced by a unit magnetic dipole ({math}`d=\frac{\left( 3\text{cos}^{2}\left( \theta \right)-1 \right)}{4\pi\left| \textbf{r} \right|^{3}}`) in spherical coordinates where {math}` \textbf{r} ` is the position vector and  is the angle with _B_{sub}`0` [8]. 
+Materials have a property called magnetic susceptibility () that reflects their ability to become magnetized in response to an external magnetic field [@Schenck1996-gu]. The change in magnetic field Bz (the subscript “z” is shown to make it explicit that we are referring to the component parallel to the _B_{sub}`0` field) is proportional to the magnetic susceptibility value, the magnetic field strength, and can be affected by the geometry and location of the tissues. It can be modeled as a convolution of the difference in magnetic susceptibility  with the component parallel to the magnetic field induced by a unit magnetic dipole ({math}`d=\frac{\left( 3\text{cos}^{2}\left( \theta \right)-1 \right)}{4\pi\left| \textbf{r} \right|^{3}}`) in spherical coordinates where {math}` \textbf{r} ` is the position vector and  is the angle with _B_{sub}`0` [@De_Rochefort2008-tb]. 
 
 ```{math}
 :label: b0Eq2
@@ -39,6 +39,6 @@ The following figure shows different susceptibility distributions in ppm for a h
 :::{figure} #fig5p3cell
 :label: b0Plot3
 :enumerator: 5.3
-Cylinder (top) and brain (bottom) of susceptibility distributions (left), simulated _B_{sub}`0` field map (middle) and the _B_{sub}`0` field map with the background field removed (right). An in-vivo susceptibility map was used for the brain and was surrounded by a bone interface, a tissue interface and the rest of the FOV was filled with air. Note that this simplistic representation still shows the field map being dominated by air-tissue interfaces even though the spatial characteristics of the field are not perfectly representative of reality. This dataset was introduced in this publication [9] and is publicly available [10], [11]. An in-vivo field map can be seen in [](#b0Plot9).
+Cylinder (top) and brain (bottom) of susceptibility distributions (left), simulated _B_{sub}`0` field map (middle) and the _B_{sub}`0` field map with the background field removed (right). An in-vivo susceptibility map was used for the brain and was surrounded by a bone interface, a tissue interface and the rest of the FOV was filled with air. Note that this simplistic representation still shows the field map being dominated by air-tissue interfaces even though the spatial characteristics of the field are not perfectly representative of reality. This dataset was introduced in this publication [@Lusebrink2021-kj] and is publicly available [@Lusebrink2020-iy;@noauthor_undated-ms]. An in-vivo field map can be seen in [](#b0Plot9).
 :::
 

5 B0 Mapping/1 B0 Inhomogeneities/3-Effects on signal.md

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-To excite the spins in the transverse plane, a carrier frequency tuned to the [Larmor frequency](https://en.wikipedia.org/wiki/Larmor_precession) is used by the transmit coil. If the frequency of the spins does not match the excitation frequency, it results in a suboptimal tip of the spins in the transverse plane. If the frequency of the spins varies across the ROI, the flip angle is affected differently across the image [12].
+To excite the spins in the transverse plane, a carrier frequency tuned to the [Larmor frequency](https://en.wikipedia.org/wiki/Larmor_precession) is used by the transmit coil. If the frequency of the spins does not match the excitation frequency, it results in a suboptimal tip of the spins in the transverse plane. If the frequency of the spins varies across the ROI, the flip angle is affected differently across the image [@Wang2006-hh].
 
 When a signal is acquired, it is demodulated to remove the carrier frequency ([Larmor frequency](https://en.wikipedia.org/wiki/Larmor_precession)) from the signal. An example of a FID is shown in [](#b0Plot4). The number of species represent the number of isochromats in the simulation. An isochromat represents an ensemble of spins with the same properties rotating at the same [Larmor frequency](https://en.wikipedia.org/wiki/Larmor_precession). For a single isochromat, if the acquired signal and demodulation frequency perfectly match, the _T_{sub}`2` signal can be recovered. If the carrier frequency is different from the expected frequency (such as when there are inhomogeneities), the demodulation introduces low-frequency variations. A non-homogeneous sample is also shown featuring many isochromats. Alternatively, a homogeneous sample with a non-homogeneous _B_{sub}`0` field could be simulated as well and would have a similar shape as the one with multiple species. In that case, the difference from the _T_{sub}`2` curve would reflect _T_{sub}`2`{sup}`*` ({math}`1/T_{2}^{*}=1/T_{2}+1/T_{2}^{'}`) effects. During the relaxation process, spins precessing at different frequencies, due to the presence  of _B_{sub}`0` inhomogeneities, will give rise to phase offsets between the spins within a voxel. This intravoxel phase dispersion leads to signal decay. 
 

5 B0 Mapping/2 Dual echo B0 mapping/01-Introduction.md

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-_B_{sub}`0` mapping estimates the _B_{sub}`0` field from the expected field for every voxel. These _B_{sub}`0` maps can be used to perform prospective _B_{sub}`0` shimming to minimize _B_{sub}`0` inhomogeneities [1], they can be used to retrospectively correct for geometric distortions (FSL FUGUE [13], [14]) (e.g.: for EPI), or to perform retrospective correction for k-space readout trajectory (e.g.: for spiral readout). Moreover, they can be used for retrospective recovery of enhanced signal decay [15], [16], for _T_{sub}`2`{sup}`*` mapping and they are also vital to quantitative susceptibility mapping (QSM) where the goal is to map the susceptibility of the subject.
+_B_{sub}`0` mapping estimates the _B_{sub}`0` field from the expected field for every voxel. These _B_{sub}`0` maps can be used to perform prospective _B_{sub}`0` shimming to minimize _B_{sub}`0` inhomogeneities [@Jezzard1995-qd], they can be used to retrospectively correct for geometric distortions (FSL FUGUE [@Jenkinson2012-np;@Smith2004-av]) (e.g.: for EPI), or to perform retrospective correction for k-space readout trajectory (e.g.: for spiral readout). Moreover, they can be used for retrospective recovery of enhanced signal decay [@An2002-ys;@Alonso-Ortiz2017-yo], for _T_{sub}`2`{sup}`*` mapping and they are also vital to quantitative susceptibility mapping (QSM) where the goal is to map the susceptibility of the subject.
 
 One of the most simple and widely adopted techniques used to perform _B_{sub}`0` mapping is the 2-echo phase difference technique. This technique is faster and simpler than most other alternatives. Before we dive into the technique, let's dip our toes in some theory.

5 B0 Mapping/2 Dual echo B0 mapping/02-Signal Theory.md

@@ -32,7 +32,7 @@ The phase ({math}`\phi`) evolution follows the following equation (not consideri
 \end{equation}
 ```
 
-where x,y,z are the coordinate locations, t is time,  is the gyromagnetic ratio, _B_{sub}`0` is the _B_{sub}`0` field offset (Tesla) and {math}`\phi_{0}` is an initial constant phase offset (e.g.: coil induced, material induced through local conductivity/permittivity). We can observe phase evolution through time in [](#b0Plot7) by looking at phase data acquired in the brain at progressively longer echo times. The phase at a single voxel changes linearly (not considering transient effects). Note that the sharp variations forming vertical lines in the previous figure are called phase wraps and occur because the phase is defined over - to . Phase-wrapping effects will be discussed in more detail in the following chapter. Wraps can also occur spatially as sharp variations as seen in the following figure. Note that the longer the echo times, the more wraps there are.
+where x,y,z are the coordinate locations, t is time,  is the gyromagnetic ratio, _B_{sub}`0` is the _B_{sub}`0` field offset (Tesla) and {math}`\phi_{0}` is an initial constant phase offset (e.g.: coil induced, material induced through local conductivity/permittivity). We can observe phase evolution through time in [](#b0Plot7) by looking at phase data acquired in the brain at progressively longer echo times. The phase at a single voxel changes linearly (not considering transient effects). Note that the sharp variations forming vertical lines in the previous figure are called phase wraps and occur because the phase is defined over - to . Phase-wrapping effects will be discussed in more detail in the following section. Wraps can also occur spatially as sharp variations as seen in the following figure. Note that the longer the echo times, the more wraps there are.
 
 :::{figure} #fig5p7cell
 :label: b0Plot7

5 B0 Mapping/2 Dual echo B0 mapping/05-Benefits and Pitfalls.md

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 When acquiring a field mapping sequence, many parameters will affect the resulting images. A minimum of two phase images is required to compute _B_{sub}`0` field maps, as the initial phase {math}`\phi_{0}\left( x,y,z \right)` is generally not known and non-zero. Multi-echo field mapping with more than two echoes will be discussed in the the advanced [_B_{sub}`0` mapping section](#b0MultiEcho). 
 
-These phase maps can be acquired by many sequences. The general principle includes the use of sequences that cause accumulation of phase. This can be done using GRE sequences or using spin-echo sequences with asymmetric echoes (e.g.: first echo at the spin echo and second echo shifted by 1-2 ms to create an accumulation of phase caused by _B_{sub}`0` inhomogeneities). The sequence parameters are chosen such that the data does not suffer much from distortions and other artifacts caused by _B_{sub}`0` inhomogeneities. High bandwidth, thin slices and multi-shot sequences are therefore preferred [17]. This means EPI sequences are generally not used for field mapping because of their sensitivity to _B_{sub}`0` inhomogeneities. 
+These phase maps can be acquired by many sequences. The general principle includes the use of sequences that cause accumulation of phase. This can be done using GRE sequences or using spin-echo sequences with asymmetric echoes (e.g.: first echo at the spin echo and second echo shifted by 1-2 ms to create an accumulation of phase caused by _B_{sub}`0` inhomogeneities). The sequence parameters are chosen such that the data does not suffer much from distortions and other artifacts caused by _B_{sub}`0` inhomogeneities. High bandwidth, thin slices and multi-shot sequences are therefore preferred [@Akcakaya2022-xw]. This means EPI sequences are generally not used for field mapping because of their sensitivity to _B_{sub}`0` inhomogeneities. 
 
 When acquiring multiple echoes, the readout direction of the even echoes can be chosen to either be in the same direction (monopolar) as the odd echoes or in opposite directions (bipolar). Using opposite directions can slightly reduce TE, but doing so can cause a slight misregistration between the even and odd echoes and we therefore recommend using readouts in the same direction. 
 
-The standard deviation of the phase ({math}`\sigma_{phase}`) is inversely proportional to the SNR of the magnitude image (SNR{sub}`mag`) [18].
+The standard deviation of the phase ({math}`\sigma_{phase}`) is inversely proportional to the SNR of the magnitude image (SNR{sub}`mag`) [@Brown2014-mv].
 
 ```{math}
 :label: b0Eq7
@@ -35,4 +35,4 @@ A high SNR image will therefore provide a more reliable phase image. With this i
 
 As echoes are usually acquired in rapid successions to avoid phase wrapping, rapid gradient switching is required which leads to [eddy currents](https://en.wikipedia.org/wiki/Eddy_current) that can impact the acquired phase data. To mitigate the issue, a single echo per RF pulse can be acquired. A dual-echo sequence would have twice the number of RF pulses (alternating between acquiring both echoes) but allows slower gradient switching and removes [eddy currents](https://en.wikipedia.org/wiki/Eddy_current) effects from the gradient work of the first echo on the second echo. However, this technique requires longer scan time.
 
-As seen in this chapter, phase wrapping can be an issue, as phase is defined over {math}`2\pi`. The next section deals with this problem.
+As seen in this section, phase wrapping can be an issue, as phase is defined over {math}`2\pi`. The next section deals with this problem.