Magnetic Resonance Imaging | 磁共振成像

📚 Magnetic Resonance Imaging | 磁共振成像

Magnetic resonance imaging (MRI) is a non-invasive medical imaging technique that uses strong magnetic fields, radiofrequency waves, and magnetic field gradients to produce high-resolution images of soft tissues inside the body. It is based on the phenomenon of nuclear magnetic resonance (NMR), in which hydrogen nuclei (protons) absorb and re-emit radiofrequency energy when placed in a magnetic field.

磁共振成像（MRI）是一种非侵入性医学成像技术，利用强磁场、射频波和磁场梯度生成体内软组织的高分辨率图像。它基于核磁共振（NMR）现象，即氢原子核（质子）在磁场中吸收并重新发射射频能量。

1. Basic Principle of MRI | MRI 的基本原理

MRI exploits the magnetic properties of hydrogen nuclei, which are abundant in water and fat molecules in the human body. When a patient is placed inside a strong, uniform magnetic field B₀, the protons tend to align with or against the field.

MRI 利用人体内水和脂肪分子中大量存在的氢原子核的磁性。当患者置于强均匀磁场 B₀ 中时，质子倾向于与磁场平行或反平行排列。

A radiofrequency (RF) pulse at the correct resonance frequency is then applied, causing the protons to absorb energy. After the pulse is switched off, the protons return to their original alignment, emitting RF signals that are detected and used to construct an image.

然后施加频率正确的射频脉冲，使质子吸收能量。脉冲关闭后，质子恢复到原来的排列状态，释放出射频信号，被检测并用于构建图像。

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2. Proton Spin and Magnetic Moment | 质子自旋与磁矩

A hydrogen nucleus consists of a single proton, which has an intrinsic angular momentum called spin. Because the proton is electrically charged, its spin gives rise to a small magnetic moment, so each proton behaves like a tiny bar magnet.

氢原子核由单个质子组成，具有称为自旋的内禀角动量。由于质子带电，其自旋产生一个小磁矩，因此每个质子就像一根微小的条形磁铁。

In the absence of an external magnetic field, these magnetic moments point in random directions, so the net magnetisation of the tissue is zero. In a strong external field, however, the moments align either parallel or antiparallel to the field.

在没有外部磁场时，这些磁矩随机取向，因此组织的净磁化为零。然而，在强外部磁场中，磁矩会平行或反平行于磁场排列。

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3. Larmor Precession and Resonance Condition | 拉莫尔进动与共振条件

When a proton is placed in a magnetic field, its magnetic moment experiences a torque that causes it to precess around the direction of the field. The precession frequency is called the Larmor frequency and is given by:

当质子置于磁场中时，其磁矩受到力矩作用，使其绕磁场方向进动。进动频率称为拉莫尔频率，由下式给出：

f = γB₀ / 2π

where f is the Larmor frequency in hertz, B₀ is the external magnetic flux density in tesla, and γ is the gyromagnetic ratio. For a hydrogen proton, γ / 2π is approximately 42.58 MHz T⁻¹.

其中 f 是以赫兹为单位的拉莫尔频率，B₀ 是以特斯拉为单位的外部磁通密度，γ 是旋磁比。对于氢质子，γ / 2π 约为 42.58 MHz T⁻¹。

Resonance occurs when an RF pulse has exactly the same frequency as the Larmor frequency. At this frequency, protons can absorb energy efficiently and flip to a higher-energy state.

当射频脉冲的频率恰好等于拉莫尔频率时发生共振。在该频率下，质子能够有效吸收能量并跃迁到较高能态。

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4. Longitudinal and Transverse Magnetisation | 纵向与横向磁化

In the equilibrium state, a slight excess of protons aligns parallel to B₀, producing a net longitudinal magnetisation M_z along the field direction. There is no net transverse magnetisation because the precessing proton moments are out of phase.

在平衡状态下，略多的质子沿 B₀ 平行排列，产生沿磁场方向的净纵向磁化 M_z。由于进动的质子磁矩相位不一致，净横向磁化为零。

An applied RF pulse at the Larmor frequency can tip the net magnetisation away from the z-axis. A 90° pulse rotates M_z completely into the transverse plane, creating a large rotating transverse magnetisation M_xy.

施加拉莫尔频率的射频脉冲可使净磁化偏离 z 轴。90° 脉冲将 M_z 完全旋转到横向平面，产生一个大的旋转横向磁化 M_xy。

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5. Radiofrequency Excitation and Resonance | 射频激发与共振

The RF pulse is produced by a transmitter coil and is applied perpendicular to B₀. It creates an oscillating magnetic field B₁ that interacts with the proton magnetic moments when its frequency matches the Larmor frequency.

射频脉冲由发射线圈产生，并垂直于 B₀ 施加。它产生一个振荡磁场 B₁，当其频率与拉莫尔频率匹配时，与质子磁矩相互作用。

The flip angle depends on the strength and duration of the RF pulse. A 180° pulse inverts the longitudinal magnetisation, while a 90° pulse maximises the transverse magnetisation. These pulses are used in different MRI sequences to control contrast.

翻转角取决于射频脉冲的强度和持续时间。180° 脉冲使纵向磁化反转，而 90° 脉冲使横向磁化最大。这些脉冲用于不同的 MRI 序列以控制对比度。

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6. Relaxation Processes: T₁ and T₂ | 弛豫过程：T₁ 与 T₂

After the RF pulse is switched off, the proton system returns to equilibrium through two independent relaxation processes. T₁ relaxation, also called spin-lattice relaxation, describes the recovery of longitudinal magnetisation M_z as protons lose energy to their surroundings.

射频脉冲关闭后，质子系统通过两个独立的弛豫过程恢复平衡。T₁ 弛豫，也称为自旋-晶格弛豫，描述质子向周围环境释放能量时纵向磁化 M_z 的恢复。

T₂ relaxation, also called spin-spin relaxation, describes the decay of transverse magnetisation M_xy caused by interactions between neighbouring proton spins that cause them to lose phase coherence.

T₂ 弛豫，也称为自旋-自旋弛豫，描述由于相邻质子自旋之间相互作用导致相位相干性丧失而引起的横向磁化 M_xy 衰减。

Different tissues have different T₁ and T₂ values. For example, fat has a short T₁ and a long T₂ relative to many tissues, while water has a long T₁ and a long T₂. These differences provide image contrast.

不同组织具有不同的 T₁ 和 T₂ 值。例如，与许多组织相比，脂肪的 T₁ 较短、T₂ 较长，而水的 T₁ 较长、T₂ 较长。这些差异提供图像对比度。

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7. Signal Detection and Free Induction Decay | 信号检测与自由感应衰减

The rotating transverse magnetisation induces a voltage in a receiver coil by electromagnetic induction. This induced signal is called the free induction decay (FID) and its amplitude decreases with time as T₂ relaxation occurs.

旋转的横向磁化通过电磁感应在接收线圈中感应出电压。该感应信号称为自由感应衰减（FID），其幅度随 T₂ 弛豫的发生而随时间减小。

The frequency of the induced signal is the Larmor frequency, and its initial amplitude is proportional to the proton density in the tissue. By measuring the FID, the MRI system can determine how much hydrogen is present.

感应信号的频率是拉莫尔频率，其初始幅度与组织中的质子密度成正比。通过测量 FID，MRI 系统可以确定氢的含量。

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8. Spatial Encoding with Gradient Fields | 梯度磁场空间编码

A uniform magnetic field alone cannot locate where signals come from. MRI uses gradient coils to superimpose small, linear variations in the magnetic field along three perpendicular axes, so the Larmor frequency becomes position-dependent.

仅靠均匀磁场无法确定信号来自何处。MRI 利用梯度线圈在三个垂直轴上叠加小的线性磁场变化，使拉莫尔频率随位置变化。

Slice selection uses a gradient along one axis while an RF pulse of a narrow frequency bandwidth is applied, so only protons in a selected slice resonate. Frequency encoding and phase encoding gradients then provide the in-plane position information.

层面选择沿一个轴施加梯度，同时施加窄频带宽度的射频脉冲，因此只有选定层面内的质子发生共振。频率编码和相位编码梯度随后提供平面内位置信息。

Because the resonance frequency is f = γ(B₀ + G·x) / 2π in the presence of a gradient G along the x-direction, the detected signal contains frequency components that identify different positions.

由于在沿 x 方向的梯度 G 存在时，共振频率为 f = γ(B₀ + G·x) / 2π，检测到的信号包含识别不同位置的频率分量。

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9. Image Reconstruction and Contrast | 图像重建与对比度

The signals received from many gradient-encoding steps are stored in a data space called k-space. A mathematical operation known as the Fourier transform converts this frequency and phase information into a spatial image.

从许多梯度编码步骤接收的信号存储在称为 k 空间的数据空间中。称为傅里叶变换的数学运算将该频率和相位信息转换为空间图像。

By changing the timing

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