MRI-1 | Metetsu Blog

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Mar 8, 2024 02:39 PM

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Magnetic Resonance Imaging

MRI_Lecture1 Proton Energy levels 质子能级磁旋比 𝛾 例题1 Precession Frequency 进动频率/旋进频率例题2 Net Magnetization 净磁化强度 Resonance共振例题3 全流程：Macroscopic Quantities - Relaxation Times 弛豫 Signals from Lipid 油脂中的信号 Spatial Encoding 空间编码例题4 Principles of Image Acquisition 图像采集原理拓展资料

MRI_Lecture1

Our body is mostly water. We can confuse water with hydrogen. We can further confuse hydrogen with the nucleus, a single proton (MRI is a medical imaging modality based on the magnetic properties of nuclei, not electrons).

Some functions:

MRI provides the spatial map of the hydrogen nuclei.

It doesn’t use ionizing radiations

Slower than CT and US, and costly.

Proton Energy levels 质子能级

质子会自旋→产生角动量和磁矩

angular momentum (J or P) and a magnetic moment (𝜇)

The proton has spin ½.

根据量子力学，角动量只能有两个值

磁旋比 𝛾

The constant of proportionality 𝛾 is the gyromagnetic ratio. Pay attention to the units of 𝛾 (rad*MHz/T) vs 𝛾/(2𝜋) (MHz/T).

没有外部磁场时→质子随机→质子磁矩随机→总和为0

有外部磁场时：

但是总的来说，会以theta角度和外部磁场B平行（称为z轴）

遇事不决，量子力学：

1，自然界会倾向于变成能量低的状态（这里是parallel状态能量低）

2，从~~不知道哪里来的~~右侧的公式，得到能量差 delta E

3，带入磁旋比，普朗克常数和磁场强度，两边取对数

4，得到一个重要公式：

例题1

1，算体积，然后根据密度算质量，再求物质的量→总原子数量

2，套公式

Precession Frequency 进动频率/旋进频率

(a)质子，量子力学视角

(b)经典力学，陀螺自转和公转，重力模拟磁场

A magnetic moment placed into an external magnetic field exhibits a motion called precession, i.e. it rotates around the magnetic field at a fixed angle.

The precession frequency is called Larmor frequency. （拉莫尔频率）

考试写f的这个

例题2

Net Magnetization 净磁化强度

多个质子在同一磁场公转，x和y轴强度相互抵消，z轴剩下一个合磁化矢量

Effects of a Radiofrequency pulse on magnetization 射频脉冲

激活系统，use electromagnetic RF (radio-frequency) pulse of:

质子可以从一个能级变为另一个能级，所需的脉冲频率必须是拉莫尔频率（外围运动的进动频率）

称为：

Resonance共振

Tips: The value of f for a 1.5 T clinical scanner is approximately 63.9 MHz

例题3

在原先的磁场，施加一个横向的拉莫尔频率的磁场B1，会从z轴转到y，并且有一个角速度

停止施加之后会恢复原来的状态

（但是怎么转过去的呢）

纵向磁化：由于磁化的横向分量之和为0，自旋核系统在平衡后形成的磁化强度仅存在纵向分量，写作M=M++M−=M0
横向磁化：由于需要检测M的大小来做成像，但纵向的M与B0方向相同，且微弱，难以测量，为了便于测量，在横向平面上施加一个射频磁场B1，使M偏转一定角度，从而分离B0和M。对自旋系统施加B1的过程称为对磁化强度矢量的激励/激发。磁矩在偏转后竖直方向上减小到Mz，而在xOy平面叠加形成横向的磁化强度Mxy，称为横向磁化。
章动：由于有B0和B1，磁化强度矢量既要绕B0进动又要绕B1进动，B1相对B0较小，所以绕X轴进动速度缓慢（由拉莫尔频率计算），故M实际的运动轨迹是一个由上向下、半径越来越大的螺旋线，这种螺旋进动被称为章动。绕x轴方向添加的磁场旋转导致磁化矢量从z轴->x轴。

全流程：

（1）均衡

（2）平衡被打破

（3）平衡恢复

（4）质子以频率f吸收能量，以频率f释放能量

The RF (excitation) pulse is applied through some RF coils (copper wires). These are also used to receive the signal. 射频(激励)脉冲通过一些射频线圈(铜线)施加。它们也用来接收信号。

Macroscopic Quantities - Relaxation Times 弛豫

When the RF pulse is turned off, the system must relax back to thermal equilibrium. This phenomenon is called relaxation(弛豫), and it is typical of many systems going from thermal equilibrium to non-equilibrium and vice-versa.

T1弛豫：z轴方向

T2弛豫：xy平面/方向

Both follow an exponential law.

不同的组织有不同的值，这也是比较不同部位的依据

（曲线大概长右边这样→）

之后称为完全恢复

T1和T2之间没有数学关系，但是T1 always >T2

In reality, due to inhomogeneities in the magnetic field 𝐵0 and different magnetic susceptibilities of different parts of the body, the relaxation time must be corrected and it usually called .

Signals from Lipid 油脂中的信号

Protons in lipids resonate at a slightly different frequency than protons in water. The reason why resonant frequencies for protons in lipids are different from those in water is that the strength of the magnetic field experienced by a proton depends not only upon the field strength, but also is affected by the geometry of the electron configuration which surrounds the proton. Electrons are spinning and, since they have an electric charge, they also create a tiny magnetic field opposite in polarity to the main magnetic field .(周围电子形成的小磁场会影响)

is the shielding constant（屏蔽常数）

氧原子和碳原子对电子的吸引能力不同，氧原子在中吸引的电子，比碳原子在脂质中吸引的多，因此周围电子形成的小磁场更小，屏蔽常数更小

Chemical shift: associated to Larmor frequency of a nuclear spin to its chemical environment (nuclear magnetic resonance (NMR) spectroscopy).

NMR + Spatial Encoding —→MRI

Spatial Encoding 空间编码

Brilliant Idea: a spatial variation of the magnetic field along the subject will result into a spatially varying Larmor frequency. This will result in an MR signal whose frequency will vary spatially and thus it can be exploited to form an image.

B在xyz三个方向求偏导数，得出三个不同梯度

循环电流产生磁场