MRI | Metetsu Blog

Magnetic Resonance Imaging

MRI_Lecture1 Some functions: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 Slice Selection 切片选择例题5 编码一点没懂 MRI_Lecture 2 MR Imaging Sequences 磁共振成像序列 Gradient-echo 梯度回波 Multi-slice gradient echo sequences 多层梯度回波序列 MRI contrast: 𝜌,,, Spin-echo 自旋回声 MRI Equipment MRI Contrast Agents MRI Safety 拓展资料

Go to the end.

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xy平面，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）

💡

纵向磁场为何消失：尝试理解：质子的自旋并非真的平行于磁场，而是一个特定角度（前文提到），因此实际上有水平和竖直分量。在施加纵向的磁场时，水平方向分量相互抵消，整体表现为向上。加入横向磁场后，在拉莫尔进动的特殊情况，parellal转化为anti-parellal，改变了自旋的方向，因此改变了横向和纵向的磁矩分量，最终平衡到一个只存在水平分量的情况这也解释了，并非所有低能量质子都变为了高能量质子，比例与磁场有关

到xy平面后，角速度怎么来的，是匀速转动吗？

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

更细致地研究T1与T2时间

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

ps. 能求导，连续，是不是能用深度学习（

例题4

127.7MHz怎么来的？

42.58MHz怎么来的？

这几个频率一个没懂

待续

Principles of Image Acquisition 图像采集原理

Slice Selection 切片选择

MRI可以从多个方向成像，非常方便，因为磁场强度B可以从三个方向求偏导，可以求变化率，变化率和物质构成有关，所以能从不同方向成像

课程讨论axial slice（轴向/纵向切片）

In this case, the gradient coil that is responsible for variations along z is 𝑮𝒛. The coil that selects the slice is called .

The RF pulse is applied at a specific frequency with a bandwidth ±∆.

通过不同的RF，选择不同的部位

（怎么理解这句）

进动频率在带宽ωs±△ωs的质子(只有这些质子)被RF脉冲旋转到横向平面

超出带宽的频率旋转的质子不受影响，因此它们的净磁化强度保持在z方向

切片厚度(T)可控制

通过改变射频脉冲的中心频率ωs值，可以将切片位置移动到患者的不同部位

例题5

编码一点没懂

Phase Encoding. 相位编码。 The magnetic gradient coil along y must be stepped across different values (Npe steps). 沿y方向的磁梯度线圈必须跨不同的值步进(Npe步进)。 Usually, one starts with a value of Gphase which is the lowest one, say Gpe1- When the acquisition is over, the RF pulse is transmitted again with the same Gslice applied at the same time. 通常，从最低的Gphase值开始，例如Gpe1-当采集结束时，再次发送射频脉冲，同时应用相同的Gslice。 Gphase is then applied with a different value, say Gpez>Gpe1This process is repeated Npe times. 然后用不同的值应用Gphase，例如Gpez> gpe1。此过程重复Npe次。 For a typical slice/image, 128 to 512 values of Gpe are collected. 对于一个典型的切片/图像，收集128到512个Gpe值。 Frequency Encoding. 频率编码。 While Gfreq is on, N, data points are collected at once. 当Gfreq开启时，一次收集数据点。 Having fixed the z-slice, a typical 2D image xy of dimension Nx x Ny = 256x256ould require 256 values of Gphase and one value Gfreq, which can encodeI Nx pixels at once. 固定z片后，一个典型的二维图像xy的维度为Nx x Ny = 256x256需要256个Gphase值和一个Gfreq值，一次可以编码Nx个像素。 The 256 values of Gfreg are collected altogether for each RF ansmission, while the 256 values of Gphase must be collected sequentiallyhat is 256 transmissions). 每次RF发射共采集256个g相位值，而256个g相位值必须依次采集(即256次发射)。 In Summary: For each RF transmission at the same frequency ωz (this selects the z-slice), N, data points are collected at once (Nx pixels) but only one value of Gphase (this encodes only one y-pixel value). 综上所述:对于相同频率ωz(选择z片)，N的每次RF传输，一次收集数据点(Nx像素)，但只有一个Gphase值(这只编码一个y像素值)。 One has to repeat the process Ny times in order to encode all Ny pixels, each time with a different value of Gphase. 为了编码所有的Ny个像素，必须重复这个过程Ny次，每次都使用不同的Gphase值。 The temporal interval in between successive transmissions/RF excitations (at the same frequency ωz) is called time ofrepetition TR. The total time to acquire a z-slice is then given by TR * Npe 连续传输/射频激励之间的时间间隔(相同频率ωz)称为重复时间TR。获得z片的总时间则由TR * Npe给出

MRI_Lecture 2

Back to the Top.

MR Imaging Sequences 磁共振成像序列

Gradient-echo 梯度回波

Different acquisition strategies can be used for different purposes within the same MRI scan

↑为什么？（因果关系）

在一个TR间隔内，要进行多次

In practice, for every RF transmission, multiple slices are acquired by tuning the RF frequency of the transmitted pulse. One can acquire multiple slices during one TR interval, by transmitting every TE within the same TR interval.

这样可以在一次TR内，做不同位置的切片（通过角速度控制）

但是是同一个方向（例如z）

Multi-slice gradient echo sequences 多层梯度回波序列

Max SNR is for 𝛼 = 90°, but this requires a long TR to allow full 𝑇1 relaxation to occur. This translates into long image acquisition time.

Ex:

If is 1 s and T_R is set to 3 ∗ to allow almost complete (>95%) relaxation, a 256x256 image will require 8 minutes to acquire (per z-slice). A 512 x 512 over 16 minutes (per z-slice), too long for clinical standards.

所以要缩减的值

恩斯特角：

MRI contrast: 𝜌,,

𝜌,都是常量，不会改变，但是其他的参数可以变

Spin-echo 自旋回声

不同物质虽然值不同，但是差异可能很小，导致对比度不明显，这时候需要使用spin-echo

如果TR特别大或者特别小（相比于），那么就相当于没有权重，纯粹是表现的差异

TE也是同样的道理

于是有了下面几种情况：

从左到右：

T1加权：TE特别小，T2权重没有，对比度来自T1恢复速度，脂肪/黄骨髓表现为亮，水和脑脊液表现为暗

T2加权：TR特别大，但是增加成像时间，T1权重没有，对比度来自T2，水和脑脊液看起来比脂肪亮

质子密度加权：小TE和大TR，对比度来自PD，高质子数高亮，脑脊液、脂肪和大多数组织看起来亮

MRI Equipment

Three major blocks: super-conducting magnet, RF coils and (magnetic field) gradient coils.

In brief:

A. The super-conducting magnet produces a net magnetization within the patient. A. 超导磁体在病人体内产生净磁化

B. The magnetic field gradient coils impose a linear variation of the proton resonant frequency as a function of position. B. 磁场梯度线圈施加质子共振频率作为位置函数的线性变化

C. The RF coils produce the magnetic energy required to create transverse magnetization and also receive the MRI signal via Faraday induction. C. 射频线圈产生产生横向磁化所需的磁能，并通过法拉第感应接收MRI信号

Super-conducting magnet

超导磁体用于高场强，一般是1.5T或者3T，实验室到7T，1T一下一般用永磁体和电阻磁体（便宜）（但是SNR低），例如Nb–Ti铌钛合金，10K超导，使用液氦和‘zero-refill operation’技术反复降温

RF Coils

射频线圈，RF部分，波长大，高频8–300 MHz，光子能量小，不产生电离

phase-modulated pulses with a carrier frequency equal to the nuclear resonance or Larmor frequency

Gradient Coils

磁场强度，空间编码，简称梯度

5 - 50 mT/m

大电流脉冲组合在梯度线圈产生显著的噪声，患者需要声音保护

MRI Contrast Agents

MRI无需造影剂即可对血管成像，但是对于一些小血管，可以使用造影剂

例如：

正造影剂, Positive contrast agents (Paramagnetic): they shorten the 𝑇1 of the tissue in which they accumulate and are therefore referred to as positive contrast agents since they increase the MRI signal on 𝑇1 -weighted scans.

Gadolinium (64-钆(ga, 二声))-based: they have the same biodistribution as contrast agents for CT and are not captured by the cells.

常用于CNS（中枢神经系统）疾病诊断，持续几十分钟至几小时，然后被肾脏迅速代谢掉

负造影剂, Negative contrast agents (Super-Paramagnetic): they reduce the MR signal in the tissue where they accumulate.

超顺磁造影剂的工作原理是在局部磁场中引起很强的不均匀性。通过这些局部不均匀性扩散的水分子经历非常快的T2和T2弛豫，因此，在药物积聚在T2加权梯度回波或T2加权自旋回波序列上的组织中，信号强度降低。

Iron oxide is metabolized by specific cells, with the tumor intensity remaining unaffected as a relatively bright area.