MRI-Tutorial
其实是错题集
1. What are the units of 𝛾?
is measured in MHz/T
is MHz*rad/T
2. In a region of space where there’s a non-zero external magnetic field 𝐵0: (multiple correct answers)
a) the individual magnetic moments are fully aligned with 𝐵0
b) the individual magnetic moments are stationary, i.e. they are fixed vectors in space and time in the lab reference system.
c) the individual magnetic moments precess at the Larmor frequency.
d) the net magnetization is fully aligned with 𝐵0.
e) Every proton populates either the parallel configuration level or the anti-parallel one.
f) The protons equally split into two different energy levels.
My answer: b, c, d, e
有自转
在非零外部磁场 的空间区域中，磁矩不会是静止不变的。这是因为磁矩倾向于与外部磁场对齐。当外部磁场存在时，如果磁矩不与磁场对齐，它们会受到力矩的作用，导致磁矩绕着磁场方向进行进动（一种旋转运动），这个现象在量子力学中被称为拉莫尔进动。因此，B选项中所述的“个别磁矩是静止的，即它们在实验室参考系中是固定不变的矢量”是不正确的。实际上，磁矩会因为外部磁场的存在而发生动态变化，除非它们已经与外部磁场完全对齐。此外，从量子力学的角度来看，磁矩的行为还受到量子效应的影响，这意味着即使在宏观层面上看似静止，微观层面上的磁矩也是动态的。在量子层面，粒子的自旋磁矩会因为量子力学的不确定性原理而表现出一定的不确定性，因此即使在外部磁场中，磁矩也不会是完全静止不变的。
3. Write down the mathematical formula for the Larmor precession frequency and clarify the difference between f and 𝜔. What is the value of the Larmor frequencies, in MHz, for an external magnetics field of 1.5, 3 and 7 Tesla?
我忘了（
其实挺简单的
无脑带入
记住的磁旋比是267.54
（记清单位是MHz，）
4. In a region of space where there’s a non-zero external magnetic field 𝐵0 along z, another magnetic field along the x-direction (RF excitation pulse) is applied. Select the correct answers:
a) The net magnetization stays aligned along z
b) The net magnetization rotates onto the transverse plane xy and is aligned along the y axis (for a tip angle of
90°)
c) Protons are moved from the parallel configuration to the anti-parallel configuration
d) Protons are moved from the anti-parallel configuration to the parallel configuration
e) The net magnetization stays in the transverse plane as long as the RF pulse is on
My answer: a, b, c, d, e
关于c：那肯定是施加磁场之后，质子能量更大，所以是从平行变成了反平行
（记忆：顺着磁场容易，反着磁场不容易，能量大）
5. Write down the expression for the tip angle and clarify the role of all the variables. If 𝛾 is fixed (for example hydrogen) and the intensity of the RF pulse is known, which variable can you control to flip the magnetization by 90°?
不记得了（
复习链接，共振那里
Calculate the tip angle (in degrees) if 𝐵1 has a value of 20 microTesla and the RF coil signal generating 𝐵1 lasts for 0.2 ms.
迎刃而解
6. In an MRI experiment where one is only interested in encoding the z coordinate (along /patient), the Larmor frequencies at two different z locations are 64.1 MHz and 64.2 MHz. Assume a linear gradient along the z direction with a value of 40 mT/m and that = = 1.5 Tesla.
a) What are the and coordinates of the two different locations?
b) What are the RF frequencies and of the two RF coils signals used to select the slice at and respectively? What are the RF frequencies and of the two MRI signals recorded from the slices at and respectively?
c) If the frequency of the detected MRI signal is = 63.8 MHz, from which slice/𝑧3 coordinate is the signal coming from?
7. The figure below shows the decay of the transverse component of the magnetization after the 𝐵1 magnetic field has been turned off. There are three curves showing the ratio 𝑀𝑡/𝑀0 for three different tissues.
Rethink about the option D.
Another example:
Understanding the core of and
The bigger, the brighter.
8. Describe in detail the roles of the magnetic field 𝐵0, 𝐵1 and the magnetic field gradients (typical values, whether they are always on or off etc), and how they are generated in a conventional MRI scanner.
The magnetic field 𝐵0 is generated by the super-conducting magnet. It is always on and it usually directed along the patient (z axis). It has typical values of 1, 3 and 7 Tesla; it is steady/constant. Its role is to induce a net, macroscopic magnetization along the patient parallel to 𝐵0.
The magnetic field 𝐵1 is generated by RF coils. These are circuits where a current/voltage is circulated at a preselected carrier frequency. This frequency will select a z-slice and only the protons of this slice will resonate (i.e. only the net magnetization of this z-slice will rotate/be affected). The 𝐵1 magnetic field is switched on/off, it is pulsed. It has typical values of 0–50 mT with durations of the order of milliseconds.
The magnetic field gradients 𝐺𝑥, 𝐺𝑦, 𝐺𝑧 are generated by the gradient coils and induce a spatial variation of the external magnetic field 𝐵0 along the three axes. Their role is to enable imaging with the mechanism of spatial encoding. They are always on during a TR interval and their values don’t change within one TR. When no patient is being scanned, the magnetic field gradients are off, while the magnetic field 𝐵0 is always on for a super-conducting magnet. Typical values are between 5 and 50 mT/m.